%================================================================ % LaTeX file with preferred layout for H1 paper drafts % use: dvips -D600 file-name %================================================================ \RequirePackage{lineno} % This is provided with the package %\documentclass[12pt]{report} \documentclass[12pt]{article} \usepackage{epsfig} \usepackage{epstopdf} \usepackage{graphicx} \usepackage{amsmath} \usepackage{hhline} \usepackage{amssymb} \usepackage{times} \usepackage{cite} \usepackage{rotate} \usepackage{multirow} \usepackage{captcont} \usepackage{subfigure} \usepackage[pagebackref=false,colorlinks=true]{hyperref} %allow html %links in the PDF document \renewcommand{\topfraction}{1.0} \renewcommand{\bottomfraction}{1.0} \renewcommand{\textfraction}{0.0} \newlength{\dinwidth} \newlength{\dinmargin} \setlength{\dinwidth}{21.0cm} \setlength{\parindent}{0.0cm} \textheight23.5cm \textwidth16.0cm \setlength{\dinmargin}{\dinwidth} \setlength{\unitlength}{1mm} 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y)_{Q^2}\,$} \newcommand{\pdff}{$(\partial F_{2} / \partial \ln Q^{2})_x\,$ } \newcommand{\Fc}{$ F_{2}~$} \newcommand{\amz}{$\alpha_s(M_Z^2)\,$} % % Some useful tex commands % \newcommand{\qsq}{\ensuremath{Q^2} } \newcommand{\gevsq}{\ensuremath{\mathrm{GeV}^2} } \newcommand{\et}{\ensuremath{E_t^*} } \newcommand{\rap}{\ensuremath{\eta^*} } \newcommand{\gp}{\ensuremath{\gamma^*}p } \newcommand{\dsiget}{\ensuremath{{\rm d}\sigma_{ep}/{\rm d}E_t^*} } \newcommand{\dsigrap}{\ensuremath{{\rm d}\sigma_{ep}/{\rm d}\eta^*} } % Journal macro \def\Journal#1#2#3#4{{#1} {\bf #2} (#3) #4} \def\NCA{\em Nuovo Cimento} \def\NIM{\em Nucl. Instrum. Methods} \def\NIMA{{\em Nucl. Instrum. Methods} {\bf A}} \def\NPB{{\em Nucl. Phys.} {\bf B}} \def\PLB{{\em Phys. Lett.} {\bf B}} \def\PRL{\em Phys. Rev. Lett.} \def\PRD{{\em Phys. Rev.} {\bf D}} \def\ZPC{{\em Z. Phys.} {\bf C}} \def\EJC{{\em Eur. Phys. J.} {\bf C}} \def\CPC{\em Comp. Phys. Commun.} \begin{titlepage} \noindent \begin{flushleft} {\tt DESY 13-211 \hfill ISSN 0418-9833} \\ {\tt December 2013} \\ \end{flushleft} \vspace{1cm} \begin{center} \begin{Large} %{\bf Measurement of the Longitudinal Structure Function \boldmath${F_L}$ at HERA}\\ %or\\ %{\bf Measurement of Neutral Current Inclusive Deep Inelastic Scattering for %Different Proton Beam Energies at HERA and of the Longitudinal Proton %Structure Function \boldmath${F_L}$}\\ %or\\ {\bf Measurement of Inclusive \boldmath${ep}$ Cross Sections at High \boldmath${Q^2}$ at \boldmath${\sqrt{s}}=225$ and $252$~GeV and of the Longitudinal Proton Structure Function \boldmath${F_L}$ at HERA} % in {\boldmath $ep$} Collisions at HERA \vspace{1cm} H1 Collaboration \end{Large} \end{center} \vspace{1cm} \begin{abstract} \noindent Inclusive $ep$ double differential cross sections for neutral current deep inelastic scattering are measured with the H1 detector at HERA. The data were taken with a lepton beam energy of $27.6$~GeV and two proton beam energies of $E_p=460$ and $575$~GeV corresponding to centre-of-mass energies of $225$ and $252$~GeV, respectively. The measurements cover the region of $6.5\times 10^{-4} \leq x \leq 0.65$ for $35\leq Q^2 \leq 800$~GeV$^2$ up to $y=0.85$. The measurements are used together with previously published H1 data at $E_p=920$~GeV and lower $Q^2$ data at $E_p=460$, $575$ and $920$~GeV to extract the longitudinal proton structure function $F_L$ in the region $1.5\leq Q^2 \leq 800$~GeV$^2$. \end{abstract} \vspace{1cm} \begin{center} Submitted to EPJC \end{center} \end{titlepage} % % COPY THE AUTHOR AND INSTITUTE LISTS % AT THE TIME OF THE T0-TALK INTO YOUR AREA % % from /h1/iww/ipublications/h1auts.tex \begin{flushleft} %% \input{Author} \end{flushleft} %\newpage %\input{h1auts} %-- H1AUTS Author list by names %-- Status: Mon Jul 1 14:40:08 CEST 2013 Number of authors = 152 V.~Andreev$^{22}$, %LPI -PD 8/88 Andreev A.~Baghdasaryan$^{34}$, %YERE-PD 09/03 Baghdasaryana S.~Baghdasaryan$^{34}$, %YERE-ST 02/10 Baghdasaryans K.~Begzsuren$^{31}$, %ULBA-PD 04/06 Begzsuren A.~Belousov$^{22}$, %LPI -HON 12/12 Belousov P.~Belov$^{10}$, %DESY-PD 05/13 Belov V.~Boudry$^{25}$, %ECPL-PD 1/93 Boudry G.~Brandt$^{46}$, %OXFU-PD 03/07 Brandt M.~Brinkmann$^{10}$, %DESY-LEFT 07/13 Brinkmann V.~Brisson$^{24}$, %ORSA-HON 01/12 Brisson D.~Britzger$^{10}$, %DESY-PD 06/13 Britzger A.~Buniatyan$^{13}$, %HDB1-PD 12/95 Buniatyan A.~Bylinkin$^{21,43}$, %ITEP-ST 09/12 Bylinkin L.~Bystritskaya$^{21}$, %ITEP-PD 05/99 Bystritskaya A.J.~Campbell$^{10}$, %DESY-PD 10/84 Campbella K.B.~Cantun~Avila$^{20}$, %MEX1-PD 05/13 Cantunavila F.~Ceccopieri$^{3}$, %BRUX-PD 10/09 Ceccopieri K.~Cerny$^{28}$, %PRG2-PD 11/08 Cernyk V.~Chekelian$^{23}$, %MPIM-PD 01/90 Chekelian J.G.~Contreras$^{20}$, %MEX1-PROF 03/98 Contreras J.B.~Dainton$^{17}$, %LIVE-PROF 01/94 Dainton K.~Daum$^{33,38}$, %WUPP-PROF 06/90 Daum E.A.~De~Wolf$^{3}$, %ANTW-LEFT 12/12 Dewolf C.~Diaconu$^{19}$, %MARS-PD 09/96 Diaconu M.~Dobre$^{4}$, %BUCH-PD 12/12 Dobre V.~Dodonov$^{10}$, %DESY-PD 04/98 Dodonov A.~Dossanov$^{11,23}$, %MPIM-LEFT 06/13 Dossanov A.~Dubak$^{23,26}$, % MPI, Podgorica G.~Eckerlin$^{10}$, %DESY-PD 8/88 Eckerlin S.~Egli$^{32}$, %PSI -PD 01/10 Egli E.~Elsen$^{10}$, %DESY-PROF 01/06 Elsen L.~Favart$^{3}$, %BRUX-PROF 10/99 Favart A.~Fedotov$^{21}$, %ITEP-PD 8/88 Fedotov J.~Feltesse$^{9}$, %SACL-HON 11/06 Feltesse J.~Ferencei$^{15}$, %KOSI-PD 08/88 Ferencei M.~Fleischer$^{10}$, %DESY-PD 07/95 Fleischer A.~Fomenko$^{22}$, %LPI -PD 02/89 Fomenko E.~Gabathuler$^{17}$, %LIVE-HON 01/12 Gabathulere J.~Gayler$^{10}$, %DESY-HON 02/05 Gayler S.~Ghazaryan$^{10}$, %DFLC-PD 09/09 Ghazaryan A.~Glazov$^{10}$, %DESY-PD 01/04 Glazov L.~Goerlich$^{6}$, %CRAC-PD 8/88 Goerlich N.~Gogitidze$^{22}$, %LPI -PD 05/91 Gogitidze M.~Gouzevitch$^{10,39}$, %DESY-PD 10/11 Gouzevitch C.~Grab$^{36}$, %ZUTH-PROF 08/07 Grab A.~Grebenyuk$^{10}$, %DESY-LEFT 07/12 Grebenyuk T.~Greenshaw$^{17}$, %LIVE-PD 8/88 Greenshaw G.~Grindhammer$^{23}$, %MPIM-HON 09/11 Grindhammer S.~Habib$^{10}$, %DESY-LEFT 11/12 Habib D.~Haidt$^{10}$, %DESY-HON 03/04 Haidt R.C.W.~Henderson$^{16}$, %LANC-PROF 10/04 Henderson M.~Herbst$^{14}$, %HDB2-PD 11/11 Herbst M.~Hildebrandt$^{32}$, %PSI -LEFT 12/12 Hildebrandtm J.~Hladk\`y$^{27}$, %PRAG-HON 12/02 Hladky D.~Hoffmann$^{19}$, %MARS-PD 07/00 Hoffmann R.~Horisberger$^{32}$, %PSI -PD 01/10 Horisberger T.~Hreus$^{3}$, %BRUX-PD 10/08 Hreus F.~Huber$^{13}$, %HDB1-PD 01/13 Huberf M.~Jacquet$^{24}$, %ORSA-PD 09/96 Jacquet X.~Janssen$^{3}$, %ANTW-PD 02/03 Janssenx A.W.~Jung$^{14,47}$, % Heidelberg , Fermilab H.~Jung$^{10,3}$, %DESY-PROF 12/99 Jungh M.~Kapichine$^{8}$, %JINR-PD 3/97 Kapichine C.~Kiesling$^{23}$, %MPIM-HON 09/11 Kiesling M.~Klein$^{17}$, %LIVE-PROF 12/06 Klein C.~Kleinwort$^{10}$, %DESY-PD 8/88 Kleinwort R.~Kogler$^{11}$, %HAM2-PD 12/10 Kogler P.~Kostka$^{35}$, %ZEUT-PD 10/87 Kostka J.~Kretzschmar$^{17}$, %LIVE-PD 03/08 Kretzschmar K.~Kr\"uger$^{10}$, %DESY-PD 01/04 Kruegerk M.P.J.~Landon$^{18}$, %QMWC-PD 10/83 Landon W.~Lange$^{35}$, %ZEUT-PD 8/88 Lange P.~Laycock$^{17}$, %LIVE-PD 11/03 Laycock A.~Lebedev$^{22}$, %LPI -HON 12/12 Lebedev S.~Levonian$^{10}$, %DESY-PD 08/88 Levonian K.~Lipka$^{10,42}$, %DESY-PD 06/01 Lipka B.~List$^{10}$, %DESY-PD 11/99 Listb J.~List$^{10}$, %DFLC-PD 10/00 Listj B.~Lobodzinski$^{10}$, %DESY-PD 01/06 Lobodzinski V.~Lubimov$^{21, \dagger}$, %ITEP-LEFT 12/12 Lubimov E.~Malinovski$^{22}$, %LPI -PD 01/89 Malinovskie H.-U.~Martyn$^{1}$, %AAC1-HON 01/12 Martyn S.J.~Maxfield$^{17}$, %LIVE-PD 8/88 Maxfield A.~Mehta$^{17}$, %LIVE-PROF 06/00 Mehta A.B.~Meyer$^{10}$, %DESY-PD 10/97 Meyeran H.~Meyer$^{33}$, %WUPP-HON 12/00 Meyerhi J.~Meyer$^{10}$, %DESY-PROF 10/84 Meyerj S.~Mikocki$^{6}$, %CRAC-PROF 10/10 Mikocki A.~Morozov$^{8}$, %JINR-PD 06/99 Morozova K.~M\"uller$^{37}$, %ZUER-PD 11/94 Muellerk Th.~Naumann$^{35}$, %ZEUT-PROF 01/05 Naumannt P.R.~Newman$^{2}$, %BIRM-PROF 10/09 Newman C.~Niebuhr$^{10}$, %DESY-PD 3/93 Niebuhr G.~Nowak$^{6}$, %CRAC-PROF 02/12 Nowakg K.~Nowak$^{11}$, %HAM2-LEFT 02/13 Nowakk B.~Olivier$^{23}$, %MPI J.E.~Olsson$^{10}$, %DESY-HON 09/10 Olsson D.~Ozerov$^{10}$, %DESY-PD 09/08 Ozerov P.~Pahl$^{10}$, %DESY-ST 10/08 Pahl C.~Pascaud$^{24}$, %ORSA-HON 09/05 Pascaud G.D.~Patel$^{17}$, %LIVE-PD 8/88 Patel E.~Perez$^{9,40}$, %SACL-PD 10/07 Perez A.~Petrukhin$^{10}$, %DESY-PD 10/09 Petrukhin I.~Picuric$^{26}$, %PODG-PROF 12/07 Picuric H.~Pirumov$^{13}$, %DESY-PD 04/13 Pirumov D.~Pitzl$^{10}$, %DESY-PD 8/88 Pitzl R.~Pla\v{c}akyt\.{e}$^{10,42}$, %DESY-PD 10/06 Placakyte B.~Pokorny$^{28}$, %PRG2-ST 10/09 Pokorny R.~Polifka$^{28,44}$, %PRG2-PD 05/11 Polifka V.~Radescu$^{10,42}$, %DESY-PD 10/06 Radescu N.~Raicevic$^{26}$, %PODG-PD 06/02 Raicevic A.~Raspereza$^{10}$, T.~Ravdandorj$^{31}$, %ULBA-PROF 09/00 Ravdandorj P.~Reimer$^{27}$, %PRAG-PD 07/90 Reimer E.~Rizvi$^{18}$, %QMWC-PROF 03/04 Rizvi P.~Robmann$^{37}$, %ZUER-PD 8/88 Robmann R.~Roosen$^{3}$, %BRUX-HON 03/12 Roosen A.~Rostovtsev$^{21}$, %ITEP-PROF 02/11 Rostovtsev M.~Rotaru$^{4}$, %BUCH-PD 06/11 Rotaru S.~Rusakov$^{22}$, %LPI -HON 01/12 Rusakov D.~\v S\'alek$^{28}$, %PRG2-PD 10/10 Salek D.P.C.~Sankey$^{5}$, %RAL -PD 01/90 Sankey M.~Sauter$^{13}$, %HDB1-PD 10/09 Sauter E.~Sauvan$^{19,45}$, %MARS-PD 11/1 Sauvan S.~Schmitt$^{10}$, %DESY-PD 09/99 Schmittst L.~Schoeffel$^{9}$, %SACL-PROF 10/10 Schoeffel A.~Sch\"oning$^{13}$, %HDB1-PROF 01/09 Schoening H.-C.~Schultz-Coulon$^{14}$, %HDB2-PROF 01/04 Schultzcoulon F.~Sefkow$^{10}$, %DFLC-PD 09/99 Sefkow S.~Shushkevich$^{10}$, %DESY-PD 08/11 Shushkevich Y.~Soloviev$^{10,22}$, %LPI -PD 08/89 Soloviev P.~Sopicki$^{6}$, %CRAC-ST 09/07 Sopicki D.~South$^{10}$, %DESY-PD 05/03 South V.~Spaskov$^{8}$, %JINR-PD 12/97 Spaskov A.~Specka$^{25}$, %ECPL-PROF 09/05 Specka M.~Steder$^{10}$, %DESY-PD 09/08 Steder B.~Stella$^{29}$, %ROME-HON 11/10 Stella U.~Straumann$^{37}$, %ZUER-PROF 09/95 Straumann T.~Sykora$^{3,28}$, %ANTW-PD 01/06 Sykora P.D.~Thompson$^{2}$, %BIRM-PD 08/99 Thompsonp D.~Traynor$^{18}$, %QMWC-PD 10/01 Traynor P.~Tru\"ol$^{37}$, %ZUER-HON 10/06 Truoel I.~Tsakov$^{30}$, %SOFI-PROF 03/12 Tsakov B.~Tseepeldorj$^{31,41}$, %ULBA-PROF 06/06 Tseepeldorj J.~Turnau$^{6}$, %CRAC-PROF 09/95 Turnau A.~Valk\'arov\'a$^{28}$, %PRG2-PD 8/88 Valkarova C.~Vall\'ee$^{19}$, %MARS-PD 06/86 Vallee P.~Van~Mechelen$^{3}$, %ANTW-PROF 01/06 Vanmechelen Y.~Vazdik$^{22}$, %LPI -PD 8/88 Vazdik D.~Wegener$^{7}$, %DORT-PROF 01/06 Wegener E.~W\"unsch$^{10}$, %DESY-PD 8/88 Wuensch J.~\v{Z}\'a\v{c}ek$^{28}$, %PRG2-PROF 10/05 Zacek Z.~Zhang$^{24}$, %ORSA-PD 10/92 Zhang R.~\v{Z}leb\v{c}\'{i}k$^{28}$, %PRG2-ST 03/12 Zlebcik H.~Zohrabyan$^{34}$, %YERE-PD 11/02 Zohrabyan and F.~Zomer$^{24}$ %ORSA-PROF 09/06 Zomer %\newpage %-- H1 Institutes \bigskip{\it $ ^{1}$ I. Physikalisches Institut der RWTH, Aachen, Germany \\ $ ^{2}$ School of Physics and Astronomy, University of Birmingham, Birmingham, UK$^{ b}$ \\ $ ^{3}$ Inter-University Institute for High Energies ULB-VUB, Brussels and Universiteit Antwerpen, Antwerpen, Belgium$^{ c}$ \\ $ ^{4}$ National Institute for Physics and Nuclear Engineering (NIPNE) , Bucharest, Romania$^{ j}$ \\ $ ^{5}$ STFC, Rutherford Appleton Laboratory, Didcot, Oxfordshire, UK$^{ b}$ \\ $ ^{6}$ Institute for Nuclear Physics, Cracow, Poland$^{ d}$ \\ $ ^{7}$ Institut f\"ur Physik, TU Dortmund, Dortmund, Germany$^{ a}$ \\ $ ^{8}$ Joint Institute for Nuclear Research, Dubna, Russia \\ $ ^{9}$ CEA, DSM/Irfu, CE-Saclay, Gif-sur-Yvette, France \\ $ ^{10}$ DESY, Hamburg, Germany \\ $ ^{11}$ Institut f\"ur Experimentalphysik, Universit\"at Hamburg, Hamburg, Germany$^{ a}$ \\ $ ^{12}$ Max-Planck-Institut f\"ur Kernphysik, Heidelberg, Germany \\ $ ^{13}$ Physikalisches Institut, Universit\"at Heidelberg, Heidelberg, Germany$^{ a}$ \\ $ ^{14}$ Kirchhoff-Institut f\"ur Physik, Universit\"at Heidelberg, Heidelberg, Germany$^{ a}$ \\ $ ^{15}$ Institute of Experimental Physics, Slovak Academy of Sciences, Ko\v{s}ice, Slovak Republic$^{ e}$ \\ $ ^{16}$ Department of Physics, University of Lancaster, Lancaster, UK$^{ b}$ \\ $ ^{17}$ Department of Physics, University of Liverpool, Liverpool, UK$^{ b}$ \\ $ ^{18}$ School of Physics and Astronomy, Queen Mary, University of London, London, UK$^{ b}$ \\ $ ^{19}$ CPPM, Aix-Marseille Univ, CNRS/IN2P3, 13288 Marseille, France \\ $ ^{20}$ Departamento de Fisica Aplicada, CINVESTAV, M\'erida, Yucat\'an, M\'exico$^{ h}$ \\ $ ^{21}$ Institute for Theoretical and Experimental Physics, Moscow, Russia$^{ i}$ \\ $ ^{22}$ Lebedev Physical Institute, Moscow, Russia \\ $ ^{23}$ Max-Planck-Institut f\"ur Physik, M\"unchen, Germany \\ $ ^{24}$ LAL, Universit\'e Paris-Sud, CNRS/IN2P3, Orsay, France \\ $ ^{25}$ LLR, Ecole Polytechnique, CNRS/IN2P3, Palaiseau, France \\ $ ^{26}$ Faculty of Science, University of Montenegro, Podgorica, Montenegro$^{ k}$ \\ $ ^{27}$ Institute of Physics, Academy of Sciences of the Czech Republic, Praha, Czech Republic$^{ f}$ \\ $ ^{28}$ Faculty of Mathematics and Physics, Charles University, Praha, Czech Republic$^{ f}$ \\ $ ^{29}$ Dipartimento di Fisica Universit\`a di Roma Tre and INFN Roma~3, Roma, Italy \\ $ ^{30}$ Institute for Nuclear Research and Nuclear Energy, Sofia, Bulgaria \\ $ ^{31}$ Institute of Physics and Technology of the Mongolian Academy of Sciences, Ulaanbaatar, Mongolia \\ $ ^{32}$ Paul Scherrer Institut, Villigen, Switzerland \\ $ ^{33}$ Fachbereich C, Universit\"at Wuppertal, Wuppertal, Germany \\ $ ^{34}$ Yerevan Physics Institute, Yerevan, Armenia \\ $ ^{35}$ DESY, Zeuthen, Germany \\ $ ^{36}$ Institut f\"ur Teilchenphysik, ETH, Z\"urich, Switzerland$^{ g}$ \\ $ ^{37}$ Physik-Institut der Universit\"at Z\"urich, Z\"urich, Switzerland$^{ g}$ \\ \bigskip $ ^{38}$ Also at Rechenzentrum, Universit\"at Wuppertal, Wuppertal, Germany \\ $ ^{39}$ Also at IPNL, Universit\'e Claude Bernard Lyon 1, CNRS/IN2P3, Villeurbanne, France \\ $ ^{40}$ Also at CERN, Geneva, Switzerland \\ $ ^{41}$ Also at Ulaanbaatar University, Ulaanbaatar, Mongolia \\ $ ^{42}$ Supported by the Initiative and Networking Fund of the Helmholtz Association (HGF) under the contract VH-NG-401 and S0-072 \\ $ ^{43}$ Also at Moscow Institute of Physics and Technology, Moscow, Russia \\ $ ^{44}$ Also at Department of Physics, University of Toronto, Toronto, Ontario, Canada M5S 1A7 \\ $ ^{45}$ Also at LAPP, Universit\'e de Savoie, CNRS/IN2P3, Annecy-le-Vieux, France \\ $ ^{46}$ Department of Physics, Oxford University, Oxford, UK$^{ b}$ \\ $ ^{47}$ Now at Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA \\ \smallskip $ ^{\dagger}$ Deceased \\ \bigskip $ ^a$ Supported by the Bundesministerium f\"ur Bildung und Forschung, FRG, under contract numbers 05H09GUF, 05H09VHC, 05H09VHF, 05H16PEA \\ $ ^b$ Supported by the UK Science and Technology Facilities Council, and formerly by the UK Particle Physics and Astronomy Research Council \\ $ ^c$ Supported by FNRS-FWO-Vlaanderen, IISN-IIKW and IWT and by Interuniversity Attraction Poles Programme, Belgian Science Policy \\ $ ^d$ Partially Supported by Polish Ministry of Science and Higher Education, grant DPN/N168/DESY/2009 \\ $ ^e$ Supported by VEGA SR grant no. 2/7062/ 27 \\ $ ^f$ Supported by the Ministry of Education of the Czech Republic under the projects LC527, INGO-LA09042 and MSM0021620859 \\ $ ^g$ Supported by the Swiss National Science Foundation \\ $ ^h$ Supported by CONACYT, M\'exico, grant 48778-F \\ $ ^i$ Russian Foundation for Basic Research (RFBR), grant no 1329.2008.2 and Rosatom \\ $ ^j$ Supported by the Romanian National Authority for Scientific Research under the contract PN 09370101 \\ $ ^k$ Partially Supported by Ministry of Science of Montenegro, no. 05-1/3-3352 \\ } \clearpage %\input{Introduction} %%%%%%%%%%%%%%%%%%%%%%% \section{Introduction} %%%%%%%%%%%%%%%%%%%%%%% \label{sec:intro} Deep inelastic scattering (DIS) data provide high precision tests of perturbative quantum chromodynamics (QCD), and have led to a detailed and comprehensive understanding of proton structure, see \cite{Perez:2012um} for a recent review. A measurement of the longitudinal proton structure function, $F_L$, provides a unique test of parton dynamics and the consistency of QCD by allowing a comparison of the gluon density obtained largely from the scaling violations of $F_2$ to an observable directly sensitive to the gluon density. %This follows from %the fact that longitudinally polarised virtual boson scattering is %forbidden at tree level due to helicity conservation, thus pure scattering %off spin half partons would predict $\tilde{F}_L=0$, whereas Previous measurements of $F_L$ have been published by the H1 and ZEUS collaborations covering the kinematic region of low Bjorken $x$, and low to medium four-momentum transfer squared, $Q^2$, using data taken at proton beam energies $E_p=460$, $575$ and $920$~GeV corresponding to centre-of-mass energies of $\sqrt{s}=225$, $252$ and $319$~GeV respectively ~\cite{h1fl,Collaboration:2010ry,Chekanov:2009na}. The new data presented here improve the experimental precision on $F_L$ in the region $35\leq Q^2 \leq 110$~GeV$^2$, and provide the first measurements of $F_L$ in the region $120\leq Q^2 \leq 800$~GeV$^2$ and $6.5\times 10^{-4}>>Additional {\sc Djangoh} study samples %>>>are produced in which the higher order QCD effects are simulated using %>>>DGLAP inspired parton showers matched to the hard LO matrix element %>>>calculation, known as MEPS. The simulated events are weighted to reproduce the cross sections predicted by the NLO QCD fit H1PDF\,2012~\cite{Aaron:2012qi}. This fit includes H1 low $Q^2$ NC data and high $Q^2$ neutral and charged current (CC) data from HERA\,I, as well as inclusive NC and CC measurements from H1 at high $Q^2$ based on the full HERA\,II integrated luminosity at $E_p=920$ GeV~\cite{Aaron:2012qi}. %All data distributions are compared to the MC expectations using %H1PDF\,2012. In both MEPS and CDM samples contributions to the cross %section from diffractive exchange are modelled using the Soft Colour %Interaction model~\cite{sci} as implemented in {\sc Lepto}. In addition the {\sc Compton~22}~\cite{Lendermann:2003rq} MC is used to simulate elastic and quasi-elastic QED Compton processes, and replaces the Compton processes simulation available in {\sc Djangoh}. The detector response to events produced by the various generator programs is simulated in detail using a program based on {\sc Geant3}~\cite{Geant}. The simulation includes a detailed time dependent modelling of detector noise conditions, beam optics, polarisation and inefficient channel maps reflecting actual running conditions throughout the data taking periods. These simulated events are then subjected to the same reconstruction, calibration, alignment and analysis chain as the real data. %\input{ExpTechnique} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Experimental Procedure} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \label{sec:expt} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{Kinematic Reconstruction} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \label{sec:kine} Accurate measurements of the event kinematic quantities $Q^2$, $x$ and $y$ are an essential component of the analysis. Since both the scattered lepton and the hadronic final state (HFS) are observed in the detector, several kinematic reconstruction methods are available allowing for calibration and cross checks. The primary inputs to the various methods employed are the scattered lepton's energy $E^{\prime}_e$ and polar scattering angle $\theta_e$, as well as the quantity $\Sigma=\sum_i(E_i-p_{z,i})$ determined from the sum over the HFS particles assuming charged particles have the pion mass, where $E_i$ and $p_{z,i}$ are the energy and longitudinal momenta respectively~\cite{hfs}. At high $Q^2$ and low $y$ the HFS is dominated by one or more jets. Therefore the complete HFS can be approximated by the sum of jet four-momenta corresponding to localised calorimetric energy sums above threshold. This technique allows a further suppression of ``hadronic noise'' in the reconstruction arising from electronic sources in the LAr calorimeter or from back-scattered low energy particles produced in secondary interactions. The most precise kinematic reconstruction method for $y\gtrsim 0.1$ is the $e$-method which relies solely on $E^{\prime}_e$ and $\theta_e$ to reconstruct the kinematic variables $Q^2$ and $y$ as \begin{linenomath} \begin{equation} Q^2_{e} = \frac{ (E^{\prime}_e \sin{\theta_e})^2}{ 1-y_e}\,, \hspace*{0.5cm} y_e =1- \frac{ E^{\prime}_e}{E_e} \sin^2\left(\frac{\theta_e}{2}\right) \,, \label{eq:emethod} \end{equation} \end{linenomath} and $x$ is determined via the relation $x=Q^2/sy$. This method is used in the analysis region $y>0.19$ since the resolution of the $e$-method degrades at low $y$. The method is also susceptible to large QED radiative corrections at the highest and lowest $y$. A cut on quantity \mbox{$E-P_z=\Sigma+E^{\prime}_e(1-\cos\theta_e)$} ensures that the radiative corrections are moderate. In the $\Sigma$-method \cite{sigma}, $y$ is reconstructed as $\Sigma/(E-P_z)$ and is therefore less sensitive to QED radiative effects. The $e\Sigma$-method \cite{esigma} is an optimum combination of the two and maintains good resolution throughout the kinematic range of the measurement with acceptably small QED radiative corrections. The kinematic variables are determined using \begin{linenomath} \begin{equation} Q^2_{e\Sigma} = Q^2_{e} = \frac{ (E^{\prime}_e \sin{\theta_e})^2}{ 1-y_e}\,, \hspace*{0.5cm} y_{e\Sigma} = 2 E_e \frac{\Sigma}{[E-P_z ]^2} \,, \label{eq:esmethod} \end{equation} \end{linenomath} and $x$ is determined as for the $e$-method above. The $e\Sigma$-method is employed to reconstruct the event kinematics for $y \leq 0.19$ in which $\Sigma$ is determined using hadronic jets defined using the longitudinally invariant $k_T$ jet algorithm~\cite{kt-jets1,kt-jets2}. %% The double angle method (DA-method)~\cite{damethod1,damethod2} provides a %% useful technique for calibrating the electromagnetic (EM) and hadronic calorimeters using %% $\theta_e$ and the polar angle of the HFS, $\gamma_h$, as input. Where the HFS %% is well contained within the detector ($y\gapprox 0.3$) the DA-method has good %% resolution and is to first order independent of the calorimeter energy %% scales. The following formulae are used to determine the kinematics: %% \begin{equation} %% Q^2_{DA} = \frac{4E_e^2\sin\gamma_h(1+\cos\theta_e)}{ \sin\gamma_h+\sin\theta_e-\sin(\theta_e+\gamma_h)}\,, %% \hspace*{0.5cm} %% y_{DA} = \frac{\sin\theta_e (1-\cos\gamma_h) }{ %% \sin\gamma_h+\sin\theta_e-\sin(\theta_e+\gamma_h)} \,. %% \label{eq:damethod} %% \end{equation} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{Polar Angle Measurement and Energy Calibration} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \label{sec:calib} The detector calibration and alignment procedures adopted for this analysis rely on the methods discussed in detail in~\cite{Aaron:2012qi} which uses the high statistics $E_p=920$ GeV data recorded just prior to the $460$ and $575$ GeV runs. The detector was not moved or opened between these run periods. The alignment and calibration constants obtained at $E_p=920$ GeV are verified using the same methods~\cite{Aaron:2012qi} for the data presented here. In this analysis the scattered lepton is detected in the LAr calorimeter by searching for a compact and isolated electromagnetic energy deposition. The polar angle of the scattered lepton, $\theta_e$, is determined using the position of its energy deposit (cluster) in the LAr calorimeter, and the event vertex reconstructed with tracks from charged particles. The relative alignment of the calorimeter and tracking chambers is verified using a sample of events with a well measured lepton track~\cite{tran} in which the COZ chamber provides an accurate $z$ reconstruction of the particle trajectory. The residual difference between the track and cluster polar angles in data and simulation is found to be less than $1$~mrad, and this value is used as the systematic uncertainty of the scattered lepton polar angle. An {\em in situ} energy calibration of electromagnetic energy depositions in the LAr calorimeter is performed for both data and simulation. Briefly, a sample of NC events in which the HFS is well contained in the detector is used with the Double Angle reconstruction method~\cite{damethod1,damethod2} to predict the scattered lepton energy ($E_{DA}$) which is then compared to the measured electromagnetic energy response allowing local calibration factors to be determined in a finely segmented grid in $z$ and $\phi$. The residual mismatch between $E_{DA}$ and $E_e^{\prime}$ after performing the calibration step are found to vary within $\simeq 0.3-1\%$ depending on the geometric location of the scattered lepton within the LAr calorimeter. An additional $0.3\%$ correlated uncertainty is considered and accounts for a possible bias in the $P_{T,DA}$ reconstruction and is determined by varying $\theta_e$ and a measurement of the inclusive hadronic polar angle, $\gamma_h$, by the angular measurement uncertainty. This has been verified by comparing the residual global shifts between data and MC in the kinematic peak of the $E_e^{\prime}$ distribution. At the lowest electron energies the calibration is validated using QED Compton interactions $ep\rightarrow e\gamma p$ with $E_e^{\prime}$ of $3-8\,{\rm GeV}$ in which the lepton track momentum $P_{\rm track}$ is compared to the measured energy $E_{e}^{\prime}$ of the cluster. The simulation on average describes the data well in this low energy region. For energies below $11$~GeV an additional uncorrelated uncertainty of $0.5\%$ is included to account for a possible nonlinearity of the energy scale. The hadronic response of the detector is calibrated by requiring a transverse momentum balance between the predicted $P_T$ in the DA-method ($P_{T,DA}$) and the measured hadronic final state using a tight selection of well reconstructed events with a single jet. The calorimeter calibration constants are then determined in a minimisation procedure across the detector acceptance separately for HFS objects inside and outside jets and for electromagnetic and hadronic contributions to the HFS~\cite{kogler}. The potential bias in the $P_{T,DA}$ reference scale of $0.3\%$ is also included as a correlated source of uncertainty. The mean transverse momentum balance between the hadronic final state and the scattered lepton both in data and simulation agree to within $1\%$ precision which is taken as the uncorrelated hadronic scale uncertainty. The hadronic SpaCal calibration is performed in a similar manner and a systematic uncertainty of $5\%$ is adopted. %\input{Measurement} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{Measurement Procedure} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \label{sec:ncmeas} The event selection and analysis of the NC sample follows closely the procedures discussed in~\cite{Aaron:2012qi}. Inelastic $ep$ interactions are required to have a well reconstructed interaction vertex to suppress beam induced background events. High \qsq neutral current events are selected by requiring each event to have a compact and isolated cluster in the electromagnetic part of the LAr calorimeter. %\footnote{Small local detector regions are disregarded in the analysis % where the cluster of the scattered electron is not fully contained % e.g. intermediate space between stacks, or where the trigger is not % fully efficient.}. The scattered lepton candidate is identified as the cluster of highest transverse momentum and must have an associated CTD track. For high electron energies the track condition is relaxed as detailed in~\ref{sec:nominalAnalysis}. The analysis is restricted to the region $322\,{\rm GeV}$. In figure~\ref{fig:contBulk} the quality of the simulation and its description of the $E_p=460$~GeV and $E_p=575$~GeV data for $y_e<0.19$ can be seen for the distributions of the $P_{T,h}/P_{T,e}$, $\theta_{\rm jets}$, and $E-P_z$ where all HFS quantities are obtained using the vector sum of jet four-momenta. The simulation provides a reasonable description of both sets of distributions. The MC simulation is normalised to the integrated luminosity of the data. \subsubsection{{\em High y} Analysis} In the {\em high y} region ($0.383$~GeV. At these energies photoproduction background contributions arise from $\pi^0\rightarrow \gamma \gamma$ decays, from charged hadrons being misidentified as electron candidates, and from real electrons originating predominantly from semi-leptonic decays of heavy flavour hadrons. These contributions increase rapidly with decreasing energy of the electron candidate. Therefore additional techniques are used to reduce this background. %% The background from $\pi^0\rightarrow \gamma \gamma$ decays lead to %% larger transverse cluster sizes compared to electrons of similar %% energy. The energy weighted cluster radius, ECRA, is calculated as a %% sum of distances of all cells contributing to the cluster from the %% cluster barycentre, weighted by the square root of the energy in each %% cell. For the region $E_e^{\prime}< 6$~GeV, the %% ECRA is required to be less than $4$cm. %% The photoproduction background is further reduced by requiring a well measured %% track associated to the calorimeter cluster, a more stringent %% requirement than is used in the {\em nominal} analysis. These tracks have %% well determined positive charge. For the region %% $E_e^{\prime}<6$~GeV the ratio of the scattered positron energy %% $E_e^{\prime}$ determined using cluster information %% to the momentum of the associated track $p_e$ is required %% to satisfy $0.7 < E_e^{\prime}/p_e < 1.5$. The background from $\pi^0\rightarrow \gamma \gamma$ decays leads to different electromagnetic shower profiles compared to electrons of similar energy. In addition genuine electrons have a momentum matched track associated to the cluster. Four cluster shape variables and the ratio of the candidate electron energy $E_e^{\prime}$ determined using cluster information, to the momentum of the associated track $p_e$, are used in a neural network multilayer perceptron~\cite{Hocker:2007ht} to discriminate signal from background. Additional information using the specific ionisation energy loss, ${\rm d}E/{\rm d}x$, of the track is also used to form a single electron discrimination variable, $D_{ele}$, such that a value of $1$ corresponds to electrons and a value of $0$ corresponds to hadrons. The neural network is trained using single particle MC simulations, and validated with samples of identified electrons and pions from $J/\psi\rightarrow e^+e^-$ and $K^0_s\rightarrow\pi^+\pi^-$ decays in data and MC~\cite{Aaron:2012cj,Sauter}. For the region $E_e^{\prime}<10$~GeV isolated electrons are selected by requiring $D_{ele}>0.80$ which is estimated to have a pion background rejection of more than $99$\% and a signal selection efficiency of better than $90$\%~\cite{Aaron:2012cj}. For the region $E_e^{\prime}>10$~GeV the scattered electron is identified as in the nominal analysis. The scattered lepton candidate is required to have positive charge corresponding to the beam lepton. The remaining background is estimated from the number of data events with opposite charge. This background is statistically subtracted from the positively charged sample. However, a charge asymmetry in photoproduction can arise due to the different detector response to particles compared to antiparticles~\cite{Adloff:2000qk,h1fl2010}. The charge asymmetry has been determined by measuring the ratio of wrongly charged scattered lepton candidates in $e^+p$ to $e^-p$ scattering at $E_p=920$~GeV data and was found to be $1.03\pm 0.05$~\cite{Aaron:2012qi}. This is cross checked in the $E_p=460$ and $575$~GeV data using photoproduction events in which the scattered electron is detected in the electron tagger. In this sample fake scattered electron candidates passing all selection criteria are detected in the LAr calorimeter with both positively and negatively charged tracks associated to the electromagnetic cluster. The charge asymmetry is obtained by comparing the two contributions. The results obtained are consistent with the asymmetry measured in the $E_p=920$~GeV data, however due to the lower statistical precision of the $E_p=460$ and $575$~GeV data sets, the uncertainty of the asymmetry is increased to $0.08$. The asymmetry is taken into account in the subtraction procedure. The efficiency with which the lepton charge is determined is well described by simulation within $0.5\%$ and is discussed in section~\ref{sys:sel}. The control of the background in the most critical region of $E_e^{\prime}<6$~GeV is demonstrated in figure~\ref{fig:contLowE} for both data sets. The MC simulation is normalised to the integrated luminosity of the data. In all cases the background dominated regions are well described in shape and overall normalisation, giving confidence that the background contributions can be reliably estimated from the wrong charge sample. At low $E-P_z$ a peak is observed arising from QED initial state radiation (ISR) which is reasonably well described. The cut $E-P_z>35$~GeV suppresses the influence of ISR on the measurement. The $D_{ele}$ distribution show two populations peaking at zero and unity arising from hadrons and real electrons respectively. The peak at $D_{ele}=1$ for the background indicates that there are real electrons in the remaining background sample. The $e$-method has the highest precision in this region of phase space and is used to reconstruct the event kinematics. Figure~\ref{fig:contHiY} shows the energy spectrum and the polar angle distribution of the scattered lepton, and the $E-P_z$ spectrum of the {\em high y} sample for the $E_p=460$ and $575$ GeV data before background subtraction. The background estimates are shown together with the contribution from the remaining QED Compton process. The NC simulation provides a good description of these distributions. In the scattered lepton energy spectrum a small discontinuity at $8$~GeV can be seen. This is a consequence of suppressing events in which two electron candidates are found, one with $E<8$~GeV and the other with $E>8$~GeV. This criterion efficiently suppresses background from the QED Compton process in the region $E_e^{\prime}<8$~GeV. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{Cross Section Measurement} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \label{sec:xsec} The simulation is used to correct the selected event samples for detector acceptance, efficiencies, migrations and QED radiation effects. The simulation provides a good description of the data and therefore is expected to give a reliable determination of the detector acceptance. The accessible kinematic ranges of the measurements depend on the resolution of the reconstructed kinematic variables. The ranges are determined by requiring the purity and stability of any measurement bin to be larger than $30\%$ as determined from signal MC. The purity is defined as the fraction of events generated and reconstructed in a measurement bin ($N^{g+r}$) from the total number of events reconstructed in the bin ($N^{r}$). The stability is the ratio of the number of events generated and reconstructed in a bin to the number of events generated in that bin ($N^{g}$). The purity and stability are typically found to be above $60\%$. The detector acceptance, $\mathcal{A}=N^{r}/N^{g}$, corrects the measured signal event yields for detector effects including resolution smearing and selection efficiency. The measured differential cross sections $\sigma(x,Q^2)$ are then determined using the relation \begin{linenomath} \begin{eqnarray} \sigma(x,Q^2) = \frac{N-B}{\mathcal{L}\cdot\mathcal{A}}\cdot{\mathcal C} \cdot \left(1+\Delta^{\rm QED}\right)\,, \end{eqnarray} \end{linenomath} where $N$ and $B$ are the selected number of data events and the estimated number of background events respectively, $\mathcal{L}$ is the integrated luminosity, $\mathcal{C}$ is the bin centre correction, and $(1+\Delta^{\rm QED})$ are the QED radiative corrections. These corrections are defined in~\cite{h19497,h1hiq2} and are calculated to first order in $\alpha$ using the program {\sc Heracles}~\cite{heracles} as implemented in {\sc Djangoh}~\cite{django} and verified with the numerical analysis programs {\sc Hector}~\cite{hector} and {\sc Eprc}~\cite{eprc}. No weak radiative corrections are applied to the measurements. The bin centre correction ${\mathcal C(x,Q^2)}$ is a factor obtained from NLO QCD expectation $\sigma^{th}$, using H1PDF\,2012~\cite{Aaron:2012qi}, and scales the bin integrated cross section to a differential cross section at the kinematic point $x,Q^2$ defined as \begin{linenomath} \begin{eqnarray} {\mathcal C}(x,Q^2) =\frac{\sigma^{th}(x,Q^2)} {\iint_{bin}{\small {\rm d}x^{\prime}{\rm d}Q^{2\prime}}\,\,\,\sigma^{th}(x^{\prime},Q^{2\prime})}\,. \end{eqnarray} \end{linenomath} The cross section measurements are finally corrected for the effects of lepton beam polarisation using the H1PDF\,2012 fit to yield cross sections with $P_e=0$. This multiplicative correction does not exceed $2.5\%$ in the region considered. In order to optimise the measurement for an extraction of the structure function $F_L$, the cross sections are measured in $y,Q^2$ bins for $y>0.38$ at $E_p=460$~GeV, and $y>0.304$ at $E_p=575$~GeV. At $E_p=920$~GeV the $y,Q^2$ binned cross sections are published for $y>0.19$~\cite{Aaron:2012qi}. This binning is constructed specifically for a measurement of $F_L$ with fine segmentation in $y$. The lower limits in $y$ for each proton beam energy are chosen such that they have the same $x$ for all three values of $E_p$. In all other cases the cross sections are measured in $Q^2,x$ bins. The bin boundaries and bin centres in the $Q^2-x$ plane are chosen to be the same in the overlapping region for $E_p=460$, $575$ and $920$~GeV for $35\leq Q^2\leq 800$~GeV$^2$. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{Systematic Uncertainties} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \label{sys:sel} The uncertainties on the measurement lead to systematic errors on the cross sections, which can be split into bin-to-bin correlated and uncorrelated parts. All the correlated systematic errors are found to be symmetric to a good approximation and are assumed so in the following. The total systematic error is formed by adding the individual errors in quadrature. The size of each systematic uncertainty source and its region of applicability are given in table~\ref{tab:syserr}. Further details can be found elsewhere~\cite{tran,shushkevich,habib,nikiforov,kogler} in which several of the sources of uncertainty have been investigated using the $E_p=920$~GeV LAr data. The results of similar studies performed using the $E_p=460$~GeV and $575$~GeV LAr data are compared to these earlier analyses to determine the systematic uncertainties. The influence of the systematic uncertainties on the cross section measurements are given in tables~\ref{tab:xsec460}-\ref{tab:xsec575}, and their origin and method of estimation are discussed below. \begin{table}[ht]\footnotesize \begin{center} \begin{tabular}{ l|c|r} \hline %\multicolumn{2}{ l }{{\bf Source}} & {\bf Uncertainty} \\ {\bf Source} & {\bf Region} & \multicolumn{1}{c} {\bf Uncertainty} \\ %jobby centre the heading ``Uncertainty'' but not the column! \hline \multirow{5}{*}{Electron energy scale} & $z_{\rm imp} \leq -150\,{\rm cm}$ & $0.5\%$ unc. $\oplus$ $0.3\%$ corr. \\ %bbe & $-150 < z_{\rm imp} \leq -60\,{\rm cm}$ & $0.3\%$ unc. $\oplus$ $0.3\%$ corr. \\ %cb1 & $-60 < z_{\rm imp} \leq +20\,{\rm cm}$ & $0.5\%$ unc. $\oplus$ $0.3\%$ corr. \\ %cb2 & $+20 < z_{\rm imp} \leq +110\,{\rm cm}$ & $0.5\%$ unc. $\oplus$ $0.3\%$ corr. \\ %cb3 & $z_{\rm imp} > +110\,{\rm cm}$ & $1.0\%$ unc. $\oplus$ $0.3\%$ corr. \\ %fb+ \hline Electron scale linearity & $E_e^{\prime}<11\,{\rm GeV}$ & $0.5\%$ \\ \hline \multirow{2}{*}{Hadronic energy scale} & LAr \& Tracks & $1.0\%$ unc. $\oplus$ $0.3\%$ corr. \\ & SpaCal & $5.0\%$ unc. $\oplus$ $0.3\%$ corr. \\ \hline Polar angle &$\theta_e$ & $1\,{\rm mrad}$ corr.\\ %&$\gamma_h$ & $3$~mrad \\ \hline \multirow{2}{*}{Noise} & $y<0.19$ & $5\%$ energy not in jets , corr.\\ & $y>0.19$ & $20\%$ corr.\\ \hline \multirow{2}{*}{Trigger efficiency} & {\em high y} & $0.3 - 2\%$ \\ & {\em nominal} & $0.3\%$ \\ \hline \multirow{2}{*}{Electron track and vertex efficiency} &{\em high y} & $1 \%$ \\ &{\em nominal} & $0.2-1\%$ \\ \hline Electron charge ID efficiency & {\em high $y$} & $0.5\%$ \\ \hline \multirow{2}{*}{Electron ID efficiency} & {\em high y} $z_{\rm imp}<20~(>20)$~cm & $0.5\%~(1\%)$ \\ & {\em nominal} $z_{\rm imp}<20~(>20)$~cm & $0.2\%~(1\%)$ \\ \hline Extra background suppression & $E_e^{\prime}<10\,{\rm GeV}$ & $D_{ele}>0.80 \pm 0.04$ corr.\\ \hline {\em High y} background subtraction & {\em high $y$} & $1.03 \pm 0.08$ corr.\\ \hline \multirow{2}{*}{QED radiative corrections } & $x<0.1 \, , \, 0.1 \leq x<0.3 \, , \, x\geq0.3$ & $0.3\%$ , $1.0\%$, $2.0\%$ \\ & {\em high y:} $y<0.8$ ($y>0.8$) & $1\%~(1.5\%)$ \\ \hline \multirow{2}{*}{Acceptance corrections} & {\em high y} & $0.5\%$ \\ & {\em nominal} & $0.2\%$ \\ \hline Luminosity & & $4\%$ corr.\\ \hline \end{tabular} \caption{ Table of applied systematic uncertainties and regions of applicability. Uncertainties which are considered point-to-point correlated are labelled corr., and all other sources are considered uncorrelated. The effect of these uncertainties on the cross section measurements is given in the tables of section~\ref{sec:results} (except for the luminosity uncertainty). } \label{tab:syserr} \end{center} \end{table} \begin{description} %{\bf Electron Energy Uncertainty:} \item[Electron Energy:] Uncertainties arise from the particular choice of calibration samples, and the linearity correction uncertainty. These uncertainties are taken from the analysis of the $920$ GeV data~\cite{Aaron:2012qi}. The uncertainty varies as a function of $z_{\rm imp}$~\cite{Aaron:2012qi}, the $z$ position of the scattered electron in the calorimeter, as given in table~\ref{tab:syserr}. The correlated part of the uncertainty of $0.3\%$ accounts for a possible bias in the $E_{DA}$ reconstruction used as a reference scale in the energy calibration procedure. This results in a systematic uncertainty which is up to $2-3\%$ at low $y$. %{\bf Hadronic Calibration Uncertainty:} \item[Hadronic Calibration:] An uncorrelated uncertainty of $1\%$ is used for the hadronic energy measurement. The uncertainty is determined by quantifying the agreement between data and simulation in the mean of the $P_{T,h}/P_{T,e}$ distribution in different kinematic regions. The correlated part of the uncertainty accounts for a possible bias in the $E_{DA}$ reconstruction used as a reference scale in the energy calibration. It is determined to be $0.3\%$ and results in a correlated systematic error on the cross section which is up to $2-3\%$ at low $y$. The resulting correlated systematic error is typically below $1\%$ for the cross sections. %{\bf Polar Angle Uncertainty:} \item[Polar Angle:] A correlated $1$~mrad uncertainty on the determination of the electron polar angle is considered. This contribution leads to a typical uncertainty on the reduced cross sections of less than $1\%$. %{\bf Noise Subtraction Uncertainty:} \item[Noise Subtraction:] Energy classified as noise in the LAr calorimeter is excluded from the HFS. For $y<0.19$ the calorimetric energy not contained within hadronic jets is classified as noise. The uncertainty on the subtracted noise is estimated to be $5\%$ of the noise contribution as determined from the analysis of the HERA\,II $E_p=920$ GeV data~\cite{Aaron:2012qi}. For $y>0.19$ the noise contribution is restricted to the sum of isolated low energy calorimetric depositions. Here the residual noise contribution is assigned an uncertainty of $20\%$, to accomodate differences between data and simulation. %{\bf {\em Nominal} Trigger Efficiency Uncertainty:} \item[{\em Nominal} Trigger Efficiency:] The uncertainty on the trigger efficiency in the {\em nominal} analysis is determined separately for both $E_p=460$ and $575$ GeV data taking periods. Three trigger requirements are employed: the global timing, the event timing and the calorimeter energy. The inefficiency of global timing criteria to suppress out of time beam related background was continuously monitored with high precision and found to be $0.3\%$ and is corrected for. Finally the event timing trigger requirements were also continuously monitored in the data. After rejection of local inefficient regions the overall trigger efficiency is close to $100\%$ and an uncertainty of $0.3\%$ is assigned. %{\bf NC {\em high y} Trigger Efficiency Uncertainty:} \item[{\em High y} Trigger Efficiency:] At low $E_e^{\prime}$ the LAr electron trigger is supplemented by the SpaCal trigger and by the Level 3 electron trigger based on the LAr Jet Trigger and the Fast Track Trigger. The same global timing conditions as mentioned above are used in the {\em high y} triggers. The SpaCal trigger and the LAr electron trigger together with the L3 electron trigger are independent since the SpaCal trigger is fired by the backward going hadronic final state particles. The efficiency of each of these two groups of triggers is determined using events triggered by the other group as a monitor sample. In the analysis events from both groups of triggers are used. The combined efficiency is calculated and is found to vary between $91\%$ and $97\%$ at $E_e^{\prime}=3\,{\rm GeV}$. The statistical uncertainty of the combined efficiency together with a $0.3\%$ uncertainty arising from the global timing conditions is adopted as uncorrelated trigger uncertainty. It varies from $0.3\%$ at high electron energies to $2\%$ at $E_e^{\prime}=3\,{\rm GeV}$. %{\bf Electron Track-Vertex Efficiency Uncertainty:} \item[Electron Track-Vertex Efficiency:] The efficiencies for reconstructing a track associated to the scattered lepton and for reconstructing the interaction vertex are determined simultaneously. The efficiency measurement follows the procedure used in the analysis of the HERA\,II $E_p=920$~GeV data and checked on the $E_p=460$ and $575$ GeV data. Three algorithms are used to determine the interaction vertex. The data and MC efficiencies are compared for each contributing algorithm. The combined efficiency in the {\em nominal} analysis is found to be larger than $99.5\%$ in the data. The residual differences between data and simulation after correction of simulation by $0.3\%$ define the uncorrelated systematic uncertainty which is $0.2\%$ and is considered to be uncorrelated. In the {\em high y} analysis a more stringent requirement on the quality of the track associated to the scattered lepton is applied. The efficiency was measured using electrons in the region of $E_e^{\prime}>18\,{\rm GeV}$ and checked at low $E_e^{\prime}$ using a sample of QED Compton events. It is found to be $96\%$ in data with a difference of $1\%$ between data and simulation. This difference was corrected for and a $1\%$ uncorrelated uncertainty is adopted. %{\bf Electron Charge Identification Efficiency Uncertainty:} \item[Electron Charge Identification Efficiency:] In the {\em high y} analysis the efficiency for correct charge identification of the scattered lepton is measured in the region $E_e^{\prime}>18\,{\rm GeV}$ which is free from photoproduction background. The simulation describes the efficiency of the data with an overall difference of $0.5\%$, and no significant time dependence is observed. This is validated using ISR events in which the incoming beam positron has reduced energy due to QED radiation, yielding a sample of events which is free from photoproduction background but has $E_e^{\prime}$ below 12~GeV. The measured cross section is corrected for the overall difference by increasing the measured values by $2\times 0.5\%$ with an uncertainty of $2\times 0.25\%$. The factor of two accounts for the fact that charge misidentification has a dual influence on the measurement by causing both a loss of signal events and an increase of the subtracted background~\cite{shushkevich}. %{\bf Electron Identification Uncertainty:} \item[Electron Identification:] A calorimetric algorithm based on longitudinal and transverse shower shape quantities is used to identify electrons in the $E_p=460$ and $575$~GeV data sample. The efficiency of this selection can be estimated using a simple track based electron finder which searches for an isolated high $p_T$ track associated to an electromagnetic energy deposition. The efficiency is well described by the simulation and the uncertainty of $0.2\%~(0.5\%)$ is assigned in the {\em nominal} ({\em high y}) analysis at $z_{\rm imp} < 20$~cm. For $z_{\rm imp} > 20$~cm the uncertainty is taken to be $1\%$ due to the lack of statistics in this region selected by the track based algorithm. \item[Extra Background Suppression:] The uncertainty on the efficiency of the $D_{ele}$ requirement has been studied with $J/\psi\rightarrow ee$ decays in data and is well described by the simulation. A variation of $\pm 0.04$ around the nominal $D_{ele}$ cut value accommodates any residual difference between data and simulation. This variation leads to a cross section uncertainty of up to $2\%$ at highest $y$. %{\bf NC {\em high y} Background Subtraction Uncertainty:} \item[{\em High y} Background Subtraction:] In the {\em high y} analysis the photoproduction background asymmetry is measured in the $E_p=460$ and $575$ GeV data, and found to be consistent with the determination using the $E_p=920$ GeV data~\cite{Aaron:2012qi,shushkevich}, albeit with reduced precision. Therefore the asymmetry is taken from the analysis of the HERA\,II data at $E_p=920$~GeV and the associated uncertainty is increased to $0.08$. The resulting uncertainty on the measured cross sections is at most $2.7\%$ at $y=0.85$ and $Q^2 = 35$~GeV$^2$. %{\bf QED Radiative Corrections Uncertainty:} \item[QED Radiative Corrections:] An error on the cross sections originating from the QED radiative corrections is taken into account. This is determined by comparing the predicted radiative corrections from the programs {\sc Heracles} (as implemented in {\sc Djangoh}), {\sc Hector}, and {\sc Eprc}. The radiative corrections due to the exchange of two or more photons between the lepton and the quark lines, which are not included in {\sc Djangoh}, vary with the polarity of the lepton beam. This variation, estimated using {\sc Eprc}, is found to be small compared to the quoted errors and is neglected~\cite{shushkevich}. %{\bf Acceptance Correction Uncertainty:} \item[Model Uncertainty of Acceptance Correction:] The MC simulation is used to determine the acceptance correction to the data and relies on a specific choice of PDFs. The assigned uncertainty is listed in table~\ref{tab:syserr}. %{\bf Luminosity Uncertainty:} \item[Luminosity:] The integrated luminosity is measured using the Bethe-Heitler process $ep\rightarrow ep\gamma$ with an uncertainty of $4\%$, of which $0.5\%$ is from the uncertainty in the theoretical calculation of this QED process. \end{description} %% In summary the typical total systematic error is substantially %% reduced compared to previous H1 %% publications~\cite{h19497,h19899,h1hiq2,h1ccpol} to about $1.5\%$ for %% the NC double differential cross sections, and $4\%$ for the CC double %% differential cross sections. For the ${\rm d} \sigma_{\rm NC(CC)} / %% {\rm d} Q^2$ measurements, the error is typically $1.3\%$ (NC) and %% $3\%$ (CC). This reduction is achieved through a better %% understanding of the response of the detector and in particular for %% the hadronic and EM calibrations, as well as the reconstruction of %% polar angles. Further detailed studies also allow reductions in %% the systematic uncertainties of the electron identification and the %% trigger efficiency. %\input{Results} %%%%%%%%%%%%%%%%% \section{Results} %%%%%%%%%%%%%%%%% \label{sec:results} %--------------------------------------------- \subsection{Double Differential Cross Sections} %--------------------------------------------- \label{sec:dxdq2} The reduced cross sections $\tilde{\sigma}_{\rm NC}(x, Q^2)$ for $P_e=0$ are measured in the kinematic range $35 \leq Q^2\leq 800\,{\rm GeV}^2$ and $0.00065\leq x\leq 0.65$ at two different centre-of-mass energies and are referred to as the LAr data. The data are presented in tables~\ref{tab:xsec460} --~\ref{tab:xsec575} and shown in figure~\ref{fig:xsec-xq2}. The figure also includes previously published H1 data~\cite{Collaboration:2010ry} in the $Q^2$ range of the new data reported here, and are referred to as the SpaCal data. The published $920$~GeV $e^+p$ LAr data~\cite{Aaron:2012qi} are scaled by a normalisation factor of $1.018$~\cite{QEDCerratum}. This correction factor arises from an error in the {\sc Compton} generator used in the determination of the integrated luminosity of the HERA-II 920 GeV data set. The new LAr data provide additional low $x$ measurements for $Q^2\geq 35$~GeV$^2$ (from the $E_p=460$ and $575$~GeV data sets). The data are compared to the H1PDF\,2012 fit~\cite{Aaron:2012qi} which provides a good description of the data. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{Measurement of $\pmb{F}_{\pmb L}$} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \label{sec:fl} According to equation~\ref{eq:Rnc} it is straightforward to determine $F_L$ by a linear fit as a function of $y^2/(1+(1-y)^2)$ to the reduced cross section measured at given values of $x$ and $Q^2$ but at different centre-of-mass energies. An example of this procedure is shown in figure~\ref{fig:rosenbluth} for six different values of $x$ at $Q^2=60$~GeV$^2$. %taking into account the experimental uncertainties. This method however does not optimally account for correlations across all measurements, and therefore an alternative procedure is applied. The structure functions $F_L$ and $F_2$ are simultaneously determined from the cross section measurements at $E_p=460,575$ and $920$~GeV using a $\chi^2$ minimisation technique as employed in~\cite{Collaboration:2010ry}. In this approach the values of $F_L$ and $F_2$ at each measured $x,Q^2$ point are free parameters of the fit. For $Q^2\leq 800$~GeV$^2$ the influence of the $xF_3$ structure function is predicted to be small and is neglected. In addition, a set of nuisance parameters $b_j$ for each correlated systematic error source $j$ is introduced. The minimisation is performed using the new measurements presented here as well as previously published data from H1~\cite{Collaboration:2010ry,Aaron:2012qi}. The $\chi^2$ function for the minimisation is \begin{linenomath} \begin{equation} \label{eq:chi2} %\chi^2 \chi^2 \left(F_{L,i},F_{2,i},b_{j}\right) = \sum_i \frac{\textstyle \left[ \left(F_{2,i}- f(y_{i}) F_{L,i}\right) - \sum_j \Gamma_{i,j} b_j - \mu_i\right]^2}{\textstyle \Delta^2_i} + \sum_j b^2_j\,, \end{equation} \end{linenomath} where $f(y)=y^2/(1+(1-y)^2)$ and $\mu_i$ is the measured reduced cross section at an $x,Q^2$ point $i$ with a combined statistical and uncorrelated systematic uncertainty $\Delta_i = \sqrt{\left(\Delta_{i, \rm stat}^2 + \Delta_{i,\rm syst}^2 \right)}$. The effect of correlated error sources $j$ on the cross section measurements is given by the systematic error matrix $\Gamma_{i,j}$. The correlations of systematic uncertainties between the SpaCal data sets at different energies are taken from~\cite{Collaboration:2010ry}. The systematic uncertainties of the LAr measurements are taken to be $100\%$ correlated among the $460\,,575$ and $920$ GeV data sets. There is no correlation between LAr and SpaCal measurements except for a common integrated luminosity normalisation of the LAr and SpaCal data at $E_p=460$ and $575$~GeV. For low $y\le 0.35$, the coefficient $f(y)$ is small compared to unity and thus $F_L$ can not be accurately measured. %In this kinematic domain, the constraint $0\le F_L\le F_2$ provides an even better bound on the value of $F_L$ than the experimental data. To avoid unphysical values for $F_L$ in this kinematic region the $\chi^2$ function is modified by adding an extra prior \cite{Collaboration:2010ry}. The minimisation of the $\chi^2$ function with respect to these variables leads to a system of linear equations which is solved analytically. This technique is identical to the linear fit discussed above when considering a single $x,~Q^2$ bin and neglecting correlations between the cross section measurements. The $\chi^2$ per degree of freedom is found to be $184/210$. %including the contribution to the $\chi^2$ from the $30$ correlated systematic error sources. The systematic sources include normalisation uncertainties for the SpaCal and LAr data sets for $E_p=460,\,575$ and $920$~GeV data which are all shifted in the minimisation procedure by less than one standard deviation with the exception of the LAr $920$~GeV data which are re-normalised by $+3.4\%$, or $1.2$ standard deviations. All other sources of uncertainty including those related to calibration scales, noise subtractions, background estimates and polar angle measurements are shifted by typically less than $0.3$ and never more than $0.8$ standard deviations. The measured structure functions are given in table~\ref{tab:flf2} over the full range in $Q^2$ from $1.5$ to $800$~GeV$^2$. Only measurements of $F_L$ with a total uncertainty less than $0.3$ for $Q^2\leq25$~GeV$^2$, or total uncertainty less than $0.4$ for $Q^2\geq35$~GeV$^2$ are considered. The table also includes the correlation coefficient $\rho$ between the $F_2$ and $F_L$ values. In figures~\ref{fig:FLxq2-a} and~\ref{fig:FLxq2-b} the measured structure functions $F_2$ and $F_L$ are shown in the regions $2\leq Q^2\leq 25$~GeV$^2$ and $Q^2\geq 35$~GeV$^2$ respectively. The new data reported here, in which the scattered electron is recorded in the LAr calorimeter, provide small additional constraints on the $F_L$ measurement for $1.5\leq Q^2\leq 25$~GeV$^2$ by means of correlations in the systematic uncertainties. The SpaCal and LAr data are used together for $35\leq Q^2 \leq 90$~GeV$^2$ . For %larger values $Q^2\geq 120$~GeV$^2$ $F_L$ is determined exclusively from the LAr cross section measurements. Therefore these data supersede the previous measurements of $F_2$ and $F_L$ in \cite{h1fl,Collaboration:2010ry}. For precision analyses of H1 data it is recommended to use the published tables of the reduced differential cross sections given in tables~\ref{tab:xsec460} to~\ref{tab:xsec575} and the full breakdown of systematic uncertainties instead of the derived quantities $F_2$ or $F_L$. %The previously published analysis of the low $Q^2$ measurements of $F_L$~\cite{Collaboration:2010ry} contained an error in the averaging procedure in which not all correlated uncertainties were taken into account. The present measurements reported here correct this error at low $Q^2$ as well as extend the range to higher $Q^2$ with the LAr data. Therefore these data supersede the previous measurements of $F_2$ and $F_L$. For precision analyses of H1 data it is recommended to use the published tables of the reduced differential cross sections given in tables~\ref{tab:xsec460} to~\ref{tab:xsec575} and the full breakdown of systematic uncertainties instead of the derived quantities $F_2$ orc $F_L$. This measurement of $F_L$ and $F_2$ at high $y$ constitutes a model independent method with no assumptions made on the values of the structure functions. Within uncertainties the $F_L$ structure function is observed to be positive everywhere and approximately equal to $20\%$ of $F_2$. Also shown are the $F_L$ and $F_2$ measurements from the ZEUS collaboration~\cite{Chekanov:2009na} which agree with the H1 data. The ZEUS data are moved to the $Q^2$ values of the H1 measurements using the H1PDF\,2012 NLO QCD fit. This QCD fit is able to provide a good description of both measurements of $F_L$ and $F_2$ across the full $Q^2$ range. In order to reduce the experimental uncertainties the $F_L$ measurements are combined at each $Q^2$ value. Furthermore the highest $Q^2$ bins are also averaged to achieve an approximately uniform experimental precision over the full kinematic range of the measurement. The $Q^2$ averaging is performed for $Q^2=300$ and $400$~GeV$^2$, and for the $Q^2=500,~600$ and $800$~GeV$^2$ values. The resulting data are given in table~\ref{tab:flave} and shown in figure~\ref{fig:FLq2} where the average $x$ for each $Q^2$ is provided on the upper scale of the figure. The data are compared to a suite of QCD predictions at NNLO: HERAPDF1.5~\cite{HERAPDF1.5}, CT10~\cite{CT10}, ABM11~\cite{ABM11}, MSTW2008~\cite{MSTW2008}, JR09~\cite{Gluck:2007ck} and NNPDF2.3~\cite{NNPDF2.3}. In all cases the perturbative calculations provide a reasonable description of the data. %A similar average of the $F_L$ measurement over $x$ has already been performed~\cite{h1fl} for $Q^2 \leq 45$~GeV$^2$. A small problem has been identified in the averaging procedure which lead to %an underestimated correlated systematic uncertainties. A similar average of $F_L$ measurements over $x$ has already been performed in~\cite{Collaboration:2010ry} for $Q^2<45$~GeV$^2$. A small problem in~\cite{Collaboration:2010ry} has been identified in the averaging procedure which lead to underestimated correlated systematic uncertainties which has been corrected in the measurements reported here. Therefore the data presented in tables~\ref{tab:flave} supersedes the corresponding table from~\cite{Collaboration:2010ry}. %the previous measurements of $F_2$ and $F_L$. %The data in tables~\ref{tab:flave} supersedes the corresponding table from~\cite{h1fl}. The cross section ratio $R$ of longitudinally to transversely polarised virtual photons is related to the structure functions $F_2$ and $F_L$ as %through the relation \begin{equation} R = \frac{\sigma_L}{\sigma_T} = \frac{F_L}{F_2-F_L} \,. \label{eq:Rflf2} \end{equation} This ratio has previously been observed to be approximately constant for $3.5 \leq Q^2 \leq 45$~GeV$^2$~\cite{Collaboration:2010ry}. The values of $R$ as a function of $Q^2$ are determined by minimising the $\chi^2$ function of equation~\ref{eq:chi2} in which $F_L$ is replaced by $$F_L=\frac{R}{1+R}F_2$$ assuming the value of $R$ is constant as a function of $x$ for a given $Q^2$. %For this reason equation~\ref{eq:chi2} becomes non-linear and therefore the minimisation cannot be solved analytically. For the same reason the uncertainties become asymmetric and a MC technique is used The minimum is found numerically in this case, using the MINUIT package \cite{minuit}. The asymmetric uncertainties are determined using a MC method in which the mean squared deviation from the measured value of $R$ is used to define the asymmetric uncertainties. The resulting value of $R(Q^2)$ is shown in figure~\ref{fig:Rq2}. % %% In the current analysis $R(Q^2)$ is determined from the reduced cross %% section measured at three centre-of-mass energies in a second $\chi^2$ %% fit in which the value of $F_2$ in each $Q^2$ bin is first averaged %% and a single common value of $R$ is assumed for the $x$ range covered %% by the measurements in the given $Q^2$ bin. This $R$ value is a free %% parameter of the fit, and minimised using the $\chi^2$ function and is %% shown as a function of $Q^2$ in figure~\ref{fig:Rq2}. % %The data are found to be consistent with a constant value across the entire $Q^2$ range shown. %The measurements at constant $y$ are compared to the prediction of the HERAPDF1.5 NNLO fit {\bf for $y=0.7$ . %The figure also includes predictions of the HERAPDF1.5 NNLO fit for values of $y$ of $0.40$ and $0.85$ which correspond to the region of $x$ in which the data are sensitive to $R$. %Only little dependence on $y$ is expected justifying the assumption made for the extraction of $R(Q^2)$.} The measurements are compared to the prediction of the HERAPDF1.5 NNLO for $\sqrt{s}=225$~GeV and $y=0.7$. { The expected small variation of $R$ in the region of $x$ in which the data are sensitive to this quantity is also shown. %Only little dependence on $y$ is observed justifying the assumption made for the extraction of $R(Q^2)$.} The data are found to be consistent with a constant value across the entire $Q^2$ range shown. The fit is repeated by assuming that $R$ is constant over the full $Q^2$ range. This yields a value of $R=0.23\pm0.04$ with $\chi^2$/ndf =$314/367$ which agrees well with the value obtained previously~\cite{Collaboration:2010ry} using only data up to $Q^2=45$~GeV$^2$, and with the ZEUS data. At NLO and NNLO QCD, analyses of DIS data constrain the gluon density through the precision measurements of $F_2$ and the reduced NC cross sections through their scaling violations. %A direct measure of $F_L$ provides an alternative means of locally determining the gluon PDF. { Since at order $\alpha_s$ the gluon density is %directly related to $F_L$ via the approximate relation~\cite{CooperSarkar:1987ds,Zijlstra:1992qd} \begin{equation} xg(x,Q^2) \approx 1.77 \frac{3\pi}{2\alpha_S(Q^2)} F_L(x,Q^2) \,, \label{eq:xgapprox} \end{equation} the direct measure of $F_L$ can be used to demonstrate its sensitivity to the gluon density by comparing the gluon obtained from the $F_L$ measurements to the predicted gluon density obtained from a NLO QCD fit to DIS data.% not including these data. In figure~\ref{fig:gluon} the gluon density extracted according to equation~\ref{eq:xgapprox} is compared to the prediction from the gluon density determined in the NLO HERA\-PDF1.5 QCD fit. } %Therefore a comparison of the gluon obtained from this measurement can be made to the predicted gluon density obtained from an NLO QCD fit to DIS data where no $F_L$ measurements have been included in the fits. %The extracted gluon density is shown in figure~\ref{fig:gluon} compared to the prediction from the gluon density determined in the NLO HERAPDF1.5 QCD fit. The uncertainty bands of the theoretical prediction includes experimental, model and parametrisation uncertainties of the fit procedure. In order to judge on the goodness of the approximation, the gluon density as obtained by applying equation~\ref{eq:xgapprox} to the $F_L$ prediction based on the NLO HERAPDF1.5 QCD fit is also shown. A reasonable agreement between the gluon density as extracted from the direct measurement of $F_L$ based on the approximate relation with the gluon derived indirectly from scaling violations is observed. %is remarkably good.} %It is striking that the local extraction of the gluon density using the direct measurements of $F_L$ and the approximate relation above agree so well with the gluon derived indirectly from scaling violations. %\input{Summary} %%%%%%%%%%%%%%%%%% \section{Conclusions} %%%%%%%%%%%%%%%%%% \label{sec:summary} The unpolarised neutral current inclusive DIS cross section for $ep$ interactions are measured at two centre-of-mass energies of $\sqrt{s}=225$ and $252$~GeV with integrated luminosities of $11.8$~pb$^{-1}$ and $5.4$~pb$^{-1}$ respectively. The measurements are performed up to the highest accessible inelasticity of $y=0.85$ where the contribution of the $F_L$ structure function to the reduced cross section is sizeable. The data are used together with previously published measurements at $\sqrt{s}=319$ GeV ($E_p=920$~GeV) to simultaneously extract the $F_L$ and $F_2$ structure functions in a model independent way. The new data extend previous measurements of $F_L$ up to %the region $Q^2 =800$~GeV$^2$ and supersede previous H1 data. Predictions of different perturbative QCD calculations at NNLO are compared to data. Good agreement is observed between the measurements and the theoretical calculations. The ratio $R$ of the longitudinally to transversely polarised virtual photon cross section is consistent with being constant over the kinematic range of the data, and is determined to be $=0.23\pm0.04$. The $F_L$ measurements are used to perform %a direct local extraction of the {a gluon density extraction based on a NLO approximation} which is found to agree reasonably well with the gluon determined from scaling violations. \section*{Acknowledgements} We are grateful to the HERA machine group whose outstanding efforts have made this experiment possible. We thank the engineers and technicians for their work in constructing and maintaining the H1 detector, our funding agencies for financial support, the DESY technical staff for continual assistance and the DESY directorate for support and for the hospitality which they extend to the non DESY members of the collaboration. We would like to give credit to all partners contributing to the EGI computing infrastructure for their support for the H1 Collaboration. We would also like to thank the members of the MSTW, CT, ABM, JR, NNPDF and HERAPDF collaborations for their help in producing theoretical predictions of $F_L$ shown in figure~\ref{fig:FLq2}. %\input{Appendix} %\input{Bibliography} %\providecommand{\href}[2]{#2}\begingroup\raggedright \begin{thebibliography}{10} %\cite{Perez:2012um} \bibitem{Perez:2012um} E.~Perez and E.~Rizvi, %``The Quark and Gluon Structure of the Proton,'' Rep.\ Prog.\ Phys.\ {\bf 76} (2013) 046201 [arXiv:1208.1178]. %%CITATION = ARXIV:1208.1178;%% %4 citations counted in INSPIRE as of 11 Jun 2013 \bibitem{h1fl} F.~D. 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B {\bf 383} (1992) 525. %%CITATION = NUPHA,B383,525;%% %327 citations counted in INSPIRE as of 02 Nov 2013 \end{thebibliography} \newpage %\bibliographystyle{unsrt} %\bibliographystyle{desy09-005} %\bibliographystyle{h1pub} %\bibliographystyle{h-physrev3} %\bibliography{Bibliography} \newpage %\input{Tables} %\input{plots/xsec460-afterPubReading} \begin{table}[htbp] \begin{center} \tiny \begin{tabular}{|r|c|c|r|r|r|r|r|r|r|r|r|r|r|r|r|} \hline $Q^2$ & $x$ & $y$ & $\tilde{\sigma}_{\rm NC}$ & $\delta_{\rm tot}$ & $\delta_{\rm stat}$ & $\delta_{\rm unc}$ & $\delta_{\rm unc}^{E}$ & $\delta_{\rm unc}^{h}$& $\delta_{\rm cor}$ & $\delta_{\rm cor}^{E^+}$ & $\delta_{\rm cor}^{\theta^+}$& $\delta_{\rm cor}^{h^+}$& $\delta_{\rm cor}^{N^+}$& $\delta_{\rm cor}^{S^+}$& $\delta_{\rm cor}^{D^+}$ \\ $(\rm GeV^2)$ & & & & $(\%)$ & $(\%)$ & $(\%)$ & $(\%)$ & $(\%)$ & $(\%)$ & $(\%)$ & $(\%)$ & $(\%)$ & $(\%)$ & $(\%)$ & $(\%)$ \\ \hline $35$ & $8.10 \times 10^{-4}$ & $0.850$ & $1.343$ & $6.5$ & $4.5$ & $3.8$ & $0.6$ & $2.8$ & $2.8$ & $-0.3$ & $-0.4$ & $0.2$ & $0.7$ & $2.3$ & $1.2$ \\ \hline $45$ & $1.04 \times 10^{-3}$ & $0.850$ & $1.173$ & $6.3$ & $4.7$ & $3.4$ & $0.4$ & $2.4$ & $2.4$ & $-0.1$ & $-0.5$ & $0.1$ & $0.6$ & $2.1$ & $1.0$ \\ $45$ & $1.18 \times 10^{-3}$ & $0.750$ & $1.187$ & $5.7$ & $5.1$ & $2.2$ & $0.6$ & $0.8$ & $1.3$ & $0.2$ & $-0.5$ & $0.0$ & $0.3$ & $0.6$ & $1.0$ \\ \hline $60$ & $1.39 \times 10^{-3}$ & $0.850$ & $1.190$ & $6.2$ & $5.0$ & $3.0$ & $0.2$ & $2.0$ & $2.0$ & $-0.1$ & $-0.3$ & $0.1$ & $0.5$ & $1.7$ & $0.8$ \\ $60$ & $1.58 \times 10^{-3}$ & $0.750$ & $1.117$ & $4.7$ & $4.0$ & $2.0$ & $0.5$ & $0.6$ & $1.4$ & $-0.2$ & $-0.6$ & $0.0$ & $0.2$ & $0.6$ & $1.0$ \\ \hline $90$ & $2.09 \times 10^{-3}$ & $0.850$ & $1.269$ & $6.3$ & $5.3$ & $2.9$ & $0.3$ & $1.8$ & $1.8$ & $-0.2$ & $-0.4$ & $0.1$ & $0.5$ & $1.4$ & $0.9$ \\ $90$ & $2.36 \times 10^{-3}$ & $0.750$ & $1.193$ & $4.6$ & $4.1$ & $1.9$ & $0.3$ & $0.5$ & $1.1$ & $-0.2$ & $-0.5$ & $0.1$ & $0.2$ & $0.3$ & $0.9$ \\ $90$ & $2.73 \times 10^{-3}$ & $0.650$ & $1.156$ & $4.2$ & $3.8$ & $1.8$ & $0.4$ & $0.2$ & $0.8$ & $-0.2$ & $-0.6$ & $0.0$ & $0.2$ & $0.3$ & $0.4$ \\ \hline $120$ & $2.78 \times 10^{-3}$ & $0.850$ & $1.249$ & $6.8$ & $6.1$ & $2.7$ & $0.1$ & $1.5$ & $1.6$ & $0.0$ & $-0.4$ & $0.1$ & $0.4$ & $0.9$ & $1.2$ \\ $120$ & $3.15 \times 10^{-3}$ & $0.750$ & $1.099$ & $5.3$ & $4.8$ & $1.9$ & $0.4$ & $0.4$ & $0.9$ & $-0.2$ & $-0.4$ & $0.0$ & $0.2$ & $0.4$ & $0.6$ \\ $120$ & $3.63 \times 10^{-3}$ & $0.650$ & $1.052$ & $4.7$ & $4.3$ & $1.9$ & $0.6$ & $0.2$ & $0.6$ & $-0.2$ & $-0.4$ & $0.0$ & $0.2$ & $0.2$ & $0.2$ \\ $120$ & $4.82 \times 10^{-3}$ & $0.490$ & $1.041$ & $3.3$ & $2.7$ & $1.8$ & $0.6$ & $0.1$ & $0.8$ & $-0.3$ & $-0.7$ & $0.0$ & $0.2$ & $0.1$ & $0.0$ \\ \hline $150$ & $3.47 \times 10^{-3}$ & $0.850$ & $1.230$ & $7.8$ & $7.1$ & $2.6$ & $0.4$ & $1.4$ & $1.9$ & $-0.2$ & $-0.3$ & $0.1$ & $0.4$ & $0.8$ & $1.6$ \\ $150$ & $3.94 \times 10^{-3}$ & $0.750$ & $1.024$ & $6.1$ & $5.8$ & $1.9$ & $0.4$ & $0.3$ & $0.8$ & $-0.2$ & $-0.4$ & $0.0$ & $0.2$ & $0.2$ & $0.6$ \\ $150$ & $4.54 \times 10^{-3}$ & $0.650$ & $1.010$ & $5.4$ & $5.0$ & $2.0$ & $0.9$ & $0.1$ & $0.5$ & $-0.2$ & $-0.4$ & $0.0$ & $0.2$ & $0.2$ & $0.1$ \\ $150$ & $6.03 \times 10^{-3}$ & $0.490$ & $1.060$ & $3.2$ & $2.5$ & $1.8$ & $0.5$ & $0.1$ & $0.7$ & $-0.3$ & $-0.6$ & $0.0$ & $0.2$ & $0.1$ & $0.0$ \\ $150$ & $8.00 \times 10^{-3}$ & $0.369$ & $0.9774$ & $3.0$ & $2.6$ & $1.4$ & $0.6$ & $0.0$ & $0.9$ & $-0.4$ & $-0.8$ & $0.0$ & $0.1$ & $0.0$ & $0.0$ \\ $150$ & $1.30 \times 10^{-2}$ & $0.227$ & $0.8384$ & $3.8$ & $3.3$ & $1.5$ & $1.2$ & $0.0$ & $1.1$ & $-0.8$ & $-0.7$ & $0.0$ & $0.0$ & $0.0$ & $0.0$ \\ $150$ & $2.00 \times 10^{-2}$ & $0.148$ & $0.7006$ & $5.2$ & $4.5$ & $2.2$ & $1.7$ & $1.0$ & $1.7$ & $-1.0$ & $-1.0$ & $-0.4$ & $-0.8$ & $0.0$ & $0.0$ \\ \hline $200$ & $4.63 \times 10^{-3}$ & $0.850$ & $1.117$ & $9.6$ & $9.1$ & $2.5$ & $0.3$ & $1.1$ & $2.1$ & $-0.1$ & $-0.4$ & $0.0$ & $0.3$ & $0.6$ & $1.9$ \\ $200$ & $5.25 \times 10^{-3}$ & $0.750$ & $1.011$ & $8.1$ & $7.7$ & $1.9$ & $0.3$ & $0.3$ & $1.1$ & $0.2$ & $-0.4$ & $0.0$ & $0.2$ & $0.1$ & $1.0$ \\ $200$ & $6.06 \times 10^{-3}$ & $0.650$ & $0.9997$ & $6.8$ & $6.5$ & $2.0$ & $0.9$ & $0.2$ & $0.6$ & $-0.1$ & $-0.5$ & $0.1$ & $0.2$ & $0.2$ & $0.0$ \\ $200$ & $8.04 \times 10^{-3}$ & $0.490$ & $0.9567$ & $3.8$ & $3.4$ & $1.7$ & $0.3$ & $0.1$ & $0.6$ & $-0.3$ & $-0.6$ & $0.0$ & $0.2$ & $0.1$ & $0.0$ \\ $200$ & $1.30 \times 10^{-2}$ & $0.303$ & $0.8430$ & $3.4$ & $3.1$ & $1.0$ & $0.6$ & $0.0$ & $0.8$ & $-0.4$ & $-0.7$ & $0.0$ & $0.0$ & $0.0$ & $0.0$ \\ $200$ & $2.00 \times 10^{-2}$ & $0.197$ & $0.6517$ & $4.1$ & $3.5$ & $1.8$ & $1.6$ & $0.0$ & $1.2$ & $-1.0$ & $-0.7$ & $0.0$ & $0.0$ & $0.0$ & $0.0$ \\ $200$ & $3.20 \times 10^{-2}$ & $0.123$ & $0.5275$ & $4.2$ & $4.0$ & $0.9$ & $0.1$ & $0.1$ & $0.6$ & $-0.1$ & $-0.5$ & $-0.1$ & $0.3$ & $0.0$ & $0.0$ \\ $200$ & $5.00 \times 10^{-2}$ & $0.079$ & $0.5297$ & $4.3$ & $4.1$ & $1.2$ & $0.9$ & $0.2$ & $0.7$ & $-0.5$ & $-0.4$ & $-0.1$ & $0.2$ & $0.0$ & $0.0$ \\ $200$ & $8.00 \times 10^{-2}$ & $0.049$ & $0.4587$ & $5.0$ & $4.7$ & $1.3$ & $0.9$ & $0.3$ & $1.0$ & $-0.6$ & $-0.7$ & $-0.2$ & $0.2$ & $0.0$ & $0.0$ \\ $200$ & $1.30 \times 10^{-1}$ & $0.030$ & $0.3610$ & $5.6$ & $5.1$ & $1.9$ & $1.5$ & $0.1$ & $1.6$ & $-0.9$ & $-0.7$ & $-0.1$ & $1.0$ & $0.0$ & $0.0$ \\ $200$ & $1.80 \times 10^{-1}$ & $0.022$ & $0.3201$ & $6.8$ & $5.8$ & $2.3$ & $1.1$ & $1.4$ & $2.6$ & $-0.7$ & $-0.9$ & $-0.4$ & $-2.3$ & $0.0$ & $0.0$ \\ $200$ & $4.00 \times 10^{-1}$ & $0.010$ & $0.1694$ & $13.1$ & $8.2$ & $4.5$ & $0.3$ & $4.0$ & $9.2$ & $0.2$ & $-1.1$ & $-0.6$ & $-9.1$ & $0.0$ & $0.0$ \\ \hline $250$ & $5.79 \times 10^{-3}$ & $0.850$ & $1.049$ & $10.9$ & $10.4$ & $2.5$ & $0.3$ & $0.9$ & $2.2$ & $-0.1$ & $-0.2$ & $0.0$ & $0.3$ & $0.6$ & $2.0$ \\ $250$ & $6.56 \times 10^{-3}$ & $0.750$ & $1.036$ & $9.1$ & $8.8$ & $1.9$ & $0.2$ & $0.3$ & $1.3$ & $-0.2$ & $-0.4$ & $0.1$ & $0.2$ & $0.2$ & $1.1$ \\ $250$ & $7.57 \times 10^{-3}$ & $0.650$ & $0.9480$ & $8.0$ & $7.7$ & $2.0$ & $0.9$ & $0.1$ & $0.5$ & $-0.2$ & $-0.4$ & $0.0$ & $0.2$ & $0.2$ & $0.0$ \\ $250$ & $1.00 \times 10^{-2}$ & $0.490$ & $0.8829$ & $4.3$ & $3.9$ & $1.7$ & $0.3$ & $0.1$ & $0.6$ & $-0.3$ & $-0.5$ & $0.0$ & $0.2$ & $0.1$ & $0.0$ \\ $250$ & $1.30 \times 10^{-2}$ & $0.379$ & $0.8281$ & $4.0$ & $3.7$ & $1.3$ & $0.4$ & $0.0$ & $0.6$ & $-0.4$ & $-0.5$ & $0.0$ & $0.1$ & $0.0$ & $0.0$ \\ $250$ & $2.00 \times 10^{-2}$ & $0.246$ & $0.6799$ & $4.0$ & $3.8$ & $1.0$ & $0.6$ & $0.0$ & $0.8$ & $-0.5$ & $-0.7$ & $0.0$ & $0.0$ & $0.0$ & $0.0$ \\ $250$ & $3.20 \times 10^{-2}$ & $0.154$ & $0.5817$ & $4.4$ & $4.1$ & $1.3$ & $1.0$ & $0.2$ & $0.9$ & $0.4$ & $-0.6$ & $0.1$ & $0.6$ & $0.0$ & $0.0$ \\ $250$ & $5.00 \times 10^{-2}$ & $0.098$ & $0.5025$ & $4.4$ & $4.1$ & $1.3$ & $0.9$ & $0.1$ & $0.9$ & $0.3$ & $-0.6$ & $0.0$ & $0.7$ & $0.0$ & $0.0$ \\ $250$ & $8.00 \times 10^{-2}$ & $0.062$ & $0.4429$ & $4.7$ & $4.4$ & $1.3$ & $1.0$ & $0.1$ & $1.0$ & $0.5$ & $-0.6$ & $-0.1$ & $0.7$ & $0.0$ & $0.0$ \\ $250$ & $1.30 \times 10^{-1}$ & $0.038$ & $0.3750$ & $4.9$ & $4.4$ & $1.4$ & $0.8$ & $0.1$ & $1.6$ & $0.3$ & $-0.5$ & $-0.1$ & $1.5$ & $0.0$ & $0.0$ \\ $250$ & $1.80 \times 10^{-1}$ & $0.027$ & $0.3582$ & $5.1$ & $4.5$ & $2.1$ & $1.3$ & $0.9$ & $1.3$ & $0.6$ & $-0.7$ & $-0.3$ & $-0.8$ & $0.0$ & $0.0$ \\ $250$ & $4.00 \times 10^{-1}$ & $0.012$ & $0.1675$ & $12.6$ & $6.6$ & $4.9$ & $2.7$ & $3.6$ & $9.5$ & $1.6$ & $-1.0$ & $-0.6$ & $-9.3$ & $0.0$ & $0.0$ \\ \hline $300$ & $6.95 \times 10^{-3}$ & $0.850$ & $0.8700$ & $13.8$ & $13.3$ & $2.4$ & $0.2$ & $0.8$ & $2.5$ & $-0.2$ & $-0.2$ & $0.0$ & $0.3$ & $0.8$ & $2.3$ \\ $300$ & $7.88 \times 10^{-3}$ & $0.750$ & $0.8274$ & $11.1$ & $10.9$ & $2.0$ & $0.2$ & $0.3$ & $1.0$ & $-0.2$ & $-0.3$ & $0.0$ & $0.2$ & $0.3$ & $0.9$ \\ $300$ & $9.09 \times 10^{-3}$ & $0.650$ & $0.8411$ & $9.8$ & $9.6$ & $1.9$ & $0.3$ & $0.1$ & $0.5$ & $0.1$ & $-0.4$ & $0.0$ & $0.2$ & $0.2$ & $0.0$ \\ $300$ & $1.21 \times 10^{-2}$ & $0.490$ & $0.9058$ & $4.8$ & $4.5$ & $1.7$ & $0.3$ & $0.1$ & $0.5$ & $-0.3$ & $-0.4$ & $0.0$ & $0.1$ & $0.0$ & $0.0$ \\ $300$ & $2.00 \times 10^{-2}$ & $0.295$ & $0.7296$ & $4.4$ & $4.2$ & $1.0$ & $0.6$ & $0.0$ & $0.8$ & $-0.6$ & $-0.5$ & $0.0$ & $0.0$ & $0.0$ & $0.0$ \\ $300$ & $3.20 \times 10^{-2}$ & $0.185$ & $0.6231$ & $4.7$ & $4.5$ & $0.9$ & $0.3$ & $0.2$ & $0.7$ & $0.3$ & $-0.3$ & $0.1$ & $0.5$ & $0.0$ & $0.0$ \\ $300$ & $5.00 \times 10^{-2}$ & $0.118$ & $0.5210$ & $4.9$ & $4.7$ & $1.1$ & $0.6$ & $0.2$ & $0.9$ & $0.4$ & $-0.5$ & $0.1$ & $0.6$ & $0.0$ & $0.0$ \\ $300$ & $8.00 \times 10^{-2}$ & $0.074$ & $0.4584$ & $5.2$ & $4.9$ & $1.4$ & $1.0$ & $0.2$ & $1.0$ & $0.6$ & $-0.6$ & $-0.1$ & $0.5$ & $0.0$ & $0.0$ \\ $300$ & $1.30 \times 10^{-1}$ & $0.045$ & $0.3695$ & $5.5$ & $5.1$ & $1.5$ & $1.0$ & $0.2$ & $1.6$ & $0.5$ & $-0.6$ & $0.0$ & $1.4$ & $0.0$ & $0.0$ \\ $300$ & $1.80 \times 10^{-1}$ & $0.033$ & $0.3330$ & $5.8$ & $5.2$ & $2.2$ & $1.5$ & $0.9$ & $1.2$ & $0.9$ & $-0.8$ & $-0.3$ & $-0.3$ & $0.0$ & $0.0$ \\ $300$ & $4.00 \times 10^{-1}$ & $0.015$ & $0.1567$ & $13.0$ & $7.7$ & $5.2$ & $3.1$ & $3.6$ & $9.1$ & $2.1$ & $-1.3$ & $-0.6$ & $-8.8$ & $0.0$ & $0.0$ \\ \hline \end{tabular} \end{center} \caption[RESULT] {\sl \label{tab:xsec460} The NC $e^+p$ reduced cross section $\tilde{\sigma}_{\rm NC}(x,Q^2)$ for $E_p=460$ GeV and $P_e=0$ with total $(\delta_{tot})$, statistical $(\delta_{\rm stat})$, total uncorrelated systematic $(\delta_{\rm unc})$ errors and two of its contributions from the electron energy error ($\delta_{unc}^{E}$) and the hadronic energy error ($\delta_{\rm unc}^{h}$). The effect of the other uncorrelated systematic errors is included in $\delta_{\rm unc}$. In addition the correlated systematic $(\delta_{\rm cor})$ and its contributions from a positive variation of one standard deviation of the electron energy error ($\delta_{cor}^{E^+}$), of the polar electron angle error ($\delta_{\rm cor}^{\theta^+}$), of the hadronic energy error ($\delta_{\rm cor}^{h^+}$), of the error due to noise subtraction ($\delta_{\rm cor}^{N^+}$), of the error due to background subtraction charge asymmetry ($\delta_{\rm cor}^{S^+}$) and of the error due to variation of the cut value on the electron discriminator $D_{ele}$ ($\delta_{\rm cor}^{D^+}$) are given. The overall normalisation uncertainty of $4\%$ is not included in the errors. %The table continues on the next page. } \end{table} \begin{table}[htbp] \begin{center} \tiny \begin{tabular}{|r|c|c|r|r|r|r|r|r|r|r|r|r|r|r|r|} \hline $Q^2$ & $x$ & $y$ & $\tilde{\sigma}_{\rm NC}$ & $\delta_{\rm tot}$ & $\delta_{\rm stat}$ & $\delta_{\rm unc}$ & $\delta_{\rm unc}^{E}$ & $\delta_{\rm unc}^{h}$& $\delta_{\rm cor}$ & $\delta_{\rm cor}^{E^+}$ & $\delta_{\rm cor}^{\theta^+}$& $\delta_{\rm cor}^{h^+}$& $\delta_{\rm cor}^{N^+}$& $\delta_{\rm cor}^{S^+}$& $\delta_{\rm cor}^{D^+}$ \\ $(\rm GeV^2)$ & & & & $(\%)$ & $(\%)$ & $(\%)$ & $(\%)$ & $(\%)$ & $(\%)$ & $(\%)$ & $(\%)$ & $(\%)$ & $(\%)$ & $(\%)$ & $(\%)$ \\ \hline $400$ & $9.27 \times 10^{-3}$ & $0.850$ & $1.025$ & $13.8$ & $13.3$ & $2.4$ & $0.6$ & $0.6$ & $2.5$ & $-0.2$ & $-0.3$ & $0.0$ & $0.2$ & $0.6$ & $2.4$ \\ $400$ & $1.05 \times 10^{-2}$ & $0.750$ & $1.074$ & $10.4$ & $10.1$ & $2.2$ & $1.0$ & $0.3$ & $0.7$ & $0.2$ & $-0.3$ & $0.1$ & $0.2$ & $0.1$ & $0.6$ \\ $400$ & $1.21 \times 10^{-2}$ & $0.650$ & $0.9263$ & $10.0$ & $9.8$ & $1.9$ & $0.2$ & $0.1$ & $0.4$ & $-0.2$ & $-0.3$ & $0.0$ & $0.2$ & $0.2$ & $0.0$ \\ $400$ & $1.61 \times 10^{-2}$ & $0.490$ & $0.8145$ & $5.7$ & $5.4$ & $1.7$ & $0.2$ & $0.0$ & $0.5$ & $-0.2$ & $-0.5$ & $0.0$ & $0.1$ & $0.0$ & $0.0$ \\ $400$ & $3.20 \times 10^{-2}$ & $0.246$ & $0.6305$ & $5.2$ & $5.0$ & $1.0$ & $0.6$ & $0.0$ & $0.8$ & $-0.6$ & $-0.6$ & $0.0$ & $0.0$ & $0.0$ & $0.0$ \\ $400$ & $5.00 \times 10^{-2}$ & $0.157$ & $0.5686$ & $5.4$ & $5.2$ & $1.0$ & $0.6$ & $0.2$ & $0.9$ & $0.5$ & $-0.5$ & $-0.1$ & $0.4$ & $0.0$ & $0.0$ \\ $400$ & $8.00 \times 10^{-2}$ & $0.098$ & $0.4493$ & $5.8$ & $5.7$ & $1.0$ & $0.4$ & $0.1$ & $0.7$ & $0.4$ & $-0.4$ & $0.1$ & $0.5$ & $0.0$ & $0.0$ \\ $400$ & $1.30 \times 10^{-1}$ & $0.061$ & $0.4300$ & $5.6$ & $5.3$ & $1.2$ & $0.4$ & $0.1$ & $1.2$ & $0.4$ & $-0.4$ & $-0.1$ & $1.1$ & $0.0$ & $0.0$ \\ $400$ & $1.80 \times 10^{-1}$ & $0.044$ & $0.3375$ & $6.2$ & $5.8$ & $1.7$ & $0.8$ & $0.7$ & $0.9$ & $0.7$ & $-0.6$ & $-0.2$ & $-0.2$ & $0.0$ & $0.0$ \\ $400$ & $4.00 \times 10^{-1}$ & $0.020$ & $0.1494$ & $13.1$ & $8.7$ & $4.6$ & $1.9$ & $3.7$ & $8.6$ & $1.9$ & $-0.9$ & $-0.7$ & $-8.3$ & $0.0$ & $0.0$ \\ \hline $500$ & $1.16 \times 10^{-2}$ & $0.850$ & $1.002$ & $15.0$ & $14.6$ & $2.4$ & $0.1$ & $0.4$ & $2.2$ & $0.2$ & $-0.2$ & $0.0$ & $0.2$ & $0.0$ & $2.2$ \\ $500$ & $1.31 \times 10^{-2}$ & $0.750$ & $0.7577$ & $13.8$ & $13.6$ & $2.1$ & $0.6$ & $0.2$ & $0.5$ & $-0.3$ & $-0.3$ & $0.0$ & $0.2$ & $0.1$ & $0.1$ \\ $500$ & $1.51 \times 10^{-2}$ & $0.650$ & $0.6938$ & $12.4$ & $12.2$ & $1.9$ & $0.3$ & $0.1$ & $0.4$ & $-0.2$ & $-0.4$ & $0.1$ & $0.2$ & $0.0$ & $0.0$ \\ $500$ & $2.01 \times 10^{-2}$ & $0.490$ & $0.7395$ & $6.7$ & $6.5$ & $1.7$ & $0.1$ & $0.0$ & $0.4$ & $-0.1$ & $-0.4$ & $0.0$ & $0.1$ & $0.0$ & $0.0$ \\ $500$ & $3.20 \times 10^{-2}$ & $0.308$ & $0.6559$ & $6.1$ & $6.0$ & $1.0$ & $0.3$ & $0.0$ & $0.6$ & $-0.3$ & $-0.5$ & $0.0$ & $0.0$ & $0.0$ & $0.0$ \\ $500$ & $5.00 \times 10^{-2}$ & $0.197$ & $0.6106$ & $6.1$ & $5.9$ & $1.3$ & $0.9$ & $0.0$ & $1.1$ & $-0.9$ & $-0.6$ & $0.0$ & $0.0$ & $0.0$ & $0.0$ \\ $500$ & $8.00 \times 10^{-2}$ & $0.123$ & $0.4712$ & $6.5$ & $6.3$ & $1.0$ & $0.5$ & $0.0$ & $0.8$ & $0.5$ & $-0.4$ & $0.0$ & $0.4$ & $0.0$ & $0.0$ \\ $500$ & $1.30 \times 10^{-1}$ & $0.076$ & $0.4112$ & $7.7$ & $7.5$ & $1.4$ & $0.6$ & $0.1$ & $1.2$ & $0.6$ & $-0.5$ & $0.0$ & $0.9$ & $0.0$ & $0.0$ \\ $500$ & $1.80 \times 10^{-1}$ & $0.055$ & $0.3045$ & $8.7$ & $8.4$ & $1.5$ & $0.6$ & $0.1$ & $1.4$ & $0.6$ & $-0.4$ & $-0.1$ & $1.1$ & $0.0$ & $0.0$ \\ $500$ & $2.50 \times 10^{-1}$ & $0.039$ & $0.2759$ & $8.5$ & $8.3$ & $1.9$ & $0.9$ & $0.8$ & $1.2$ & $0.9$ & $-0.6$ & $-0.2$ & $-0.3$ & $0.0$ & $0.0$ \\ $500$ & $4.00 \times 10^{-1}$ & $0.025$ & $0.1311$ & $13.7$ & $11.8$ & $4.1$ & $1.9$ & $3.1$ & $5.8$ & $1.8$ & $-0.7$ & $-0.7$ & $-5.3$ & $0.0$ & $0.0$ \\ $500$ & $6.50 \times 10^{-1}$ & $0.015$ & $0.01698$ & $27.9$ & $23.0$ & $7.0$ & $2.8$ & $5.9$ & $14.3$ & $2.8$ & $-1.4$ & $-1.0$ & $-13.9$ & $0.0$ & $0.0$ \\ \hline $650$ & $1.51 \times 10^{-2}$ & $0.850$ & $0.8058$ & $19.6$ & $19.4$ & $2.7$ & $0.5$ & $0.5$ & $1.1$ & $-0.1$ & $0.2$ & $0.1$ & $0.3$ & $0.7$ & $0.7$ \\ $650$ & $1.71 \times 10^{-2}$ & $0.750$ & $0.9192$ & $14.0$ & $13.9$ & $2.0$ & $0.1$ & $0.2$ & $0.4$ & $0.1$ & $-0.3$ & $0.0$ & $0.2$ & $0.2$ & $0.0$ \\ $650$ & $1.97 \times 10^{-2}$ & $0.650$ & $0.9125$ & $12.1$ & $12.0$ & $1.9$ & $0.0$ & $0.1$ & $0.4$ & $-0.1$ & $-0.4$ & $0.0$ & $0.1$ & $0.1$ & $0.0$ \\ $650$ & $2.61 \times 10^{-2}$ & $0.490$ & $0.6085$ & $8.0$ & $7.8$ & $1.8$ & $0.5$ & $0.0$ & $0.5$ & $-0.2$ & $-0.4$ & $0.0$ & $0.1$ & $0.0$ & $0.0$ \\ $650$ & $5.00 \times 10^{-2}$ & $0.256$ & $0.4952$ & $7.9$ & $7.8$ & $1.1$ & $0.6$ & $0.0$ & $0.8$ & $-0.6$ & $-0.6$ & $0.0$ & $0.0$ & $0.0$ & $0.0$ \\ $650$ & $8.00 \times 10^{-2}$ & $0.160$ & $0.4515$ & $7.9$ & $7.8$ & $1.0$ & $0.4$ & $0.2$ & $0.8$ & $0.5$ & $-0.4$ & $0.1$ & $0.5$ & $0.0$ & $0.0$ \\ $650$ & $1.30 \times 10^{-1}$ & $0.098$ & $0.3732$ & $9.5$ & $9.3$ & $1.4$ & $0.6$ & $0.2$ & $0.8$ & $0.6$ & $-0.4$ & $-0.1$ & $0.3$ & $0.0$ & $0.0$ \\ $650$ & $1.80 \times 10^{-1}$ & $0.071$ & $0.3397$ & $9.7$ & $9.5$ & $1.5$ & $0.5$ & $0.2$ & $1.1$ & $0.6$ & $-0.5$ & $0.0$ & $0.9$ & $0.0$ & $0.0$ \\ $650$ & $2.50 \times 10^{-1}$ & $0.051$ & $0.2520$ & $10.3$ & $10.1$ & $1.7$ & $0.7$ & $0.5$ & $0.9$ & $0.7$ & $-0.3$ & $0.1$ & $0.5$ & $0.0$ & $0.0$ \\ $650$ & $4.00 \times 10^{-1}$ & $0.032$ & $0.1915$ & $12.8$ & $11.2$ & $3.9$ & $1.9$ & $2.7$ & $4.8$ & $1.9$ & $-0.8$ & $-0.7$ & $-4.3$ & $0.0$ & $0.0$ \\ $650$ & $6.50 \times 10^{-1}$ & $0.020$ & $0.02382$ & $27.6$ & $22.4$ & $7.8$ & $3.7$ & $6.4$ & $14.0$ & $3.5$ & $-1.1$ & $-1.2$ & $-13.5$ & $0.0$ & $0.0$ \\ \hline $800$ & $1.85 \times 10^{-2}$ & $0.850$ & $0.2872$ & $37.1$ & $36.9$ & $3.9$ & $1.1$ & $0.4$ & $0.5$ & $0.2$ & $-0.3$ & $0.0$ & $0.2$ & $0.3$ & $0.1$ \\ $800$ & $2.10 \times 10^{-2}$ & $0.750$ & $0.6634$ & $19.2$ & $19.0$ & $2.3$ & $0.2$ & $0.2$ & $0.3$ & $-0.1$ & $-0.2$ & $0.1$ & $0.2$ & $0.0$ & $0.0$ \\ $800$ & $2.42 \times 10^{-2}$ & $0.650$ & $0.6620$ & $16.0$ & $15.9$ & $2.1$ & $0.4$ & $0.1$ & $0.4$ & $-0.3$ & $-0.2$ & $0.0$ & $0.1$ & $0.0$ & $0.0$ \\ $800$ & $3.21 \times 10^{-2}$ & $0.490$ & $0.6172$ & $8.8$ & $8.6$ & $1.8$ & $0.6$ & $0.0$ & $0.4$ & $-0.3$ & $-0.3$ & $0.0$ & $0.1$ & $0.0$ & $0.0$ \\ $800$ & $5.00 \times 10^{-2}$ & $0.315$ & $0.4847$ & $9.1$ & $9.0$ & $1.2$ & $0.7$ & $0.0$ & $0.6$ & $-0.5$ & $-0.3$ & $0.0$ & $0.0$ & $0.0$ & $0.0$ \\ $800$ & $8.00 \times 10^{-2}$ & $0.197$ & $0.4527$ & $9.3$ & $9.1$ & $1.3$ & $0.8$ & $0.0$ & $0.7$ & $-0.5$ & $-0.6$ & $0.0$ & $0.0$ & $0.0$ & $0.0$ \\ $800$ & $1.30 \times 10^{-1}$ & $0.121$ & $0.3868$ & $10.8$ & $10.6$ & $1.4$ & $0.5$ & $0.3$ & $0.9$ & $0.7$ & $-0.4$ & $-0.2$ & $0.4$ & $0.0$ & $0.0$ \\ $800$ & $1.80 \times 10^{-1}$ & $0.087$ & $0.3642$ & $11.0$ & $10.9$ & $1.5$ & $0.2$ & $0.1$ & $0.8$ & $0.4$ & $-0.3$ & $0.0$ & $0.6$ & $0.0$ & $0.0$ \\ $800$ & $2.50 \times 10^{-1}$ & $0.063$ & $0.2749$ & $11.7$ & $11.6$ & $1.7$ & $0.6$ & $0.6$ & $1.0$ & $0.8$ & $-0.4$ & $-0.2$ & $0.5$ & $0.0$ & $0.0$ \\ $800$ & $4.00 \times 10^{-1}$ & $0.039$ & $0.1262$ & $16.7$ & $15.8$ & $3.5$ & $1.5$ & $2.3$ & $3.9$ & $1.5$ & $-0.4$ & $-0.6$ & $-3.5$ & $0.0$ & $0.0$ \\ $800$ & $6.50 \times 10^{-1}$ & $0.024$ & $0.01953$ & $31.8$ & $28.9$ & $7.1$ & $2.9$ & $5.9$ & $11.4$ & $2.8$ & $-0.7$ & $-1.0$ & $-11.0$ & $0.0$ & $0.0$ \\ \hline \end{tabular} \end{center} \captcont{\sl continued.} %\caption{Continued from table~\ref{tab:xsec460}.} \end{table} %\input{plots/xsec575-afterPubReading} \begin{table}[htbp] \begin{center} \tiny \begin{tabular}{|r|c|c|r|r|r|r|r|r|r|r|r|r|r|r|r|} \hline $Q^2$ & $x$ & $y$ & $\tilde{\sigma}_{\rm NC}$ & $\delta_{\rm tot}$ & $\delta_{\rm stat}$ & $\delta_{\rm unc}$ & $\delta_{\rm unc}^{E}$ & $\delta_{\rm unc}^{h}$& $\delta_{\rm cor}$ & $\delta_{\rm cor}^{E^+}$ & $\delta_{\rm cor}^{\theta^+}$& $\delta_{\rm cor}^{h^+}$& $\delta_{\rm cor}^{N^+}$& $\delta_{\rm cor}^{S^+}$& $\delta_{\rm cor}^{D^+}$ \\ $(\rm GeV^2)$ & & & & $(\%)$ & $(\%)$ & $(\%)$ & $(\%)$ & $(\%)$ & $(\%)$ & $(\%)$ & $(\%)$ & $(\%)$ & $(\%)$ & $(\%)$ & $(\%)$ \\ \hline $35$ & $6.50 \times 10^{-4}$ & $0.848$ & $1.303$ & $8.6$ & $7.1$ & $3.8$ & $0.5$ & $2.7$ & $3.1$ & $-0.2$ & $-0.5$ & $0.2$ & $0.6$ & $2.7$ & $1.2$ \\ \hline $45$ & $8.40 \times 10^{-4}$ & $0.848$ & $1.413$ & $7.2$ & $6.0$ & $3.4$ & $0.4$ & $2.2$ & $2.0$ & $-0.2$ & $-0.4$ & $0.1$ & $0.5$ & $1.6$ & $1.1$ \\ $45$ & $9.30 \times 10^{-4}$ & $0.760$ & $1.235$ & $8.2$ & $7.7$ & $2.6$ & $0.5$ & $0.7$ & $1.4$ & $-0.2$ & $-0.6$ & $0.1$ & $0.3$ & $0.7$ & $0.9$ \\ \hline $60$ & $1.11 \times 10^{-3}$ & $0.848$ & $1.259$ & $8.0$ & $7.1$ & $3.2$ & $0.3$ & $2.0$ & $1.8$ & $-0.1$ & $-0.4$ & $0.1$ & $0.5$ & $1.5$ & $0.8$ \\ $60$ & $1.24 \times 10^{-3}$ & $0.760$ & $1.411$ & $6.4$ & $5.8$ & $2.3$ & $0.7$ & $0.6$ & $1.3$ & $-0.4$ & $-0.5$ & $0.0$ & $0.2$ & $0.6$ & $1.0$ \\ $60$ & $1.39 \times 10^{-3}$ & $0.680$ & $1.268$ & $7.5$ & $7.2$ & $2.0$ & $0.5$ & $0.2$ & $1.1$ & $-0.2$ & $-0.6$ & $0.0$ & $0.2$ & $0.5$ & $0.7$ \\ \hline $90$ & $1.67 \times 10^{-3}$ & $0.848$ & $1.310$ & $8.6$ & $7.9$ & $2.9$ & $0.3$ & $1.7$ & $1.7$ & $-0.2$ & $-0.4$ & $0.1$ & $0.4$ & $1.4$ & $0.8$ \\ $90$ & $1.86 \times 10^{-3}$ & $0.760$ & $1.326$ & $6.9$ & $6.5$ & $2.1$ & $0.3$ & $0.5$ & $1.1$ & $-0.1$ & $-0.5$ & $0.0$ & $0.3$ & $0.3$ & $0.9$ \\ $90$ & $2.09 \times 10^{-3}$ & $0.680$ & $1.316$ & $6.2$ & $5.8$ & $1.9$ & $0.5$ & $0.2$ & $1.0$ & $-0.2$ & $-0.6$ & $0.0$ & $0.2$ & $0.2$ & $0.7$ \\ $90$ & $2.36 \times 10^{-3}$ & $0.600$ & $1.342$ & $6.4$ & $6.0$ & $2.0$ & $0.8$ & $0.1$ & $0.8$ & $-0.2$ & $-0.8$ & $0.0$ & $0.2$ & $0.1$ & $0.0$ \\ \hline $120$ & $2.23 \times 10^{-3}$ & $0.848$ & $1.374$ & $9.0$ & $8.4$ & $2.7$ & $0.3$ & $1.5$ & $1.4$ & $-0.2$ & $-0.4$ & $0.1$ & $0.4$ & $0.6$ & $1.1$ \\ $120$ & $2.49 \times 10^{-3}$ & $0.760$ & $1.173$ & $8.0$ & $7.7$ & $2.0$ & $0.6$ & $0.4$ & $0.8$ & $-0.3$ & $-0.3$ & $0.0$ & $0.2$ & $0.3$ & $0.6$ \\ $120$ & $2.78 \times 10^{-3}$ & $0.680$ & $1.161$ & $7.2$ & $6.9$ & $1.9$ & $0.4$ & $0.2$ & $0.6$ & $0.1$ & $-0.4$ & $0.0$ & $0.2$ & $0.2$ & $0.3$ \\ $120$ & $3.15 \times 10^{-3}$ & $0.600$ & $1.115$ & $6.8$ & $6.5$ & $1.8$ & $0.4$ & $0.1$ & $0.7$ & $-0.3$ & $-0.6$ & $0.0$ & $0.2$ & $0.3$ & $0.0$ \\ $120$ & $3.63 \times 10^{-3}$ & $0.520$ & $1.185$ & $6.0$ & $5.7$ & $1.8$ & $0.5$ & $0.1$ & $0.8$ & $-0.4$ & $-0.7$ & $0.0$ & $0.2$ & $0.1$ & $0.0$ \\ $120$ & $4.82 \times 10^{-3}$ & $0.392$ & $1.074$ & $5.5$ & $5.1$ & $1.6$ & $0.5$ & $0.0$ & $1.0$ & $-0.3$ & $-0.9$ & $0.0$ & $0.2$ & $0.0$ & $0.0$ \\ \hline $150$ & $2.79 \times 10^{-3}$ & $0.848$ & $1.291$ & $10.8$ & $10.3$ & $2.6$ & $0.3$ & $1.2$ & $1.8$ & $-0.1$ & $-0.3$ & $0.1$ & $0.4$ & $0.8$ & $1.5$ \\ $150$ & $3.11 \times 10^{-3}$ & $0.760$ & $1.171$ & $9.8$ & $9.5$ & $2.0$ & $0.3$ & $0.4$ & $1.0$ & $-0.2$ & $-0.5$ & $0.1$ & $0.3$ & $0.5$ & $0.6$ \\ $150$ & $3.47 \times 10^{-3}$ & $0.680$ & $1.324$ & $7.9$ & $7.6$ & $2.3$ & $1.3$ & $0.2$ & $0.6$ & $-0.1$ & $-0.5$ & $0.0$ & $0.2$ & $0.3$ & $0.2$ \\ $150$ & $3.94 \times 10^{-3}$ & $0.600$ & $1.244$ & $7.2$ & $6.9$ & $1.8$ & $0.2$ & $0.1$ & $0.6$ & $-0.2$ & $-0.5$ & $0.0$ & $0.1$ & $0.2$ & $0.0$ \\ $150$ & $4.54 \times 10^{-3}$ & $0.520$ & $1.041$ & $7.1$ & $6.8$ & $1.8$ & $0.3$ & $0.1$ & $0.7$ & $-0.3$ & $-0.6$ & $0.0$ & $0.2$ & $0.2$ & $0.0$ \\ $150$ & $6.03 \times 10^{-3}$ & $0.392$ & $1.020$ & $4.0$ & $3.6$ & $1.4$ & $0.7$ & $0.0$ & $0.8$ & $-0.5$ & $-0.6$ & $0.0$ & $0.1$ & $0.0$ & $0.0$ \\ $150$ & $8.00 \times 10^{-3}$ & $0.295$ & $0.9700$ & $4.2$ & $3.9$ & $1.1$ & $0.8$ & $0.0$ & $0.9$ & $-0.5$ & $-0.8$ & $0.0$ & $0.0$ & $0.0$ & $0.0$ \\ $150$ & $1.30 \times 10^{-2}$ & $0.182$ & $0.8609$ & $5.7$ & $5.2$ & $1.8$ & $1.4$ & $0.9$ & $1.2$ & $-0.9$ & $-0.6$ & $-0.2$ & $-0.5$ & $0.0$ & $0.0$ \\ $150$ & $2.00 \times 10^{-2}$ & $0.118$ & $0.7980$ & $7.8$ & $6.9$ & $2.8$ & $2.5$ & $1.0$ & $2.0$ & $-1.6$ & $-1.0$ & $-0.3$ & $-0.8$ & $0.0$ & $0.0$ \\ \hline $200$ & $3.72 \times 10^{-3}$ & $0.848$ & $1.296$ & $13.3$ & $12.9$ & $2.6$ & $0.1$ & $1.2$ & $2.0$ & $-0.2$ & $-0.3$ & $0.1$ & $0.3$ & $0.9$ & $1.7$ \\ $200$ & $4.15 \times 10^{-3}$ & $0.760$ & $1.288$ & $11.8$ & $11.5$ & $2.1$ & $0.2$ & $0.3$ & $1.2$ & $0.2$ & $-0.5$ & $0.0$ & $0.2$ & $0.1$ & $1.0$ \\ $200$ & $4.63 \times 10^{-3}$ & $0.680$ & $1.051$ & $11.3$ & $11.1$ & $2.2$ & $1.1$ & $0.2$ & $0.5$ & $0.2$ & $-0.3$ & $0.0$ & $0.2$ & $0.3$ & $0.2$ \\ $200$ & $5.25 \times 10^{-3}$ & $0.600$ & $1.169$ & $9.1$ & $8.9$ & $1.8$ & $0.2$ & $0.1$ & $0.5$ & $-0.2$ & $-0.4$ & $0.0$ & $0.2$ & $0.1$ & $0.0$ \\ $200$ & $6.06 \times 10^{-3}$ & $0.520$ & $1.110$ & $8.3$ & $8.1$ & $1.8$ & $0.2$ & $0.1$ & $0.5$ & $-0.2$ & $-0.4$ & $0.0$ & $0.2$ & $0.1$ & $0.0$ \\ $200$ & $8.04 \times 10^{-3}$ & $0.392$ & $0.9625$ & $4.8$ & $4.6$ & $1.3$ & $0.4$ & $0.0$ & $0.8$ & $-0.3$ & $-0.7$ & $0.0$ & $0.1$ & $0.1$ & $0.0$ \\ $200$ & $1.30 \times 10^{-2}$ & $0.242$ & $0.8743$ & $4.7$ & $4.4$ & $1.3$ & $1.0$ & $0.0$ & $1.0$ & $-0.6$ & $-0.7$ & $0.0$ & $0.0$ & $0.0$ & $0.0$ \\ $200$ & $2.00 \times 10^{-2}$ & $0.157$ & $0.7573$ & $5.1$ & $4.9$ & $0.9$ & $0.3$ & $0.0$ & $0.8$ & $0.2$ & $-0.6$ & $-0.1$ & $0.5$ & $0.0$ & $0.0$ \\ $200$ & $3.20 \times 10^{-2}$ & $0.098$ & $0.6151$ & $5.6$ & $5.5$ & $1.0$ & $0.5$ & $0.0$ & $0.6$ & $-0.3$ & $-0.5$ & $-0.1$ & $0.3$ & $0.0$ & $0.0$ \\ $200$ & $5.00 \times 10^{-2}$ & $0.063$ & $0.5041$ & $6.5$ & $6.4$ & $1.2$ & $0.6$ & $0.5$ & $0.8$ & $-0.4$ & $-0.6$ & $-0.2$ & $-0.1$ & $0.0$ & $0.0$ \\ $200$ & $8.00 \times 10^{-2}$ & $0.039$ & $0.4211$ & $7.7$ & $7.3$ & $1.7$ & $1.4$ & $0.2$ & $1.5$ & $-0.9$ & $-0.6$ & $-0.1$ & $1.1$ & $0.0$ & $0.0$ \\ $200$ & $1.30 \times 10^{-1}$ & $0.024$ & $0.3857$ & $7.6$ & $7.2$ & $1.9$ & $1.5$ & $0.2$ & $1.5$ & $-0.7$ & $-0.9$ & $-0.2$ & $0.9$ & $0.0$ & $0.0$ \\ $200$ & $1.80 \times 10^{-1}$ & $0.018$ & $0.3034$ & $10.4$ & $9.3$ & $2.6$ & $0.6$ & $2.1$ & $3.7$ & $-0.5$ & $-0.8$ & $-0.3$ & $-3.6$ & $0.0$ & $0.0$ \\ $200$ & $4.00 \times 10^{-1}$ & $0.008$ & $0.1910$ & $13.2$ & $11.0$ & $3.7$ & $0.7$ & $3.1$ & $6.3$ & $-0.5$ & $-1.2$ & $-0.4$ & $-6.1$ & $0.0$ & $0.0$ \\ \hline $250$ & $4.64 \times 10^{-3}$ & $0.848$ & $0.8545$ & $19.8$ & $19.5$ & $2.5$ & $0.2$ & $1.0$ & $2.5$ & $0.1$ & $-0.3$ & $0.1$ & $0.3$ & $1.4$ & $2.0$ \\ $250$ & $5.18 \times 10^{-3}$ & $0.760$ & $1.080$ & $14.3$ & $14.1$ & $2.2$ & $0.2$ & $0.3$ & $1.5$ & $0.1$ & $-0.4$ & $0.1$ & $0.2$ & $0.0$ & $1.4$ \\ $250$ & $5.79 \times 10^{-3}$ & $0.680$ & $0.9481$ & $13.9$ & $13.7$ & $2.3$ & $1.2$ & $0.1$ & $0.5$ & $-0.2$ & $-0.3$ & $0.0$ & $0.2$ & $0.2$ & $0.0$ \\ $250$ & $6.56 \times 10^{-3}$ & $0.600$ & $0.9475$ & $11.6$ & $11.5$ & $1.8$ & $0.2$ & $0.1$ & $0.5$ & $-0.1$ & $-0.4$ & $0.0$ & $0.2$ & $0.1$ & $0.0$ \\ $250$ & $7.57 \times 10^{-3}$ & $0.520$ & $1.018$ & $9.8$ & $9.6$ & $1.8$ & $0.2$ & $0.1$ & $0.6$ & $-0.2$ & $-0.5$ & $0.0$ & $0.2$ & $0.1$ & $0.0$ \\ $250$ & $1.00 \times 10^{-2}$ & $0.392$ & $0.9523$ & $5.3$ & $5.1$ & $1.2$ & $0.4$ & $0.0$ & $0.6$ & $-0.3$ & $-0.5$ & $0.0$ & $0.1$ & $0.0$ & $0.0$ \\ $250$ & $1.30 \times 10^{-2}$ & $0.303$ & $0.8513$ & $5.3$ & $5.1$ & $1.1$ & $0.6$ & $0.0$ & $0.8$ & $-0.6$ & $-0.5$ & $0.0$ & $0.0$ & $0.0$ & $0.0$ \\ $250$ & $2.00 \times 10^{-2}$ & $0.197$ & $0.7707$ & $5.5$ & $5.2$ & $1.5$ & $1.2$ & $0.0$ & $1.1$ & $-0.9$ & $-0.6$ & $0.0$ & $0.0$ & $0.0$ & $0.0$ \\ $250$ & $3.20 \times 10^{-2}$ & $0.123$ & $0.6210$ & $5.9$ & $5.7$ & $1.4$ & $1.0$ & $0.3$ & $1.0$ & $0.4$ & $-0.6$ & $0.0$ & $0.6$ & $0.0$ & $0.0$ \\ $250$ & $5.00 \times 10^{-2}$ & $0.079$ & $0.5412$ & $6.1$ & $5.9$ & $1.4$ & $1.0$ & $0.1$ & $0.9$ & $0.5$ & $-0.6$ & $0.0$ & $0.6$ & $0.0$ & $0.0$ \\ $250$ & $8.00 \times 10^{-2}$ & $0.049$ & $0.4602$ & $6.7$ & $6.4$ & $1.3$ & $0.9$ & $0.1$ & $1.3$ & $0.3$ & $-0.5$ & $-0.1$ & $1.2$ & $0.0$ & $0.0$ \\ $250$ & $1.30 \times 10^{-1}$ & $0.030$ & $0.3906$ & $6.6$ & $6.2$ & $1.4$ & $0.7$ & $0.2$ & $1.8$ & $0.3$ & $-0.5$ & $0.0$ & $1.8$ & $0.0$ & $0.0$ \\ $250$ & $1.80 \times 10^{-1}$ & $0.022$ & $0.3514$ & $7.8$ & $6.9$ & $2.5$ & $1.5$ & $1.5$ & $2.5$ & $0.7$ & $-0.6$ & $-0.4$ & $-2.3$ & $0.0$ & $0.0$ \\ $250$ & $4.00 \times 10^{-1}$ & $0.010$ & $0.1556$ & $13.0$ & $10.1$ & $4.2$ & $2.5$ & $2.7$ & $7.1$ & $1.5$ & $-1.0$ & $-0.5$ & $-6.8$ & $0.0$ & $0.0$ \\ \hline \end{tabular} \end{center} \caption[RESULT] {\sl \label{tab:xsec575} The NC $e^+p$ reduced cross section $\tilde{\sigma}_{\rm NC}(x,Q^2)$ for $E_p=575$ GeV and $P_e=0$ with total $(\delta_{tot})$, statistical $(\delta_{\rm stat})$, total uncorrelated systematic $(\delta_{\rm unc})$ errors and two of its contributions from the electron energy error ($\delta_{unc}^{E}$) and the hadronic energy error ($\delta_{\rm unc}^{h}$). The effect of the other uncorrelated systematic errors is included in $\delta_{\rm unc}$. In addition the correlated systematic $(\delta_{\rm cor})$ and its contributions from a positive variation of one standard deviation of the electron energy error ($\delta_{cor}^{E^+}$), of the polar electron angle error ($\delta_{\rm cor}^{\theta^+}$), of the hadronic energy error ($\delta_{\rm cor}^{h^+}$), of the error due to noise subtraction ($\delta_{\rm cor}^{N^+}$), of the error due to background subtraction charge asymmetry ($\delta_{\rm cor}^{S^+}$) and of the error due to variation of the cut value on the electron discriminator $D_{ele}$ ($\delta_{\rm cor}^{D^+}$) are given. The overall normalisation uncertainty of $4\%$ is not included in the errors. %The table continues on the next page. } \end{table} \begin{table}[htbp] \begin{center} \tiny \begin{tabular}{|r|c|c|r|r|r|r|r|r|r|r|r|r|r|r|r|} \hline $Q^2$ & $x$ & $y$ & $\tilde{\sigma}_{\rm NC}$ & $\delta_{\rm tot}$ & $\delta_{\rm stat}$ & $\delta_{\rm unc}$ & $\delta_{\rm unc}^{E}$ & $\delta_{\rm unc}^{h}$& $\delta_{\rm cor}$ & $\delta_{\rm cor}^{E^+}$ & $\delta_{\rm cor}^{\theta^+}$& $\delta_{\rm cor}^{h^+}$& $\delta_{\rm cor}^{N^+}$& $\delta_{\rm cor}^{S^+}$& $\delta_{\rm cor}^{D^+}$ \\ $(\rm GeV^2)$ & & & & $(\%)$ & $(\%)$ & $(\%)$ & $(\%)$ & $(\%)$ & $(\%)$ & $(\%)$ & $(\%)$ & $(\%)$ & $(\%)$ & $(\%)$ & $(\%)$ \\ \hline $300$ & $5.57 \times 10^{-3}$ & $0.848$ & $1.208$ & $16.0$ & $15.7$ & $2.5$ & $0.6$ & $0.8$ & $2.1$ & $-0.3$ & $-0.3$ & $0.1$ & $0.3$ & $0.2$ & $2.1$ \\ $300$ & $6.22 \times 10^{-3}$ & $0.760$ & $0.8707$ & $18.1$ & $18.0$ & $2.1$ & $0.2$ & $0.3$ & $1.3$ & $-0.2$ & $-0.4$ & $0.1$ & $0.2$ & $0.4$ & $1.1$ \\ $300$ & $6.95 \times 10^{-3}$ & $0.680$ & $0.9694$ & $15.0$ & $14.8$ & $2.1$ & $0.8$ & $0.1$ & $0.5$ & $-0.1$ & $-0.5$ & $0.0$ & $0.2$ & $0.0$ & $0.0$ \\ $300$ & $7.88 \times 10^{-3}$ & $0.600$ & $1.035$ & $12.9$ & $12.7$ & $1.9$ & $0.1$ & $0.1$ & $0.5$ & $0.1$ & $-0.5$ & $0.0$ & $0.2$ & $0.0$ & $0.0$ \\ $300$ & $9.09 \times 10^{-3}$ & $0.520$ & $0.8632$ & $12.1$ & $12.0$ & $1.8$ & $0.3$ & $0.1$ & $0.6$ & $-0.3$ & $-0.5$ & $0.0$ & $0.1$ & $0.0$ & $0.0$ \\ $300$ & $1.21 \times 10^{-2}$ & $0.392$ & $0.9079$ & $6.2$ & $6.0$ & $1.3$ & $0.4$ & $0.0$ & $0.6$ & $-0.4$ & $-0.5$ & $0.0$ & $0.1$ & $0.0$ & $0.0$ \\ $300$ & $2.00 \times 10^{-2}$ & $0.236$ & $0.6653$ & $6.5$ & $6.3$ & $1.0$ & $0.6$ & $0.0$ & $0.9$ & $-0.6$ & $-0.7$ & $0.0$ & $0.0$ & $0.0$ & $0.0$ \\ $300$ & $3.20 \times 10^{-2}$ & $0.148$ & $0.6171$ & $6.7$ & $6.6$ & $1.0$ & $0.5$ & $0.1$ & $0.8$ & $0.3$ & $-0.4$ & $0.0$ & $0.6$ & $0.0$ & $0.0$ \\ $300$ & $5.00 \times 10^{-2}$ & $0.094$ & $0.5364$ & $6.9$ & $6.8$ & $1.2$ & $0.8$ & $0.0$ & $0.9$ & $0.5$ & $-0.6$ & $-0.1$ & $0.5$ & $0.0$ & $0.0$ \\ $300$ & $8.00 \times 10^{-2}$ & $0.059$ & $0.4802$ & $7.4$ & $7.2$ & $1.3$ & $0.9$ & $0.0$ & $1.2$ & $0.5$ & $-0.6$ & $-0.1$ & $0.9$ & $0.0$ & $0.0$ \\ $300$ & $1.30 \times 10^{-1}$ & $0.036$ & $0.3762$ & $7.6$ & $7.2$ & $1.5$ & $1.0$ & $0.1$ & $1.9$ & $0.4$ & $-0.6$ & $-0.1$ & $1.7$ & $0.0$ & $0.0$ \\ $300$ & $1.80 \times 10^{-1}$ & $0.026$ & $0.3190$ & $8.7$ & $8.1$ & $2.5$ & $1.8$ & $1.1$ & $2.0$ & $1.1$ & $-0.9$ & $-0.3$ & $-1.4$ & $0.0$ & $0.0$ \\ $300$ & $4.00 \times 10^{-1}$ & $0.012$ & $0.1469$ & $15.5$ & $12.0$ & $4.8$ & $2.8$ & $3.4$ & $8.6$ & $1.7$ & $-1.1$ & $-0.6$ & $-8.4$ & $0.0$ & $0.0$ \\ \hline $400$ & $7.43 \times 10^{-3}$ & $0.848$ & $0.8123$ & $23.1$ & $22.9$ & $2.6$ & $0.3$ & $0.7$ & $2.3$ & $-0.3$ & $-0.3$ & $0.1$ & $0.3$ & $0.6$ & $2.2$ \\ $400$ & $8.29 \times 10^{-3}$ & $0.760$ & $0.5949$ & $23.1$ & $23.0$ & $2.3$ & $0.6$ & $0.2$ & $0.8$ & $-0.1$ & $-0.3$ & $0.0$ & $0.2$ & $0.0$ & $0.8$ \\ $400$ & $9.27 \times 10^{-3}$ & $0.680$ & $1.013$ & $16.1$ & $16.0$ & $2.0$ & $0.4$ & $0.2$ & $0.4$ & $0.2$ & $-0.2$ & $0.0$ & $0.2$ & $0.2$ & $0.0$ \\ $400$ & $1.05 \times 10^{-2}$ & $0.600$ & $0.8806$ & $15.6$ & $15.5$ & $1.9$ & $0.3$ & $0.1$ & $0.5$ & $-0.2$ & $-0.4$ & $0.0$ & $0.2$ & $0.0$ & $0.0$ \\ $400$ & $1.21 \times 10^{-2}$ & $0.520$ & $0.9991$ & $13.0$ & $12.9$ & $1.9$ & $0.1$ & $0.1$ & $0.5$ & $0.2$ & $-0.4$ & $0.0$ & $0.1$ & $0.0$ & $0.0$ \\ $400$ & $1.61 \times 10^{-2}$ & $0.392$ & $0.8791$ & $7.1$ & $7.0$ & $1.2$ & $0.3$ & $0.0$ & $0.6$ & $-0.3$ & $-0.5$ & $0.0$ & $0.1$ & $0.0$ & $0.0$ \\ $400$ & $3.20 \times 10^{-2}$ & $0.197$ & $0.6501$ & $7.3$ & $7.2$ & $1.1$ & $0.8$ & $0.0$ & $1.0$ & $-0.8$ & $-0.6$ & $0.0$ & $0.0$ & $0.0$ & $0.0$ \\ $400$ & $5.00 \times 10^{-2}$ & $0.126$ & $0.5099$ & $8.0$ & $7.9$ & $1.1$ & $0.6$ & $0.1$ & $1.0$ & $0.6$ & $-0.6$ & $0.0$ & $0.5$ & $0.0$ & $0.0$ \\ $400$ & $8.00 \times 10^{-2}$ & $0.079$ & $0.4452$ & $8.6$ & $8.5$ & $1.1$ & $0.6$ & $0.1$ & $1.1$ & $0.6$ & $-0.6$ & $-0.1$ & $0.7$ & $0.0$ & $0.0$ \\ $400$ & $1.30 \times 10^{-1}$ & $0.049$ & $0.3769$ & $8.5$ & $8.2$ & $1.3$ & $0.4$ & $0.2$ & $1.7$ & $0.4$ & $-0.4$ & $0.0$ & $1.6$ & $0.0$ & $0.0$ \\ $400$ & $1.80 \times 10^{-1}$ & $0.035$ & $0.3421$ & $8.9$ & $8.6$ & $2.0$ & $1.0$ & $1.1$ & $1.6$ & $0.9$ & $-0.6$ & $-0.3$ & $-1.1$ & $0.0$ & $0.0$ \\ $400$ & $4.00 \times 10^{-1}$ & $0.016$ & $0.1488$ & $16.6$ & $13.4$ & $4.6$ & $2.0$ & $3.5$ & $8.6$ & $1.9$ & $-0.9$ & $-0.7$ & $-8.4$ & $0.0$ & $0.0$ \\ \hline $500$ & $9.29 \times 10^{-3}$ & $0.848$ & $0.7285$ & $27.8$ & $27.6$ & $2.7$ & $0.3$ & $0.5$ & $2.1$ & $0.0$ & $-0.1$ & $0.1$ & $0.2$ & $0.4$ & $2.1$ \\ $500$ & $1.04 \times 10^{-2}$ & $0.760$ & $0.7348$ & $22.8$ & $22.7$ & $2.3$ & $1.0$ & $0.3$ & $0.5$ & $-0.2$ & $-0.4$ & $0.1$ & $0.2$ & $0.0$ & $0.1$ \\ $500$ & $1.16 \times 10^{-2}$ & $0.680$ & $1.177$ & $16.2$ & $16.1$ & $2.0$ & $0.1$ & $0.1$ & $0.4$ & $-0.1$ & $-0.3$ & $0.0$ & $0.2$ & $0.0$ & $0.0$ \\ $500$ & $1.31 \times 10^{-2}$ & $0.600$ & $0.8538$ & $17.7$ & $17.6$ & $1.9$ & $0.2$ & $0.1$ & $0.5$ & $-0.2$ & $-0.4$ & $0.0$ & $0.1$ & $0.2$ & $0.0$ \\ $500$ & $1.51 \times 10^{-2}$ & $0.520$ & $1.040$ & $14.2$ & $14.1$ & $1.9$ & $0.4$ & $0.1$ & $0.4$ & $-0.3$ & $-0.3$ & $0.0$ & $0.1$ & $0.0$ & $0.0$ \\ $500$ & $2.01 \times 10^{-2}$ & $0.392$ & $0.7340$ & $9.1$ & $9.0$ & $1.3$ & $0.4$ & $0.0$ & $0.6$ & $-0.4$ & $-0.4$ & $0.0$ & $0.1$ & $0.0$ & $0.0$ \\ $500$ & $3.20 \times 10^{-2}$ & $0.246$ & $0.6891$ & $8.4$ & $8.3$ & $1.1$ & $0.7$ & $0.0$ & $0.8$ & $-0.7$ & $-0.4$ & $0.0$ & $0.0$ & $0.0$ & $0.0$ \\ $500$ & $5.00 \times 10^{-2}$ & $0.157$ & $0.5602$ & $8.9$ & $8.8$ & $1.0$ & $0.3$ & $0.4$ & $0.8$ & $0.3$ & $-0.3$ & $0.1$ & $0.7$ & $0.0$ & $0.0$ \\ $500$ & $8.00 \times 10^{-2}$ & $0.098$ & $0.4454$ & $9.8$ & $9.7$ & $1.0$ & $0.5$ & $0.2$ & $0.7$ & $0.5$ & $-0.3$ & $-0.1$ & $0.3$ & $0.0$ & $0.0$ \\ $500$ & $1.30 \times 10^{-1}$ & $0.061$ & $0.3831$ & $11.5$ & $11.4$ & $1.3$ & $0.5$ & $0.2$ & $1.4$ & $0.5$ & $-0.4$ & $0.1$ & $1.3$ & $0.0$ & $0.0$ \\ $500$ & $1.80 \times 10^{-1}$ & $0.044$ & $0.3467$ & $11.6$ & $11.3$ & $1.5$ & $0.6$ & $0.1$ & $1.6$ & $0.6$ & $-0.5$ & $-0.1$ & $1.4$ & $0.0$ & $0.0$ \\ $500$ & $2.50 \times 10^{-1}$ & $0.032$ & $0.2290$ & $13.8$ & $13.5$ & $2.0$ & $0.8$ & $1.2$ & $1.7$ & $0.8$ & $-0.4$ & $-0.3$ & $-1.4$ & $0.0$ & $0.0$ \\ $500$ & $4.00 \times 10^{-1}$ & $0.020$ & $0.1687$ & $18.1$ & $16.3$ & $4.2$ & $1.8$ & $3.2$ & $6.7$ & $1.8$ & $-0.6$ & $-0.7$ & $-6.3$ & $0.0$ & $0.0$ \\ $500$ & $6.50 \times 10^{-1}$ & $0.012$ & $0.02022$ & $31.5$ & $28.9$ & $5.5$ & $2.3$ & $4.3$ & $11.2$ & $2.3$ & $-0.9$ & $-0.7$ & $-10.9$ & $0.0$ & $0.0$ \\ \hline $650$ & $1.21 \times 10^{-2}$ & $0.848$ & $0.4914$ & $38.7$ & $38.5$ & $3.0$ & $0.4$ & $0.4$ & $1.0$ & $0.2$ & $0.0$ & $0.0$ & $0.2$ & $0.5$ & $0.8$ \\ $650$ & $1.35 \times 10^{-2}$ & $0.760$ & $0.6986$ & $28.3$ & $28.2$ & $2.2$ & $0.3$ & $0.2$ & $0.6$ & $-0.2$ & $-0.2$ & $0.1$ & $0.2$ & $0.4$ & $0.0$ \\ $650$ & $1.51 \times 10^{-2}$ & $0.680$ & $0.6789$ & $25.2$ & $25.1$ & $2.1$ & $0.2$ & $0.1$ & $0.5$ & $0.1$ & $-0.3$ & $0.0$ & $0.2$ & $0.3$ & $0.0$ \\ $650$ & $1.71 \times 10^{-2}$ & $0.600$ & $0.6957$ & $21.4$ & $21.3$ & $2.0$ & $0.3$ & $0.1$ & $0.5$ & $-0.2$ & $-0.4$ & $0.0$ & $0.1$ & $0.0$ & $0.0$ \\ $650$ & $1.97 \times 10^{-2}$ & $0.520$ & $0.4817$ & $22.7$ & $22.6$ & $2.0$ & $0.6$ & $0.1$ & $0.6$ & $-0.4$ & $-0.4$ & $0.0$ & $0.1$ & $0.0$ & $0.0$ \\ $650$ & $2.61 \times 10^{-2}$ & $0.392$ & $0.6348$ & $10.8$ & $10.7$ & $1.3$ & $0.4$ & $0.0$ & $0.5$ & $-0.2$ & $-0.5$ & $0.0$ & $0.1$ & $0.0$ & $0.0$ \\ $650$ & $5.00 \times 10^{-2}$ & $0.205$ & $0.4685$ & $11.7$ & $11.6$ & $1.3$ & $0.9$ & $0.0$ & $1.0$ & $-0.8$ & $-0.6$ & $0.0$ & $0.0$ & $0.0$ & $0.0$ \\ $650$ & $8.00 \times 10^{-2}$ & $0.128$ & $0.4525$ & $11.4$ & $11.3$ & $1.1$ & $0.5$ & $0.0$ & $0.9$ & $0.6$ & $-0.4$ & $-0.1$ & $0.5$ & $0.0$ & $0.0$ \\ $650$ & $1.30 \times 10^{-1}$ & $0.079$ & $0.3975$ & $13.4$ & $13.3$ & $1.4$ & $0.6$ & $0.0$ & $1.2$ & $0.6$ & $-0.5$ & $0.0$ & $0.9$ & $0.0$ & $0.0$ \\ $650$ & $1.80 \times 10^{-1}$ & $0.057$ & $0.3285$ & $14.0$ & $13.9$ & $1.4$ & $0.3$ & $0.2$ & $1.4$ & $0.4$ & $-0.2$ & $0.0$ & $1.4$ & $0.0$ & $0.0$ \\ $650$ & $2.50 \times 10^{-1}$ & $0.041$ & $0.2401$ & $15.5$ & $15.3$ & $2.0$ & $1.0$ & $0.9$ & $1.3$ & $1.0$ & $-0.6$ & $-0.3$ & $-0.6$ & $0.0$ & $0.0$ \\ $650$ & $4.00 \times 10^{-1}$ & $0.026$ & $0.1563$ & $20.4$ & $18.9$ & $4.5$ & $2.1$ & $3.3$ & $6.2$ & $2.2$ & $-0.9$ & $-0.9$ & $-5.7$ & $0.0$ & $0.0$ \\ $650$ & $6.50 \times 10^{-1}$ & $0.016$ & $0.02266$ & $35.8$ & $33.3$ & $6.0$ & $2.3$ & $4.9$ & $11.4$ & $2.2$ & $-0.9$ & $-0.8$ & $-11.1$ & $0.0$ & $0.0$ \\ \hline $800$ & $1.49 \times 10^{-2}$ & $0.848$ & $0.6679$ & $31.9$ & $31.8$ & $3.1$ & $0.9$ & $0.4$ & $0.5$ & $-0.4$ & $-0.2$ & $0.1$ & $0.2$ & $0.0$ & $0.1$ \\ $800$ & $1.66 \times 10^{-2}$ & $0.760$ & $0.4843$ & $38.5$ & $38.4$ & $2.7$ & $0.6$ & $0.2$ & $0.7$ & $0.6$ & $-0.3$ & $0.1$ & $0.3$ & $0.0$ & $0.0$ \\ $800$ & $1.85 \times 10^{-2}$ & $0.680$ & $0.6761$ & $27.1$ & $27.0$ & $2.2$ & $0.2$ & $0.1$ & $0.4$ & $-0.2$ & $-0.3$ & $0.0$ & $0.1$ & $0.0$ & $0.0$ \\ $800$ & $2.10 \times 10^{-2}$ & $0.600$ & $0.6604$ & $24.5$ & $24.4$ & $2.1$ & $0.1$ & $0.1$ & $0.5$ & $-0.1$ & $-0.5$ & $0.0$ & $0.1$ & $0.0$ & $0.0$ \\ $800$ & $2.42 \times 10^{-2}$ & $0.520$ & $0.6435$ & $21.9$ & $21.8$ & $1.9$ & $0.1$ & $0.0$ & $0.6$ & $0.0$ & $-0.6$ & $0.0$ & $0.1$ & $0.0$ & $0.0$ \\ $800$ & $3.21 \times 10^{-2}$ & $0.392$ & $0.4923$ & $13.6$ & $13.5$ & $1.4$ & $0.5$ & $0.0$ & $0.4$ & $-0.3$ & $-0.3$ & $0.0$ & $0.1$ & $0.0$ & $0.0$ \\ $800$ & $5.00 \times 10^{-2}$ & $0.252$ & $0.5837$ & $12.0$ & $11.9$ & $1.2$ & $0.7$ & $0.0$ & $0.8$ & $-0.6$ & $-0.6$ & $0.0$ & $0.0$ & $0.0$ & $0.0$ \\ $800$ & $8.00 \times 10^{-2}$ & $0.157$ & $0.5522$ & $12.0$ & $12.0$ & $1.1$ & $0.4$ & $0.1$ & $0.8$ & $0.6$ & $-0.4$ & $0.1$ & $0.3$ & $0.0$ & $0.0$ \\ $800$ & $1.30 \times 10^{-1}$ & $0.097$ & $0.2926$ & $18.3$ & $18.3$ & $1.3$ & $0.1$ & $0.1$ & $0.7$ & $0.4$ & $-0.2$ & $-0.1$ & $0.6$ & $0.0$ & $0.0$ \\ $800$ & $1.80 \times 10^{-1}$ & $0.070$ & $0.2636$ & $18.7$ & $18.6$ & $1.5$ & $0.5$ & $0.1$ & $1.5$ & $0.7$ & $-0.5$ & $0.0$ & $1.2$ & $0.0$ & $0.0$ \\ $800$ & $2.50 \times 10^{-1}$ & $0.050$ & $0.1811$ & $20.5$ & $20.4$ & $1.9$ & $0.8$ & $0.8$ & $1.3$ & $1.1$ & $-0.5$ & $-0.2$ & $-0.5$ & $0.0$ & $0.0$ \\ $800$ & $4.00 \times 10^{-1}$ & $0.032$ & $0.1614$ & $22.2$ & $21.3$ & $3.8$ & $1.5$ & $2.7$ & $4.9$ & $1.5$ & $-0.4$ & $-0.5$ & $-4.6$ & $0.0$ & $0.0$ \\ $800$ & $6.50 \times 10^{-1}$ & $0.019$ & $0.02134$ & $43.1$ & $40.8$ & $6.7$ & $2.6$ & $5.4$ & $12.1$ & $2.7$ & $-0.6$ & $-1.1$ & $-11.8$ & $0.0$ & $0.0$ \\ \hline \end{tabular} \end{center} %\caption{Continued from table~\ref{tab:xsec575}.} \captcont{\sl continued.} \end{table} %\input{plots/flf2615-afterPubReading} \begin{table}[htbp] \begin{center} \tiny \begin{tabular}{|r|c|c|r|r|r|r|r|r|r|r|r|r|} \hline $Q^2$ & $x$ & $F_{L}$ & $\Delta_{\rm stat}F_{L}$ & $\Delta_{\rm uncor}F_{L}$ & $\Delta_{\rm cor}F_{L}$ & $\Delta_{\rm tot}F_{L}$ & $F_{2}$ & $\Delta_{\rm stat}F_{2}$ & $\Delta_{\rm uncor}F_{2}$ & $\Delta_{\rm cor}F_{2}$ & $\Delta_{\rm tot}F_{2}$ & $\rho$ \\ (GeV$^2$) & & & & & & & & & & & & \\ \hline $ 1.5 $&$ 0.279 \times 10^{-4} $&$ 0.088 $&$ 0.113 $&$ 0.186 $&$ 0.053 $&$ 0.224 $&$ 0.732 $&$ 0.066 $&$ 0.096 $&$ 0.028 $&$ 0.120 $&$ 0.882$\\ $ 2.0 $&$ 0.372 \times 10^{-4} $&$ 0.110 $&$ 0.069 $&$ 0.131 $&$ 0.062 $&$ 0.160 $&$ 0.843 $&$ 0.028 $&$ 0.051 $&$ 0.032 $&$ 0.066 $&$ 0.855$\\ $ 2.0 $&$ 0.415 \times 10^{-4} $&$ 0.437 $&$ 0.110 $&$ 0.181 $&$ 0.071 $&$ 0.223 $&$ 0.904 $&$ 0.039 $&$ 0.060 $&$ 0.030 $&$ 0.078 $&$ 0.852$\\ $ 2.0 $&$ 0.464 \times 10^{-4} $&$ 0.043 $&$ 0.052 $&$ 0.104 $&$ 0.033 $&$ 0.121 $&$ 0.740 $&$ 0.033 $&$ 0.052 $&$ 0.009 $&$ 0.062 $&$ 0.822$\\ $ 2.5 $&$ 0.465 \times 10^{-4} $&$ 0.013 $&$ 0.057 $&$ 0.120 $&$ 0.046 $&$ 0.141 $&$ 0.846 $&$ 0.022 $&$ 0.045 $&$ 0.016 $&$ 0.053 $&$ 0.856$\\ $ 2.5 $&$ 0.519 \times 10^{-4} $&$ 0.103 $&$ 0.062 $&$ 0.129 $&$ 0.042 $&$ 0.149 $&$ 0.897 $&$ 0.023 $&$ 0.045 $&$ 0.016 $&$ 0.053 $&$ 0.860$\\ $ 2.5 $&$ 0.580 \times 10^{-4} $&$ 0.174 $&$ 0.047 $&$ 0.090 $&$ 0.058 $&$ 0.117 $&$ 0.889 $&$ 0.021 $&$ 0.034 $&$ 0.028 $&$ 0.049 $&$ 0.821$\\ $ 2.5 $&$ 0.658 \times 10^{-4} $&$ 0.169 $&$ 0.043 $&$ 0.099 $&$ 0.063 $&$ 0.125 $&$ 0.865 $&$ 0.019 $&$ 0.035 $&$ 0.031 $&$ 0.050 $&$ 0.840$\\ $ 2.5 $&$ 0.759 \times 10^{-4} $&$ 0.413 $&$ 0.096 $&$ 0.155 $&$ 0.079 $&$ 0.198 $&$ 0.877 $&$ 0.024 $&$ 0.035 $&$ 0.026 $&$ 0.050 $&$ 0.783$\\ $ 3.5 $&$ 0.651 \times 10^{-4} $&$ 0.130 $&$ 0.065 $&$ 0.135 $&$ 0.052 $&$ 0.158 $&$ 0.973 $&$ 0.025 $&$ 0.050 $&$ 0.022 $&$ 0.060 $&$ 0.846$\\ $ 3.5 $&$ 0.727 \times 10^{-4} $&$ 0.199 $&$ 0.061 $&$ 0.133 $&$ 0.044 $&$ 0.152 $&$ 0.989 $&$ 0.024 $&$ 0.047 $&$ 0.021 $&$ 0.057 $&$ 0.850$\\ $ 3.5 $&$ 0.812 \times 10^{-4} $&$ 0.253 $&$ 0.044 $&$ 0.094 $&$ 0.041 $&$ 0.112 $&$ 0.981 $&$ 0.019 $&$ 0.036 $&$ 0.016 $&$ 0.044 $&$ 0.811$\\ $ 3.5 $&$ 0.921 \times 10^{-4} $&$ 0.230 $&$ 0.037 $&$ 0.099 $&$ 0.037 $&$ 0.112 $&$ 0.968 $&$ 0.015 $&$ 0.033 $&$ 0.014 $&$ 0.039 $&$ 0.816$\\ $ 3.5 $&$ 0.106 \times 10^{-3} $&$ 0.155 $&$ 0.049 $&$ 0.123 $&$ 0.046 $&$ 0.141 $&$ 0.934 $&$ 0.015 $&$ 0.032 $&$ 0.010 $&$ 0.037 $&$ 0.797$\\ $ 3.5 $&$ 0.141 \times 10^{-3} $&$ 0.665 $&$ 0.112 $&$ 0.221 $&$ 0.123 $&$ 0.276 $&$ 0.937 $&$ 0.011 $&$ 0.028 $&$ 0.012 $&$ 0.032 $&$ 0.735$\\ $ 5.0 $&$ 0.931 \times 10^{-4} $&$ 0.411 $&$ 0.081 $&$ 0.162 $&$ 0.068 $&$ 0.193 $&$ 1.149 $&$ 0.031 $&$ 0.060 $&$ 0.031 $&$ 0.075 $&$ 0.846$\\ $ 5.0 $&$ 0.104 \times 10^{-3} $&$ 0.344 $&$ 0.065 $&$ 0.142 $&$ 0.044 $&$ 0.163 $&$ 1.072 $&$ 0.027 $&$ 0.052 $&$ 0.024 $&$ 0.063 $&$ 0.859$\\ $ 5.0 $&$ 0.116 \times 10^{-3} $&$ 0.258 $&$ 0.048 $&$ 0.108 $&$ 0.049 $&$ 0.128 $&$ 1.127 $&$ 0.021 $&$ 0.042 $&$ 0.018 $&$ 0.050 $&$ 0.828$\\ $ 5.0 $&$ 0.131 \times 10^{-3} $&$ 0.306 $&$ 0.037 $&$ 0.109 $&$ 0.041 $&$ 0.122 $&$ 1.082 $&$ 0.016 $&$ 0.037 $&$ 0.017 $&$ 0.044 $&$ 0.830$\\ $ 5.0 $&$ 0.152 \times 10^{-3} $&$ 0.224 $&$ 0.044 $&$ 0.134 $&$ 0.045 $&$ 0.148 $&$ 1.060 $&$ 0.014 $&$ 0.034 $&$ 0.015 $&$ 0.040 $&$ 0.834$\\ $ 5.0 $&$ 0.201 \times 10^{-3} $&$ 0.533 $&$ 0.057 $&$ 0.203 $&$ 0.084 $&$ 0.227 $&$ 1.018 $&$ 0.008 $&$ 0.028 $&$ 0.012 $&$ 0.032 $&$ 0.809$\\ $ 6.5 $&$ 0.121 \times 10^{-3} $&$ 0.435 $&$ 0.096 $&$ 0.179 $&$ 0.077 $&$ 0.218 $&$ 1.215 $&$ 0.037 $&$ 0.066 $&$ 0.027 $&$ 0.080 $&$ 0.853$\\ $ 6.5 $&$ 0.135 \times 10^{-3} $&$ 0.199 $&$ 0.071 $&$ 0.151 $&$ 0.042 $&$ 0.172 $&$ 1.103 $&$ 0.030 $&$ 0.055 $&$ 0.020 $&$ 0.066 $&$ 0.862$\\ $ 6.5 $&$ 0.151 \times 10^{-3} $&$ 0.137 $&$ 0.051 $&$ 0.114 $&$ 0.054 $&$ 0.136 $&$ 1.135 $&$ 0.023 $&$ 0.044 $&$ 0.023 $&$ 0.055 $&$ 0.844$\\ $ 6.5 $&$ 0.171 \times 10^{-3} $&$ 0.357 $&$ 0.040 $&$ 0.119 $&$ 0.044 $&$ 0.133 $&$ 1.158 $&$ 0.017 $&$ 0.041 $&$ 0.020 $&$ 0.048 $&$ 0.844$\\ $ 6.5 $&$ 0.197 \times 10^{-3} $&$ 0.318 $&$ 0.044 $&$ 0.145 $&$ 0.053 $&$ 0.161 $&$ 1.147 $&$ 0.014 $&$ 0.038 $&$ 0.019 $&$ 0.044 $&$ 0.855$\\ $ 6.5 $&$ 0.262 \times 10^{-3} $&$ 0.188 $&$ 0.046 $&$ 0.205 $&$ 0.090 $&$ 0.229 $&$ 1.044 $&$ 0.007 $&$ 0.029 $&$ 0.017 $&$ 0.034 $&$ 0.842$\\ $ 8.5 $&$ 0.158 \times 10^{-3} $&$ 0.499 $&$ 0.109 $&$ 0.195 $&$ 0.095 $&$ 0.243 $&$ 1.352 $&$ 0.044 $&$ 0.074 $&$ 0.033 $&$ 0.092 $&$ 0.845$\\ $ 8.5 $&$ 0.177 \times 10^{-3} $&$ 0.489 $&$ 0.089 $&$ 0.184 $&$ 0.051 $&$ 0.210 $&$ 1.335 $&$ 0.038 $&$ 0.067 $&$ 0.022 $&$ 0.080 $&$ 0.862$\\ $ 8.5 $&$ 0.197 \times 10^{-3} $&$ 0.271 $&$ 0.057 $&$ 0.123 $&$ 0.058 $&$ 0.147 $&$ 1.196 $&$ 0.027 $&$ 0.048 $&$ 0.021 $&$ 0.059 $&$ 0.841$\\ $ 8.5 $&$ 0.224 \times 10^{-3} $&$ 0.242 $&$ 0.045 $&$ 0.125 $&$ 0.042 $&$ 0.139 $&$ 1.158 $&$ 0.019 $&$ 0.043 $&$ 0.017 $&$ 0.050 $&$ 0.849$\\ $ 8.5 $&$ 0.258 \times 10^{-3} $&$-0.123 $&$ 0.045 $&$ 0.140 $&$ 0.051 $&$ 0.156 $&$ 1.038 $&$ 0.015 $&$ 0.036 $&$ 0.016 $&$ 0.042 $&$ 0.853$\\ $ 8.5 $&$ 0.342 \times 10^{-3} $&$ 0.167 $&$ 0.045 $&$ 0.216 $&$ 0.089 $&$ 0.238 $&$ 1.095 $&$ 0.007 $&$ 0.030 $&$ 0.017 $&$ 0.035 $&$ 0.846$\\ $ 12 $&$ 0.223 \times 10^{-3} $&$ 0.094 $&$ 0.101 $&$ 0.159 $&$ 0.084 $&$ 0.206 $&$ 1.314 $&$ 0.039 $&$ 0.041 $&$ 0.044 $&$ 0.072 $&$ 0.855$\\ $ 12 $&$ 0.249 \times 10^{-3} $&$ 0.544 $&$ 0.098 $&$ 0.155 $&$ 0.058 $&$ 0.193 $&$ 1.389 $&$ 0.035 $&$ 0.035 $&$ 0.028 $&$ 0.057 $&$ 0.835$\\ $ 12 $&$ 0.278 \times 10^{-3} $&$ 0.281 $&$ 0.059 $&$ 0.098 $&$ 0.047 $&$ 0.124 $&$ 1.310 $&$ 0.024 $&$ 0.024 $&$ 0.019 $&$ 0.039 $&$ 0.757$\\ $ 12 $&$ 0.316 \times 10^{-3} $&$ 0.248 $&$ 0.050 $&$ 0.100 $&$ 0.038 $&$ 0.118 $&$ 1.258 $&$ 0.019 $&$ 0.022 $&$ 0.015 $&$ 0.033 $&$ 0.733$\\ $ 12 $&$ 0.364 \times 10^{-3} $&$ 0.435 $&$ 0.055 $&$ 0.121 $&$ 0.041 $&$ 0.139 $&$ 1.268 $&$ 0.016 $&$ 0.022 $&$ 0.013 $&$ 0.030 $&$ 0.728$\\ $ 12 $&$ 0.483 \times 10^{-3} $&$ 0.414 $&$ 0.050 $&$ 0.162 $&$ 0.064 $&$ 0.181 $&$ 1.189 $&$ 0.007 $&$ 0.016 $&$ 0.012 $&$ 0.021 $&$ 0.651$\\ $ 15 $&$ 0.279 \times 10^{-3} $&$ 0.510 $&$ 0.109 $&$ 0.183 $&$ 0.085 $&$ 0.230 $&$ 1.485 $&$ 0.040 $&$ 0.047 $&$ 0.049 $&$ 0.079 $&$ 0.854$\\ $ 15 $&$ 0.312 \times 10^{-3} $&$ 0.148 $&$ 0.088 $&$ 0.150 $&$ 0.052 $&$ 0.181 $&$ 1.370 $&$ 0.032 $&$ 0.035 $&$ 0.027 $&$ 0.054 $&$ 0.834$\\ $ 15 $&$ 0.348 \times 10^{-3} $&$ 0.188 $&$ 0.061 $&$ 0.099 $&$ 0.039 $&$ 0.122 $&$ 1.329 $&$ 0.023 $&$ 0.023 $&$ 0.017 $&$ 0.036 $&$ 0.748$\\ $ 15 $&$ 0.395 \times 10^{-3} $&$ 0.419 $&$ 0.051 $&$ 0.100 $&$ 0.036 $&$ 0.118 $&$ 1.321 $&$ 0.017 $&$ 0.021 $&$ 0.015 $&$ 0.031 $&$ 0.710$\\ $ 15 $&$ 0.455 \times 10^{-3} $&$ 0.257 $&$ 0.062 $&$ 0.117 $&$ 0.045 $&$ 0.140 $&$ 1.269 $&$ 0.015 $&$ 0.018 $&$ 0.013 $&$ 0.027 $&$ 0.693$\\ $ 15 $&$ 0.604 \times 10^{-3} $&$ 0.066 $&$ 0.054 $&$ 0.157 $&$ 0.066 $&$ 0.179 $&$ 1.180 $&$ 0.007 $&$ 0.014 $&$ 0.012 $&$ 0.019 $&$ 0.620$\\ $ 20 $&$ 0.372 \times 10^{-3} $&$ 0.216 $&$ 0.116 $&$ 0.197 $&$ 0.065 $&$ 0.238 $&$ 1.452 $&$ 0.041 $&$ 0.051 $&$ 0.033 $&$ 0.073 $&$ 0.877$\\ $ 20 $&$ 0.415 \times 10^{-3} $&$ 0.322 $&$ 0.092 $&$ 0.158 $&$ 0.044 $&$ 0.188 $&$ 1.424 $&$ 0.032 $&$ 0.037 $&$ 0.021 $&$ 0.054 $&$ 0.837$\\ $ 20 $&$ 0.464 \times 10^{-3} $&$ 0.412 $&$ 0.070 $&$ 0.108 $&$ 0.037 $&$ 0.134 $&$ 1.396 $&$ 0.024 $&$ 0.025 $&$ 0.015 $&$ 0.037 $&$ 0.752$\\ $ 20 $&$ 0.526 \times 10^{-3} $&$ 0.358 $&$ 0.052 $&$ 0.103 $&$ 0.037 $&$ 0.121 $&$ 1.354 $&$ 0.018 $&$ 0.021 $&$ 0.015 $&$ 0.032 $&$ 0.708$\\ $ 20 $&$ 0.607 \times 10^{-3} $&$ 0.304 $&$ 0.062 $&$ 0.119 $&$ 0.041 $&$ 0.140 $&$ 1.295 $&$ 0.015 $&$ 0.019 $&$ 0.013 $&$ 0.027 $&$ 0.693$\\ $ 20 $&$ 0.805 \times 10^{-3} $&$ 0.212 $&$ 0.060 $&$ 0.163 $&$ 0.068 $&$ 0.186 $&$ 1.222 $&$ 0.007 $&$ 0.014 $&$ 0.012 $&$ 0.019 $&$ 0.608$\\ $ 25 $&$ 0.493 \times 10^{-3} $&$ 0.363 $&$ 0.072 $&$ 0.157 $&$ 0.043 $&$ 0.178 $&$ 1.484 $&$ 0.022 $&$ 0.040 $&$ 0.024 $&$ 0.052 $&$ 0.851$\\ $ 25 $&$ 0.616 \times 10^{-3} $&$ 0.284 $&$ 0.043 $&$ 0.089 $&$ 0.031 $&$ 0.103 $&$ 1.382 $&$ 0.013 $&$ 0.021 $&$ 0.014 $&$ 0.028 $&$ 0.698$\\ $ 25 $&$ 0.759 \times 10^{-3} $&$ 0.296 $&$ 0.065 $&$ 0.124 $&$ 0.042 $&$ 0.146 $&$ 1.330 $&$ 0.015 $&$ 0.020 $&$ 0.013 $&$ 0.028 $&$ 0.700$\\ $ 25 $&$ 0.101 \times 10^{-2} $&$ 0.168 $&$ 0.064 $&$ 0.167 $&$ 0.068 $&$ 0.191 $&$ 1.236 $&$ 0.007 $&$ 0.014 $&$ 0.012 $&$ 0.020 $&$ 0.616$\\ \hline \end{tabular} \end{center} %\captcont{ \caption{\sl \label{tab:flf2} The proton structure functions $F_L$ and $F_2$ measured at the given values of $Q^2$ and $x$ without model assumptions. $\Delta_{\rm stat}F_{L}$, $\Delta_{\rm uncor}F_{L}$, $\Delta_{\rm cor}F_{L}$ and $\Delta_{\rm tot}F_{L}$ are the statistical, uncorrelated systematic, correlated systematic, and total uncertainty on $F_L$ respectively. $\Delta_{\rm stat}F_{2}$, $\Delta_{\rm uncor}F_{2}$, $\Delta_{\rm cor}F_{2}$ and $\Delta_{\rm tot}F_{2}$ are the statistical, uncorrelated systematic and total uncertainty on $F_2$, respectively. The correlation coefficient between the $F_L$ and $F_2$ values ,$\rho$, is also given.} \end{table} \begin{table}[htbp] \begin{center} \tiny \begin{tabular}{|r|c|c|r|r|r|r|r|r|r|r|r|r|} \hline $Q^2$ & $x$ & $F_{L}$ & $\Delta_{\rm stat}F_{L}$ & $\Delta_{\rm uncor}F_{L}$ & $\Delta_{\rm cor}F_{L}$ & $\Delta_{\rm tot}F_{L}$ & $F_{2}$ & $\Delta_{\rm stat}F_{2}$ & $\Delta_{\rm uncor}F_{2}$ & $\Delta_{\rm cor}F_{2}$ & $\Delta_{\rm tot}F_{2}$ & $\rho$ \\ (GeV$^2$) & & & & & & & & & & & & \\ \hline $ 35 $&$ 0.651 \times 10^{-3} $&$ 0.453 $&$ 0.124 $&$ 0.214 $&$ 0.091 $&$ 0.264 $&$ 1.612 $&$ 0.043 $&$ 0.058 $&$ 0.030 $&$ 0.078 $&$ 0.889$\\ $ 35 $&$ 0.727 \times 10^{-3} $&$ 0.041 $&$ 0.144 $&$ 0.232 $&$ 0.065 $&$ 0.281 $&$ 1.419 $&$ 0.038 $&$ 0.048 $&$ 0.020 $&$ 0.065 $&$ 0.884$\\ $ 35 $&$ 0.812 \times 10^{-3} $&$ 0.106 $&$ 0.075 $&$ 0.107 $&$ 0.054 $&$ 0.142 $&$ 1.411 $&$ 0.026 $&$ 0.027 $&$ 0.019 $&$ 0.042 $&$ 0.753$\\ $ 35 $&$ 0.921 \times 10^{-3} $&$ 0.436 $&$ 0.080 $&$ 0.125 $&$ 0.040 $&$ 0.153 $&$ 1.405 $&$ 0.022 $&$ 0.024 $&$ 0.014 $&$ 0.035 $&$ 0.727$\\ $ 35 $&$ 0.106 \times 10^{-2} $&$ 0.196 $&$ 0.072 $&$ 0.130 $&$ 0.042 $&$ 0.155 $&$ 1.325 $&$ 0.017 $&$ 0.021 $&$ 0.012 $&$ 0.030 $&$ 0.698$\\ $ 35 $&$ 0.141 \times 10^{-2} $&$ 0.057 $&$ 0.067 $&$ 0.170 $&$ 0.065 $&$ 0.194 $&$ 1.226 $&$ 0.008 $&$ 0.015 $&$ 0.011 $&$ 0.021 $&$ 0.639$\\ $ 45 $&$ 0.837 \times 10^{-3} $&$ 0.179 $&$ 0.117 $&$ 0.188 $&$ 0.061 $&$ 0.230 $&$ 1.518 $&$ 0.042 $&$ 0.054 $&$ 0.022 $&$ 0.072 $&$ 0.875$\\ $ 45 $&$ 0.934 \times 10^{-3} $&$ 0.516 $&$ 0.167 $&$ 0.238 $&$ 0.058 $&$ 0.296 $&$ 1.517 $&$ 0.043 $&$ 0.052 $&$ 0.022 $&$ 0.071 $&$ 0.869$\\ $ 45 $&$ 0.104 \times 10^{-2} $&$ 0.366 $&$ 0.084 $&$ 0.107 $&$ 0.054 $&$ 0.146 $&$ 1.430 $&$ 0.029 $&$ 0.027 $&$ 0.016 $&$ 0.042 $&$ 0.731$\\ $ 45 $&$ 0.118 \times 10^{-2} $&$ 0.396 $&$ 0.108 $&$ 0.118 $&$ 0.042 $&$ 0.165 $&$ 1.395 $&$ 0.025 $&$ 0.025 $&$ 0.014 $&$ 0.038 $&$ 0.732$\\ $ 45 $&$ 0.137 \times 10^{-2} $&$ 0.255 $&$ 0.100 $&$ 0.151 $&$ 0.047 $&$ 0.187 $&$ 1.350 $&$ 0.021 $&$ 0.023 $&$ 0.013 $&$ 0.034 $&$ 0.729$\\ $ 45 $&$ 0.181 \times 10^{-2} $&$ 0.099 $&$ 0.075 $&$ 0.175 $&$ 0.065 $&$ 0.202 $&$ 1.210 $&$ 0.009 $&$ 0.016 $&$ 0.011 $&$ 0.021 $&$ 0.659$\\ $ 60 $&$ 0.112 \times 10^{-2} $&$ 0.282 $&$ 0.146 $&$ 0.179 $&$ 0.051 $&$ 0.237 $&$ 1.446 $&$ 0.058 $&$ 0.058 $&$ 0.021 $&$ 0.084 $&$ 0.851$\\ $ 60 $&$ 0.125 \times 10^{-2} $&$ 0.279 $&$ 0.165 $&$ 0.198 $&$ 0.055 $&$ 0.263 $&$ 1.548 $&$ 0.048 $&$ 0.050 $&$ 0.018 $&$ 0.072 $&$ 0.844$\\ $ 60 $&$ 0.139 \times 10^{-2} $&$ 0.383 $&$ 0.095 $&$ 0.105 $&$ 0.049 $&$ 0.150 $&$ 1.450 $&$ 0.033 $&$ 0.030 $&$ 0.016 $&$ 0.047 $&$ 0.731$\\ $ 60 $&$ 0.158 \times 10^{-2} $&$ 0.464 $&$ 0.102 $&$ 0.101 $&$ 0.047 $&$ 0.151 $&$ 1.369 $&$ 0.027 $&$ 0.024 $&$ 0.014 $&$ 0.039 $&$ 0.711$\\ $ 60 $&$ 0.182 \times 10^{-2} $&$ 0.159 $&$ 0.230 $&$ 0.320 $&$ 0.047 $&$ 0.397 $&$ 1.288 $&$ 0.028 $&$ 0.033 $&$ 0.012 $&$ 0.045 $&$ 0.818$\\ $ 60 $&$ 0.242 \times 10^{-2} $&$-0.044 $&$ 0.094 $&$ 0.185 $&$ 0.069 $&$ 0.218 $&$ 1.186 $&$ 0.011 $&$ 0.016 $&$ 0.011 $&$ 0.023 $&$ 0.683$\\ $ 90 $&$ 0.187 \times 10^{-2} $&$ 0.041 $&$ 0.222 $&$ 0.207 $&$ 0.045 $&$ 0.307 $&$ 1.330 $&$ 0.095 $&$ 0.077 $&$ 0.017 $&$ 0.123 $&$ 0.862$\\ $ 90 $&$ 0.209 \times 10^{-2} $&$ 0.060 $&$ 0.109 $&$ 0.119 $&$ 0.041 $&$ 0.166 $&$ 1.313 $&$ 0.051 $&$ 0.045 $&$ 0.014 $&$ 0.069 $&$ 0.801$\\ $ 90 $&$ 0.237 \times 10^{-2} $&$ 0.007 $&$ 0.109 $&$ 0.101 $&$ 0.040 $&$ 0.154 $&$ 1.218 $&$ 0.037 $&$ 0.029 $&$ 0.012 $&$ 0.048 $&$ 0.769$\\ $ 90 $&$ 0.273 \times 10^{-2} $&$ 0.447 $&$ 0.143 $&$ 0.135 $&$ 0.048 $&$ 0.202 $&$ 1.325 $&$ 0.031 $&$ 0.027 $&$ 0.013 $&$ 0.043 $&$ 0.717$\\ $ 90 $&$ 0.362 \times 10^{-2} $&$ 0.163 $&$ 0.167 $&$ 0.233 $&$ 0.058 $&$ 0.293 $&$ 1.145 $&$ 0.015 $&$ 0.017 $&$ 0.011 $&$ 0.025 $&$ 0.699$\\ $ 120 $&$ 0.220 \times 10^{-2} $&$ 0.070 $&$ 0.067 $&$ 0.241 $&$ 0.041 $&$ 0.253 $&$ 1.400 $&$ 0.019 $&$ 0.060 $&$ 0.027 $&$ 0.069 $&$ 0.908$\\ $ 120 $&$ 0.250 \times 10^{-2} $&$ 0.450 $&$ 0.096 $&$ 0.252 $&$ 0.037 $&$ 0.272 $&$ 1.414 $&$ 0.022 $&$ 0.051 $&$ 0.025 $&$ 0.061 $&$ 0.875$\\ $ 120 $&$ 0.280 \times 10^{-2} $&$ 0.136 $&$ 0.094 $&$ 0.103 $&$ 0.036 $&$ 0.144 $&$ 1.299 $&$ 0.022 $&$ 0.025 $&$ 0.021 $&$ 0.039 $&$ 0.711$\\ $ 120 $&$ 0.320 \times 10^{-2} $&$ 0.073 $&$ 0.175 $&$ 0.342 $&$ 0.032 $&$ 0.385 $&$ 1.129 $&$ 0.103 $&$ 0.146 $&$ 0.018 $&$ 0.179 $&$ 0.963$\\ $ 120 $&$ 0.360 \times 10^{-2} $&$ 0.480 $&$ 0.178 $&$ 0.234 $&$ 0.039 $&$ 0.296 $&$ 1.245 $&$ 0.062 $&$ 0.063 $&$ 0.012 $&$ 0.089 $&$ 0.886$\\ $ 120 $&$ 0.480 \times 10^{-2} $&$ 0.152 $&$ 0.166 $&$ 0.212 $&$ 0.071 $&$ 0.278 $&$ 1.069 $&$ 0.024 $&$ 0.024 $&$ 0.010 $&$ 0.035 $&$ 0.762$\\ $ 150 $&$ 0.280 \times 10^{-2} $&$ 0.123 $&$ 0.083 $&$ 0.270 $&$ 0.046 $&$ 0.286 $&$ 1.357 $&$ 0.024 $&$ 0.065 $&$ 0.025 $&$ 0.074 $&$ 0.931$\\ $ 150 $&$ 0.310 \times 10^{-2} $&$ 0.306 $&$ 0.099 $&$ 0.290 $&$ 0.035 $&$ 0.308 $&$ 1.330 $&$ 0.022 $&$ 0.056 $&$ 0.023 $&$ 0.065 $&$ 0.904$\\ $ 150 $&$ 0.350 \times 10^{-2} $&$ 0.038 $&$ 0.085 $&$ 0.127 $&$ 0.038 $&$ 0.157 $&$ 1.274 $&$ 0.017 $&$ 0.027 $&$ 0.021 $&$ 0.038 $&$ 0.728$\\ $ 150 $&$ 0.390 \times 10^{-2} $&$ 0.401 $&$ 0.095 $&$ 0.124 $&$ 0.029 $&$ 0.159 $&$ 1.266 $&$ 0.015 $&$ 0.022 $&$ 0.020 $&$ 0.033 $&$ 0.675$\\ $ 150 $&$ 0.450 \times 10^{-2} $&$ 0.554 $&$ 0.114 $&$ 0.153 $&$ 0.038 $&$ 0.195 $&$ 1.209 $&$ 0.014 $&$ 0.023 $&$ 0.020 $&$ 0.034 $&$ 0.668$\\ $ 150 $&$ 0.600 \times 10^{-2} $&$ 0.137 $&$ 0.118 $&$ 0.194 $&$ 0.060 $&$ 0.235 $&$ 1.069 $&$ 0.009 $&$ 0.020 $&$ 0.018 $&$ 0.028 $&$ 0.677$\\ $ 200 $&$ 0.370 \times 10^{-2} $&$-0.039 $&$ 0.110 $&$ 0.305 $&$ 0.044 $&$ 0.327 $&$ 1.231 $&$ 0.033 $&$ 0.072 $&$ 0.023 $&$ 0.083 $&$ 0.944$\\ $ 200 $&$ 0.410 \times 10^{-2} $&$-0.157 $&$ 0.141 $&$ 0.321 $&$ 0.033 $&$ 0.352 $&$ 1.160 $&$ 0.032 $&$ 0.059 $&$ 0.020 $&$ 0.070 $&$ 0.929$\\ $ 200 $&$ 0.460 \times 10^{-2} $&$ 0.146 $&$ 0.115 $&$ 0.131 $&$ 0.038 $&$ 0.179 $&$ 1.188 $&$ 0.023 $&$ 0.025 $&$ 0.019 $&$ 0.039 $&$ 0.758$\\ $ 200 $&$ 0.520 \times 10^{-2} $&$ 0.184 $&$ 0.126 $&$ 0.138 $&$ 0.033 $&$ 0.189 $&$ 1.136 $&$ 0.019 $&$ 0.022 $&$ 0.019 $&$ 0.035 $&$ 0.719$\\ $ 200 $&$ 0.610 \times 10^{-2} $&$ 0.253 $&$ 0.141 $&$ 0.169 $&$ 0.033 $&$ 0.223 $&$ 1.107 $&$ 0.016 $&$ 0.021 $&$ 0.018 $&$ 0.032 $&$ 0.690$\\ $ 200 $&$ 0.800 \times 10^{-2} $&$ 0.228 $&$ 0.126 $&$ 0.203 $&$ 0.057 $&$ 0.246 $&$ 0.995 $&$ 0.008 $&$ 0.018 $&$ 0.017 $&$ 0.026 $&$ 0.654$\\ $ 250 $&$ 0.460 \times 10^{-2} $&$ 0.620 $&$ 0.136 $&$ 0.365 $&$ 0.052 $&$ 0.393 $&$ 1.340 $&$ 0.041 $&$ 0.086 $&$ 0.025 $&$ 0.099 $&$ 0.950$\\ $ 250 $&$ 0.520 \times 10^{-2} $&$ 0.214 $&$ 0.159 $&$ 0.349 $&$ 0.039 $&$ 0.385 $&$ 1.186 $&$ 0.037 $&$ 0.065 $&$ 0.020 $&$ 0.077 $&$ 0.931$\\ $ 250 $&$ 0.580 \times 10^{-2} $&$ 0.243 $&$ 0.130 $&$ 0.142 $&$ 0.038 $&$ 0.196 $&$ 1.176 $&$ 0.026 $&$ 0.027 $&$ 0.019 $&$ 0.041 $&$ 0.770$\\ $ 250 $&$ 0.660 \times 10^{-2} $&$ 0.163 $&$ 0.145 $&$ 0.146 $&$ 0.030 $&$ 0.208 $&$ 1.087 $&$ 0.022 $&$ 0.022 $&$ 0.016 $&$ 0.035 $&$ 0.742$\\ $ 250 $&$ 0.760 \times 10^{-2} $&$ 0.117 $&$ 0.159 $&$ 0.173 $&$ 0.031 $&$ 0.237 $&$ 0.998 $&$ 0.018 $&$ 0.020 $&$ 0.016 $&$ 0.032 $&$ 0.714$\\ $ 250 $&$ 0.100 \times 10^{-1} $&$ 0.105 $&$ 0.139 $&$ 0.197 $&$ 0.050 $&$ 0.246 $&$ 0.914 $&$ 0.008 $&$ 0.015 $&$ 0.015 $&$ 0.023 $&$ 0.650$\\ $ 250 $&$ 0.130 \times 10^{-1} $&$ 0.140 $&$ 0.228 $&$ 0.280 $&$ 0.095 $&$ 0.374 $&$ 0.842 $&$ 0.008 $&$ 0.014 $&$ 0.014 $&$ 0.021 $&$ 0.650$\\ $ 300 $&$ 0.560 \times 10^{-2} $&$-0.038 $&$ 0.161 $&$ 0.316 $&$ 0.041 $&$ 0.357 $&$ 1.138 $&$ 0.048 $&$ 0.075 $&$ 0.021 $&$ 0.091 $&$ 0.942$\\ $ 300 $&$ 0.690 \times 10^{-2} $&$ 0.345 $&$ 0.151 $&$ 0.149 $&$ 0.039 $&$ 0.216 $&$ 1.118 $&$ 0.030 $&$ 0.028 $&$ 0.019 $&$ 0.045 $&$ 0.781$\\ $ 300 $&$ 0.790 \times 10^{-2} $&$ 0.377 $&$ 0.168 $&$ 0.148 $&$ 0.027 $&$ 0.225 $&$ 1.058 $&$ 0.025 $&$ 0.022 $&$ 0.016 $&$ 0.037 $&$ 0.752$\\ $ 300 $&$ 0.910 \times 10^{-2} $&$ 0.349 $&$ 0.193 $&$ 0.176 $&$ 0.028 $&$ 0.263 $&$ 0.967 $&$ 0.021 $&$ 0.019 $&$ 0.015 $&$ 0.033 $&$ 0.734$\\ $ 300 $&$ 0.121 \times 10^{-1} $&$-0.324 $&$ 0.157 $&$ 0.200 $&$ 0.047 $&$ 0.258 $&$ 0.839 $&$ 0.009 $&$ 0.014 $&$ 0.014 $&$ 0.022 $&$ 0.663$\\ $ 400 $&$ 0.930 \times 10^{-2} $&$-0.093 $&$ 0.164 $&$ 0.135 $&$ 0.033 $&$ 0.215 $&$ 0.950 $&$ 0.033 $&$ 0.025 $&$ 0.015 $&$ 0.044 $&$ 0.790$\\ $ 400 $&$ 0.105 \times 10^{-1} $&$-0.199 $&$ 0.180 $&$ 0.131 $&$ 0.020 $&$ 0.223 $&$ 0.923 $&$ 0.028 $&$ 0.019 $&$ 0.014 $&$ 0.037 $&$ 0.760$\\ $ 400 $&$ 0.121 \times 10^{-1} $&$-0.051 $&$ 0.207 $&$ 0.179 $&$ 0.027 $&$ 0.275 $&$ 0.913 $&$ 0.023 $&$ 0.021 $&$ 0.015 $&$ 0.034 $&$ 0.736$\\ $ 400 $&$ 0.161 \times 10^{-1} $&$-0.180 $&$ 0.182 $&$ 0.202 $&$ 0.043 $&$ 0.276 $&$ 0.788 $&$ 0.011 $&$ 0.013 $&$ 0.012 $&$ 0.021 $&$ 0.680$\\ $ 500 $&$ 0.116 \times 10^{-1} $&$-0.255 $&$ 0.184 $&$ 0.119 $&$ 0.028 $&$ 0.221 $&$ 0.868 $&$ 0.037 $&$ 0.022 $&$ 0.014 $&$ 0.046 $&$ 0.790$\\ $ 500 $&$ 0.131 \times 10^{-1} $&$ 0.340 $&$ 0.207 $&$ 0.143 $&$ 0.019 $&$ 0.252 $&$ 0.946 $&$ 0.033 $&$ 0.022 $&$ 0.015 $&$ 0.042 $&$ 0.755$\\ $ 500 $&$ 0.152 \times 10^{-1} $&$ 0.279 $&$ 0.244 $&$ 0.149 $&$ 0.021 $&$ 0.287 $&$ 0.860 $&$ 0.028 $&$ 0.017 $&$ 0.012 $&$ 0.035 $&$ 0.742$\\ $ 500 $&$ 0.201 \times 10^{-1} $&$ 0.192 $&$ 0.214 $&$ 0.211 $&$ 0.043 $&$ 0.304 $&$ 0.770 $&$ 0.013 $&$ 0.014 $&$ 0.013 $&$ 0.023 $&$ 0.691$\\ $ 650 $&$ 0.151 \times 10^{-1} $&$ 0.229 $&$ 0.219 $&$ 0.145 $&$ 0.018 $&$ 0.263 $&$ 0.917 $&$ 0.043 $&$ 0.026 $&$ 0.013 $&$ 0.052 $&$ 0.804$\\ $ 650 $&$ 0.171 \times 10^{-1} $&$-0.229 $&$ 0.209 $&$ 0.132 $&$ 0.016 $&$ 0.248 $&$ 0.743 $&$ 0.033 $&$ 0.021 $&$ 0.012 $&$ 0.041 $&$ 0.769$\\ $ 650 $&$ 0.197 \times 10^{-1} $&$-0.204 $&$ 0.254 $&$ 0.148 $&$ 0.019 $&$ 0.294 $&$ 0.735 $&$ 0.030 $&$ 0.017 $&$ 0.011 $&$ 0.036 $&$ 0.750$\\ $ 650 $&$ 0.261 \times 10^{-1} $&$ 0.651 $&$ 0.244 $&$ 0.201 $&$ 0.036 $&$ 0.318 $&$ 0.739 $&$ 0.016 $&$ 0.014 $&$ 0.012 $&$ 0.024 $&$ 0.698$\\ $ 800 $&$ 0.185 \times 10^{-1} $&$ 0.625 $&$ 0.228 $&$ 0.158 $&$ 0.014 $&$ 0.278 $&$ 0.821 $&$ 0.045 $&$ 0.028 $&$ 0.013 $&$ 0.054 $&$ 0.812$\\ $ 800 $&$ 0.210 \times 10^{-1} $&$ 0.205 $&$ 0.230 $&$ 0.167 $&$ 0.015 $&$ 0.285 $&$ 0.762 $&$ 0.036 $&$ 0.026 $&$ 0.012 $&$ 0.046 $&$ 0.774$\\ $ 800 $&$ 0.242 \times 10^{-1} $&$ 0.123 $&$ 0.281 $&$ 0.148 $&$ 0.016 $&$ 0.318 $&$ 0.698 $&$ 0.033 $&$ 0.017 $&$ 0.010 $&$ 0.039 $&$ 0.753$\\ $ 800 $&$ 0.322 \times 10^{-1} $&$ 0.276 $&$ 0.253 $&$ 0.202 $&$ 0.031 $&$ 0.325 $&$ 0.642 $&$ 0.016 $&$ 0.014 $&$ 0.010 $&$ 0.023 $&$ 0.714$\\ \hline \end{tabular} \end{center} %% \caption{\label{tab:flf2a} The proton structure functions $F_L$ and $F_2$ %% measured at the given values of $Q^2$ and $x$ without model assumptions. %% $\Delta_{\rm stat}F_{L}$, $\Delta_{\rm uncor}F_{L}$, %% $\Delta_{\rm cor}F_{L}$ and $\Delta_{\rm tot}F_{L}$ %% are the statistical, uncorrelated systematic, correlated systematic, and total uncertainty on $F_L$ %% respectively. %% $\Delta_{\rm stat}F_{2}$, $\Delta_{\rm uncor}F_{2}$, %% $\Delta_{\rm cor}F_{2}$ and $\Delta_{\rm tot}F_{2}$ %% are the statistical, uncorrelated systematic and total uncertainty on $F_2$, %% respectively. %% $\rho$ is the correlation coefficient between the $F_L$ and $F_2$ values.} %\caption{\label{tab:flf2b} Continued from table~\ref{tab:flf2a}. } \captcont{\sl continued.} \end{table} \begin{table}[htbp] \begin{center} \tiny \begin{tabular}{|r|c|c|r|r|r|r|} \hline $Q^2$ & $x$ & $F_{L}$ & $\Delta_{\rm stat}$ & $\Delta_{\rm uncor}$ & $\Delta_{\rm cor}$ & $\Delta_{\rm tot}$ \\ (GeV$^2$) & & & & & & \\ \hline %\input{plots/ave_fl-afterPubReading} $ 1.5 $ &$ 0.279 \times 10^{-4}$ & $ 0.088 $ &$ 0.113 $ &$ 0.186 $ &$ 0.053 $ &$0.224$ \\ $ 2.0 $ &$ 0.427 \times 10^{-4}$ & $ 0.127 $ &$ 0.039 $ &$ 0.074 $ &$ 0.044 $ &$0.095$ \\ $ 2.5 $ &$ 0.588 \times 10^{-4}$ & $ 0.156 $ &$ 0.025 $ &$ 0.050 $ &$ 0.053 $ &$0.077$ \\ $ 3.5 $ &$ 0.877 \times 10^{-4}$ & $ 0.227 $ &$ 0.021 $ &$ 0.049 $ &$ 0.040 $ &$0.067$ \\ $ 5.0 $ &$ 0.129 \times 10^{-3}$ & $ 0.314 $ &$ 0.022 $ &$ 0.055 $ &$ 0.045 $ &$0.074$ \\ $ 6.5 $ &$ 0.169 \times 10^{-3}$ & $ 0.264 $ &$ 0.023 $ &$ 0.058 $ &$ 0.050 $ &$0.080$ \\ $ 8.5 $ &$ 0.224 \times 10^{-3}$ & $ 0.216 $ &$ 0.025 $ &$ 0.062 $ &$ 0.051 $ &$0.084$ \\ $ 12 $ &$ 0.319 \times 10^{-3}$ & $ 0.324 $ &$ 0.026 $ &$ 0.051 $ &$ 0.044 $ &$0.072$ \\ $ 15 $ &$ 0.402 \times 10^{-3}$ & $ 0.266 $ &$ 0.027 $ &$ 0.051 $ &$ 0.042 $ &$0.071$ \\ $ 20 $ &$ 0.540 \times 10^{-3}$ & $ 0.327 $ &$ 0.029 $ &$ 0.053 $ &$ 0.040 $ &$0.072$ \\ $ 25 $ &$ 0.687 \times 10^{-3}$ & $ 0.282 $ &$ 0.029 $ &$ 0.061 $ &$ 0.037 $ &$0.077$ \\ $ 35 $ &$ 0.958 \times 10^{-3}$ & $ 0.213 $ &$ 0.035 $ &$ 0.059 $ &$ 0.040 $ &$0.080$ \\ $ 45 $ &$ 0.121 \times 10^{-2}$ & $ 0.303 $ &$ 0.043 $ &$ 0.060 $ &$ 0.044 $ &$0.086$ \\ $ 60 $ &$ 0.157 \times 10^{-2}$ & $ 0.315 $ &$ 0.051 $ &$ 0.060 $ &$ 0.044 $ &$0.090$ \\ $ 90 $ &$ 0.243 \times 10^{-2}$ & $ 0.125 $ &$ 0.061 $ &$ 0.062 $ &$ 0.039 $ &$0.095$ \\ $ 120 $ &$ 0.303 \times 10^{-2}$ & $ 0.198 $ &$ 0.054 $ &$ 0.077 $ &$ 0.029 $ &$0.098$ \\ $ 150 $ &$ 0.402 \times 10^{-2}$ & $ 0.264 $ &$ 0.044 $ &$ 0.068 $ &$ 0.035 $ &$0.088$ \\ $ 200 $ &$ 0.541 \times 10^{-2}$ & $ 0.150 $ &$ 0.056 $ &$ 0.073 $ &$ 0.034 $ &$0.099$ \\ $ 250 $ &$ 0.736 \times 10^{-2}$ & $ 0.196 $ &$ 0.061 $ &$ 0.075 $ &$ 0.033 $ &$0.102$ \\ $ 346 $ &$ 0.986 \times 10^{-2}$ & $ 0.039 $ &$ 0.059 $ &$ 0.057 $ &$ 0.029 $ &$0.087$ \\ $ 636 $ &$ 0.184 \times 10^{-1}$ & $ 0.152 $ &$ 0.066 $ &$ 0.045 $ &$ 0.020 $ &$0.082$ \\ \hline \end{tabular} \caption{\sl The proton structure function $F_L(x,Q^2)$ obtained by averaging $F_L$ data from table~\ref{tab:flf2} at the given values of $Q^2$ and $x$. $\Delta_{\rm stat}$, $\Delta_{\rm uncor}$, $\Delta_{\rm cor}$ and $\Delta_{\rm tot}$ are the statistical, uncorrelated systematic, correlated systematic, and total uncertainty on $F_L$, respectively.} \label{tab:flave} \end{center} \end{table} \newpage %\input{Figures} %---------------- Fig1 Bulk y<0.19 of E, theta , E-PZ ----------------- \begin{figure}[htbp] \begin{center} %\subfigure[\label{fig:contBulk460}]{\includegraphics[width=\columnwidth]{plots/ControlHists-jets-y019-460-040FL} } %\subfigure[\label{fig:contBulk575}]{\includegraphics[width=\columnwidth]{plots/ControlHists-jets-y019-575-040FL} } %\subfigure[\label{fig:contBulk460}]{\includegraphics[width=\columnwidth]{plots/ControlHists-jets-y019-460-060FL} } %\subfigure[\label{fig:contBulk575}]{\includegraphics[width=\columnwidth]{plots/ControlHists-jets-y019-575-060FL} } %\subfigure[\label{fig:contBulk460}]{\includegraphics[width=\columnwidth]{plots/ControlHists-jets-y019-460-100FL-MLP-ComptMC} } %\subfigure[\label{fig:contBulk575}]{\includegraphics[width=\columnwidth]{plots/ControlHists-jets-y019-575-100FL-MLP-ComptMC} } \subfigure[\label{fig:contBulk460}]{\includegraphics[width=\columnwidth]{d13-211f1a.eps} } \subfigure[\label{fig:contBulk575}]{\includegraphics[width=\columnwidth]{d13-211f1b.eps} } \end{center} \caption{\sl Distributions of $P_{\rm T,h}/P_{\rm T,e}$, $\theta_{\rm jets}$ and $E-P_z$ for (a) $E_p=460$~GeV and (b) $E_p=575$~GeV for $y<0.19$ data (solid points) and simulation and estimated background (histograms) normalised to the integrated luminosity of the data. The estimated QED Compton background contribution is shown as shaded histogram.} \label{fig:contBulk} \end{figure} %---------------- Fig2 high E<6 of E-PZ, ECRA, E/p ----------------- \begin{figure}[htbp] \begin{center} %\subfigure[\label{fig:contLoE460}]{\includegraphics[width=\columnwidth]{plots/ControlHists-E36-460-040FL} } %\subfigure[\label{fig:contLoE575}]{\includegraphics[width=\columnwidth]{plots/ControlHists-E36-575-040FL} } %\subfigure[\label{fig:contLoE460}]{\includegraphics[width=\columnwidth]{plots/ControlHists-E36-460-090FL-MLP} } %\subfigure[\label{fig:contLoE575}]{\includegraphics[width=\columnwidth]{plots/ControlHists-E36-575-090FL-MLP} } %\subfigure[\label{fig:contLoE460}]{\includegraphics[width=\columnwidth]{plots/ControlHists-E36-460-100FL-MLP} } %\subfigure[\label{fig:contLoE575}]{\includegraphics[width=\columnwidth]{plots/ControlHists-E36-575-100FL-MLP} } \subfigure[\label{fig:contLoE460}]{\includegraphics[width=\columnwidth]{d13-211f2a.eps} } \subfigure[\label{fig:contLoE575}]{\includegraphics[width=\columnwidth]{d13-211f2b.eps} } \end{center} \caption{\sl Distributions of $E-P_z$, $D_{ele}$, and $E^\prime_e/p_e$ for the sample of events with $E^\prime_e<6$~GeV. The selection requirements on $E-P_z$ and $D_{ele}$ are shown as vertical lines with all other selection criteria applied. The distributions are shown for (a) $E_p=460$~GeV and (b) $E_p=575$~GeV for data (solid points) and simulation and estimated background (histograms) normalised to the integrated luminosity of the data. The estimated background is shown as shaded histogram and includes the photoproduction contribution estimated using wrong charge scattered lepton candidates as well as the QED Compton contribution.} \label{fig:contLowE} \end{figure} %---------------- Fig3 high y of E, theta , E-PZ ----------------- \begin{figure}[htbp] \begin{center} %\subfigure[\label{fig:contHiY460}]{\includegraphics[width=\columnwidth]{plots/ControlHists-hiy-E6-460-040FL} } %\subfigure[\label{fig:contHiY575}]{\includegraphics[width=\columnwidth]{plots/ControlHists-hiy-E6-575-040FL} } %\subfigure[\label{fig:contHiY460}]{\includegraphics[width=\columnwidth]{plots/ControlHists-hiy-E6-460-080FL-ComptLine} } %\subfigure[\label{fig:contHiY575}]{\includegraphics[width=\columnwidth]{plots/ControlHists-hiy-E6-575-080FL-ComptLine} } %\subfigure[\label{fig:contHiY460}]{\includegraphics[width=\columnwidth]{plots/ControlHists-hiy-E6-460-100FL-MLP-ComptLine} } %\subfigure[\label{fig:contHiY575}]{\includegraphics[width=\columnwidth]{plots/ControlHists-hiy-E6-575-100FL-MLP-ComptLine} } \subfigure[\label{fig:contHiY460}]{\includegraphics[width=\columnwidth]{d13-211f3a.eps} } \subfigure[\label{fig:contHiY575}]{\includegraphics[width=\columnwidth]{d13-211f3b.eps} } \end{center} \caption{\sl Distributions of $E^\prime_e$, $\theta_e$ and $E-P_z$ for (a) $E_p=460$~GeV and (b) $E_p=575$~GeV for $high~y$ data (solid points) and simulation and estimated background (histograms) normalised to the integrated luminosity of the data. The estimated background is shown as shaded histogram and includes the photoproduction contribution estimated using wrong charge scattered lepton candidates and the QED Compton contribution (dashed line).} \label{fig:contHiY} \end{figure} %---------------- Fig4 cross section 920/460/575 (x,Q2) ----------------- \begin{figure}[htbp] \begin{center} \includegraphics[width=\columnwidth]{d13-211f4.eps} \end{center} \caption{\sl The reduced cross section $\tilde{\sigma}_{NC}(x,Q^2)+0.3i$ measured at three proton beam energies $E_p=460$~GeV (diamonds, i=0), $575$~GeV (squares, i=1) and $920$~GeV (circles, i=2). The previously published H1 SpaCal data are shown by the open symbols. %The open symbols represent the previously published H1 SpaCal data, and t The solid symbols are the H1 LAr data. The new measurements reported here correspond to the filled diamonds and squares. The inner error bars represent the statistical errors, the full error bars include the statistical and systematic uncertainties added in quadrature, excluding the normalisation uncertainty. The curves represent the prediction from the H1PDF2012 NLO QCD fit.} \label{fig:xsec-xq2} \end{figure} %---------------- Fig5 Rosenbluth plot (Q2=150) ----------------- \begin{figure}[htbp] \begin{center} \includegraphics[width=\columnwidth]{d13-211f5.eps} \end{center} \caption{\sl The reduced cross section $\tilde{\sigma}_{NC}(x,Q^2)$ as a function of $y^2/(1 + (1-y)^2)$ for six values of $x$ at $Q^2 = 60$~GeV$^2$, measured for proton beam energies of $E_p = 920,~575$ and $460$~GeV. The inner error bars denote the statistical error, the outer error bars show statistical and systematic uncertainties added in quadrature. The luminosity uncertainty is not included in the error bars. The negative slopes of the linear fits (solid line) which were performed using total errors, illustrate the non-vanishing values of the structure function $F_L(x,Q^2)$.} \label{fig:rosenbluth} \end{figure} %---------------- Fig6 F2 & FL(x,Q2) ----------------- \begin{figure}[htbp] \begin{center} \includegraphics[width=\columnwidth]{d13-211f6.eps} \end{center} \caption{\sl The proton structure functions $F_L(x,Q^2)$ (solid symbols) and $F_2(x,Q^2)$ (open symbols) measured by H1 (circles) and ZEUS (diamonds) in the region $2\leq Q^2 \leq 25$~GeV$^2$. The inner error bars represent the statistical uncertainties, the full error bars include the statistical and systematic uncertainties added in quadrature, including all correlated and uncorrelated uncertainties. The curves represent the prediction from the H1PDF2012 NLO QCD fit.} \label{fig:FLxq2-a} \end{figure} %---------------- Fig7 F2 & FL(x,Q2) ----------------- \begin{figure}[htbp] \begin{center} \includegraphics[width=\columnwidth]{d13-211f7.eps} \end{center} \caption{\sl The proton structure functions $F_L(x,Q^2)$ (solid symbols) and $F_2(x,Q^2)$ (open symbols) measured by H1 (circles) and ZEUS (diamonds) in the region $35\leq Q^2 \leq 800$~GeV$^2$. The inner error bars represent the statistical uncertainties, the full error bars include the statistical and systematic uncertainties added in quadrature, including all correlated and uncorrelated uncertainties. The curves represent the prediction from the H1PDF2012 NLO QCD fit. } \label{fig:FLxq2-b} \end{figure} %---------------- Fig8 FL(Q2) ----------------- \begin{figure}[htbp] \begin{center} \includegraphics[width=\columnwidth]{d13-211f8.eps} \end{center} \caption{\sl The proton structure function $F_L$ averaged over $x$ at different $Q^2$ (solid points). The average value of $x$ for each $Q^2$ is given above each data point. The inner error bars represent the statistical uncertainties, the full error bars include the statistical and systematic uncertainties added in quadrature, including all correlated and uncorrelated uncertainties. The $F_L$ measurements by ZEUS are also shown (open points). The data are compared to NNLO predictions from a selection of PDF sets as indicated.} \label{fig:FLq2} \end{figure} %% %---------------- Fig9 R(x,Q2) ----------------- %% \begin{figure}[htbp] %% \begin{center} %% \includegraphics[width=\columnwidth]{plots/R_doubleQ2x} %% \end{center} %% \caption{\sl The structure function ratio $R(x,Q^2)$ (solid points) in %% the region $35\leq Q^2 \leq 800$~GeV$^2$. The inner error bars %% represent the statistical uncertainties, the full error bars include %% the statistical and systematic uncertainties added in quadrature, %% excluding the normalisation uncertainty. The curves represent the %% prediction from the H1PDF2012 NLO QCD fit.} %% \label{fig:Rxq2} %% \end{figure} %---------------- Fig9 R(Q2) ----------------- \begin{figure}[htbp] \begin{center} \includegraphics[width=\columnwidth]{d13-211f9.eps} \end{center} \caption{\sl The ratio $R(Q^2)$ averaged over $x$ in the region $1.5\leq Q^2 \leq 800$~GeV$^2$ (solid points). The error bars represent the full errors as obtained by the Monte Carlo procedure described in the text. The ZEUS data are also shown (open symbols). The ZEUS data point at $Q^2=45$~GeV$^2$ is slightly shifted for better visibility of the erros. The solid curve represents the prediction from the HERAPDF1.5 NNLO QCD fit and its uncertainty for $\sqrt{s}=225$~Gev$^2$ and $y=0.7$. The additional dashed and dotted curves show the variations of $R$ in the region of $x$ where the data are sensitive to this quantity. % y=0.85 is the lowest x where we have 2 measurements of FL % y=0.70 is the highest x where we have 2 measurements of FL } \label{fig:Rq2} \end{figure} %---------------- Fig10 g(Q2) ----------------- \begin{figure}[htbp] \begin{center} \includegraphics[width=\columnwidth]{d13-211f10.eps} \end{center} \caption{\sl The gluon density $xg(x,Q^2)$ averaged over $x$ in the region $1.5\leq Q^2 \leq 800$~GeV$^2$ (solid points). The average value of $x$ for each $Q^2$ is given above each data point. The inner error bars represent the statistical uncertainties, the full error bars include the statistical and systematic uncertainties added in quadrature, including all correlated and uncorrelated uncertainties. The shaded regions represent the prediction from the HERAPDF1.5 NLO QCD fit. The dashed line corresponds to $xg$ as obtained by applying equation \ref{eq:xgapprox} to the $F_L$ prediction based on the HERAPDF1.5 NLO QCD fit. } \label{fig:gluon} \end{figure} \end{document}