%================================================================ % LaTeX file with prefered layout for H1 paper drafts % use: dvips -D600 file-name %================================================================ %%%%%%%%%%%%% LATEX HEADER %%%%%%%%%%%%% DO NOT DELET NOT CHANGE ANYTHING IN THE HEADER %%%%%%%%%%%%% UNLESS CLEARLY RECOMMENDED \documentclass[12pt]{article} \usepackage{epsfig} \usepackage{amsmath} \usepackage{hhline} \usepackage{amssymb} \usepackage{times} \usepackage{cite} %%%%%%%%%%%% Comment the next two lines to remove the line numbering %\usepackage[]{lineno} %\linenumbers %%%%%%%%%%%% \renewcommand{\topfraction}{1.0} \renewcommand{\bottomfraction}{1.0} \renewcommand{\textfraction}{0.0} \newlength{\dinwidth} \newlength{\dinmargin} \setlength{\dinwidth}{21.0cm} \textheight23.5cm \textwidth16.0cm \setlength{\dinmargin}{\dinwidth} \setlength{\unitlength}{1mm} \addtolength{\dinmargin}{-\textwidth} \setlength{\dinmargin}{0.5\dinmargin} \oddsidemargin -1.0in \addtolength{\oddsidemargin}{\dinmargin} \setlength{\evensidemargin}{\oddsidemargin} \setlength{\marginparwidth}{0.9\dinmargin} \marginparsep 8pt \marginparpush 5pt \topmargin -42pt \headheight 12pt \headsep 30pt \footskip 24pt \parskip 3mm plus 2mm minus 2mm \usepackage{graphicx} \usepackage{lscape} \usepackage{fancybox} \usepackage{verbatim} \usepackage{booktabs} %\usepackage{a4} %%%%%%%%%%%%%%%% END OF LATEX HEADER \begin{document} %%%%%%%%%%%%%%%% \newcommand{\pom}{{I\!\!P}} \newcommand{\reg}{{I\!\!R}} \newcommand{\slowpi}{\pi_{\mathit{slow}}} %\newcommand{\gevsq}{\mathrm{GeV}^2} \newcommand{\fiidiii}{F_2^{D(3)}} \newcommand{\fiidiiiarg}{\fiidiii\,(\beta,\,Q^2,\,x)} \newcommand{\n}{1.19\pm 0.06 (stat.) \pm0.07 (syst.)} \newcommand{\nz}{1.30\pm 0.08 (stat.)^{+0.08}_{-0.14} (syst.)} \newcommand{\fiidiiiful}{F_2^{D(4)}\,(\beta,\,Q^2,\,x,\,t)} \newcommand{\fiipom}{\tilde F_2^D} \newcommand{\ALPHA}{1.10\pm0.03 (stat.) \pm0.04 (syst.)} \newcommand{\ALPHAZ}{1.15\pm0.04 (stat.)^{+0.04}_{-0.07} (syst.)} \newcommand{\fiipomarg}{\fiipom\,(\beta,\,Q^2)} \newcommand{\pomflux}{f_{\pom / p}} \newcommand{\nxpom}{1.19\pm 0.06 (stat.) \pm0.07 (syst.)} \newcommand {\gapprox} {\raisebox{-0.7ex}{$\stackrel {\textstyle>}{\sim}$}} \newcommand {\lapprox} {\raisebox{-0.7ex}{$\stackrel {\textstyle<}{\sim}$}} \def\gsim{\,\lower.25ex\hbox{$\scriptstyle\sim$}\kern-1.30ex% \raise 0.55ex\hbox{$\scriptstyle >$}\,} \def\lsim{\,\lower.25ex\hbox{$\scriptstyle\sim$}\kern-1.30ex% \raise 0.55ex\hbox{$\scriptstyle <$}\,} \newcommand{\pomfluxarg}{f_{\pom / p}\,(x_\pom)} \newcommand{\dsf}{\mbox{$F_2^{D(3)}$}} \newcommand{\dsfva}{\mbox{$F_2^{D(3)}(\beta,Q^2,x_{I\!\!P})$}} \newcommand{\dsfvb}{\mbox{$F_2^{D(3)}(\beta,Q^2,x)$}} \newcommand{\dsfpom}{$F_2^{I\!\!P}$} \newcommand{\gap}{\stackrel{>}{\sim}} \newcommand{\lap}{\stackrel{<}{\sim}} \newcommand{\fem}{$F_2^{em}$} \newcommand{\tsnmp}{$\tilde{\sigma}_{NC}(e^{\mp})$} \newcommand{\tsnm}{$\tilde{\sigma}_{NC}(e^-)$} \newcommand{\tsnp}{$\tilde{\sigma}_{NC}(e^+)$} \newcommand{\st}{$\star$} \newcommand{\sst}{$\star \star$} \newcommand{\ssst}{$\star \star \star$} \newcommand{\sssst}{$\star \star \star \star$} \newcommand{\tw}{\theta_W} \newcommand{\sw}{\sin{\theta_W}} \newcommand{\cw}{\cos{\theta_W}} \newcommand{\sww}{\sin^2{\theta_W}} \newcommand{\cww}{\cos^2{\theta_W}} \newcommand{\trm}{m_{\perp}} \newcommand{\trp}{p_{\perp}} \newcommand{\trmm}{m_{\perp}^2} \newcommand{\trpp}{p_{\perp}^2} \newcommand{\alp}{\alpha_s} \newcommand{\alps}{\alpha_s} \newcommand{\sqrts}{$\sqrt{s}$} \newcommand{\LO}{$O(\alpha_s^0)$} \newcommand{\Oa}{$O(\alpha_s)$} \newcommand{\Oaa}{$O(\alpha_s^2)$} \newcommand{\PT}{p_{\perp}} \newcommand{\JPSI}{J/\psi} \newcommand{\sh}{\hat{s}} %\newcommand{\th}{\hat{t}} \newcommand{\uh}{\hat{u}} \newcommand{\MP}{m_{J/\psi}} %\newcommand{\PO}{\mbox{l}\!\mbox{P}} \newcommand{\PO}{I\!\!P} \newcommand{\xbj}{x} \newcommand{\xpom}{x_{\PO}} \newcommand{\ttbs}{\char'134} \newcommand{\xpomlo}{3\times10^{-4}} \newcommand{\xpomup}{0.05} \newcommand{\dgr}{^\circ} \newcommand{\pbarnt}{\,\mbox{{\rm pb$^{-1}$}}} \newcommand{\gev}{\,\mbox{GeV}} \newcommand{\WBoson}{\mbox{$W$}} \newcommand{\fbarn}{\,\mbox{{\rm fb}}} \newcommand{\fbarnt}{\,\mbox{{\rm fb$^{-1}$}}} \newcommand{\dsdx}[1]{$ d\sigma\!/\!d #1\,$} \newcommand{\dsd}[1]{${\rm d}\sigma\!/\!{\rm d} #1\,$} \newcommand{\dds}{$d\sigma\!/\!d x\, d Q^2\,$} \newcommand{\eV}{\mbox{e\hspace{-0.08em}V}} % % Some useful tex commands % \newcommand{\qsq}{\ensuremath{Q^2} } %\newcommand{\qsq}{{$Q^2$}} \newcommand{\gevsq}{\ensuremath{\mathrm{GeV}^2} } \newcommand{\et}{\ensuremath{E_t^*} } \newcommand{\rap}{\ensuremath{\eta^*} } \newcommand{\gp}{\ensuremath{\gamma^*}p } \newcommand{\dsiget}{\ensuremath{{\rm d}\sigma_{ep}/{\rm d}E_t^*} } \newcommand{\dsigrap}{\ensuremath{{\rm d}\sigma_{ep}/{\rm d}\eta^*} } %%% Dstar stuff \newcommand{\dstar}{\ensuremath{D^*}} \newcommand{\dstarp}{\ensuremath{D^{*+}}} \newcommand{\dstarm}{\ensuremath{D^{*-}}} \newcommand{\dstarpm}{\ensuremath{D^{*\pm}}} \newcommand{\zDs}{\ensuremath{z(\dstar )}} \newcommand{\Wgp}{\ensuremath{W_{\gamma p}}} \newcommand{\ptds}{\ensuremath{p_t(\dstar )}} \newcommand{\etads}{\ensuremath{\eta(\dstar )}} \newcommand{\ptj}{\ensuremath{p_t(\mbox{jet})}} \newcommand{\ptjn}[1]{\ensuremath{p_t(\mbox{jet$_{#1}$})}} \newcommand{\etaj}{\ensuremath{\eta(\mbox{jet})}} \newcommand{\detadsj}{\ensuremath{\eta(\dstar )\, \mbox{-}\, \etaj}} % Journal macro \def\Journal#1#2#3#4{{#1} {\bf #2} (#3) #4} \def\NCA{ Nuovo Cimento} \def\NIM{ Nucl. Instrum. Methods} \def\NIMA{{ Nucl. Instrum. Methods} {\bf A}} \def\NPB{{ Nucl. Phys.} {\bf B}} \def\PLB{{ Phys. Lett.} {\bf B}} \def\PRL{ Phys. Rev. Lett.} \def\PRD{{ Phys. Rev.} {\bf D}} \def\ZPC{{ Z. Phys.} {\bf C}} \def\EJC{{ Eur. Phys. J.} {\bf C}} \def\CPC{ Comp. Phys. Commun.} %%%%%%%%%%%%%%%% extra stuff \newcommand{\ord}{{\cal O}} \renewcommand{\L}{{\cal L}} \newcommand{\rpv}{\slash\hspace{-3.1mm}{R}_{p}} \newcommand{\brpv}{\slash\hspace{-3.8mm}{R}_{p}} \newcommand{\GeV}{\mathrm{GeV}} \newcommand{\TeV}{\mathrm{TeV}} \newcommand{\pb}{\mathrm{pb}} \newcommand{\cm}{\mathrm{cm}} \newcommand{\m}{\mathrm{m}} \newcommand{\hdick}{\noalign{\hrule height1.4pt}} % \newcommand{\nn}{\nonumber} \newcommand{\beq}{\begin{equation}} \newcommand{\eeq}{\end{equation}} \newcommand{\bea}{\begin{eqnarray}} \newcommand{\eea}{\end{eqnarray}} \newcommand{\eq}[1]{eq.~(\ref{#1})} \newcommand{\tf}[1]{\parbox{8mm}{\hfill #1}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{titlepage} \noindent \begin{flushleft} {\tt DESY 11-114 \hfill ISSN 0418-9833} \\ {\tt July 2011} \\ \end{flushleft} \noindent %Date: \\ \today \\ %Version: 2.9 \\ %%.2...; 1st draft: 1.0, 1.1...; 2nd Draft 2.0..., Final Reading 3.0,3.1... \\ %Editors: H.~Pirumov, V.~Radescu, A.~Sch\"oning \\ %Referees: J.~List, R.~Placakyte \\ %Final Reading Friday, July 1st, 8h30, spokesperson office \\ \noindent \vspace{2cm} \begin{center} \begin{Large}{\bf Search for Contact Interactions \\ in {\boldmath $e^\pm p$} Collisions at HERA} \\ \vspace*{2cm} {H1 Collaboration} \end{Large} \end{center} \vspace{2cm} \begin{abstract} A search for physics beyond the Standard Model in neutral current deep inelastic scattering at high negative four-momentum transfer squared \qsq is performed in $e^{\pm}p$ collisions at HERA. % The differential cross section \dsd {\qsq}, measured using the full H1 data sample corresponding to an integrated luminosity of $446$~pb$^{-1}$, is compared to the Standard Model prediction. % No significant deviation is observed. Limits on various models predicting new phenomena at high \qsq are derived. % For general four-fermion $eeqq$ contact interaction models, lower limits on the compositeness scale $\Lambda$ are set in the range $3.6~\TeV$ to $7.2~\TeV$. % Leptoquarks with masses $M_{\rm LQ}$ and couplings $\lambda$ are constrained to $M_{\rm LQ}/\lambda > 0.41-1.86~\TeV$ and limits on squarks in $R$-parity violating supersymmetric models are derived. % A lower limit on the %effective Planck gravitational scale in (4+n) dimensions of %$M_S > 0.9~\TeV$ $M_{S} > 0.9~\TeV$ is established for low-scale quantum gravity effects in models with large extra dimensions. % For the light quark radius an upper bound of $R_q< 0.65 \cdot 10^{-18}~\m$ is determined. \end{abstract} \vspace{1.5cm} \begin{center} Submitted to \PLB \end{center} \end{titlepage} \newpage \noindent %-- H1AUTS Author list by names %-- Status: Wed Jun 1 14:13:45 CEST 2011 Number of authors = 203 F.D.~Aaron$^{5,48}$, %BUCH-PD 11/06 Aaron C.~Alexa$^{5}$, %BUCH-PD 06/06 Alexa V.~Andreev$^{25}$, %LPI -PD 8/88 Andreev S.~Backovic$^{30}$, %PODG-PD 03/02 Backovic A.~Baghdasaryan$^{38}$, %YERE-PD 09/03 Baghdasaryana S.~Baghdasaryan$^{38}$, %YERE-ST 02/10 Baghdasaryans E.~Barrelet$^{29}$, %PARI-PD 11/99 Barrelet W.~Bartel$^{11}$, %DESY-PD 8/88 Bartel K.~Begzsuren$^{35}$, %ULBA-PD 04/06 Begzsuren A.~Belousov$^{25}$, %LPI -PD 8/88 Belousov P.~Belov$^{11}$, %DESY-ST 07/10 Belov J.C.~Bizot$^{27}$, %ORSA-PD 8/88 Bizot V.~Boudry$^{28}$, %ECPL-PD 1/93 Boudry I.~Bozovic-Jelisavcic$^{2}$, %BEOG-PD 03/06 Bozovicjelisavcic J.~Bracinik$^{3}$, %BIRM-PD 01/2 Bracinik G.~Brandt$^{11}$, %DESY-PD 01/20 Brandt M.~Brinkmann$^{11}$, %DESY-PD 03/10 Brinkmann V.~Brisson$^{27}$, %ORSA-PD 8/88 Brisson D.~Britzger$^{11}$, %DESY-ST 10/09 Britzger D.~Bruncko$^{16}$, %KOSI-PD 8/88 Bruncko A.~Bunyatyan$^{13,38}$, %MPIH-PD 12/95 Bunyatyan G.~Buschhorn$^{26, \dagger}$, %MPIM-LEFT 05/11 Buschhorn L.~Bystritskaya$^{24}$, %ITEP-PD 05/99 Bystritskaya A.J.~Campbell$^{11}$, %DESY-PD 8/88 Campbella \newline K.B.~Cantun~Avila$^{22}$, %MEX1-ST 04/06 Cantunavila F.~Ceccopieri$^{4}$, %BRUX-PD 10/09 Ceccopieri K.~Cerny$^{32}$, %PRG2-PD 09/08 Cernyk V.~Cerny$^{16,47}$, %KOSI-PD 06/04 Cernyv V.~Chekelian$^{26}$, %MPIM-PD 01/90 Chekelian J.G.~Contreras$^{22}$, %MEX1-PD 04/97 Contreras \newline J.A.~Coughlan$^{6}$, %RAL -PD 8/88 Coughlan J.~Cvach$^{31}$, %PRAG-PD 8/88 Cvach J.B.~Dainton$^{18}$, %LIVE-PD 8/88 Dainton K.~Daum$^{37,43}$, %WUPP-PD 06/96 Daum B.~Delcourt$^{27}$, %ORSA-PD 8/88 Delcourt J.~Delvax$^{4}$, %BRUX-PD 11/10 Delvax \newline E.A.~De~Wolf$^{4}$, %ANTW-PD 3/93 Dewolf C.~Diaconu$^{21}$, %MARS-PD 01/05 Diaconu M.~Dobre$^{12,50,51}$, %HAM2-ST 07/09 Dobre V.~Dodonov$^{13}$, %MPIH-PD 04/98 Dodonov A.~Dossanov$^{26}$, %MPIM-ST 01/07 Dossanov A.~Dubak$^{30,46}$, %PODG-PD 10/03 Dubak G.~Eckerlin$^{11}$, %DESY-PD 8/88 Eckerlin S.~Egli$^{36}$, %PSI -PD 01/10 Egli A.~Eliseev$^{25}$, %LPI -PD 01/06 Eliseev E.~Elsen$^{11}$, %DESY-PD 8/88 Elsen L.~Favart$^{4}$, %BRUX-PD 8/88 Favart A.~Fedotov$^{24}$, %ITEP-PD 8/88 Fedotov R.~Felst$^{11}$, %DESY-PD 11/0 Felst \newline J.~Feltesse$^{10}$, %SACL-PD 03/05 Feltesse J.~Ferencei$^{16}$, %KOSI-PD 01/05 Ferencei D.-J.~Fischer$^{11}$, %DESY-ST 03/08 Fischer M.~Fleischer$^{11}$, %DESY-PD 07/0 Fleischer A.~Fomenko$^{25}$, %LPI -PD 8/88 Fomenko E.~Gabathuler$^{18}$, %LIVE-PD 10/89 Gabathulere J.~Gayler$^{11}$, %DESY-PD 8/88 Gayler S.~Ghazaryan$^{11}$, %DFLC-PD 09/09 Ghazaryan A.~Glazov$^{11}$, %DESY-PD 01/04 Glazov L.~Goerlich$^{7}$, %CRAC-PD 8/88 Goerlich N.~Gogitidze$^{25}$, %LPI -PD 8/88 Gogitidze M.~Gouzevitch$^{11,45}$, %DESY-PD 09/10 Gouzevitch C.~Grab$^{40}$, %ZUTH-PD 8/88 Grab A.~Grebenyuk$^{11}$, %DESY-ST 03/09 Grebenyuk T.~Greenshaw$^{18}$, %LIVE-PD 8/88 Greenshaw B.R.~Grell$^{11}$, %DESY-LEFT 10/10 Grell G.~Grindhammer$^{26}$, %MPIM-PD 8/88 Grindhammer S.~Habib$^{11}$, %DESY-PD 09/09 Habib D.~Haidt$^{11}$, %DESY-PD 8/88 Haidt C.~Helebrant$^{11}$, %DFLC-LEFT 01/11 Helebrant R.C.W.~Henderson$^{17}$, %LANC-PD 8/88 Henderson E.~Hennekemper$^{15}$, %HDB2-ST 11/07 Hennekemper H.~Henschel$^{39}$, %ZEUT-PD 06/99 Henschel M.~Herbst$^{15}$, %HDB2-ST 06/08 Herbst G.~Herrera$^{23}$, %MEX2-PD 07/98 Herrera M.~Hildebrandt$^{36}$, %PSI -PD 01/10 Hildebrandtm K.H.~Hiller$^{39}$, %ZEUT-PD 8/88 Hiller D.~Hoffmann$^{21}$, %MARS-PD 10/0 Hoffmann R.~Horisberger$^{36}$, %PSI -PD 01/10 Horisberger T.~Hreus$^{4,44}$, %BRUX-PD 10/08 Hreus F.~Huber$^{14}$, %HDB1-ST 09/09 Huberf M.~Jacquet$^{27}$, %ORSA-PD 09/96 Jacquet X.~Janssen$^{4}$, %ANTW-PD 02/03 Janssenx L.~J\"onsson$^{20}$, %LUND-PD 8/88 Joensson H.~Jung$^{11,4,52}$, %DESY-PD 07/00 Jungh M.~Kapichine$^{9}$, %JINR-PD 3/97 Kapichine I.R.~Kenyon$^{3}$, %BIRM-PD 8/88 Kenyon C.~Kiesling$^{26}$, %MPIM-PD 8/88 Kiesling M.~Klein$^{18}$, %LIVE-PD 8/88 Klein C.~Kleinwort$^{11}$, %DESY-PD 8/88 Kleinwort T.~Kluge$^{18}$, %LIVE-PD 05/04 Kluge R.~Kogler$^{11}$, %DESY-PD 12/10 Kogler P.~Kostka$^{39}$, %ZEUT-PD 8/88 Kostka M.~Kraemer$^{11}$, %DESY-PD 10/09 Kraemer J.~Kretzschmar$^{18}$, %LIVE-PD 01/08 Kretzschmar K.~Kr\"uger$^{15}$, %HDB2-PD 01/04 Kruegerk M.P.J.~Landon$^{19}$, %QMWC-PD 8/88 Landon W.~Lange$^{39}$, %ZEUT-PD 8/88 Lange G.~La\v{s}tovi\v{c}ka-Medin$^{30}$, %PODG-PD 06/04 Lastovickamedin \newline P.~Laycock$^{18}$, %LIVE-PD 11/03 Laycock A.~Lebedev$^{25}$, %LPI -PD 8/88 Lebedev V.~Lendermann$^{15}$, %HDB2-PD 01/2 Lendermann S.~Levonian$^{11}$, %DESY-PD 8/88 Levonian K.~Lipka$^{11,50}$, %DESY-PD 01/03 Lipka B.~List$^{11}$, %DESY-LEFT 01/11 Listb J.~List$^{11}$, %DFLC-PD 01/05 Listj R.~Lopez-Fernandez$^{23}$, %MEX2-PD 03/2 Lopezfernandez V.~Lubimov$^{24}$, %ITEP-PD 01/95 Lubimov A.~Makankine$^{9}$, %JINR-PD 11/02 Makankine E.~Malinovski$^{25}$, %LPI -PD 01/89 Malinovskie P.~Marage$^{4}$, %BRUX-LEFT 10/10 Marage \newline H.-U.~Martyn$^{1}$, %AAC1-PD 8/88 Martyn S.J.~Maxfield$^{18}$, %LIVE-PD 8/88 Maxfield A.~Mehta$^{18}$, %LIVE-PD 8/88 Mehta A.B.~Meyer$^{11}$, %DESY-PD 01/00 Meyeran H.~Meyer$^{37}$, %WUPP-PD 8/88 Meyerhi J.~Meyer$^{11}$, %DESY-PD 8/88 Meyerj S.~Mikocki$^{7}$, %CRAC-PD 8/88 Mikocki I.~Milcewicz-Mika$^{7}$, %CRAC-ST 10/02 Milcewicz F.~Moreau$^{28}$, %ECPL-PD 01/90 Moreau A.~Morozov$^{9}$, %JINR-PD 06/99 Morozova J.V.~Morris$^{6}$, %RAL -PD 8/88 Morris M.~Mudrinic$^{2}$, %BEOG-LEFT 01/11 Mudrinic K.~M\"uller$^{41}$, %ZUER-PD 8/88 Muellerk Th.~Naumann$^{39}$, %ZEUT-PD 01/89 Naumannt P.R.~Newman$^{3}$, %BIRM-PD 10/92 Newman C.~Niebuhr$^{11}$, %DESY-PD 3/93 Niebuhr D.~Nikitin$^{9}$, %JINR-PD 06/08 Nikitin G.~Nowak$^{7}$, %CRAC-PD 8/88 Nowakg K.~Nowak$^{11}$, %DESY-PD 10/09 Nowakk \newline J.E.~Olsson$^{11}$, %DESY-PD 8/88 Olsson D.~Ozerov$^{24}$, %ITEP-PD 08/08 Ozerov P.~Pahl$^{11}$, %DESY-ST 10/08 Pahl V.~Palichik$^{9}$, %JINR-PD 01/04 Palichik I.~Panagoulias$^{l,}$$^{11,42}$, %DESY-ST 08/04 Panagoulias M.~Pandurovic$^{2}$, %BEOG-PD 03/11 Pandurovic \newline Th.~Papadopoulou$^{l,}$$^{11,42}$, %DESY-PD 06/04 Papadopoulou C.~Pascaud$^{27}$, %ORSA-PD 8/88 Pascaud G.D.~Patel$^{18}$, %LIVE-PD 8/88 Patel E.~Perez$^{10,45}$, %SACL-PD 10/07 Perez A.~Petrukhin$^{11}$, %DESY-PD 10/09 Petrukhin I.~Picuric$^{30}$, %PODG-PD 01/06 Picuric S.~Piec$^{11}$, %DESY-PD 11/09 Piec H.~Pirumov$^{14}$, %HDB1-ST 09/09 Pirumov D.~Pitzl$^{11}$, %DESY-PD 8/88 Pitzl R.~Pla\v{c}akyt\.{e}$^{12}$, %HAM2-PD 07/10 Placakyte B.~Pokorny$^{32}$, %PRG2-ST 10/09 Pokorny R.~Polifka$^{32}$, %PRG2-ST 10/06 Polifka B.~Povh$^{13}$, %MPIH-PD 8/88 Povh V.~Radescu$^{14}$, %HDB1-PD 10/06 Radescu N.~Raicevic$^{30}$, %PODG-PD 03/2 Raicevic T.~Ravdandorj$^{35}$, %ULBA-PD 06/06 Ravdandorj P.~Reimer$^{31}$, %PRAG-PD 8/88 Reimer E.~Rizvi$^{19}$, %QMWC-PD 01/05 Rizvi P.~Robmann$^{41}$, %ZUER-PD 8/88 Robmann R.~Roosen$^{4}$, %BRUX-PD 8/88 Roosen A.~Rostovtsev$^{24}$, %ITEP-PD 8/88 Rostovtsev M.~Rotaru$^{5}$, %BUCH-ST 02/07 Rotaru J.E.~Ruiz~Tabasco$^{22}$, %MEX1-PD 05/10 Ruiztabascojuliaelis S.~Rusakov$^{25}$, %LPI -PD 8/88 Rusakov D.~\v S\'alek$^{32}$, %PRG2-PD 10/10 Salek D.P.C.~Sankey$^{6}$, %RAL -PD 8/88 Sankey M.~Sauter$^{14}$, %HDB1-PD 10/09 Sauter E.~Sauvan$^{21}$, %MARS-PD 11/1 Sauvan S.~Schmitt$^{11}$, %DESY-PD 09/07 Schmittst L.~Schoeffel$^{10}$, %SACL-PD 12/98 Schoeffel A.~Sch\"oning$^{14}$, %HDB1-PD 04/09 Schoening H.-C.~Schultz-Coulon$^{15}$, %HDB2-PD 01/04 Schultzcoulon F.~Sefkow$^{11}$, %DFLC-PD 09/99 Sefkow L.N.~Shtarkov$^{25}$, %LPI -PD 8/88 Shtarkov S.~Shushkevich$^{26}$, %MPIM-ST 08/07 Shushkevich T.~Sloan$^{17}$, %LANC-PD 1/96 Sloan I.~Smiljanic$^{2}$, %BEOG-LEFT 01/11 Smiljanic Y.~Soloviev$^{25}$, %LPI -PD 8/88 Soloviev \newline P.~Sopicki$^{7}$, %CRAC-ST 09/07 Sopicki D.~South$^{11}$, %DESY-PD 07/10 South V.~Spaskov$^{9}$, %JINR-PD 12/97 Spaskov A.~Specka$^{28}$, %ECPL-PD 3/95 Specka Z.~Staykova$^{4}$, %ANTW-PD 10/10 Staykova M.~Steder$^{11}$, %DESY-PD 09/08 Steder B.~Stella$^{33}$, %ROME-PD 8/88 Stella G.~Stoicea$^{5}$, %BUCH-PD 02/08 Stoicea U.~Straumann$^{41}$, %ZUER-PD 8/88 Straumann T.~Sykora$^{4,32}$, %ANTW-PD 01/06 Sykora P.D.~Thompson$^{3}$, %BIRM-PD 08/99 Thompsonp T.H.~Tran$^{27}$, %ORSA-PD 03/10 Tran D.~Traynor$^{19}$, %QMWC-PD 12/01 Traynor \newline P.~Tru\"ol$^{41}$, %ZUER-PD 8/88 Truoel I.~Tsakov$^{34}$, %SOFI-PD 04/03 Tsakov B.~Tseepeldorj$^{35,49}$, %ULBA-PD 06/06 Tseepeldorj J.~Turnau$^{7}$, %CRAC-PD 8/88 Turnau K.~Urban$^{15}$, %HDB2-LEFT 07/10 Urbank A.~Valk\'arov\'a$^{32}$, %PRG2-PD 8/88 Valkarova C.~Vall\'ee$^{21}$, %MARS-PD 8/88 Vallee \newline P.~Van~Mechelen$^{4}$, %ANTW-PD 12/98 Vanmechelen Y.~Vazdik$^{25}$, %LPI -PD 8/88 Vazdik D.~Wegener$^{8}$, %DORT-PD 8/88 Wegener E.~W\"unsch$^{11}$, %DESY-PD 8/88 Wuensch J.~\v{Z}\'a\v{c}ek$^{32}$, %PRG2-PD 8/88 Zacek J.~Z\'ale\v{s}\'ak$^{31}$, %PRAG-PD 01/05 Zalesak Z.~Zhang$^{27}$, %ORSA-PD 10/92 Zhang A.~Zhokin$^{24}$, %ITEP-PD 04/99 Zhokine H.~Zohrabyan$^{38}$, %YERE-PD 11/02 Zohrabyan and F.~Zomer$^{27}$ %ORSA-PD 8/88 Zomer %-- H1 Institutes \noindent \bigskip{\it \\ $ ^{1}$ I. Physikalisches Institut der RWTH, Aachen, Germany \\ $ ^{2}$ Vinca Institute of Nuclear Sciences, University of Belgrade, 1100 Belgrade, Serbia \\ $ ^{3}$ School of Physics and Astronomy, University of Birmingham, Birmingham, UK$^{ b}$ \\ $ ^{4}$ Inter-University Institute for High Energies ULB-VUB, Brussels and Universiteit Antwerpen, Antwerpen, Belgium$^{ c}$ \\ $ ^{5}$ National Institute for Physics and Nuclear Engineering (NIPNE) , Bucharest, Romania$^{ m}$ \\ $ ^{6}$ Rutherford Appleton Laboratory, Chilton, Didcot, UK$^{ b}$ \\ $ ^{7}$ Institute for Nuclear Physics, Cracow, Poland$^{ d}$ \\ $ ^{8}$ Institut f\"ur Physik, TU Dortmund, Dortmund, Germany$^{ a}$ \\ $ ^{9}$ Joint Institute for Nuclear Research, Dubna, Russia \\ $ ^{10}$ CEA, DSM/Irfu, CE-Saclay, Gif-sur-Yvette, France \\ $ ^{11}$ DESY, Hamburg, Germany \\ $ ^{12}$ Institut f\"ur Experimentalphysik, Universit\"at Hamburg, Hamburg, Germany$^{ a}$ \\ $ ^{13}$ Max-Planck-Institut f\"ur Kernphysik, Heidelberg, Germany \\ $ ^{14}$ Physikalisches Institut, Universit\"at Heidelberg, Heidelberg, Germany$^{ a}$ \\ $ ^{15}$ Kirchhoff-Institut f\"ur Physik, Universit\"at Heidelberg, Heidelberg, Germany$^{ a}$ \\ $ ^{16}$ Institute of Experimental Physics, Slovak Academy of Sciences, Ko\v{s}ice, Slovak Republic$^{ f}$ \\ $ ^{17}$ Department of Physics, University of Lancaster, Lancaster, UK$^{ b}$ \\ $ ^{18}$ Department of Physics, University of Liverpool, Liverpool, UK$^{ b}$ \\ $ ^{19}$ Queen Mary and Westfield College, London, UK$^{ b}$ \\ $ ^{20}$ Physics Department, University of Lund, Lund, Sweden$^{ g}$ \\ $ ^{21}$ CPPM, Aix-Marseille Universit\'e, CNRS/IN2P3, Marseille, France \\ $ ^{22}$ Departamento de Fisica Aplicada, CINVESTAV, M\'erida, Yucat\'an, M\'exico$^{ j}$ \\ $ ^{23}$ Departamento de Fisica, CINVESTAV IPN, M\'exico City, M\'exico$^{ j}$ \\ $ ^{24}$ Institute for Theoretical and Experimental Physics, Moscow, Russia$^{ k}$ \\ $ ^{25}$ Lebedev Physical Institute, Moscow, Russia$^{ e}$ \\ $ ^{26}$ Max-Planck-Institut f\"ur Physik, M\"unchen, Germany \\ $ ^{27}$ LAL, Universit\'e Paris-Sud, CNRS/IN2P3, Orsay, France \\ $ ^{28}$ LLR, Ecole Polytechnique, CNRS/IN2P3, Palaiseau, France \\ $ ^{29}$ LPNHE, Universit\'e Pierre et Marie Curie Paris 6, Universit\'e Denis Diderot Paris 7, CNRS/IN2P3, Paris, France \\ $ ^{30}$ Faculty of Science, University of Montenegro, Podgorica, Montenegro$^{ n}$ \\ $ ^{31}$ Institute of Physics, Academy of Sciences of the Czech Republic, Praha, Czech Republic$^{ h}$ \\ $ ^{32}$ Faculty of Mathematics and Physics, Charles University, Praha, Czech Republic$^{ h}$ \\ $ ^{33}$ Dipartimento di Fisica Universit\`a di Roma Tre and INFN Roma~3, Roma, Italy \\ $ ^{34}$ Institute for Nuclear Research and Nuclear Energy, Sofia, Bulgaria$^{ e}$ \\ $ ^{35}$ Institute of Physics and Technology of the Mongolian Academy of Sciences, Ulaanbaatar, Mongolia \\ $ ^{36}$ Paul Scherrer Institut, Villigen, Switzerland \\ $ ^{37}$ Fachbereich C, Universit\"at Wuppertal, Wuppertal, Germany \\ $ ^{38}$ Yerevan Physics Institute, Yerevan, Armenia \\ $ ^{39}$ DESY, Zeuthen, Germany \\ $ ^{40}$ Institut f\"ur Teilchenphysik, ETH, Z\"urich, Switzerland$^{ i}$ \\ $ ^{41}$ Physik-Institut der Universit\"at Z\"urich, Z\"urich, Switzerland$^{ i}$ \\ \bigskip \noindent $ ^{42}$ Also at Physics Department, National Technical University, Zografou Campus, GR-15773 Athens, Greece \\ $ ^{43}$ Also at Rechenzentrum, Universit\"at Wuppertal, Wuppertal, Germany \\ $ ^{44}$ Also at University of P.J. \v{S}af\'{a}rik, Ko\v{s}ice, Slovak Republic \\ $ ^{45}$ Also at CERN, Geneva, Switzerland \\ $ ^{46}$ Also at Max-Planck-Institut f\"ur Physik, M\"unchen, Germany \\ $ ^{47}$ Also at Comenius University, Bratislava, Slovak Republic \\ $ ^{48}$ Also at Faculty of Physics, University of Bucharest, Bucharest, Romania \\ $ ^{49}$ Also at Ulaanbaatar University, Ulaanbaatar, Mongolia \\ $ ^{50}$ Supported by the Initiative and Networking Fund of the Helmholtz Association (HGF) under the contract VH-NG-401. \\ $ ^{51}$ Absent on leave from NIPNE-HH, Bucharest, Romania \\ $ ^{52}$ On leave of absence at CERN, Geneva, Switzerland \\ \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 the Deutsche Forschungsgemeinschaft \\ $ ^f$ Supported by VEGA SR grant no. 2/7062/ 27 \\ $ ^g$ Supported by the Swedish Natural Science Research Council \\ $ ^h$ Supported by the Ministry of Education of the Czech Republic under the projects LC527, INGO-LA09042 and MSM0021620859 \\ $ ^i$ Supported by the Swiss National Science Foundation \\ $ ^j$ Supported by CONACYT, M\'exico, grant 48778-F \\ $ ^k$ Russian Foundation for Basic Research (RFBR), grant no 1329.2008.2 \\ $ ^l$ This project is co-funded by the European Social Fund (75\%) and National Resources (25\%) - (EPEAEK II) - PYTHAGORAS II \\ $ ^m$ Supported by the Romanian National Authority for Scientific Research under the contract PN 09370101 \\ $ ^n$ Partially Supported by Ministry of Science of Montenegro, no. 05-1/3-3352 \\ } \newpage %\clearpage \section{Introduction} Deep inelastic neutral current (NC) scattering $e^\pm p \rightarrow e^\pm X$ at high negative four-momentum transfer squared \qsq allows the structure of $e q$ interactions to be probed at short distances and to search for new phenomena beyond the Standard Model (SM). % Using the concept of four-fermion contact interactions (CI) the interference of the photon and $Z$-boson fields with any new particle field associated to larger scales can be investigated. %% Results from searches for contact interactions in $ep$ interactions at HERA have been previously reported by the H1 \cite{h1ci2003,h1ci2000} and ZEUS \cite{zeusci2004,zeusci2000} collaborations. % Therein, genuine contact interaction models, models with leptoquarks and supersymmetric scalar quarks (squarks), low-scale quantum gravity models with large extra dimensions and compositeness models of quarks have been investigated by searching for deviations from the SM expectation at high $Q^2$. Contact interaction studies have been also performed at LEP~\cite{LEP}. %% Such models have also been investigated in direct searches at HERA, the Tevatron and the LHC. % Searches for leptoquarks involving lepton flavour violation \cite{h1lfv} and %scalar squarks in $R$-parity violating ($\rpv$) supersymmetric models \cite{h1rpv} have been published by the H1 collaboration using the full HERA data. % Searches for leptoquark pair production in proton-proton collisions at a centre--of--mass energy of $\sqrt{s}=7$~TeV were reported by the ATLAS \cite{atlaslq} and CMS \cite{cmslq} collaborations, excluding first generation scalar leptoquarks up to $376$~TeV and $384$~TeV, respectively. % These results surpass limits obtained at the Tevatron \cite{d0lq}. % Stringent limits on low-scale quantum gravity models with large extra dimensions using di-jet, di-electron and di-photon final states have been reported by the D{\O} collaboration \cite{d0led2008,d0led2009} and recently, by the CMS collaboration, excluding mass scales below $1.6$-$2.3$~TeV depending on the model~\cite{cmsled}. %% The analysis in this paper is based on the full H1 data sample collected in the years 1994-2007, which corresponds to an integrated luminosity of $\L=446$~pb$^{-1}$ and represents a factor of $3(12)$ increase in statistics for $e^+p$ ($e^-p$) collisions with respect to the previous publications \cite{h1ci2003}. % The same method is used as in previous analysis which is superseded by the results presented in this paper. %% %\cite{dummy} \section{Contact Interaction Models} New physics phenomena in fermion-fermion scattering experiments may manifest themselves in deviations of the differential cross section \dsd {\qsq} from the SM expectation, and may be related to new heavy particles with masses $M_X$ much larger than the electroweak scale. % In the low energy limit $\sqrt{s} \ll M_X$ such phenomena can be described by an effective four-fermion CI model. % Different implementations of this effective model are summarised in the following. %% \subsection{General contact interactions and compositeness} In $ep$ scattering, the most general chiral invariant Lagrangian for neutral current vector-like four-fermion contact interactions can be written in the form~\cite{elpr,haberl}: % \begin{eqnarray} {\cal L}_V &=& \sum_{q } \sum_{a,\,b\, =\, L,\,R} \eta^q_{ab}\, (\bar{e}_a\gamma_\mu e_a)(\bar{q}_b\gamma^\mu q_b) \ , \label{lcontact} \end{eqnarray} % where $\eta^{q}_{ab}$ are the CI coupling coefficients, $a$ and $b$ indicate the left-handed and right-handed fermion helicities and the first sum is over all quark flavours. % In the kinematic region of interest mainly the valence quarks ($u$ and $d$) contribute. %% In the case of general models of fermion compositeness or substructure the CI coupling coefficients are defined as: % \begin{equation} \eta^q_{ab} = \epsilon^q_{ab}\, \frac{4\pi}{\Lambda^2} \ . \label{eq:composit} \end{equation} % %Here the coupling strength is conventionally set to one \cite{elpr}. % New physics models are then characterised by a common compositeness scale $\Lambda$ and the coefficients $\epsilon^q_{ab}$, which describe the chiral structure of the coupling and may take the values $\pm 1$ or $0$, depending on the scenario, for example pure left-handed (L), right-handed (R), or vector (V) and axial-vector (A) couplings. % Depending on the model and the sign of the coefficients, the new physics processes interfere either constructively or destructively with the SM processes. %% \subsection{Leptoquarks} Leptoquarks, colour triplet scalar or vector bosons carrying lepton and baryon number, appear naturally in extensions of the SM which aim to unify the lepton and quark sectors. % For leptoquark masses $M_{\rm LQ}$ much larger than the probing scale $M_{\rm LQ} \gg \sqrt{s}$, the coupling $\lambda$ is related to the CI coupling coefficients via: % \begin{equation} \eta^{q}_{ab} = \epsilon^{q}_{ab}\, \frac{\lambda^2}{M_{\rm LQ}^2} \ . \end{equation} % The classification of the leptoquarks follows the Buchm\"uller-R\"uckl-Wyler (BRW) model~\cite{brw}, in which the coefficients $\epsilon^{q}_{ab}$ depend on the leptoquark type~\cite{kalinowski} and take values $0$, $\pm \frac{1}{2}$, $\pm 1$, $\pm 2$. %% Two leptoquark types, $S_{0}^{L}$ and $\tilde{S}_{1/2}^{L}$, have quantum numbers identical to %supersymmetric scalar the squarks $\tilde{d}$ and $\tilde{u}$. % For these leptoquarks the couplings $\lambda$ correspond to the Yukawa couplings, $\lambda'_{ijk}$, which describe the ~$\rpv$ supersymmetric $L_iQ_j \bar{D}_k$ interaction \cite{rpv}. % Here $i$, $j$ and $k$ are the family indices and $L_i$, $Q_j$ and $\bar{D}_k$ are the super-fields containing the left-handed leptons, the left-handed up-type quarks and the right-handed down-type quarks, respectively, together with their supersymmetric partners. %% \subsection{Large extra dimensions} In some string inspired models the small nature of the gravitational force is explained by the existence of compactified extra dimensions~\cite{add}. % In these models the gravitational scale %$M_S$ $M_{S}$ in $4+n$ dimensions is related to the size $R$ of the compactified extra dimensions via the Planck scale %$M_P^2 \sim R^n\,M_S^{2+n}$. $M_P^2 \sim R^n\,M_{S}^{2+n}$. % SM particles reside on a four-dimensional brane, while the spin $2$ graviton propagates into the extra spatial dimensions creating a tower of Kaluza-Klein states. % Assuming that the ultraviolet cut-off scale of the tower is of similar size to the gravitational scale, an effective contact-type interaction~\cite{giudice} term can be defined with a coupling coefficient: % \begin{equation} % \eta_G = \frac{\lambda}{M^4_S} \ . \eta_G = \frac{\lambda}{M^4_{S}} \ . \end{equation} % The coupling $\lambda$ depends on details of the theory and is conventionally set to $\pm 1$. %% \subsection{Quark Radius} % A clear manifestation of substructure would be the observation of finite size effects like the measurement of electroweak charge distributions of fermions. % Finite size effects are typically described by a standard form factor in the $eq$ scattering cross section: \begin{eqnarray} f(Q^2) & = & 1 - \frac{{\langle R^2 \rangle}}{6}\,Q^2 \ , \end{eqnarray} which relates the decrease of the scattering cross sections at high $Q^2$ to the mean squared radius $\langle R^2 \rangle$ of the electroweak charge distribution. % This form factor modifies the \qsq dependence of the $ep$ scattering cross section similarly to the CI models described above. %% \section{Data and Analysis Method} The analysed data sample is recorded in $e^+p$ and $e^-p$ collisions corresponding to an integrated luminosity of $281$~pb$^{-1}$ and $165$~pb$^{-1}$, respectively. % The measurement of the differential neutral current cross-section, \dsd {\qsq}, which is used to probe possible CI signatures %is a repetition of follows the previous measurements based on data recorded in the years 1994-2000 \cite{h1xsec,h1xe+p,h1xe-p} and includes new data recorded from 2003-2007. % A list of the analysed data sets is given in table~\ref{datasets}. % \begin{table}[htb] \begin{center} %\vspace*{-2mm} \begin{tabular}{cccl@{\,}c} \toprule Reaction & $\L_{int}~[\pb^{-1}]$ & $\sqrt{s}~[\GeV]$ & \multicolumn{2}{c}{Polarisation $(P_e~[\%])$} \\[.2ex] \midrule $e^+p \to e^+X$ & $36$ & $301$ & \multicolumn{2}{c}{Unpolarised} \\[.2ex] $e^-p \to e^-X$ & $16$ & $319$ & \multicolumn{2}{c}{Unpolarised} \\[.2ex] $e^+p \to e^+X$ & $65$ & $319$ & \multicolumn{2}{c}{Unpolarised} \\[.2ex] $e^-p \to e^-X$ & $46$ & $319$ & Right & $(P_e=+37)$ \\[.2ex] $e^-p \to e^-X$ & $103$ & $319$ & Left & $(P_e=-26)$ \\[.2ex] $e^+p \to e^+X$ & $98$ & $319$ & Right & $(P_e=+33)$ \\[.2ex] $e^+p \to e^+X$ & $82$ & $319$ & Left & $(P_e=-38)$ \\ \bottomrule \end{tabular} \end{center} \caption{%H1 Data samples recorded in the years 1994-2007 with corresponding integrated luminosities, centre-of-mass energies and average longitudinal polarisations.} \label{datasets} \end{table} % The data collected from the year 2003 onwards were taken with a longitudinally polarised lepton beam, with typical polarisation values of $\pm 35\%$. % The average luminosity weighted polarisations of the $e^+p$ and $e^-p$ data sets are small. % Due to the different chiral structure of hypothetical new particles with respect to the irreducible SM background, the sensitivity to possible new physics phenomena is increased by up to $15$ percent by analysing the data sets with left and right longitudinal lepton polarisation separately. Contact interactions are investigated by searching for deviations in the NC differential cross section \dsd{Q^2} from the SM expectation at high negative four-momentum transfer squared $Q^2>200$~GeV$^2$. % The SM cross section of neutral current scattering factorises into the electroweak matrix element of the hard $eq$ interaction process and the parton distribution function (PDF) of the proton. % The \qsq dependence of the PDF is calculated using perturbative QCD \cite{DGLAP}. %% For the CI analysis the parton densities at high values of $Q^2$, corresponding to high values of $x$, are of special importance. % In this analysis the CTEQ6m~\cite{cteq6} PDF is used to calculate both the SM and signal expectations. % The CTEQ6m set was obtained by fitting several experimental data sets. % At high $x$ %, the region relevant for this analysis, this PDF is mostly constrained by fixed target experiments and also by $W$-boson production and jet data from the Tevatron experiments, which are not sensitive to possible $eq$ contact interaction processes. %signals. % CTEQ6m also includes early $e^\pm p$ scattering data at high \qsq from the H1~({$\L=52~\textrm{pb}^{-1}$) and ZEUS~({$ \L=30~\textrm{pb}^{-1}$) experiments. % However, since the $e^+ p$ ($e^- p$) data sets analysed here are $6(10)$ times larger, the residual correlations between the HERA data and the CTEQ6m PDF are small and are neglected in the following. % Furthermore, the CTEQ6m parton densities can be regarded as unbiased with respect to possible contact interaction effects. % CTEQ6m is chosen as it describes many experimental data and in particular, the HERA data in the region \qsq$<200$~GeV$^2$, which are not used in this analysis. % The results of this analysis are verified using an alternative PDF not based on HERA high \qsq data, as described in section~\ref{sec:results}. %% The single differential cross sections \dsd{\qsq} are measured for $e^+p$ and $e^-p$ scattering up to \qsq$=30000$~GeV$^2$ and compared to the SM expectation. % The ratio of the data to the SM expectation is shown in figure~\ref{fig:dsdq2norm}. % Good agreement between data and the SM is observed, in particular in the high \qsq region, which is the focus of this analysis. %% In the next step, a quantitative test of the SM and the CI models is performed by investigating the measured cross sections ${\rm d}\sigma / {\rm d}Q^2$ following the analysis method described in \cite{h1ci2003} by applying a minimisation of the $\chi^2$ function \cite{h1lowx}: \begin{equation} \chi^2(\eta,\varepsilon) = \sum_i \frac {\left( {\sigma}_i^{\rm exp}- {\sigma}_i^{\rm th}(\eta)\, (1-\sum_k \Delta_{ik}(\varepsilon_k)) \right)^2} {\delta^{2}_{i,\rm{stat}}\,{\sigma}_i^{\rm exp}{\sigma}_i^{\rm th}(\eta)\, (1-\sum_k \Delta_{ik}(\varepsilon_k)) + {(\delta_{i,\rm{uncor}}\,{\sigma}_i^{\rm exp})}^2} + \sum_k \varepsilon_k^2 \ . \label{chi2} \end{equation} Here ${\sigma}_i^{\rm exp}$ and ${\sigma}_i^{\rm th}(\eta)$ are the experimental and theoretical cross sections, respectively, for the measurement point $i$, and ${\delta}_{i,\rm{stat}}$ and ${\delta}_{i,\rm{uncor}}$ correspond to the relative statistical and uncorrelated systematic errors, respectively. % The theoretical cross section includes both the SM and the contact interaction term, and it depends on the coupling coefficient $\eta$, which is varied in the fit. % The functions $\Delta_{ik}(\varepsilon_k)$ describe the correlated systematic errors for point $i$ associated to a source $k$ and depend on the fit parameters $\varepsilon_k$. % In particular, the normalisations of the individual data sets described in table~\ref{datasets} are free parameters, only constrained by the individual luminosity measurements. % Since the precise cross section measurements at low \qsq determine the normalisations, new physics signals are mainly tested by exploiting the shape of the \qsq distribution. %% Statistical and systematic uncertainties are taken into account in the fit procedure. % The following sources of experimental uncertainties are accounted for \cite{h1xsec,h1xe-p,h1xe+p,theses}: the electromagnetic energy scale uncertainty of $1-3\%$, the polar angle uncertainty of the scattered lepton of $2-3$~mrad, the uncertainty on the electron identification of $0.5-2\%$, the hadronic energy scale uncertainty of $2-7\%$ the uncertainty from the luminosity measurement of $1.6-3.8\%$ and the uncertainty on the electron beam polarisation of $1-2.3\%$. % The effect of the above systematic uncertainties on the SM expectation is determined by varying the experimental quantities by $\pm 1$ standard deviation in the MC samples and propagating these variations through the whole analysis. The uncorrelated systematic uncertainties of the measurements vary as function of $Q^2$ between $1-11\%$ $(1.6-13\%)$ for $e^+p$ ($e^-p$) scattering. % The dominant sources of the correlated systematic errors are the PDF uncertainty (about $8\%$), %and the uncertainties from the luminosity measurement and from the experimental uncertainties on the energy scale and the polar angle of the scattered lepton. %In addition, also the experimental uncertainties of up to $3\%$ each from the energy scale and from %the polar angle measurement contribute to the correlated systematic error. All other experimental systematic uncertainties are found to have a negligible impact on the analysis. %E 2.6 theta 3.4 %\bf (?? -- add the correlated part) \rm %All statistical and systematic uncertainties are taken %into account in the fitting procedure. %The dominant experimental error comes from the electromagnetic %energy scale uncertainty with some %smaller contribution from the measurement of the electron polar angle. %Other experimental uncertainties coming from the lepton identification and %the trigger employed in the analysis are negligible. % uncorrelated 10.85% 13.01% %Electron energy(corr) 1.33% 0.51% %Electron theta(corr) 0.26% 0.46% %PDF(corr) 7.6% 8.4% %lumi 3.1% 3.8% \section{Results} \label{sec:results} % The data used in this analysis are found to be consistent with the expectation from the SM alone ($\eta=0$ in equation~\ref{chi2}) based on the CTEQ6m PDF, yielding a $\chi^2/dof=16.4/17$ $(7.0/17)$ for the $e^+p$ $(e^-p)$ data. % The normalisation constants of the individual data sets agree well with the SM expectation within the PDF uncertainties. %% For each CI model the effective scale parameters and couplings describing the new physics scale are determined by a fit to the differential NC cross section. % All scale parameters are found to be consistent with the SM and limits are calculated at $95\%$ confidence levels (CL) using the frequentist method as described in the previous publication \cite{h1ci2003}. %% Lower limits on the compositeness scale $\Lambda$ in the context of the general contact interaction model are presented in table~\ref{etafits} and figure~\ref{fig:lqlimits}. % The results are presented for eight scenarios, which differ in their chiral structure as determined by the CI coupling coefficients $\eta^{q}_{ab}$. %The limits are given for both signs of coupling constants, where %$\Lambda^+$ ($\Lambda^-$) denotes the positive (negative) sign. % Depending on the model and the sign of the coefficients, limits on $\Lambda$ are obtained in the range $3.6~\TeV$ to $7.2~\TeV$. % In figure~\ref{fig:dsdq2normvv}, differential cross section measurements for $e^+p$ and $e^-p$ scattering normalised to the SM expectation are compared to the predictions corresponding to the $95$\% CL exclusion limits of the VV model, $\Lambda^+_{VV}>5.6~\TeV$ and $\Lambda^-_{VV}>7.2~\TeV$. %% For leptoquark-type contact interactions, the notation, quantum numbers and lower limits on $M_{\rm LQ}/\lambda$ are presented in table~\ref{lqfits}. % The limits are in the range $M_{\rm LQ}/\lambda > 0.41-1.86~\TeV$. % Leptoquarks coupling to $u$ quarks are probed with higher sensitivity, corresponding to more stringent limits than those coupling to $d$ quarks due to the different quark densities in the proton. % In figure~\ref{fig:dsdq2normlq}, the normalised differential $e^\pm p$ cross section measurements are compared to the predicted cross sections corresponding to the $95\%$ CL exclusion limits of the $S_1^L$ and $V_1^L$ leptoquarks. % At high \qsq the existence of a $S_1^L$ ($V_1^L$) leptoquark would lead to an increase (decrease) of the $e^\pm p$ cross sections, which is not observed. % For a Yukawa coupling of electromagnetic strength, $\lambda=0.3$, scalar and vector leptoquark masses up to $0.33~\TeV$ and $0.56~\TeV$ are excluded, respectively, comparable or exceeding limits obtained by Tevatron and LHC. % The leptoquarks $S_0^L$ and $\tilde{S}_{1/2}^L$ may also be interpreted as squarks in the framework of $\rpv$ supersymmetry and the corresponding limits in terms of the ratio $M_{\tilde{q}}/\lambda'$ are given in table~\ref{sqfits}. % For a Yukawa coupling of electromagnetic strength, the corresponding lower limit on the $\tilde{u}$ mass of $0.33$~TeV is similar to that obtained recently by the H1 collaboration in a direct search \cite{h1rpv}. %% %Schael 2007, s~_R m>490 GeV Lower limits in a model with large extra dimensions on the gravitational scale $M_{S}$ in $4+n$~dimensions assuming a positive ($\lambda = +1$) or negative ($\lambda = -1$) coupling are given in table~\ref{ledfits}. % Mass scales $M_{S}<0.9~\gev$ are excluded at $95\%$ CL. % The corresponding cross section predictions normalised to the SM expectation are compared to the $e^{\pm}p$ data in figure~\ref{fig:dsdq2normled}. %% Finally, an upper limit at $95\%$~CL on the quark radius $R_q < 0.65 \cdot 10^{-18}$~m is derived assuming point-like leptons. % The corresponding cross section predictions normalised to the SM expectation are compared to the $e^{\pm}p$ data in figure~\ref{fig:dsdq2normrad}. %% % Voica %The above results were also verified using the dedicated H1 PDF, where %a good agreement was found between results based on the dedicated H1 PDF set %and the CTEQ6m PDF. The above results are also verified using a dedicated H1 PDF set based on data collected in the years 1994-2007. % This PDF set was obtained from a next-to-leading order QCD fit to the H1 data \cite{h1lowx} with $Q^2<200$~GeV$^2$, excluding the high \qsq data used in this analysis. % Both the SM expectation and limits derived using the dedicated H1 PDF agree well with those obtained using the CTEQ6m PDF within the uncertainties. %% \section{Summary} Neutral current deep inelastic $e^-p$ and $e^+p$ scattering cross section measurements are analysed to search for new phenomena mediated via contact interactions. % The data are well described by the Standard Model expectations. % Limits on the %strength parameters of various contact interaction models are presented at $95\%$ CL. %% Lower limits on the compositeness scale $\Lambda$ are derived within a general contact interaction analysis. % The limits range between $3.6~\TeV$ and $7.2~\TeV$ depending on the chiral structure, corresponding to an increase by a factor of about two compared to previous HERA searches. % The study of leptoquark exchange yields lower limits on the ratio $M_{\rm LQ}/\lambda$ between $0.41~\TeV$ and $1.86~\TeV$, considerably improving constraints from the previous analysis. % Squarks in the framework of $R$-parity violating supersymmetry with masses satisfying $M_{\tilde u}/\lambda'_{1j1} < 1.10~\TeV$ and $M_{\tilde d}/\lambda'_{11k} < 0.66~\TeV$ are excluded. % Possible effects of low-scale quantum gravity with gravitons propagating into extra spatial dimensions are also investigated, where lower limits %on the effective Planck on the gravitational scale in $4+n$~dimensions $M_{S}>0.9~\TeV$ are found. % Finally, a form factor approach yields an upper limit on the size of light $u$ and $d$ quarks of $R_q< 0.65\cdot 10^{-18}~\m$, assuming point-like leptons. %% Using the full HERA data set, limits derived in this analysis are more stringent than previous results by H1 and ZEUS. % The results can also be compared to those obtained by the LEP, Tevatron and, most recently, LHC collaborations. % For most models with Yukawa couplings of electromagnetic strength, or stronger, the analysis presented here provides the most stringent limits on first generation leptoquarks. %% \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. \clearpage % % References for Contact Interaction paper % \begin{thebibliography}{99} % H1 CI paper \bibitem{h1ci2003} C.~Adloff {\it et al.} [H1 Collaboration], % ``Searches and electroweak measurements at HERA,'' Phys.\ Lett.\ B {\bf 568} (2003) 35 [hep-ex/0305015]. %%CITATION = HEP-EX 0003002;%% \bibitem{h1ci2000} C.~Adloff {\it et al.} [H1 Collaboration], % ``Search for compositeness, leptoquarks and large extra dimensions in e q contact interactions at HERA,'' Phys.\ Lett.\ B {\bf 479} (2000) 358 [hep-ex/0003002]. %%CITATION = HEP-EX 0003002;%% \bibitem{zeusci2004} S.~Chekanov {\it et al.} [ZEUS Collaboration], % ``Search for contact interactions, large extra dimensions and finite quark % radius in e p collisions at HERA,'' Phys.\ Lett.\ B {\bf 591} (2004) 23 [hep-ex/0401009]. %%CITATION = PHLTA,B591,23;%% \bibitem{zeusci2000} J.~Breitweg {\it et al.} [ZEUS Collaboration], % ``Search for contact interactions in deep inelastic e+ p $\to$ e+ X scattering at HERA,'' Eur.\ Phys.\ J.\ C {\bf 14} (2000) 239 [hep-ex/9905039]. %%CITATION = HEP-EX 9905039;%% \bibitem{LEP} K.~Cheung, Phys.\ Lett.\ B {\bf 517} (2001) 167 [hep-ph/0106251]. %%% \bibitem{h1lfv} F.~D.~Aaron {\it et al.} [H1 Collaboration], % ``Search for Lepton Flavour Violation at HERA,'' accepted by Phys.\ Lett. 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The $\Lambda^{+}$ limits correspond to the upper signs and the $\Lambda^{-}$ limits correspond to the lower signs of the chiral coefficients \mbox{[$\epsilon^q_{LL}$, $\epsilon^q_{LR}$, $\epsilon^q_{RL}$, $\epsilon^q_{RR}$]}.} \label{etafits} \end{table} \clearpage % leptoquarks \begin{table}[htb] %\label{tab:LQ} \begin{center} \begin{tabular}{l c c c c c} % \hdick \\[-1.5ex] \hline \\[-1.5ex] \multicolumn{5}{c}{\bf\large H1 Search for Heavy Leptoquarks} \\ [1ex] % \hdick \\[-1.5ex] & \multicolumn{2}{c}{$\eta^q_{ab}=\epsilon^q_{ab}~\lambda^2 /M_{\rm LQ}^2$ } & %& $e^-p$ $(319~\GeV)$ & $e^+p$ $(319~\GeV)$ & \\[.5ex] LQ & $\epsilon^u_{ab}$ & $\epsilon^d_{ab}$ & $F$ %& $M_{\rm LQ}/\lambda ~ [ \GeV ]$ %& $M_{\rm LQ}/\lambda ~ [ \GeV ]$ & $M_{\rm LQ}/\lambda ~ [ \TeV ]$ \\[1ex] % \hdick \\[-1.5ex] \hline \\[-1.5ex] $S_0^L$ & \ $\epsilon^u_{LL} = +\frac{1}{2}$ \ & & $2$ & $1.10$ \\[.2em] $S_0^R$ & \ $\epsilon^u_{RR} = +\frac{1}{2}$ \ & & $2$ & $1.10$ \\[.2em] $\tilde{S}_0^R$ & & \ $\epsilon^d_{RR} = +\frac{1}{2}$ \ & $2$ & $0.41$ \\[.2em] $S_{1/2}^L$ & \ $\epsilon^u_{LR} = -\frac{1}{2}$ \ & & $0$ & $0.87$ \\[.2em] $S_{1/2}^R$ & \ $\epsilon^u_{RL} = -\frac{1}{2}$ \ & \ $\epsilon^d_{RL} = -\frac{1}{2}$ \ & $0$ & $0.59$ \\[.2em] $\tilde{S}_{1/2}^L$ & & \ $\epsilon^d_{LR} = -\frac{1}{2}$ \ & $0$ & $0.66$ \\[.2em] $S_1^L$ & \ $\epsilon^u_{LL} = +\frac{1}{2}$ \ & \ $\epsilon^d_{LL} = +1$ \ & $2$ & $0.71$ \\[1ex] \hline \\[-1.5ex] $V_0^L$ & & \ $\epsilon^d_{LL} = -1$ \ & $0$ & $1.06$ \\[.2em] $V_0^R$ & & \ $\epsilon^d_{RR} = -1$ \ & $0$ & $0.91$ \\[.2em] $\tilde{V}_0^R$ & \ $\epsilon^u_{RR} = -1$ \ & & $0$ & $1.35$ \\[.2em] $V_{1/2}^L$ & & \ $\epsilon^d_{LR} = +1$ \ & $2$ & $0.51$ \\[.2em] $V_{1/2}^R$ & \ $\epsilon^u_{RL} = +1$ \ & \ $\epsilon^d_{RL} = +1$ \ & $2$ & $1.44$ \\[.2em] $\tilde{V}_{1/2}^L$ & \ $\epsilon^u_{LR} = +1$ \ & & $2$ & $1.58$ \\[.2em] $V_1^L$ & \ $\epsilon^u_{LL} = -2$ \ & \ $\epsilon^d_{LL} = -1$ \ & $0$ & $1.86$ \\[1ex] \hline \end{tabular} \end{center} \caption{Lower limits at $95\%$~CL on $M_{\rm LQ}/\lambda$ for scalar ($S$) and vector ($V$) leptoquarks, where $L$ and $R$ denote the lepton chirality and the subscript ($0,\ 1/2,\ 1$) is the weak isospin. For each leptoquark type, the relevant coefficients $\epsilon^{q}_{ab}$ and fermion number $F = L + 3B$ are indicated. Leptoquarks with identical quantum numbers except for weak hypercharge are distinguished using a tilde, for example $V_0^R$ and $\tilde{V}_0^R$. Quantum numbers and helicities refer to $e^-q$ and $e^-\bar{q}$ states.} \label{lqfits} \end{table} \vspace{1cm} % squarks \begin{table}[htb] \begin{center} \begin{tabular}{lccc} % \hdick \\[-1.5ex] \hline \\[-1.5ex] \multicolumn{4}{c}{\bf\large H1 Search for {\boldmath$\brpv$} Squarks } \\ [1ex] %\hdick \\[-1.5ex] % & %& $e^-p$ $(319~\GeV)$ & $e^+p$ $(319~\GeV)$ % & \\[.5ex] \ Channel & Coupling & $\epsilon^q_{ab}$ %& $M_{\tilde q}/\lambda' ~ [ \GeV ]$ %& $M_{\tilde q}/\lambda' ~ [ \GeV ]$ & $M_{\tilde q}/\lambda' ~ [ \TeV ]$\\[1ex] % \hdick \\[-1.5ex] \hline \\[-1.5ex] $e^+ d \to \tilde u^{\,(k)}$ & $\lambda'_{11k}$ & \ $\epsilon^u_{LL} = +\frac{1}{2}$ \ & $1.10$ \\[.2em] $e^- u \to \tilde{d}^{\,(j)}$ & $\lambda'_{1j1}$ & \ $\epsilon^d_{LR} = -\frac{1}{2}$ \ & $0.66$ \\[1ex] \hline \end{tabular} \end{center} \caption{Lower limits at $95\%$~CL on $M_{\tilde q}/\lambda'$ for the $R_p$ violating couplings $\lambda'_{ijk}$~\cite{rpv}, where $i,j,k$ are family indices. The coefficients $\epsilon^q_{ab}$ are also shown. The $\lambda'_{11k}$ ($\lambda'_{1j1}$) coupling corresponds to the $S_{0}^{L}$ ($\tilde{S}_{1/2}^{L}$) leptoquark coupling shown in table~\ref{lqfits}.} \label{sqfits} \end{table} % large extra dimensions \begin{table}[ht] \begin{center} \begin{tabular}{p{0.165\textwidth}cp{0.2\textwidth}} % \hdick \\[-1.5ex] \hline \\[-1.5ex] \multicolumn{3}{c}{\bf\large H1 Search for Large Extra Dimensions} \\ [1ex] %\hdick \\[-1.5ex] %& \ $e^- p$ $(319~\GeV)$ \ & \ $e^+ p$ $(319~\GeV)$ \ & $\eta_{G} = \lambda/M_{S}^{4}$\\ \multicolumn{1}{c}{coupling $\lambda$} & & \multicolumn{1}{c}{$M_{S}~[\TeV]$} %& \ $M_S~[\TeV]$ \ & \ $M_S~[\TeV]$ \ \\[1ex] % \hdick \\[-1.5ex] \hline \\[-1.5ex] \multicolumn{1}{c}{$+1$} & & \multicolumn{1}{c}{$0.90$} \\[.2em] \multicolumn{1}{c}{$-1$} & & \multicolumn{1}{c}{$0.92$} \\[.2em] \hline \end{tabular} \end{center} \caption{Lower limits at $95\%$~CL on a model with large extra dimensions on the gravitational scale $M_{S}$ in $4+n$ dimensions, assuming positive ($\lambda = +1$) or negative ($\lambda = -1$) couplings.} \label{ledfits} \end{table} \vspace{1cm} \vfill \clearpage \begin{figure} %\includegraphics[width=\textwidth]{plots/xsec_ratio_comb_pol_v2.eps} \includegraphics[width=\textwidth]{d11-114f1.eps} \caption{The ratio of the measured cross section to the Standard Model prediction determined using the CTEQ6m PDF set for $e^+p \rightarrow e^+X$ and $e^-p \rightarrow e^-X$ scattering. The top figure%plot corresponds to the full H1 data with an average longitudinal polarisation of $P \approx 0$. The middle and bottom figures%plots represent polarised H1 data taken from the year 2003 onwards for different lepton charge and polarisation data sets. The error bars represent the statistical and uncorrelated systematic errors added in quadrature. The bands indicate the PDF uncertainties of the Standard Model cross section predictions.} \label{fig:dsdq2norm} \end{figure} \begin{figure} %\includegraphics[width=\textwidth]{plots/comp_excl_pol_v2.eps} \includegraphics[width=\textwidth]{d11-114f2.eps} \caption{Lower limits at $95\%$~CL on the compositeness scale $\Lambda$ for various chiral models, obtained from the full H1 data. Limits are given for both signs $\Lambda^+$ and $\Lambda^-$ of the chiral coefficients.} \label{fig:lqlimits} \end{figure} \begin{figure} %\includegraphics[width=\textwidth]{plots/vv_comb_pol_v2.eps} \includegraphics[width=\textwidth]{d11-114f3.eps} \caption{The measured neutral current cross section ${\rm d}\sigma/{\rm d}Q^2$ normalised to the Standard Model expectation. H1 $e^{\pm}p$ scattering data are compared with curves corresponding to $95$\%~CL exclusion limits obtained from the full H1 data for the $VV$ compositeness scale model, for both signs $\Lambda^+$ and $\Lambda^-$ of the chiral coefficients. The error bars represent the statistical and uncorrelated systematic errors added in quadrature.} \label{fig:dsdq2normvv} \end{figure} \begin{figure} %\includegraphics[width=\textwidth]{plots/lq_comb_pol_v2} \includegraphics[width=\textwidth]{d11-114f4.eps} \caption{The measured neutral current cross section ${\rm d}\sigma/{\rm d}Q^2$ normalised to the Standard Model expectation. H1 $e^{\pm}p$ scattering data are compared with curves corresponding to $95\%$~CL exclusion limits obtained from the full H1 data on the ratio $M_{\rm LQ}/\lambda$ for the $S^L_{1}$ and $V^L_{1}$ leptoquarks. The error bars represent the statistical and uncorrelated systematic errors added in quadrature.} \label{fig:dsdq2normlq} \end{figure} \begin{figure} %\includegraphics[width=\textwidth]{plots/kk_comb_pol_v2} \includegraphics[width=\textwidth]{d11-114f5.eps} \caption{The measured neutral current cross section ${\rm d}\sigma/{\rm d}Q^2$ normalised to the Standard Model expectation. H1 $e^{\pm}p$ scattering data are compared with curves corresponding to $95\%$~CL exclusion limits obtained from the full H1 data on the gravitational scale, $M_{S}$ for both positive ($\lambda = +1$) and negative ($\lambda = -1$) couplings. The error bars represent the statistical and uncorrelated systematic errors added in quadrature.} \label{fig:dsdq2normled} \end{figure} \begin{figure} %\includegraphics[width=\textwidth]{plots/qr_comb_pol_v2} \includegraphics[width=\textwidth]{d11-114f6.eps} \caption{The measured neutral current cross section ${\rm d}\sigma/{\rm d}Q^2$ normalised to the Standard Model expectation. H1 $e^{\pm}p$ scattering data are compared with curves corresponding to $95\%$~CL exclusion limits obtained from the full H1 data on the quark radius, $R_q$ assuming point-like leptons. The error bars represent the statistical and uncorrelated systematic errors added in quadrature.} \label{fig:dsdq2normrad} \end{figure} \end{document}