%================================================================ % LaTeX file with prefered layout for H1+ZEUS 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} \usepackage{colordvi} \usepackage{captcont} %%%%%%%%%%%% 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 \def\figurename{Fig.} \def\tablename{Table} %%%%%%%%%%%%%%%% END OF LATEX HEADER %===============================title page============================= \begin{document} %%%%%%%%%%%%%%%% Pre-defined commands, you can use for the most obvious notations \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{\eV}{\mbox{e\hspace{-0.08em}V}} % % 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^*} } %%% 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{\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.} %%%%%%%%%%%%% my new commands and def%%%%%%%%%%%%%%%% \newcommand{\be}{\begin{equation}} \newcommand{\ee}{\end{equation}} \newcommand{\ba}{\begin{eqnarray}} \newcommand{\ea}{\end{eqnarray}} \def\ra{\rightarrow} \def\Q2{\mbox{$Q^2$}} \def\xbj{\mbox{$x_{Bj}$}} \def\Pom{\mbox{I$\!$P}} \def\Pem{\mbox{$I\!\!P$}} \def\Pma{I\!\!P} \def\xip{\mbox{$x_{\Pma}$}} \def\pbi{pb$^-1$} \def\chisq{\chi^2} \begin{titlepage} \noindent \begin{flushleft} {\tt DESY 12-100 \hfill ISSN 0418-9833} \\ {\tt June 2012} \\ \end{flushleft} \noindent \vspace{2cm} \begin{center} \begin{Large} {\bf Combined inclusive diffractive cross sections measured with forward proton spectrometers in deep inelastic {\boldmath $ep$} scattering at HERA\\} \vspace{2cm} H1 and ZEUS Collaborations \end{Large} \end{center} \vspace{2cm} \begin{abstract} A combination of the inclusive diffractive cross section measurements made by the H1 and ZEUS Collaborations at HERA is presented. The analysis uses samples of diffractive deep inelastic $ep$ scattering data at a centre-of-mass energy $\sqrt{s}$~=~318 GeV where leading protons are detected by dedicated spectrometers. Correlations of systematic uncertainties are taken into account, resulting in an improved precision of the cross section measurement which reaches 6\% for the most precise points. The combined data cover the range $2.5 < Q^2 < 200$ GeV$^2$ in photon virtuality, $0.00035 < \xip < 0.09$ in proton fractional momentum loss, $0.09 < |t| < 0.55$ GeV$^2$ in squared four-momentum transfer at the proton vertex and $0.0018 < \beta < 0.816$ in $\beta=x/\xip$, where $x$ is the Bjorken scaling variable. \end{abstract} \vspace{1.5cm} %\begin{center} %Draft 2.0 (after 1st EB, circulated to EB) %\end{center} \begin{center} Submitted to \EJC \end{center} \end{titlepage} \begin{flushleft} %\input{DESY-09-100_auth} F.D.~Aaron$^{13,a4}$, %BUCH-LEFT 01/12 Aaron H.~Abramowicz$^{71, a45}$, I.~Abt$^{56}$, L.~Adamczyk$^{35}$, M.~Adamus$^{84}$, R.~Aggarwal$^{14, a12}$, C.~Alexa$^{13}$, %BUCH-PD 06/06 Alexa V.~Andreev$^{53}$, %LPI -PD 8/88 Andreev S.~Antonelli$^{10}$, P.~Antonioli$^{9}$, A.~Antonov$^{54}$, M.~Arneodo$^{77}$, O.~Arslan$^{11}$, V.~Aushev$^{38, 39, a37}$, Y.~Aushev,$^{39, a37, a38}$, O.~Bachynska$^{29}$, S.~Backovic$^{64}$, %PODG-LEFT 08/11 Backovic A.~Baghdasaryan$^{86}$, %YERE-PD 09/03 Baghdasaryana S.~Baghdasaryan$^{86}$, %YERE-ST 02/10 Baghdasaryans A.~Bamberger$^{25}$, A.N.~Barakbaev$^{2}$, G.~Barbagli$^{23}$, G.~Bari$^{9}$, F.~Barreiro$^{49}$, E.~Barrelet$^{63}$, %PARI-LEFT 01/12 Barrelet W.~Bartel$^{29}$, %DESY-HON 02/03 Bartel N.~Bartosik$^{29}$, D.~Bartsch$^{11}$, M.~Basile$^{10}$, K.~Begzsuren$^{80}$, %ULBA-PD 04/06 Begzsuren O.~Behnke$^{29}$, J.~Behr$^{29}$, U.~Behrens$^{29}$, L.~Bellagamba$^{9}$, A.~Belousov$^{53}$, %LPI -PROF 08/87 Belousov P.~Belov$^{29}$, %DESY-ST 07/10 Belov A.~Bertolin$^{60}$, S.~Bhadra$^{88}$, M.~Bindi$^{10}$, J.C.~Bizot$^{57}$, %ORSA-LEFT 01/12 Bizot C.~Blohm$^{29}$, V.~Bokhonov$^{38, a37}$, K.~Bondarenko$^{39}$, E.G.~Boos$^{2}$, K.~Borras$^{29}$, D.~Boscherini$^{9}$, D.~Bot$^{29}$, V.~Boudry$^{62}$, %ECPL-PD 1/93 Boudry I.~Bozovic-Jelisavcic$^{6}$, %BEOG-PROF 04/07 Bozovicjelisavcic T.~Bo{\l}d$^{35}$, N.~Br\"ummer$^{16}$, J.~Bracinik$^{8}$, %BIRM-LEFT 01/12 Bracinik G.~Brandt$^{29}$, %DESY-LEFT 06/11 Brandt M.~Brinkmann$^{29}$, %DESY-PD 03/10 Brinkmann V.~Brisson$^{57}$, %ORSA-HON 01/12 Brisson D.~Britzger$^{29}$, %DESY-ST 10/09 Britzger I.~Brock$^{11}$, E.~Brownson$^{48}$, R.~Brugnera$^{61}$, D.~Bruncko$^{34}$, %KOSI-LEFT 01/12 Bruncko A.~Bruni$^{9}$, G.~Bruni$^{9}$, B.~Brzozowska$^{83}$, A.~Bunyatyan$^{32, 86}$, %MPIH-PD 12/95 Bunyatyan P.J.~Bussey$^{27}$, A.~Bylinkin$^{52}$, %ITEP-DIP 09/10 Bylinkin B.~Bylsma$^{16}$, L.~Bystritskaya$^{52}$, %ITEP-PD 05/99 Bystritskaya A.~Caldwell$^{56}$, A.J.~Campbell$^{29}$, %DESY-PD 10/84 Campbella K.B.~Cantun~Avila$^{89}$, %MEX1-ST 04/06 Cantunavila M.~Capua$^{17}$, R.~Carlin$^{61}$, C.D.~Catterall$^{88}$, F.~Ceccopieri$^{4}$, %BRUX-PD 10/09 Ceccopieri K.~Cerny$^{66}$, %PRG2-PD 11/08 Cernyk V.~Cerny$^{34}$, %KOSI-LEFT 01/12 Cernyv S.~Chekanov$^{5}$, V.~Chekelian$^{56}$, %MPIM-PD 01/90 Chekelian J.~Chwastowski$^{18, a14}$, J.~Ciborowski$^{83, a49}$, R.~Ciesielski$^{29, a17}$, L.~Cifarelli$^{10}$, F.~Cindolo$^{9}$, A.~Contin$^{10}$, J.G.~Contreras$^{89}$, %MEX1-PROF 03/98 Contreras A.M.~Cooper-Sarkar$^{58}$, N.~Coppola$^{29, a18}$, M.~Corradi$^{9}$, F.~Corriveau$^{51}$, M.~Costa$^{76}$, J.A.~Coughlan$^{59}$, %RAL -LEFT 01/12 Coughlan J.~Cvach$^{65}$, %PRAG-HON 01/10 Cvach G.~D'Agostini$^{69}$, J.B.~Dainton$^{41}$, %LIVE-PROF 01/94 Dainton F.~Dal~Corso$^{60}$, K.~Daum$^{85,a1}$, %WUPP-PROF 06/90 Daum B.~Delcourt$^{57}$, %ORSA-LEFT 01/12 Delcourt J.~Delvax$^{4}$, %BRUX-LEFT 10/11 Delvax R.K.~Dementiev$^{55}$, M.~Derrick$^{5}$, R.C.E.~Devenish$^{58}$, S.~De~Pasquale$^{10, a10}$, E.A.~De~Wolf$^{4}$, %ANTW-HON 10/10 Dewolf J.~del~Peso$^{49}$, C.~Diaconu$^{50}$, %MARS-PD 09/96 Diaconu M.~Dobre$^{28, a6, a7}$, %HAM2-ST 07/09 Dobre D.~Dobur$^{25, a29}$, V.~Dodonov$^{32}$, %MPIH-PD 04/98 Dodonov B.A.~Dolgoshein~$^{54, \dagger}$, G.~Dolinska$^{39}$, A.~Dossanov$^{28, 56}$, %MPIM-ST 05/07 Dossanov A.T.~Doyle$^{27}$, V.~Drugakov$^{90}$, A.~Dubak$^{64}$, %PODG-LEFT 07/11 Dubak L.S.~Durkin$^{16}$, S.~Dusini$^{60}$, G.~Eckerlin$^{29}$, %DESY-PD 8/88 Eckerlin S.~Egli$^{82}$, %PSI -PD 01/10 Egli Y.~Eisenberg$^{67}$, A.~Eliseev$^{53}$, %LPI -LEFT 12/11 Eliseev E.~Elsen$^{29}$, %DESY-PROF 01/06 Elsen P.F.~Ermolov~$^{55, \dagger}$, A.~Eskreys~$^{18, \dagger}$, S.~Fang$^{29, a19}$, L.~Favart$^{4}$, %BRUX-PROF 10/99 Favart S.~Fazio$^{17}$, A.~Fedotov$^{52}$, %ITEP-PD 8/88 Fedotov R.~Felst$^{29}$, %DESY-HON 06/02 Felst J.~Feltesse$^{26}$, %SACL-HON 11/06 Feltesse J.~Ferencei$^{34}$, %KOSI-PD 08/88 Ferencei J.~Ferrando$^{27}$, M.I.~Ferrero$^{76}$, J.~Figiel$^{18}$, D.-J.~Fischer$^{29}$, %DESY-PD 07/11 Fischer M.~Fleischer$^{29}$, %DESY-PD 07/95 Fleischer A.~Fomenko$^{53}$, %LPI -PD 02/89 Fomenko M.~Forrest$^{27, a32}$, B.~Foster$^{58, a41}$, E.~Gabathuler$^{41}$, %LIVE-HON 01/12 Gabathulere G.~Gach$^{35}$, A.~Galas$^{18}$, E.~Gallo$^{23}$, A.~Garfagnini$^{61}$, J.~Gayler$^{29}$, %DESY-HON 02/05 Gayler A.~Geiser$^{29}$, S.~Ghazaryan$^{29}$, %DFLC-PD 09/09 Ghazaryan I.~Gialas$^{15, a33}$, A.~Gizhko$^{39, a39}$, L.K.~Gladilin$^{55, a40}$, D.~Gladkov$^{54}$, C.~Glasman$^{49}$, A.~Glazov$^{29}$, %DESY-PD 01/04 Glazov L.~Goerlich$^{18}$, %CRAC-PD 8/88 Goerlich N.~Gogitidze$^{53}$, %LPI -PD 05/91 Gogitidze O.~Gogota$^{39}$, Yu.A.~Golubkov$^{55}$, P.~G\"ottlicher$^{29, a20}$, M.~Gouzevitch$^{29, a2}$, %DESY-PD 10/11 Gouzevitch C.~Grab$^{91}$, %ZUTH-PROF 08/07 Grab I.~Grabowska-Bo{\l}d$^{35}$, A.~Grebenyuk$^{29}$, %DESY-PD 03/12 Grebenyuk J.~Grebenyuk$^{29}$, T.~Greenshaw$^{41}$, %LIVE-PD 8/88 Greenshaw I.~Gregor$^{29}$, G.~Grigorescu$^{3}$, G.~Grindhammer$^{56}$, %MPIM-HON 09/11 Grindhammer G.~Grzelak$^{83}$, O.~Gueta$^{71}$, M.~Guzik$^{35}$, C.~Gwenlan$^{58, a42}$, A.~H\"uttmann$^{29}$, T.~Haas$^{29}$, S.~Habib$^{29}$, %DESY-PD 10/09 Habib D.~Haidt$^{29}$, %DESY-HON 03/04 Haidt W.~Hain$^{29}$, R.~Hamatsu$^{75}$, J.C.~Hart$^{59}$, H.~Hartmann$^{11}$, G.~Hartner$^{88}$, R.C.W.~Henderson$^{40}$, %LANC-PROF 10/04 Henderson E.~Hennekemper$^{31}$, %HDB2-PD 07/11 Hennekemper H.~Henschel$^{90}$, %ZEUT-LEFT 02/12 Henschel M.~Herbst$^{31}$, %HDB2-PD 11/11 Herbst G.~Herrera$^{47}$, %MEX2-PD 07/98 Herrera M.~Hildebrandt$^{82}$, %PSI -PD 01/10 Hildebrandtm E.~Hilger$^{11}$, K.H.~Hiller$^{90}$, %ZEUT-PD 01/92 Hiller J.~Hladk\'y$^{65}$, D.~Hochman$^{67}$, D.~Hoffmann$^{50}$, %MARS-PD 07/00 Hoffmann R.~Hori$^{74}$, R.~Horisberger$^{82}$, %PSI -PD 01/10 Horisberger T.~Hreus$^{4}$, %BRUX-PD 10/08 Hreus F.~Huber$^{30}$, %HDB1-ST 09/09 Huberf Z.A.~Ibrahim$^{36}$, Y.~Iga$^{72}$, R.~Ingbir$^{71}$, M.~Ishitsuka$^{73}$, M.~Jacquet$^{57}$, %ORSA-PD 09/96 Jacquet H.-P.~Jakob$^{11}$, X.~Janssen$^{4}$, %ANTW-PD 02/03 Janssenx F.~Januschek$^{29}$, T.W.~Jones$^{44}$, L.~J\"onsson$^{46}$, %LUND-PROF 01/01 Joensson M.~J\"ungst$^{11}$, H.~Jung$^{29, 4}$, %DESY-PROF 12/99 Jungh I.~Kadenko$^{39}$, B.~Kahle$^{29}$, S.~Kananov$^{71}$, T.~Kanno$^{73}$, M.~Kapichine$^{22}$, %JINR-PD 3/97 Kapichine U.~Karshon$^{67}$, F.~Karstens$^{25, a30}$, I.I.~Katkov$^{29, a21}$, P.~Kaur$^{14, a12}$, M.~Kaur$^{14}$, I.R.~Kenyon$^{8}$, %BIRM-LEFT 01/12 Kenyon A.~Keramidas$^{3}$, L.A.~Khein$^{55}$, C.~Kiesling$^{56}$, %MPIM-HON 09/11 Kiesling J.Y.~Kim$^{37}$, D.~Kisielewska$^{35}$, S.~Kitamura$^{75, a47}$, R.~Klanner$^{28}$, M.~Klein$^{41}$, %LIVE-PROF 12/06 Klein U.~Klein$^{29, a22}$, C.~Kleinwort$^{29}$, %DESY-PD 8/88 Kleinwort E.~Koffeman$^{3}$, R.~Kogler$^{28}$, %HAM2-PD 12/10 Kogler N.~Kondrashova$^{39, a39}$, O.~Kononenko$^{39}$, P.~Kooijman$^{3}$, Ie.~Korol$^{39}$, I.A.~Korzhavina$^{55, a40}$, P.~Kostka$^{90}$, %ZEUT-PD 10/87 Kostka A.~Kota\'nski$^{19, a15}$, U.~K\"otz$^{29}$, H.~Kowalski$^{29}$, M.~Kr\"amer$^{29}$, %DESY-PD 10/09 Kraemer J.~Kretzschmar$^{41}$, %LIVE-PD 03/08 Kretzschmar K.~Kr\"uger$^{31}$, %HDB2-PD 01/04 Kruegerk O.~Kuprash$^{29}$, M.~Kuze$^{73}$, M.P.J.~Landon$^{42}$, %QMWC-PD 10/83 Landon W.~Lange$^{90}$, %ZEUT-PD 8/88 Lange G.~La\v{s}tovi\v{c}ka-Medin$^{64}$, %PODG-LEFT 01/12 Lastovickamedin P.~Laycock$^{41}$, %LIVE-PD 11/03 Laycock A.~Lebedev$^{53}$, %LPI -PROF 04/89 Lebedev A.~Lee$^{16}$, V.~Lendermann$^{31}$, %HDB2-LEFT 01/12 Lendermann B.B.~Levchenko$^{55}$, S.~Levonian$^{29}$, %DESY-PD 08/88 Levonian A.~Levy$^{71}$, V.~Libov$^{29}$, S.~Limentani$^{61}$, T.Y.~Ling$^{16}$, K.~Lipka$^{29, a6}$, %DESY-PD 06/01 Lipka M.~Lisovyi$^{29}$, B.~List$^{29}$, %DESY-PD 11/99 Listb J.~List$^{29}$, %DFLC-PD 10/00 Listj E.~Lobodzinska$^{29}$, B.~Lobodzinski$^{29}$, %DESY-PD 01/06 Lobodzinski W.~Lohmann$^{90}$, B.~L\"ohr$^{29}$, E.~Lohrmann$^{28}$, K.R.~Long$^{43}$, A.~Longhin$^{60, a43}$, D.~Lontkovskyi$^{29}$, R.~Lopez-Fernandez$^{47}$, %MEX2-PD 03/2 Lopezfernandez V.~Lubimov$^{52}$, %ITEP-HON 01/12 Lubimov O.Yu.~Lukina$^{55}$, J.~Maeda$^{73, a46}$, S.~Magill$^{5}$, I.~Makarenko$^{29}$, E.~Malinovski$^{53}$, %LPI -PD 01/89 Malinovskie J.~Malka$^{29}$, R.~Mankel$^{29}$, A.~Margotti$^{9}$, G.~Marini$^{69}$, J.F.~Martin$^{78}$, H.-U.~Martyn$^{1}$, %AAC1-HON 01/12 Martyn A.~Mastroberardino$^{17}$, M.C.K.~Mattingly$^{7}$, S.J.~Maxfield$^{41}$, %LIVE-PD 8/88 Maxfield A.~Mehta$^{41}$, %LIVE-PROF 06/00 Mehta I.-A.~Melzer-Pellmann$^{29}$, S.~Mergelmeyer$^{11}$, A.B.~Meyer$^{29}$, %DESY-PD 10/97 Meyeran H.~Meyer$^{85}$, %WUPP-HON 12/00 Meyerhi J.~Meyer$^{29}$, %DESY-PROF 10/84 Meyerj S.~Miglioranzi$^{29, a23}$, S.~Mikocki$^{18}$, %CRAC-PROF 10/10 Mikocki I.~Milcewicz-Mika$^{18}$, %CRAC-PD 12/11 Milcewicz F.~Mohamad Idris$^{36}$, V.~Monaco$^{76}$, A.~Montanari$^{29}$, F.~Moreau$^{62}$, %ECPL-LEFT 01/12 Moreau A.~Morozov$^{22}$, %JINR-PD 06/99 Morozova J.V.~Morris$^{59}$, %RAL -HON 01/10 Morris J.D.~Morris$^{12, a11}$, K.~Mujkic$^{29, a24}$, K.~M\"uller$^{92}$, %ZUER-PD 11/94 Muellerk B.~Musgrave$^{5}$, K.~Nagano$^{79}$, T.~Namsoo$^{29, a25}$, R.~Nania$^{9}$, Th.~Naumann$^{90}$, %ZEUT-PROF 01/05 Naumannt P.R.~Newman$^{8}$, %BIRM-PROF 10/09 Newman C.~Niebuhr$^{29}$, %DESY-PD 3/93 Niebuhr A.~Nigro$^{69}$, D.~Nikitin$^{22}$, %JINR-PD 06/08 Nikitin Y.~Ning$^{33}$, T.~Nobe$^{73}$, D.~Notz$^{29}$, G.~Nowak$^{18}$, %CRAC-PROF 02/12 Nowakg K.~Nowak$^{29,a6}$, %HAM2-PD 03/10 Nowakk R.J.~Nowak$^{83}$, A.E.~Nuncio-Quiroz$^{11}$, B.Y.~Oh$^{81}$, N.~Okazaki$^{74}$, K.~Olkiewicz$^{18}$, J.E.~Olsson$^{29}$, %DESY-HON 09/10 Olsson Yu.~Onishchuk$^{39}$, D.~Ozerov$^{29}$, %DESY-PD 09/08 Ozerov P.~Pahl$^{29}$, %DESY-ST 10/08 Pahl V.~Palichik$^{22}$, %JINR-PD 01/04 Palichik M.~Pandurovic$^{6}$, %BEOG-PD 03/11 Pandurovic K.~Papageorgiu$^{15}$, A.~Parenti$^{29}$, C.~Pascaud$^{57}$, %ORSA-HON 09/05 Pascaud G.D.~Patel$^{41}$, %LIVE-PD 8/88 Patel E.~Paul$^{11}$, J.M.~Pawlak$^{83}$, B.~Pawlik$^{18}$, P.~G.~Pelfer$^{24}$, A.~Pellegrino$^{3}$, E.~Perez$^{26, a3}$, %SACL-PD 10/07 Perez W.~Perla\'nski$^{83, a50}$, H.~Perrey$^{29}$, A.~Petrukhin$^{29}$, %DESY-PD 10/09 Petrukhin I.~Picuric$^{64}$, %PODG-PROF 12/07 Picuric K.~Piotrzkowski$^{45}$, H.~Pirumov$^{30}$, %HDB1-ST 09/09 Pirumov D.~Pitzl$^{29}$, %DESY-PD 8/88 Pitzl R.~Pla\v{c}akyt\.{e}$^{29,a6}$, %DESY-PD 10/06 Placakyte P.~Pluci\'nski$^{84, a51}$, B.~Pokorny$^{66}$, %PRG2-ST 10/09 Pokorny N.S.~Pokrovskiy$^{2}$, R.~Polifka$^{66, a8}$, %PRG2-PD 05/11 Polifka A.~Polini$^{9}$, B.~Povh$^{32}$, %MPIH-PROF 09/95 Povh A.S.~Proskuryakov$^{55}$, M.~Przybycie\'n$^{35}$, V.~Radescu$^{29,a6}$, %DESY-PD 10/06 Radescu N.~Raicevic$^{64}$, %PODG-PD 06/02 Raicevic A.~Raval$^{29}$, T.~Ravdandorj$^{80}$, %ULBA-PROF 09/00 Ravdandorj D.D.~Reeder$^{48}$, P.~Reimer$^{65}$, %PRAG-PD 07/90 Reimer B.~Reisert$^{56}$, Z.~Ren$^{33}$, J.~Repond$^{5}$, Y.D.~Ri$^{75, a48}$, E.~Rizvi$^{42}$, %QMWC-PROF 03/04 Rizvi A.~Robertson$^{58}$, P.~Robmann$^{92}$, %ZUER-PD 8/88 Robmann P.~Roloff$^{29, a23}$, R.~Roosen$^{4}$, %BRUX-HON 03/12 Roosen A.~Rostovtsev$^{52}$, %ITEP-PROF 02/11 Rostovtsev M.~Rotaru$^{13}$, %BUCH-PD 06/11 Rotaru I.~Rubinsky$^{29}$, J.E.~Ruiz~Tabasco$^{89}$, %MEX1-PD 05/10 Ruiztabascojuliaelis S.~Rusakov$^{53}$, %LPI -HON 01/12 Rusakov M.~Ruspa$^{77}$, R.~Sacchi$^{76}$, D.~\v{S}\'alek$^{66}$, %PRG2-PD 10/10 Salek U.~Samson$^{11}$, D.P.C.~Sankey$^{59}$, %RAL -PD 01/90 Sankey G.~Sartorelli$^{10}$, M.~Sauter$^{30}$, %HDB1-PD 10/09 Sauter E.~Sauvan$^{50, a9}$, %MARS-PD 11/1 Sauvan A.A.~Savin$^{48}$, D.H.~Saxon$^{27}$, M.~Schioppa$^{17}$, S.~Schlenstedt$^{90}$, P.~Schleper$^{28}$, W.B.~Schmidke$^{56}$, S.~Schmitt$^{29}$, %DESY-PD 09/99 Schmittst U.~Schneekloth$^{29}$, L.~Schoeffel$^{26}$, %SACL-PROF 10/10 Schoeffel V.~Sch\"onberg$^{11}$, A.~Sch\"oning$^{30}$, %HDB1-PROF 01/09 Schoening T.~Sch\"orner-Sadenius$^{29}$, H.-C.~Schultz-Coulon$^{31}$, %HDB2-PROF 01/04 Schultzcoulon J.~Schwartz$^{51}$, F.~Sciulli$^{33}$, F.~Sefkow$^{29}$, %DFLC-PD 09/99 Sefkow L.M.~Shcheglova$^{55}$, R.~Shehzadi$^{11}$, S.~Shimizu$^{74, a23}$, L.N.~Shtarkov$^{53}$, %LPI -LEFT 01/12 Shtarkov S.~Shushkevich$^{29}$, %DESY-PD 08/11 Shushkevich I.~Singh$^{14, a12}$, I.O.~Skillicorn$^{27}$, W.~S{\l}omi\'nski$^{19, a16}$, T.~Sloan$^{40}$, %LANC-LEFT 01/12 Sloan W.H.~Smith$^{48}$, V.~Sola$^{28}$, A.~Solano$^{76}$, Y.~Soloviev$^{25,53}$, %LPI -PD 08/89 Soloviev D.~Son$^{20}$, P.~Sopicki$^{18}$, %CRAC-ST 09/07 Sopicki V.~Sosnovtsev$^{54}$, D.~South$^{29}$, %DESY-PD 05/03 South V.~Spaskov$^{22}$, %JINR-PD 12/97 Spaskov A.~Specka$^{62}$, %ECPL-PROF 09/05 Specka A.~Spiridonov$^{29, a26}$, H.~Stadie$^{28}$, L.~Stanco$^{60}$, Z.~Staykova$^{4}$, %ANTW-PD 10/10 Staykova M.~Steder$^{29}$, %DESY-PD 09/08 Steder N.~Stefaniuk$^{39}$, B.~Stella$^{68}$, %ROME-HON 11/10 Stella A.~Stern$^{71}$, T.P.~Stewart$^{78}$, A.~Stifutkin$^{54}$, G.~Stoicea$^{13}$, %BUCH-PD 02/08 Stoicea P.~Stopa$^{18}$, U.~Straumann$^{92}$, %ZUER-PROF 09/95 Straumann S.~Suchkov$^{54}$, G.~Susinno$^{17}$, L.~Suszycki$^{35}$, T.~Sykora$^{4, 66}$, %ANTW-PD 01/06 Sykora J.~Sztuk-Dambietz$^{28}$, J.~Szuba$^{29, a27}$, D.~Szuba$^{28}$, A.D.~Tapper$^{43}$, E.~Tassi$^{17, a13}$, J.~Terr\'on$^{49}$, T.~Theedt$^{29}$, P.D.~Thompson$^{8}$, %BIRM-PD 08/99 Thompsonp H.~Tiecke$^{3}$, K.~Tokushuku$^{79, a34}$, J.~Tomaszewska$^{29, a28}$, T.H.~Tran$^{57}$, %ORSA-LEFT 10/11 Tran D.~Traynor$^{42}$, %QMWC-PD 10/01 Traynor P.~Tru\"ol$^{92}$, %ZUER-HON 10/06 Truoel V.~Trusov$^{39}$, I.~Tsakov$^{70}$, %SOFI-PROF 03/12 Tsakov B.~Tseepeldorj$^{80, a5}$, %ULBA-PROF 06/06 Tseepeldorj T.~Tsurugai$^{87}$, M.~Turcato$^{28}$, O.~Turkot$^{39, a39}$, J.~Turnau$^{18}$, %CRAC-PROF 09/95 Turnau T.~Tymieniecka$^{84, a52}$, M.~V\'azquez$^{3, a23}$, A.~Valk\'arov\'a$^{66}$, %PRG2-PD 8/88 Valkarova C.~Vall\'ee$^{50}$, %MARS-PD 06/86 Vallee P.~Van~Mechelen$^{4}$, %ANTW-PROF 01/06 Vanmechelen Y.~Vazdik$^{53}$, %LPI -PD 8/88 Vazdik A.~Verbytskyi$^{29}$, O.~Viazlo$^{39}$, N.N.~Vlasov$^{25, a31}$, R.~Walczak$^{58}$, W.A.T.~Wan Abdullah$^{36}$, D.~Wegener$^{21}$, %DORT-PROF 01/06 Wegener J.J.~Whitmore$^{81, a44}$, K.~Wichmann$^{29}$, L.~Wiggers$^{3}$, M.~Wing$^{44}$, M.~Wlasenko$^{11}$, G.~Wolf$^{29}$, H.~Wolfe$^{48}$, K.~Wrona$^{29}$, E.~W\"unsch$^{29}$, %DESY-PD 8/88 Wuensch A.G.~Yag\"ues-Molina$^{29}$, S.~Yamada$^{79}$, Y.~Yamazaki$^{79, a35}$, R.~Yoshida$^{5}$, C.~Youngman$^{29}$, O.~Zabiegalov$^{39, a39}$, J.~\v{Z}\'a\v{c}ek$^{66}$, %PRG2-PROF 10/05 Zacek J.~Z\'ale\v{s}\'ak$^{65}$, %PRAG-PD 01/05 Zalesak L.~Zawiejski$^{18}$, O.~Zenaiev$^{29}$, W.~Zeuner$^{29, a23}$, Z.~Zhang$^{57}$, %ORSA-PD 10/92 Zhang B.O.~Zhautykov$^{2}$, N.~Zhmak$^{38, a37}$, A.~Zhokin$^{52}$, %ITEP-LEFT 06/11 Zhokine A.~Zichichi$^{10}$, R.~\v{Z}leb\v{c}\'ik$^{66}$, %PRG2-ST 03/12 Zlebcik H.~Zohrabyan$^{86}$, %YERE-PD 11/02 Zohrabyan Z.~Zolkapli$^{36}$, F.~Zomer$^{57}$, %ORSA-PROF 09/06 Zomer D.S.~Zotkin$^{55}$ and A.F.~\.Zarnecki$^{83}$ \bigskip{\it % H1 institutes %$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $^{1}$ I. Physikalisches Institut der RWTH, Aachen, Germany \\ $^{2}$ {\it Institute of Physics and Technology of Ministry of Education and Science of Kazakhstan, Almaty, Kazakhstan}\\ $^{3}$ {\it NIKHEF and University of Amsterdam, Amsterdam, Netherlands}~$^{b29}$\\ $^{4}$ Inter-University Institute for High Energies ULB-VUB, Brussels and Universiteit Antwerpen, Antwerpen, Belgium~$^{b2}$ \\ $^{5}$ {\it Argonne National Laboratory, Argonne, Illinois 60439-4815, USA}~$^{b13}$\\ $^{6}$ Vinca Institute of Nuclear Sciences, University of Belgrade, 1100 Belgrade, Serbia \\ $^{7}$ {\it Andrews University, Berrien Springs, Michigan 49104-0380, USA}\\ $^{8}$ School of Physics and Astronomy, University of Birmingham, Birmingham, UK~$^{b16}$ \\ $^{9}$ {\it INFN Bologna, Bologna, Italy}~$^{b14}$\\ $^{10}$ {\it University and INFN Bologna, Bologna, Italy}~$^{b14}$\\ $^{11}$ {\it Physikalisches Institut der Universit\"at Bonn, Bonn, Germany}~$^{b15}$\\ $^{12}$ {\it H.H.~Wills Physics Laboratory, University of Bristol, Bristol, United Kingdom}~$^{b16}$\\ $^{13}$ National Institute for Physics and Nuclear Engineering (NIPNE) , Bucharest, Romania~$^{b11}$ \\ $^{14}$ {\it Panjab University, Department of Physics, Chandigarh, India}\\ $^{15}$ {\it Department of Engineering in Management and Finance, Univ. of the Aegean, Chios, Greece}\\ $^{16}$ {\it Physics Department, Ohio State University, Columbus, Ohio 43210, USA}~$^{b13}$\\ $^{17}$ {\it Calabria University, Physics Department and INFN, Cosenza, Italy}~$^{b14}$\\ $^{18}$ The Henryk Niewodniczanski Institute of Nuclear Physics, Polish Academy of Sciences, Cracow, Poland~$^{b4}$ \\ $^{19}$ {\it Department of Physics, Jagellonian University, Cracow, Poland}\\ $^{20}$ {\it Kyungpook National University, Center for High Energy Physics, Daegu, South Korea}~$^{b23}$\\ $^{21}$ Institut f\"ur Physik, TU Dortmund, Dortmund, Germany~$^{b1}$ \\ $^{22}$ Joint Institute for Nuclear Research, Dubna, Russia \\ $^{23}$ {\it INFN Florence, Florence, Italy}~$^{b14}$\\ $^{24}$ {\it University and INFN Florence, Florence, Italy}~$^{b14}$\\ $^{25}$ {\it Fakult\"at f\"ur Physik der Universit\"at Freiburg i.Br., Freiburg i.Br., Germany}\\ $^{26}$ CEA, DSM/Irfu, CE-Saclay, Gif-sur-Yvette, France \\ $^{27}$ {\it School of Physics and Astronomy, University of Glasgow, Glasgow, United Kingdom}~$^{b16}$\\ $^{28}$ Institut f\"ur Experimentalphysik, Universit\"at Hamburg, Hamburg, Germany~$^{b1}$$^{,}$$^{b21}$\\ $^{29}$ {\it Deutsches Elektronen-Synchrotron DESY, Hamburg, Germany}\\ $^{30}$ Physikalisches Institut, Universit\"at Heidelberg, Heidelberg, Germany~$^{b1}$ \\ $^{31}$ Kirchhoff-Institut f\"ur Physik, Universit\"at Heidelberg, Heidelberg, Germany~$^{b1}$ \\ $^{32}$ Max-Planck-Institut f\"ur Kernphysik, Heidelberg, Germany \\ $^{33}$ {\it Nevis Laboratories, Columbia University, Irvington on Hudson, New York 10027, USA}~$^{b18}$\\ $^{34}$ Institute of Experimental Physics, Slovak Academy of Sciences, Ko\v{s}ice, Slovak Republic~$^{b5}$ \\ $^{35}$ {\it AGH-University of Science and Technology, Faculty of Physics and Applied Computer Science, Krakow, Poland}~$^{b20}$\\ $^{36}$ {\it Jabatan Fizik, Universiti Malaya, 50603 Kuala Lumpur, Malaysia}~$^{b17}$\\ $^{37}$ {\it Institute for Universe and Elementary Particles, Chonnam National University, Kwangju, South Korea}\\ $^{38}$ {\it Institute for Nuclear Research, National Academy of Sciences, Kyiv, Ukraine}\\ $^{39}$ {\it Department of Nuclear Physics, National Taras Shevchenko University of Kyiv, Kyiv, Ukraine}\\ $^{40}$ Department of Physics, University of Lancaster, Lancaster, UK~$^{b16}$ \\ $^{41}$ Department of Physics, University of Liverpool, Liverpool, UK~$^{b16}$ \\ $^{42}$ School of Physics and Astronomy, Queen Mary, University of London, London, UK~$^{b16}$ \\ $^{43}$ {\it Imperial College London, High Energy Nuclear Physics Group, London, United Kingdom}~$^{b16}$\\ $^{44}$ {\it Physics and Astronomy Department, University College London, London, United Kingdom}~$^{b16}$\\ $^{45}$ {\it Institut de Physique Nucl\'{a14}aire, Universit\'{a14} Catholique de Louvain, Louvain-la-Neuve,\\ Belgium}~$^{b24}$\\ $^{46}$ Physics Department, University of Lund, Lund, Sweden~$^{b6}$ \\ $^{47}$ Departamento de Fisica, CINVESTAV IPN, M\'exico City, M\'exico~$^{b9}$ \\ $^{48}$ {\it Department of Physics, University of Wisconsin, Madison, Wisconsin 53706, USA}~$^{b13}$\\ $^{49}$ {\it Departamento de F\'{\i}sica Te\'orica, Universidad Aut\'onoma de Madrid, Madrid, Spain}~$^{b25}$\\ $^{50}$ CPPM, Aix-Marseille Univ, CNRS/IN2P3, 13288 Marseille, France \\ $^{51}$ {\it Department of Physics, McGill University, Montr\'eal, Qu\'ebec, Canada H3A 2T8}~$^{b26}$\\ $^{52}$ Institute for Theoretical and Experimental Physics, Moscow, Russia~$^{b10}$ \\ $^{53}$ Lebedev Physical Institute, Moscow, Russia \\ $^{54}$ {\it Moscow Engineering Physics Institute, Moscow, Russia}~$^{b27}$\\ $^{55}$ {\it Lomonosov Moscow State University, Skobeltsyn Institute of Nuclear Physics, Moscow, Russia}~$^{b28}$\\ $^{56}$ {\it Max-Planck-Institut f\"ur Physik, M\"unchen, Germany}\\ $^{57}$ LAL, Universit\'e Paris-Sud, CNRS/IN2P3, Orsay, France \\ $^{58}$ {\it Department of Physics, University of Oxford, Oxford, United Kingdom}~$^{b16}$\\ $^{59}$ STFC, Rutherford Appleton Laboratory, Didcot, Oxfordshire, UK~$^{b16}$ \\ $^{60}$ {\it INFN Padova, Padova, Italy}~$^{b14}$\\ $^{61}$ {\it Dipartimento di Fisica dell' Universit\`a and INFN, Padova, Italy}~$^{b14}$\\ $^{62}$ LLR, Ecole Polytechnique, CNRS/IN2P3, Palaiseau, France \\ $^{63}$ LPNHE, Universit\'e Pierre et Marie Curie Paris 6, Universit\'e Denis Diderot Paris 7, CNRS/IN2P3, Paris, France \\ $^{64}$ Faculty of Science University of Montenegro, Podgorica, Montenegro~$^{b12}$ \\ $^{65}$ Institute of Physics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic~$^{b7}$ \\ $^{66}$ Faculty of Mathematics and Physics of Charles University, Praha, Czech Republic~$^{b7}$ \\ $^{67}$ {\it Department of Particle Physics and Astrophysics, Weizmann Institute, Rehovot, Israel}\\ $^{68}$ Dipartimento di Fisica Universit\`a di Roma Tre and INFN Roma~3, Roma, Italy \\ $^{69}$ {\it Dipartimento di Fisica, Universit\`a 'La Sapienza' and INFN, Rome, Italy}~$^{b14}$\\ $^{70}$ Institute for Nuclear Research and Nuclear Energy, Sofia, Bulgaria \\ $^{71}$ {\it Raymond and Beverly Sackler Faculty of Exact Sciences, School of Physics, Tel Aviv University, Tel Aviv, Israel}~$^{b30}$\\ $^{72}$ {\it Polytechnic University, Tokyo, Japan}~$^{b22}$\\ $^{73}$ {\it Department of Physics, Tokyo Institute of Technology, Tokyo, Japan}~$^{b22}$\\ $^{74}$ {\it Department of Physics, University of Tokyo, Tokyo, Japan}~$^{b22}$\\ $^{75}$ {\it Tokyo Metropolitan University, Department of Physics, Tokyo, Japan}~$^{b22}$\\ $^{76}$ {\it Universit\`a di Torino and INFN, Torino, Italy}~$^{b14}$\\ $^{77}$ {\it Universit\`a del Piemonte Orientale, Novara, and INFN, Torino, Italy}~$^{b14}$\\ $^{78}$ {\it Department of Physics, University of Toronto, Toronto, Ontario, Canada M5S 1A7}~$^{b26}$\\ $^{79}$ {\it Institute of Particle and Nuclear Studies, KEK, Tsukuba, Japan}~$^{b22}$\\ $^{80}$ Institute of Physics and Technology of the Mongolian Academy of Sciences, Ulaanbaatar, Mongolia \\ $^{81}$ {\it Department of Physics, Pennsylvania State University, University Park, Pennsylvania 16802, USA}~$^{b18}$\\ $^{82}$ Paul Scherrer Institut, Villigen, Switzerland \\ $^{83}$ {\it Faculty of Physics, University of Warsaw, Warsaw, Poland}\\ $^{84}$ {\it National Centre for Nuclear Research, Warsaw, Poland}\\ $^{85}$ Fachbereich C, Universit\"at Wuppertal, Wuppertal, Germany \\ $^{86}$ Yerevan Physics Institute, Yerevan, Armenia \\ $^{87}$ {\it Meiji Gakuin University, Faculty of General Education, Yokohama, Japan}~$^{b22}$\\ $^{88}$ {\it Department of Physics, York University, Ontario, Canada M3J 1P3}~$^{b26}$\\ $^{89}$ Departamento de Fisica Aplicada, CINVESTAV, M\'erida, Yucat\'an, M\'exico~$^{b9}$ \\ $^{90}$ {\it Deutsches Elektronen-Synchrotron DESY, Zeuthen, Germany}\\ $^{91}$ Institut f\"ur Teilchenphysik, ETH, Z\"urich, Switzerland~$^{b8}$ \\ $^{92}$ Physik-Institut der Universit\"at Z\"urich, Z\"urich, Switzerland~$^{b8}$ \\ %$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ \bigskip % references to H1 members %################################ $ ^{a1}$ Also at Rechenzentrum, Universit\"at Wuppertal, Wuppertal, Germany \\ $ ^{a2}$ Also at IPNL, Universit\'e Claude Bernard Lyon 1, CNRS/IN2P3, Villeurbanne, France \\ $ ^{a3}$ Also at CERN, Geneva, Switzerland \\ $ ^{a4}$ Also at Faculty of Physics, University of Bucharest, Bucharest, Romania \\ $ ^{a5}$ Also at Ulaanbaatar University, Ulaanbaatar, Mongolia \\ $ ^{a6}$ Supported by the Initiative and Networking Fund of the Helmholtz Association (HGF) under the contract VH-NG-401 and S0-072. \\ $ ^{a7}$ Absent on leave from NIPNE-HH, Bucharest, Romania \\ $ ^{a8}$ Also at Department of Physics, University of Toronto, Toronto, Ontario, Canada M5S 1A7 \\ $ ^{a9}$ Also at LAPP, Universit\'e de Savoie, CNRS/IN2P3, Annecy-le-Vieux, France \\ % rerefrences to ZEUS members $^{a10}$ Now at University of Salerno, Italy\\ $^{a11}$ Now at Queen Mary University of London, United Kingdom\\ $^{a12}$ Also funded by Max Planck Institute for Physics, Munich, Germany\\ $^{a13}$ Also Senior Alexander von Humboldt Research Fellow at Hamburg University, Institute of Experimental Physics, Hamburg, Germany\\ $^{a14}$ Also at Cracow University of Technology, Faculty of Physics, Mathemathics and Applied Computer Science, Poland\\ $^{a15}$ Supported by the research grant No. 1 P03B 04529 (2005-2008)\\ $^{a16}$ Supported by the Polish National Science Centre, project No. DEC-2011/01/BST2/03643\\ $^{a17}$ Now at Rockefeller University, New York, NY 10065, USA\\ $^{a18}$ Now at DESY group FS-CFEL-1\\ $^{a19}$ Now at Institute of High Energy Physics, Beijing, China\\ $^{a20}$ Now at DESY group FEB, Hamburg, Germany\\ $^{a21}$ Also at Moscow State University, Russia\\ $^{a22}$ Now at University of Liverpool, United Kingdom\\ $^{a23}$ Now at CERN, Geneva, Switzerland\\ $^{a24}$ Also affiliated with Universtiy College London, UK\\ $^{a25}$ Now at Goldman Sachs, London, UK\\ $^{a26}$ Also at Institute of Theoretical and Experimental Physics, Moscow, Russia\\ $^{a27}$ Also at FPACS, AGH-UST, Cracow, Poland\\ $^{a28}$ Partially supported by Warsaw University, Poland\\ $^{a29}$ Now at Istituto Nucleare di Fisica Nazionale (INFN), Pisa, Italy\\ $^{a30}$ Now at Haase Energie Technik AG, Neum\"unster, Germany\\ $^{a31}$ Now at Department of Physics, University of Bonn, Germany\\ $^{a32}$ Now at Biodiversit\"at und Klimaforschungszentrum (BiK-F), Frankfurt, Germany\\ $^{a33}$ Also affiliated with DESY, Germany\\ $^{a34}$ Also at University of Tokyo, Japan\\ $^{a35}$ Now at Kobe University, Japan\\ %$^{\dagger}$ deceased \\ $^{a37}$ Supported by DESY, Germany\\ $^{a38}$ Member of National Technical University of Ukraine, Kyiv Polytechnic Institute, Kyiv, Ukraine\\ $^{a39}$ Member of National University of Kyiv - Mohyla Academy, Kyiv, Ukraine\\ $^{a40}$ Partly supported by the Russian Foundation for Basic Research, grant 11-02-91345-DFG\_a\\ $^{a41}$ Alexander von Humboldt Professor; also at DESY and University of Oxford\\ $^{a42}$ STFC Advanced Fellow\\ $^{a43}$ Now at LNF, Frascati, Italy\\ $^{a44}$ This material was based on work supported by the National Science Foundation, while working at the Foundation.\\ $^{a45}$ Also at Max Planck Institute for Physics, Munich, Germany, External Scientific Member\\ $^{a46}$ Now at Tokyo Metropolitan University, Japan\\ $^{a47}$ Now at Nihon Institute of Medical Science, Japan\\ $^{a48}$ Now at Osaka University, Osaka, Japan\\ $^{a49}$ Also at Lodz University, Poland\\ % \L\'{a24}d\'{a35} $^{a50}$ Member of Lodz University, Poland\\ % \L\'{a24}d\'{a35} $^{a51}$ Now at Department of Physics, Stockholm University, Stockholm, Sweden\\ $^{a52}$ Also at Cardinal Stefan Wyszy\'nski University, Warsaw, Poland\\ %################################ \bigskip % H1 references concerning institutes; %@@@@@@@@@@@@@@@@@@@@@@@@@@ $^{b1}$ Supported by the Bundesministerium f\"ur Bildung und Forschung, FRG, under contract numbers 05H09GUF, 05H09VHC, 05H09VHF, 05H16PEA \\ $^{b2}$ Supported by FNRS-FWO-Vlaanderen, IISN-IIKW and IWT and by Interuniversity Attraction Poles Programme, Belgian Science Policy \\ % here modified by hand $^{b4}$ Partially Supported by Polish Ministry of Science and Higher Education, grant DPN/N168/DESY/2009 \\ $^{b4}$ Supported by Polish Ministry of Science and Higher Education, grants DPN/N168/DESY/2009 and DPN/N188/DESY/2009 \\ $^{b5}$ Supported by VEGA SR grant no. 2/7062/ 27 \\ $^{b6}$ Supported by the Swedish Natural Science Research Council \\ $^{b7}$ Supported by the Ministry of Education of the Czech Republic under the projects LC527, INGO-LA09042 and MSM0021620859 \\ $^{b8}$ Supported by the Swiss National Science Foundation \\ $^{b9}$ Supported by CONACYT, M\'exico, grant 48778-F \\ $^{b10}$ Russian Foundation for Basic Research (RFBR), grant no 1329.2008.2 and Rosatom \\ $^{b11}$ Supported by the Romanian National Authority for Scientific Research under the contract PN 09370101 \\ $^{b12}$ Partially Supported by Ministry of Science of Montenegro, no. 05-1/3-3352 \\ % ZEUS references concerning institutes; $^{b13}$ Supported by the US Department of Energy\\ $^{b14}$ Supported by the Italian National Institute for Nuclear Physics (INFN) \\ $^{b15}$ Supported by the German Federal Ministry for Education and Research (BMBF), under contract No. 05 H09PDF\\ $^{b16}$ Supported by the Science and Technology Facilities Council, UK\\ $^{b17}$ Supported by an FRGS grant from the Malaysian government\\ $^{b18}$ Supported by the US National Science Foundation. Any opinion, findings and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.\\ % removed by hand because included in teh H1 similar note for INP Cracow %$^{b19}$ Supported by the Polish Ministry of Science and Higher Education as a scientific project No. DPN/N188/DESY/2009\\ $^{b20}$ Supported by the Polish Ministry of Science and Higher Education and its grants for Scientific Research\\ $^{b21}$ Supported by the German Federal Ministry for Education and Research (BMBF), under contract No. 05h09GUF, and the SFB 676 of the Deutsche Forschungsgemeinschaft (DFG) \\ $^{b22}$ Supported by the Japanese Ministry of Education, Culture, Sports, Science and Technology (MEXT) and its grants for Scientific Research\\ $^{b23}$ Supported by the Korean Ministry of Education and Korea Science and Engineering Foundation\\ $^{b24}$ Supported by FNRS and its associated funds (IISN and FRIA) and by an Inter-University Attraction Poles Programme subsidised by the Belgian Federal Science Policy Office\\ $^{b25}$ Supported by the Spanish Ministry of Education and Science through funds provided by CICYT\\ $^{b26}$ Supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) \\ $^{b27}$ Partially supported by the German Federal Ministry for Education and Research (BMBF)\\ $^{b28}$ Supported by RF Presidential grant N 4142.2010.2 for Leading Scientific Schools, by the Russian Ministry of Education and Science through its grant for Scientific Research on High Energy Physics and under contract No.02.740.11.0244 \\ $^{b29}$ Supported by the Netherlands Foundation for Research on Matter (FOM)\\ $^{b30}$ Supported by the Israel Science Foundation\\ %@@@@@@@@@@@@@@@@@@@@@@@@@@ \vspace{0.2cm} $^{\dagger}$ deceased \\ } \end{flushleft} % \newpage %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Introduction} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \label{sec-int} Diffractive collisions in deep inelastic electron-proton scattering (DIS), $ep \to eXp$, have been studied extensively at the HERA collider. %and provide an essential input for the understanding of quantum %chromodynamics (QCD) at high parton densities. They can be viewed as resulting from processes in which the exchanged photon probes a colour-singlet combination of partons. The photon virtuality, $Q^2$, supplies a hard scale, which allows the application of perturbative quantum chromodynamics (QCD). %A hard scattering QCD collinear factorisation theorem~\cite{qcdf,qcdf1} %allows the definition of diffractive parton distribution functions (DPDFs) %for a given scattered proton four-momentum. Diffractive reactions in DIS are a tool to investigate low-momentum partons in the proton, notably through the study of diffractive parton distribution functions (DPDFs), determined by a QCD analysis of the data. %The latter are the densities of partons in the %proton when the final state of the process contains a fast proton of %specified four-momentum. In diffractive $ep$ scattering the virtual photon dissociates %through its interaction with the proton. %FIXME:INTRODUCE PDISS AND ADD MORE INTRODUCTION, INTRODUCE Q2 and MX %and CONNECTION BETWEEN y and W and beta/Mx. %The diffractive dissociation of virtual photons, $\gamma^{\star}p \to Xp$ %(figure~\ref{fig:diagram}), produces a hadronic system $X$ with mass $M_X$ at a photon-proton centre-of-mass energy $W$ and squared four-momentum transfer $t$ at the proton vertex (figure~\ref{fig-diagram}), producing a hadronic system $X$ with mass $M_X$. The fractional longitudinal momentum loss of the proton is denoted as $\xip$, while the fraction of this momentum %carried by the struck quark taking part in the interaction with the photon is denoted as $\beta$. %and the mass of the dissociated system $X$ is denoted $M_X$. These variables are related to Bjorken $x$ by $x=\beta \, \xip$. The variable $\beta$ is related to $M_X$ and $Q^2$ by $\beta\simeq Q^2/(Q^2+M_X^2)$. The variables $W, Q^2$ and the inelasticity $y$ are related by $W^2\simeq sy-Q^2$, where $s$ is the square of the $ep$ centre-of-mass energy. \begin{figure}[!h] \vfill \begin{center} \hskip 3.0cm \includegraphics[scale = 0.33]{d12-100f1.eps} \end{center} \vspace{-0.3cm} \caption{ Diagram of the reaction $ep \rightarrow eXp$. } \label{fig-diagram} \vfill \end{figure} %In processes of the type $ep \to eXp$, the exchanged virtual %The diffractive dissociation of virtual photons, $\gamma^{\star}p \to Xp$ %(figure~\ref{fig:diagram}), produces a hadronic system $X$ with mass $M_X$ Similarly to inclusive DIS, %cross section measurements for the reaction $ep \to eXp$ diffractive cross section measurements are conventionally expressed in terms of the reduced diffractive cross section, $\sigma_r^{D(4)}$, which is related to the measured $ep$ cross section by \begin{eqnarray} \frac{{\rm d} \sigma^{ep \rightarrow eXp}}{{\rm d} \beta {\rm d} Q^2 {\rm d} \xip {\rm d} t} = \frac{4\pi\alpha^2}{\beta Q^4} \ \ \left[1-y+\frac{y^2}{2}\right] \ \ \sigma_r^{D(4)}(\beta,Q^2,\xip,t) \ . \label{sigma-2} \end{eqnarray} The reduced cross section $\sigma_r^{D(3)}(\beta,Q^2,\xip)$ is obtained by integrating $\sigma_r^{D(4)}(\beta,Q^2,\xip,t)$ over $t$. % in the $t$-range of the measurement. At small and moderate values of the inelasticity $y$, $\sigma_r^{D(3)}$ is approximately equal to the diffractive structure function $F_2^{D(3)}$ to good approximation. Experimentally, diffractive $ep$ scattering is characterised by the presence of a leading proton in the final state carrying most of the proton beam energy and by a depletion of hadronic activity in the pseudo-rapidity\footnote{The pseudo-rapidity is defined as $\eta=-\ln\tan\theta/2$ where the polar angle $\theta$ is measured with respect to the proton beam direction.} distribution of particles (large rapidity gap, LRG) in the forward (proton) direction. Both of these signatures have been exploited in various analyses by H1 and ZEUS to select diffractive samples either by tagging the outgoing proton in dedicated proton spectrometers~\cite{h1-fps1,h1-fps2,zeus-lps1,zeus-lrglps} or by requiring the presence of a large rapidity gap~\cite{zeus-lrglps,h1-lrg1,h1-lrg2}. %distribution of hadronic final state particles %in the forward region. %Alternatively, a method is %used to determine statistically the number of diffractive events, based on %the expected difference in shape of the distributions of the invariant %mass, $M_X$, for diffractive and non-diffractive %events~\cite{h1-mx, zeus-mx1,zeus-mx2}. The two methods differ partially in the accessible kinematic ranges (higher $\xpom$ for the proton-tagged data) and substantially in their dominant sources of systematic uncertainties. In LRG-based measurements, the largest uncertainty arises from proton dissociative events, $ep \rightarrow eXN$, in which the proton dissociates into a low mass state $N$. % %the admixture of low mass %leading baryon systems other than protons. These include %proton excitations to low mass states as well as leading %neutrons produced via charge exchange reactions. All such %contributions are collectively referred to here as `proton dissociation', %$ep \rightarrow eXN$, with the baryon state %$N$ having mass $M_N$. % %Due to the limitations in the instrumentation very near to the %beam-pipe, % Such events cannot always be distinguished from those % in which the proton is scattered elastically and provide % a background which affects the normalisation of the % measured cross section. %Events with %high $M_X$ are not accessible since the %non-diffractive background grows with $M_X$ and the rapidity gap becomes %more and more forward (and eventually becomes confined to the %beam-pipe). %; a large rapidity %gap is still present and the $M_X$ measurement is unaffected. % Conversely, Low $\xip$ samples selected by the proton spectrometers have little or no proton dissociation contribution, but their precision is limited statistically by the small acceptances and systematically by large uncertainties in the proton tagging efficiency, which strongly depends on the proton-beam optics. %Proton spectrometers also allow a measurement of $t$, %and give access to higher $x_{\spom}$ than the other methods, The results from both methods are found to be consistent~\cite{h1-fps1,h1-fps2,zeus-lrglps,h1-lrg2,martapaul}. Combining measurements can provide more precise and kinematically extended data than the individual measurements. % The combined results can % eventually be used to extract the DPDFs. A first step, % presented in this paper, is taken towards such a perspective by In this paper, a combination of the H1~\cite{h1-fps2, h1-fps1} and the ZEUS~\cite{zeus-lrglps,zeus-lps1} proton spectrometer results is presented. %\footnote{ %In these studies the main detectors are used to reconstruct $Q^2$ and $x$ %whereas $M_X$, $\beta$, $\xip$ and $t$ derive from the proton spectrometers %or from the joint information of the proton spectrometers and the main %detectors.} %(the Forward Proton Spectrometer, FPS, for H1 and %the Leading Proton Spectrometer, LPS, for ZEUS). % At low $\xip$, these combined proton-tagged data, which are free from proton dissociation contribution, can be used % to assess the normalisation of the diffractive cross section in DIS. %Because of the variety of the selection methods, subject to different %systematic uncertainties, %the complementary features of the data and the statistical limitations %of some samples. The combination is performed using the weighted averaging method introduced in~\cite{glazov} and extended in~\cite{:2009wt,Aaron:2009bp}. %This also provides a model independent %check of the data consistency. The correlated systematic uncertainties and global normalisations are constrained in the fit such that one coherent data set is obtained. Since H1 and ZEUS have employed different experimental techniques, using different detectors and methods of kinematic reconstruction, the combination leads to significantly reduced uncertainties. %The kinematic range of the combined data is: photon virtualities $2.5 < Q^2 < 200$ GeV$^2$, values of the fraction of the proton's momentum carried by the diffractive exchange of $0.0009 < \xip < 0.09$, values of the fraction of the momentum of the diffractive exchange carried by the struck parton of $0.0018 < \beta < 0.56$ %and values of the square of the four-momentum exchanged at the proton vertex $0.09 < |t| < 0.55$ GeV$^2$. The kinematic range of the combined data is: $2.5 \leq Q^2 \leq 200$~GeV$^2$, $0.0018 \leq \beta \leq 0.816$, $0.00035 \leq x_{\pom} \leq 0.09$ and $0.09 < |t| < 0.55$~GeV$^2$. The latter requirement restricts the analysis to the $t$ range directly accessible by both the H1 and ZEUS proton spectrometers. %$2.5 \le Q^2 \le 200$ GeV$^2$, $0.0009 \le \xip \le 0.09$, $0.0018 \le \beta \le 0.56$ and $0.09 \le |t| \le 0.55$ GeV$^2$. %To select diffractive events, either the final-state proton %can be detected (LPS method) or the different characteristics %of the system $X$ in diffractive and non-diffractive events (hadronic %methods) can be exploited. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Combination of the H1 and ZEUS measurements} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{Data samples} The H1~\cite{H1_det} and ZEUS~\cite{ZEUS_det} detectors were general purpose instruments which consisted of tracking systems surrounded by electromagnetic and hadronic calorimeters and muon detectors, ensuring close to 4$\pi$ coverage about the $ep$ interaction point. Both detectors were equipped with proton spectrometers; the Leading Proton Spectrometer (LPS) for ZEUS, the Forward Proton Spectrometer (FPS) and the Very Forward Proton Spectrometer (VFPS) for H1. These spectrometers were located $60$ to $220$~m away from the main detectors in the forward (proton beam) direction. %A detailed descriptions of the H1 and ZEUS detectors can be found elsewhere~\cite{H1_det,ZEUS_det}. The combination is based on the cross sections measured with the H1 FPS~\cite{h1-fps1,h1-fps2} and the ZEUS LPS~\cite{zeus-lps1,zeus-lrglps}. The bulk of the data~\cite{h1-fps1,h1-fps2,zeus-lrglps} was taken at electron and proton beam energies of $E_e\simeq27.5$~GeV and $E_p=920$~GeV, respectively, corresponding to an $ep$ centre-of-mass energy of $\sqrt{s} = 318$~GeV. The earlier ZEUS LPS data~\cite{zeus-lps1} collected at $E_p=820$~GeV are corrected to a common $\sqrt{s} = 318$~GeV by using the extrapolation procedure described in section~\ref{sec-grid}. The three-fold differential reduced cross sections, $\sigma_r^{D(3)}$($\beta$,~$Q^2$,~$\xip$), are combined. For the original measurements, the main H1 and ZEUS detectors are used to reconstruct $Q^2, W$ and $x$, whereas $M_X$, $\beta$, $\xip$ and $t$ are derived from the proton spectrometer measurement or from combined information of the proton spectrometers and the main detectors. %A summary of the features of the data is given in table~\ref{tab-data}. In table~\ref{tab-data} the data sets used for the combination are listed together with their kinematic ranges and integrated luminosities. %The H1 data taken with the VFPS~\cite{h1-vfps} are still under analysis and are %not included in the combination; anyhow, they cover %a different kinematic region and are expected to have little %influence in the range of the combined FPS+LPS data. \begin{table} \begin{center} \begin{footnotesize} \renewcommand{\arraystretch}{1.2} \begin{tabular}{|c|c|c|c|c|c|c|c|} \hline Data Set & $Q^2$ range & $\xip$ range & $y$ range & $\beta$ range & $t$ range & Luminosity & Ref.\\ & [GeV$^2$] & & & & [GeV$^2$] & [pb$^{-1}$] & \\ \hline H1 FPS HERA II & $4 - 700$ & $< 0.1$ & $0.03 - 0.8$ & $0.001 - 1$ & $0.1 - 0.7$ & $156.6$ & ~\cite{h1-fps2}\\ \hline H1 FPS HERA I & $2 - 50$ & $< 0.1$ & $0.02 - 0.6$ & $0.004 - 1$ & $0.08 - 0.5$ & $28.4$ & ~\cite{h1-fps1}\\ \hline\hline & & & $W$ range & $M_X$ range & & & \\ & & & [GeV] & [GeV] & & & \\\hline ZEUS LPS 2 & $2.5 - 120$ & $0.0002 - 0.1$ & $40 - 240$ & $2 - 40$ & $0.09 - 0.55$ & $32.6$ &~\cite{zeus-lrglps} \\ \hline ZEUS LPS 1 & $2 - 100$ & $<0.1$ & $25 - 240$ & $>1.5$ & $0.075 - 0.35$ & $3.6$ &~\cite{zeus-lps1}\\ \hline \end{tabular} \end{footnotesize} \end{center} \vspace{-0.3cm} \caption{H1 and ZEUS data sets used for the combination.} \label{tab-data} \end{table} \subsubsection{Restricted {\boldmath $t$} range} \label{sec-t} In the individual analyses~\cite{h1-fps1,h1-fps2,zeus-lrglps,zeus-lps1} the reduced cross sections are directly measured for ranges of the squared four-momentum transfer $t$ visible to the proton spectrometers (see table~\ref{tab-data}) and extrapolated to the range\footnote{The smallest kinematically accessible value of $|t|$ is denoted as $|t_{min}|$.} $|t_{min}| < |t| < 1$ GeV$^2$ (denoted in the following as `the full $t$ range'), assuming an exponential $t$ dependence of the diffractive cross section and using the exponential slope measured from the data. Due to the uncertainties of the slope parameters measured by H1~\cite{h1-fps2, h1-fps1} and ZEUS~\cite{zeus-lrglps,zeus-lps1}, this extrapolation introduces an additional uncertainty in the normalisation of the cross section. %Such extrapolation, which depends on the exponential slope of the $t$ %distribution and on its uncertainty, introduces an extra uncertainty in the %normalisation of the cross section. To reduce this source of systematic uncertainty, the H1 and ZEUS cross sections are combined in the restricted $t$ range $0.09 < |t| < 0.55$ GeV$^2$ covered by the proton spectrometer acceptances of both detectors for the bulk of the data. %MK The correction factors from the visible $t$ range of the `FPS HERA I' and `LPS 1' data samples to the restricted $t$ range are evaluated by using the $t$ dependencies as a function of $x_{\pom}$ measured for each sample. The correction factors for the most precise `FPS HERA II' data are applied in bins of $\beta, Q^2$ and $\xpom$. For the `LPS 2' sample the restricted range coincides with the visible range. %MK Because of the uncertainty on the exponential slope parameter, such factors introduce uncertainties of 2.2\%, 1.1\% and 5\% on the `FPS HERA II', `FPS HERA I' and `LPS 1' data, respectively, which are included in the normalisation uncertainty on each sample. The total normalisation uncertainties of the data samples are listed in table~\ref{tab-t}. In the restricted $t$ range, these uncertainties are in general smaller and the average normalisations are in better agreement than in the full $t$ range; the ratio of the `FPS HERA II' to the `LPS 2' data averaged over the measured data points, which is $0.85 \pm 0.01$(stat) $\pm 0.03 $(sys) $^{+0.09}_{-0.12}$(norm)~ in the full $t$ range~\cite{h1-fps2}, becomes $0.91 \pm 0.01$ (stat) $\pm 0.03$ (sys) $\pm 0.08$ (norm)~ in the restricted $t$ range. Within the uncertainties, the ratio does not show any significant $\beta$, $Q^2$ or $\xip$ dependence. %The correction factors from the full $t$ range to the restricted $t$ range are within $\pm5$\% for `FPS HERA I', within %(+5\%/-8\%) for `FPS HERA II' and within (+17\%/-3\%) for `LPS 1'. The restricted range coincides with the visible range of the %`LPS 2' data. The correction factors are evaluated %using the $t$ dependence measured at each $\beta, Q^2, x_{\pom}$ and introduce %an uncertainty which is summed up in the normalisation uncertainty of each sample. %\vspace*{1.0cm} \begin{table} \begin{center} \renewcommand{\arraystretch}{1.2} \begin{tabular}{|c|c|c|} \hline Data Set & $|t_{min}| < |t| < 1$ GeV$^2$ & $0.09 < |t| < 0.55$ GeV$^2$ \\ \hline FPS HERA II & $\pm 6 \%$ & $\pm 5\%$ \\ FPS HERA I & $\pm 10 \%$ & $\pm 10 \%$\\ LPS 2 & $+11\%$, $-7\%$ & $\pm 7 \%$\\ LPS 1 & $+12\%$, $-10\%$& $\pm 11 \%$\\ \hline \end{tabular} \vspace{-0.3cm} \end{center} \caption{Normalisation uncertainties in the full range $|t| < 1$ GeV$^2$ and in the restricted $t$ range for the data used for the combination.} \label{tab-t} \end{table} \subsubsection{Extrapolation to a common ({\boldmath $Q^2$, $\xip$, $\beta$}) grid} \label{sec-grid} %The averaging procedure works under the assumption that there is %a single true value of the cross section for a single data point.~Therefore, %cross section values from different data sets are needed %at the same ($\beta$, $Q^2$, $\xip$) bin. The original binning schemes of the $\sigma_r^{D(3)}$ measurements are very different. In the H1 case the measurements are extracted at fixed $\beta$, whereas for ZEUS the cross section is measured at fixed $M_X$; also the $Q^2$~and $\xip$~central values differ. Therefore, prior to the combination, the H1 and ZEUS data are transformed to a common grid of ($\beta, Q^2, x_{\pom}$) points. %\footnote{The same procedure could not be applied to the $\sigma_r^{D(4)}$ %measurements, for which reaching a common %($\beta, Q^2, \xip, t$) grid would imply extrapolating in %$\xip$ and $t$ separately: this cannot be done rigorously as the $\xip$ %and $t$ dependences are connected through the slope of the Pomeron %trajectory~(Section~\ref{sec-kine}).} The grid points are based on the original binning scheme of the `FPS HERA II' data. The ($Q^2, \xip$) grid points at the lowest $Q^2$ value of $2.5$~GeV$^2$ and at the lowest and highest $ x_{\pom}$ values, which are beyond the `FPS HERA II' data grid, are taken from the `LPS 2' measurement. %The older H1 FPS HERA-1~\cite{H1FPS1} and ZEUS LPS1~\cite{ZEUSLPS1} data are extrapolated to the selected common %grid of points. %MK % The matching is done between % the original grid and the common grid of ($\beta, Q^2, x_{\pom}$) using the nearest grid point. % taken for all the variables linearly. %MK The transformation of a measurement from the original $i^{th}$ point ($\beta_i, Q^2_i, \xip_i$) to the nearest grid point ($\beta_{grid}, Q^2_{grid}, \xip_{grid}$) is performed by multiplying the measured cross section by the ratio $\sigma_r^{D(3)}$($\beta_{grid}, Q^2_{grid}, \xip_{grid}$)/ $\sigma_r^{D(3)}$($\beta_{i}, Q^2_{i}, \xip_{i}$) calculated with the Next-to-Leading-Order (NLO) DPDF `ZEUS SJ' parameterisation~\cite{zeus-qcdfits}. Most of the corrections are smaller than $10$\%, while a few points undergo corrections up to $\sim~30$\%. The procedure is checked by using the NLO DPDF `H1 Fit B' parameterisation~\cite{h1-lrg1}. %The resulting cross section difference is of the order of %$1.2$\% on average and up to $8$\% for a few data points. The resulting difference is treated as a procedural uncertainty on the combined cross section, as discussed in Section~\ref{sec-procedurals}. The cross sections from all the data sets are shown in figure~\ref{fig-q2dep-allinputs} after correcting to $0.09 < |t| < 0.55$ GeV$^2$ and transforming to the common grid. \subsection{Combination method} \label{sec-comb} The combination is based on the $\chisq$~minimisation method described in~\cite{glazov} and used for previous combined HERA results~\cite{:2009wt}. The averaging procedure is based on the assumption that at a given kinematic point the H1 and ZEUS experiments are measuring the same cross section. ~The correlated systematic uncertainties are floated coherently. ~The procedure allows a model independent check of the data consistency and leads to a significant reduction of the correlated uncertainties. For an individual data set, the $\chisq$~function is defined as: \begin{equation} \chi^2_{exp} (\pmb{m},\pmb{b}) = \sum_i \frac{\left[ m^i - \sum_j \gamma^i_j m^i b_j - \mu^i \right]^2} {\delta^2_{i,stat} \mu^i \left( m^i - \sum_j \gamma^i_j m^i b_j \right) + \left( \delta_{i,uncor} m^i \right)^2} + \sum_j b^2_j~. \label{eq-chi} \end{equation} \noindent Here $\mu^i$ is the measured cross section value at a point $i$ ($\beta_i$,~$Q^2_i$,~$\xip_i$), and $\gamma^i_j$, $\delta_{i,stat}$ and $\delta_{i,uncor}$ are the relative correlated systematic, relative statistical and relative uncorrelated systematic uncertainties, respectively. The vector $\pmb{m}$ of quantities $m^i$ expresses the values of the combined cross section for each point $i$ and the vector $\pmb{b}$ of quantities $b_j$ expresses the shifts of the correlated systematic uncertainty sources, $j$, in units of the standard deviation. % The summation over $j$ extends over all correlated systematic sources. The relative uncertainties $\gamma^i_j$ and $\delta_{i,uncor}$ are multiplied by the %expectation combined cross section $m^i$ in order to take into account the fact that the correlated and uncorrelated systematic uncertainties are to a good approximation proportional to the central values (multiplicative uncertainties). On the other hand, the statistical uncertainties scale with the square root of the expected number of events, which is determined by the expected cross section, corrected for the biases due to the correlated systematic uncertainties. This is taken into account by the $\delta^2_{i,stat} \mu^i ( m^i - \sum_j \gamma^i_j m^i b_j )$ term. %The second term in the expression for $\chi^2_{exp}$ is the sum of the %resulting shifts of the systematic uncertainties. %The $\chisq$~function defined in Eq.~(\ref{eq-chi}) has by construction a %minimum $\chi^2_{exp} = 0$~for $m^i = \mu^i$ and $b_j = 0$. If several analyses provide measurements at the same ($\beta$,~$Q^2$, $\xip$) values, % they can be combined by using the formula above, generalised % for the case of multiple data sets. Then a $\chi^2_{tot}$ is built~\cite{Aaron:2009bp} from the sum of the $\chi^2_{exp}$ of each data set, assuming the individual data sets to be statistically uncorrelated. The $\chi^2_{tot}$ is minimised with respect to the $m^i$ and $b_j$ from each data set with an iterative procedure. ~The ratio $\chi^2_{min} / n_{dof}$ is a measure of the consistency of the data sets.~The number of degrees of freedom, $n_{dof}$, is calculated as the difference between the total number of measurements and the number of averaged points. The uncertainties of the combined cross sections are evaluated from the $\chi^2_{min}+1$ criteria~\cite{glazov,Aaron:2009bp,:2009wt}. % Possible tensions between the data sets can be investigated by means of % unbiased pull distributions, defined as in~\cite{:2009wt}. % such that for data with no correlated systematic uncertainties they are expected to follow % Gaussian distributions with zero mean and unit width. % When correlated systematic uncertainties are present and % since the corresponding parameters are floated, this can lead to narrowed pull distributions. For some of the ($\beta, Q^2, x_{\pom}$) points there is only one measurement; %Note that through however, because of the systematic uncertainty correlations such measurements may %nevertheless be shifted with respect to the original values, and the uncertainties may be reduced. % in the averaging procedure. %~For the measurement at the point $i$ of the data set $e$, the pull is defined as: %\begin{equation} %p^{i,e} = \frac{\mu^{i,e} - \mu^{i,ave} (1 - \sum_j \gamma^{i,e}_j b_{j,ave})} %{\sqrt{ \Delta^2_{i,e} - \Delta^2_{i,ave}}}~, %\label{eq-pull} %\end{equation} %where $ \Delta^2_{i,e}$ ($ \Delta^2_{i,ave}$) is the quadratic sum of the %statistical and uncorrelated systematic uncertainty for the measurement $e$ (average).~The %pull value is $p^{i,e} \neq 0$ under the condition that measurements from more %than one data set average at the same point $i$.~This means that if only one %input data set $e$ contributes to the point $i$, the value of the combined %cross section in that point is $\mu^{i,ave} = \mu^{i,e} / (1 - \sum_j \gamma^{i,e}_j b_{j,ave})$. %For the correlated systematic source $j$ the pull is given by: %The definition of pull for the correlated systematic sources in given by: %\begin{equation} %p_s = \frac{b_{j,ave}} %{\sqrt{ 1 - \Delta^2_{b_j,ave}}}~, %\label{eq:pull:s} %\end{equation} %where $\Delta^2_{b_j,ave}$ is the uncertainty on the source $j$ after the averaging procedure. \subsection{Uncertainties} \subsubsection{Experimental systematic uncertainties and their correlations} \label{sec-corrsys} The input cross sections are published with their statistical and systematic uncertainties. The statistical uncertainties correspond to $\delta_{i,stat}$ in Eq.~(\ref{eq-chi}). The systematic uncertainties are classified as point-to-point correlated or point-to-point uncorrelated, corresponding to $\gamma^i_j$ and $\delta_{i,uncor}$ respectively, according to the information provided in the corresponding publications, as follows: \begin{itemize} \item for the two older analyses, `FPS HERA I' and `LPS 1', only the total systematic uncertainties are given~\cite{h1-fps1,zeus-lps1}, with no information on the single contributions and point-to-point correlations. For these two samples only the normalisation uncertainties~(table~\ref{tab-t}) are considered among the correlated systematics, while the remaining uncertainties are treated as uncorrelated; \item for the sample `FPS HERA II' all the systematic sources discussed in~\cite{h1-fps2} are treated as point-to-point correlated. The hadronic energy scale uncertainty is taken as correlated separately for $\xip < 0.012$ and $\xip > 0.012$. This is to account for the different sensitivity to this systematic source for the two $\xip$ regions, where different methods are used to reconstruct the variable $\beta$, which are typically sensitive to different regions of the H1 central calorimeter. For $\xpom<0.012$, where the mass $M_X$ of the hadronic final state is used to reconstruct $\beta$, the effect on the cross section due to the hadronic energy scale uncertainty is 4\% on average and reaches 6.7\%. For $\xpom>0.012$, where $\beta$ is reconstructed with the leading proton energy measured by the FPS, the cross section shows almost no sensitivity to the hadronic energy scale; %where the scaling variable $x$ is obtained by combining the information from %the scattered electron and from the angles of the electron and the hadronic final state and the variable %$\xip$ is evaluated using the leading proton energy. %: an average effect of 4\% reaching 6-7\% in some bins for $\xip<0.012$, where $\beta$ is reconstructed with the main %detector, and almost no sensitivity for $\xip>0.012$, where $\beta$ is reconstructed %with the FPS; \item in the `LPS 2' case, the total systematic uncertainties quoted in~\cite{zeus-lrglps} are %split between decomposed in correlated and uncorrelated %sources following the prescriptions in~\cite{zeus-qcdfits}. They are symmetrised %MK %\footnote{The result of % the average is found to be insensitive to the details of the symmetrisation procedure.} by taking the average of the positive and negative uncertainties. \end{itemize} In the H1 `FPS HERA II' analysis, the systematic effects related to the leading proton measurement are considered as correlated and derived from the variation of the acceptance in the $\xpom$ and $t$ bins when %applying the positive and negative shifts of shifting the FPS energy scale and transverse momentum within the estimated uncertainties~\cite{h1-fps2}. % In the ZEUS `LPS 2' case the effect of this uncertainty on the % cross section is derived from the uncertainty on the alignment procedure of the LPS stations and the beam optics. % the key variable measured with the LPS is the % longitudinal momentum of the scattered proton, the uncertainty on which % derives from the alignment procedure. % In the ZEUS `LPS 2' case, the systematic uncertainty of the leading proton measurement %%on the cross section is covered by the uncertainty on the alignment procedure of the LPS stations %is expressed in terms of the uncertainty on the LPS station alignment and that on the proton beam optics % simulation. In the ZEUS 'LPS 2' case, the systematic uncertainty related to the leading proton measurement is dominated by the incomplete knowledge of the beam optics, of the position of the beamline aperture limitations and of the intrinsic transverse-momentum spread of the proton beam at the interaction point. The beam optics contribution is largely independent of the kinematic variables and therefore is taken as a normalisation uncertainty~\cite{zeus-lrglps}. The other contributions are quantified by varying the cut on the distance of closest approach of the reconstructed proton track to the beampipe, and the value of the intrinsic transverse-momentum spread assumed in the simulation. They are treated as uncorrelated uncertainties. %The former uncertainty is treated as uncorrelated and % the resulting uncertainty on the spectrometer acceptance is estimated % by varying the distance of closest approach of the LPS % stations to the proton beam. %The effect of the latter uncertainty is found to be largely independent of %the kinematic variables and therefore % is taken as a normalisation uncertainty~\cite{zeus-lrglps}. %%MK of the LPS stations to the proton beam ??? or of the scattered proton to the beam pipe ??? %largely covered by the uncertainty on the beam optics. %All the systematic uncertainties are treated as independent between the H1 and ZEUS measurements. All the H1 systematic uncertainties are treated as independent of the ZEUS uncertainties, and vice versa. Possible effects due to correlations between the two experiments are taken into account in the procedural uncertainties, discussed in Section~\ref{sec-procedurals}. In total, 23 independent sources of correlated systematic uncertainties are considered, including the global normalisation for each sample. The full list is given in table~\ref{tab-sys}. \subsubsection{Procedural uncertainties} \label{sec-procedurals} The following uncertainties on the combined cross sections due to the combination procedure are studied: \begin{itemize} \item The $\chi^2$ function given by Eq.~(\ref{eq-chi}) treats all systematic uncertainties as multiplicative, i.e. proportional to the expected central values. While this generally holds for the normalisation uncertainties, it may not be the case for the other uncertainties.~To study the sensitivity of the average result to this issue, an alternative averaging is performed. Only the normalisation uncertainty and those related to the $t$ reconstruction % ($\delta_{p_x,FPS}$, $\delta_{p_y,FPS}$, $\delta_{t,FPS}$, $\delta_{t,LPS}$), (the uncertainties on the `FPS HERA II' proton $p_x$, $p_y$ reconstruction and on the `FPS HERA II' and `LPS 2' $t$ reweighting) which, for the reasons explained in Section~\ref{sec-t}, can affect the normalisation, are taken as multiplicative, while all other uncertainties are treated as additive. The difference between this average and the nominal result is of the order of 1\% on average and 6.4\% at most. \item The H1 and ZEUS experiments use similar methods for detector calibration, apply similar reweighting to the Monte Carlo models used for the acceptance corrections and employ similar Monte Carlo models for QED radiative corrections, for the hadronic final state simulation and for background subtraction. Such similarities may lead to correlations between the measurements of the two experiments. %Three systematic sources are identified which are most likely to be correlated between the two experiments. Three systematic source are identified as the most likely to be correlated between the two experiments. These are %related to the electromagnetic energy scale and the reweighting of the simulation in $\xip$ and $t$. Averages are formed for each of the $2^3$ possible assumptions on the presence of correlations of these systematic uncertainties %whether these systematics are correlated or uncorrelated between the experiments and are compared with the nominal average for which all sources are assumed to be uncorrelated. The maximum difference between the nominal and the alternative averages is taken as an uncertainty. It is 1.4\% on average and 6.6\% at most, with no particular dependence on the kinematics. \item The bias introduced by transforming the data to the common grid (see Section~\ref{sec-grid}) is studied by using correction factors obtained from the NLO DPDF `H1 Fit B'~\cite{h1-lrg1} parameterisation. For a few bins this changes the result by up to 8\%, but % Though in a few bins the difference increases up to 8\%, the average effect is 1.2\%. \item The averaging procedure shifts the H1 hadronic energy scale at $\xip < 0.012$ by substantially more than $1\sigma$ of the nominal value (see Section~\ref{sec-res}). To study the sensitivity of the average result to the treatment of the uncertainty on the H1 hadronic energy scale, an alternative averaging is performed for which this uncertainty is considered as point-to-point uncorrelated. The difference between the alternative and nominal results is 0.9\% on average and reaches 8.7\% at low $\xpom$. \end{itemize} For each combined data point the difference between the average obtained by considering each of the procedural effects and the nominal average is calculated and summed in quadrature. The effect of the procedural uncertainties is 2.9\% on average and 9.3\% at most. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Results} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \label{sec-res} In the minimisation procedure, 352 data points are combined to 191 cross section measurements.~The data show good consistency, with $\chi^2_{min} / n_{dof} = 133 / 161$. %~For a standard weighted average the resulting $\chi^2 / n_{dof}$ is 134/161. The distributions of pulls~\cite{:2009wt}, shown in figure~\ref{fig-pulls} for each data set, exhibit no significant tensions. For data with no correlated systematic uncertainties pulls are expected to follow Gaussian distributions with zero mean and unit width. Correlated systematic uncertainties lead to narrowed pull distributions. ~The effects of the combination on the correlated systematic uncertainties are summarised in table~\ref{tab-sys} in terms of shifts in units of the original uncertainty and of values of the final uncertainties as percentages of the originals. %in $\sigma$ units and in percent of the original uncertainty. The combined cross section values are given in table~\ref{tab-results} together with statistical, uncorrelated systematic, correlated systematic, experimental, procedural and total uncertainties. The experimental uncertainty is obtained as the quadratic sum of the statistical, uncorrelated systematic and correlated systematic uncertainties. The total uncertainty is defined as the quadratic sum of the experimental and procedural uncertainties. The full information about correlations can be found elsewhere~\cite{website}. As the global normalisations of the input data sets are fitted as correlated systematic uncertainties, the normalisation uncertainty on the combined data is included in the correlated systematic uncertainty given in table~\ref{tab-results}. Most of the 23 correlated systematic uncertainties shift by less than $0.5~\sigma$ of the nominal value in the averaging procedure. None of them shifts by substantially more than $1 \sigma$, with the exception of the hadronic energy scale for $\xip<0.012$ for the `FPS HERA II' sample. Detailed studies show that there is a tension between the H1 `FPS HERA II' and ZEUS `LPS 2' data at low $\xip$; the average ratio of the H1 to ZEUS cross sections is above $1.0$ for $\beta>0.1$ and below $0.9$ for $\beta<0.1$. The H1 cross section uncertainty is positively correlated with the hadronic energy scale for $\beta>0.1$ and anti-correlated for $\beta<0.1$. As a result, the combination shifts the H1 cross sections for $\xip<0.012$ in the direction opposite to the cross section uncertainty due to the H1 hadronic energy scale. Conversely the combined statistical and uncorrelated uncertainty on the ZEUS data is much larger than the ZEUS hadronic energy scale uncertainty; consequently the fit is less sensitive to the ZEUS hadronic energy scale. %If such error source is taken as correlated %across the whole $\xip$ region (i.e. without splitting between $\xip<0.012$ and %$\xip > 0.012$) the resulting shift is $1.7 \sigma$. This significant effect, %together with the observation that only the lowest $\xip$ combined points %show relevant displacements (up to 15\%) with respect to the input measurements, is the reason to split the $\xip$ range in the %fit of this error parameter. The influence of several correlated systematic uncertainties is reduced significantly for the combined result. Specifically, the uncertainty on the FPS proton energy measurement and the normalisation uncertainties on the `FPS HERA I' and `LPS 1' samples are reduced by more than a factor of 2. The H1 hadronic energy scale uncertainty for the low $\xip$-range ($\xip<0.012$) and the ZEUS hadronic energy scale uncertainty are reduced to around 55\% of those for the individual data sets. % Two facts explain these significant reductions. Since H1 and ZEUS use different reconstruction methods, similar systematic sources influence the measured cross section differently. % as a function of the kinematics.~ Therefore, requiring the cross sections to be consistent at all ($\beta$, $Q^2$, $\xip$) points constrains the systematic uncertainties efficiently. %~In addition, the `FPS HERA II' sample has superior precision compared to the others for most regions of the phase space. The less precise measurements are fitted to the more precise one, with a simultaneous reduction of the correlated systematic uncertainty.~This reduction propagates also to the average points based only on the less precise data sets. Due to this cross calibration effect, the combined measurement shows an average improvement of the experimental uncertainty of about 27\% with respect to the most precise single data set, `FPS HERA II', though the latter data set contains five times more events than the second largest data set, `LPS 2'. The correlated part of the experimental uncertainty is reduced from about 69\% in~\cite{h1-fps2} to 49\% in the combined measurement. The statistical, experimental and procedural uncertainties on the combined data are on average 11\%, 13.8\% and 2.9\%, respectively. The total uncertainty on the cross section is 14.3\% on average and is 6\% for the most precise points. The normalisation uncertainty, which contributes to the correlated systematic uncertainty on the combined data, is on average 4\%. The combined result extends the kinematic coverage with respect to the H1 and ZEUS measurements taken separately %such that and the resulting cross section covers the region $2.5 \leq Q^2 \leq 200$~GeV$^2$, $0.0018 \leq \beta \leq 0.816$ and $0.00035 \leq x_{\pom} \leq 0.09$, for $0.09 < |t| < 0.55$~GeV$^2$. Figure~\ref{fig-q2sel-all} shows the combined cross section as a function of $Q^2$~at $x_{\pom} = 0.05$, for different values of $\beta$, compared with the individual measurements used for the combination.~The reduction of the total uncertainty of the HERA measurement compared to the input cross sections is visible. ~The derivative of the reduced cross section as a function of $\log(Q^2)$ decreases with $\beta$, %~The rate of the %growth of the reduced cross section with $Q^2$ ~depends on $\beta$~ a feature characteristic of the scaling violations in diffractive DIS, which are now measured precisely from proton-tagged as well as LRG data. Figures~\ref{fig-q2dep-comb} and~\ref{fig-xpdep-comb} show the HERA combined diffractive reduced cross sections as a function of $Q^2$ and $\xip$, respectively. At low $\xip \lesssim 0.01$, % where in the framework of Regge phenomenology~\cite{regge} % the diffractive reactions are ascribed to the exchange of a leading (pomeron) trajectory and where the proton spectrometer data are free from proton dissociation contributions, the combined data provide the most precise determination of the absolute normalisation of the diffractive cross section. %This combined data are very valuable in the scenario of inclusive diffraction %at HERA. Diffractive interactions are often discussed in the framework of Regge %phenomenology~\cite{regge} in terms of the exchange of a `pomeron' with %vacuum quantum numbers. Similar reactions, in which %sub-leading Reggeon and pion trajectories are exchanged, %have a negligible cross section at the smallest $\xip$ values. %The LPS and FPS data, and hence the combined data, %extend to $\xip \sim 0.1$ and are therefore also %sensitive to such non-leading contributions. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Conclusions} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% The reduced diffractive cross sections, $\sigma_r^{D(3)}(ep \to eXp)$, measured by the H1 and ZEUS Collaborations by using proton spectrometers to detect the leading protons are combined. The input data from the two experiments are consistent with a $\chi^2_{min} / n_{dof} = 133 / 161$. % Correlations of systematic uncertainties are taken into account by the combination method, The combination of the measurements results in more precise and kinematically extended diffractive DIS data in the $t$-range $0.09 < |t| < 0.55$~GeV$^2$. The total uncertainty on the cross section measurement is 6\% for the most precise points. The combined data provide the most precise determination of the absolute normalisation of the $ep\rightarrow eXp$ cross section. % $2.5 \leq Q^2 \leq 200$~GeV$^2$, $0.0018 \leq \beta \leq 0.816$, $0.00035 \leq x_{\pom} \leq 0.09$ and $0.09 < |t| < % 0.55$~GeV$^2$. %These combined data are very valuable in the scenario of inclusive diffraction at HERA and beyond.~They can provide the absolute normalisation of the diffractive cross section in DIS and can help to quantify background contributions in the samples selected with hadronic methods (large rapidity gap technique and $M_X$ method). %The combination of H1 and ZEUS %diffractive cross sections measured with proton spectrometers %results in a dataset for sigma of improved precision which is %compatible with the original datasets. This is the first step %towards a combination of diffractive cross sections from other %experimental methods and may eventually result in a common fit %and the extraction of unique diffractive deep inelastic %scattering structure functions." %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section*{Acknowledgements} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% We are grateful to the HERA machine group whose outstanding efforts have made these experiments possible. We appreciate the contributions to the construction and maintenance of the H1 and ZEUS detectors of many people who are not listed as authors. We thank our funding agencies for financial support, the DESY technical staff for continuous assistance and the DESY directorate for their support and for the hospitality they extended to the non-DESY members of the collaborations. % WE EXPECIALLY THANK THE HERA MACHINE GROUPS FOR THE SUPPORT % WITH THE LPS AND FPS DATA TAKING? %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{thebibliography}{99} \bibitem{h1-fps1} H1 Collaboration, A. Aktas {\it et al.}, Eur. Phys. J.{} {\bf C48},~749~(2006). \bibitem{h1-fps2} H1 Collaboration, A. Aktas {\it et al.}, Eur. Phys. J.{} {\bf C71},~1578~(2011). % \bibitem{h1-vfps} % H1 Collaboration, F.D. Aaron {\it et al.}, H1prelim-10-014{}. % FIXME: instrumental conference proceedings % \bibitem{h1-vfps1} % T.~Hreus, Proceedings of the DIS 2010 workshop, Pos DIS2010 (2010) 068, % arXiv:1008,2785 [hep-ex]. \bibitem{zeus-lps1} ZEUS Collaboration, S.~Chekanov {\it et al.}, Eur. Phys. J.{} {\bf C38},~43~(2004). \bibitem{zeus-lrglps} ZEUS Collaboration, S.~Chekanov {\it et al.}, Nucl. Phys.{} {\bf B816},~1~(2009). \bibitem{h1-lrg1} H1 Collaboration, A. Aktas {\it et al.}, Eur. Phys. J.{} {\bf C48},~715~(2006). \bibitem{h1-lrg2} H1 Collaboration, F.D. Aaron {\it et al.}, DESY-12-041, arXiv:1203.4495. %\bibitem{h1-mx} %H1 Collaboration, A. Aktas {\it et al.}, %H1prelim-06-014.{} %\bibitem{zeus-mx1} %ZEUS Collaboration, S. Chekanov {\it et al.}, %Nucl. Phys.{} {\bf B713},~3~(2005). %\bibitem{zeus-mx2} %ZEUS Collaboration, S.~Chekanov {\it et al.}, %Nucl. Phys.{} {\bf B 800},~1~(2008). \bibitem{martapaul} P.~Newman and M.~Ruspa, arXiv:0903.2957. \bibitem{glazov} A.~Glazov, AIP Conf. Proc. {\bf 792}, 237 (2005). \bibitem{Aaron:2009bp} H1 Collaboration, F. D. Aaron {\it et al.}, Eur. Phys. J.{} {\bf C63},~625~(2009). \bibitem{:2009wt} H1 and ZEUS Collaborations, F. D. Aaron {\it et al.}, JHEP{} {\bf 1001},~109~(2010). \bibitem{H1_det} H1 Collaboration, I.~Abt {\it et al.}, % ``The H1 detector at HERA,'' Nucl.\ Instrum.\ Meth.\ {\bf A386} (1997) 310;\\ % H1 Collaboration, I.~Abt {\it et al.}, % ``The Tracking, calorimeter and muon detectors of the H1 experiment at HERA,'' Nucl.\ Instrum.\ Meth.\ {\bf A386} (1997) 348; \\ % R.~D.~Appuhn {\it et al.} [H1 SPACAL Group], %``The H1 lead/scintillating-fibre calorimeter,'' Nucl.\ Instrum.\ Meth.\ {\bf A386} (1997) 397. \bibitem{ZEUS_det} ZEUS Collaboration, U.~Holm (ed.), {\it The ZEUS Detector}, Status Report (unpublished), DESY (1993), available on http://www-zeus.desy.de/bluebook/bluebook.html. \bibitem{zeus-qcdfits} ZEUS Collaboration, S.~Chekanov {\it et al.}, Nucl. Phys.{} {\bf B831},~1~(2010). \bibitem{website} The combined data together with the full correlation information is provided at the URL http://www.desy.de/h1zeus. % \bibitem{regge} % P.D.B.~Collins, % {\em An Introduction to {Regge} Theory and High Energy Physics,\rm{ % Cambridge University Press, Cambridge (1977).}} \end{thebibliography} %%%%%%%%%%%%%%%%%%%%%%%%%%% TABLES %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \newpage % \begin{table}[!ht] % \begin{center} % \begin{footnotesize} % \begin{tabular}{|l|c|c|c|} % \hline % Source & Symbol & Shift ($\sigma$ units) & Reduction \% \\ % \hline % FPS HERA II hadronic energy scale $\xip<0.012$ & $\delta_{had1,H1}$ & -1.61 & 56.9 \\ % FPS HERA II hadronic energy scale $\xip>0.012$ & $\delta_{had12,H1}$ & 0.13 & 99.8 \\ % FPS HERA II electromagnetic energy scale & $\delta_{ele,H1}$ & 0.49 & 85.9 \\ % FPS HERA II electron angle & $\delta_{\theta,H1}$ & 0.67 & 66.6 \\ % FPS HERA II $\beta$~reweighting & $\delta_{\beta,H1}$ & 0.15 & 90.4 \\ % FPS HERA II $\xip$~reweighting & $\delta_{\xip,H1}$ & 0.05 & 98.3 \\ % FPS HERA II $t$~reweighting & $\delta_{t,FPS}$ & 0.70 & 79.8 \\ % FPS HERA II $Q^2$~reweighting & $\delta_{Q^2,H1}$ & 0.09 & 97.6 \\ % FPS HERA II proton energy & $\delta_{E_p,FPS}$ & 0.05 & 45.6 \\ % FPS HERA II proton $p_x$ & $\delta_{p_x,FPS}$ & 0.62 & 74.5 \\ % FPS HERA II proton $p_y$ & $\delta_{p_y,FPS}$ & 0.27 & 86.5 \\ % FPS HERA II vertex reconstruction & $\delta_{vtx,FPS}$ & 0.07 & 97.0 \\ % FPS HERA II background subtraction & $\delta_{bgd,FPS}$ & 0.84 & 89.9 \\ % FPS HERA II bin centre corrections & $\delta_{bcc,FPS}$ & -1.05 & 87.3 \\ % FPS HERA II global normalisation & $\delta_{norm,FPSHERAII}$ & -0.39 & 84.4 \\ % FPS HERA I global normalisation & $\delta_{norm,FPSHERAI}$ & 0.81 & 48.9 \\ % \hline % LPS 2 hadronic energy scale & $\delta_{had,ZEUS}$ & -0.02 & 55.0 \\ % LPS 2 electromagnetic energy scale & $\delta_{ele,ZEUS}$ & -0.14 & 62.4 \\ % LPS 2 $\xip$~reweighting & $\delta_{x_{\pom},ZEUS}$ & -0.32 & 98.2\\ % LPS 2 $t$~reweighting & $\delta_{t,LPS}$ & -0.26 & 86.4 \\ % LPS 2 background subtraction & $\delta_{bgd,ZEUS}$ & 0.40 & 94.9 \\ % LPS 2 global normalisation & $\delta_{norm,LPS2}$ & -0.53 & 67.7 \\ % LPS 1 global normalisation & $\delta_{norm,LPS1}$ & 0.86 & 44.1 \\ % \hline \begin{table}[!ht] \begin{center} \begin{normalsize} \begin{tabular}{|l|r|c|} \hline Source & Shift ($\sigma$ units) & Reduction factor \% \\ \hline FPS HERA II hadronic energy scale $\xip<0.012$ & $-1.61~~~~$ & $56.9$ \\ FPS HERA II hadronic energy scale $\xip>0.012$ & $~0.13~~~~$ & $99.8$ \\ FPS HERA II electromagnetic energy scale & $~0.49~~~~$ & $85.9$ \\ FPS HERA II electron angle & $~0.67~~~~$ & $66.6$ \\ FPS HERA II $\beta$~reweighting & $~0.15~~~~$ & $90.4$ \\ FPS HERA II $\xip$~reweighting & $~0.05~~~~$ & $98.3$ \\ FPS HERA II $t$~reweighting & $~0.70~~~~$ & $79.8$ \\ FPS HERA II $Q^2$~reweighting & $~0.09~~~~$ & $97.6$ \\ FPS HERA II proton energy & $~0.05~~~~$ & $45.6$ \\ FPS HERA II proton $p_x$ & $~0.62~~~~$ & $74.5$ \\ FPS HERA II proton $p_y$ & $~0.27~~~~$ & $86.5$ \\ FPS HERA II vertex reconstruction & $~0.07~~~~$ & $97.0$ \\ FPS HERA II background subtraction & $~0.84~~~~$ & $89.9$ \\ FPS HERA II bin centre corrections & $-1.05~~~~$ & $87.3$ \\ FPS HERA II global normalisation & $-0.39~~~~$ & $84.4$ \\ FPS HERA I global normalisation & $~0.81~~~~$ & $48.9$ \\ \hline LPS 2 hadronic energy scale & $-0.02~~~~$ & $55.0$ \\ LPS 2 electromagnetic energy scale & $-0.14~~~~$ & $62.4$ \\ LPS 2 $\xip$~reweighting & $-0.32~~~~$ & $98.2$ \\ LPS 2 $t$~reweighting & $-0.26~~~~$ & $86.4$ \\ LPS 2 background subtraction & $~0.40~~~~$ & $94.9$ \\ LPS 2 global normalisation & $-0.53~~~~$ & $67.7$ \\ LPS 1 global normalisation & $~0.86~~~~$ & $44.1$ \\ \hline \end{tabular} \end{normalsize} \caption{Sources of point-to-point correlated systematic uncertainties considered in the combination. For each source the shifts resulting from the combination in units of the original uncertainty and the values of the final uncertainties as percentages of the original are given.} \label{tab-sys} \end{center} \end{table} %\include{tab_latex_03corFR_kk} %\include{tab_latex_03corFR2} \begin{table}[ht!] \begin{center} %\setlength{\extrarowheight}{1.5pt} \begin{tabular}{|c|c|c|c|r@{.}l|r@{.}l|r@{.}l|r@{.}l|r@{.}l|r@{.}l|} \hline $Q^2$ & $\beta$ & $x_{I\!\!P}$ & $x_{I\!\!P} \sigma_r^{D(3)}$ & \multicolumn{2}{c|}{$\delta_{stat}$} & \multicolumn{2}{c|}{$\delta_{uncor}$} & \multicolumn{2}{c|}{$\delta_{cor}$} & \multicolumn{2}{c|}{$\delta_{exp}$} & \multicolumn{2}{c|}{$\delta_{proc}$} & \multicolumn{2}{c|}{$\delta_{tot}$} \\ (GeV$^2$) & & & & \multicolumn{2}{c|}{(\%)} & \multicolumn{2}{c|}{(\%)} & \multicolumn{2}{c|}{(\%)} & \multicolumn{2}{c|}{(\%)} & \multicolumn{2}{c|}{(\%)} & \multicolumn{2}{c|}{(\%)} \\ \hline 2.5 & 0.0018 & 0.0500 & 0.0110 & 19& & 5&8 & 4&7 & 21& & 7&6 & 22& \\ 2.5 & 0.0018 & 0.0750 & 0.0166 & 14& & 6&9 & 5&3 & 17& & 7&6 & 18& \\ 2.5 & 0.0018 & 0.0900 & 0.0128 & 14& & 9&6 & 5&1 & 18& & 7&9 & 20& \\ 2.5 & 0.0056 & 0.0085 & 0.0101 & 19& & 11& & 7&6 & 23& & 9&3 & 25& \\ 2.5 & 0.0056 & 0.0160 & 0.0093 & 12& & 6&9 & 5&1 & 14& & 3&9 & 15& \\ 2.5 & 0.0056 & 0.0250 & 0.0096 & 16& & 9&8 & 5&0 & 20& & 4&6 & 20& \\ 2.5 & 0.0056 & 0.0350 & 0.0110 & 18& & 11& & 4&9 & 22& & 2&3 & 22& \\ 2.5 & 0.0056 & 0.0500 & 0.0117 & 9&8 & 6&4 & 5&3 & 13& & 1&5 & 13& \\ 2.5 & 0.0056 & 0.0750 & 0.0143 & 14& & 11& & 5&7 & 19& & 4&7 & 19& \\ 2.5 & 0.0056 & 0.0900 & 0.0154 & 15& & 6&4 & 5&7 & 17& & 4&3 & 17& \\ 2.5 & 0.0178 & 0.0025 & 0.0099 & 14& & 6&8 & 4&5 & 16& & 8&2 & 18& \\ 2.5 & 0.0178 & 0.0085 & 0.0076 & 8&3 & 7&1 & 4&5 & 12& & 1&7 & 12& \\ 2.5 & 0.0178 & 0.0160 & 0.0073 & 8&2 & 9&5 & 4&5 & 13& & 1&4 & 13& \\ 2.5 & 0.0178 & 0.0250 & 0.0071 & 8&8 & 9&2 & 4&5 & 14& & 1&4 & 14& \\ 2.5 & 0.0178 & 0.0350 & 0.0095 & 15& & 29& & 4&9 & 33& & 2&3 & 33& \\ 2.5 & 0.0178 & 0.0500 & 0.0114 & 7&8 & 7&1 & 4&5 & 11& & 2&2 & 12& \\ 2.5 & 0.0178 & 0.0750 & 0.0123 & 11& & 7&8 & 4&9 & 14& & 1&7 & 14& \\ 2.5 & 0.0562 & 0.0009 & 0.0114 & 13& & 8&6 & 5&2 & 16& & 3&4 & 17& \\ 2.5 & 0.0562 & 0.0025 & 0.0074 & 9&3 & 5&7 & 4&8 & 12& & 2&8 & 12& \\ 2.5 & 0.0562 & 0.0085 & 0.0064 & 9&6 & 6&7 & 4&5 & 13& & 2&3 & 13& \\ 2.5 & 0.0562 & 0.0160 & 0.0068 & 10& & 10& & 4&6 & 15& & 4&4 & 16& \\ 2.5 & 0.0562 & 0.0250 & 0.0063 & 14& & 14& & 4&9 & 20& & 1&9 & 20& \\ 2.5 & 0.1780 & 0.0003 & 0.0156 & 8&8 & 5&4 & 4&7 & 11& & 2&6 & 12& \\ 2.5 & 0.1780 & 0.0009 & 0.0102 & 5&9 & 4&3 & 4&4 & 8&5 & 2&2 & 8&8 \\ 2.5 & 0.1780 & 0.0025 & 0.0068 & 8&0 & 6&3 & 4&7 & 11& & 2&6 & 12& \\ 2.5 & 0.1780 & 0.0085 & 0.0074 & 9&3 & 10& & 4&8 & 15& & 3&9 & 15& \\ 2.5 & 0.1780 & 0.0160 & 0.0116 & 18& & 7&5 & 5&0 & 20& & 2&3 & 20& \\ 2.5 & 0.5620 & 0.0003 & 0.0214 & 16& & 8&8 & 5&0 & 19& & 2&3 & 19& \\ 2.5 & 0.5620 & 0.0009 & 0.0172 & 19& & 23& & 5&0 & 31& & 2&3 & 31& \\ 2.5 & 0.5620 & 0.0025 & 0.0110 & 21& & 28& & 4&9 & 36& & 2&3 & 36& \\ 5.1 & 0.0018 & 0.0500 & 0.0199 & 5&9 & 0&0 & 6&6 & 8&9 & 1&8 & 9&1 \\ 5.1 & 0.0018 & 0.0750 & 0.0232 & 6&7 & 0&0 & 5&1 & 8&4 & 2&1 & 8&7 \\ 5.1 & 0.0056 & 0.0160 & 0.0135 & 3&9 & 0&6 & 5&9 & 7&1 & 2&0 & 7&4 \\ \hline \end{tabular} \caption{Combined reduced cross sections $\xip \sigma_r^{D(3)}(\beta,Q^2,x_{\pom})$ for diffractive $ep$ scattering, $ep \to e X p$. The values indicated by ~$\delta_{stat}$, $\delta_{uncor}$, $\delta_{cor}$, $\delta_{exp}$, $\delta_{proc}$ and $\delta_{tot}$ represent the statistical, uncorrelated systematic, correlated systematic, experimental, procedural and total uncertainties, respectively.} \label{tab-results} \end{center} \end{table} \begin{table}[ht!] \begin{center} %\setlength{\extrarowheight}{1.5pt} \begin{tabular}{|c|c|c|c|r@{.}l|r@{.}l|r@{.}l|r@{.}l|r@{.}l|r@{.}l|} \hline $Q^2$ & $\beta$ & $x_{I\!\!P}$ & $x_{I\!\!P} \sigma_r^{D(3)}$ & \multicolumn{2}{c|}{$\delta_{stat}$} & \multicolumn{2}{c|}{$\delta_{uncor}$} & \multicolumn{2}{c|}{$\delta_{cor}$} & \multicolumn{2}{c|}{$\delta_{exp}$} & \multicolumn{2}{c|}{$\delta_{proc}$} & \multicolumn{2}{c|}{$\delta_{tot}$} \\ (GeV$^2$) & & & & \multicolumn{2}{c|}{(\%)} & \multicolumn{2}{c|}{(\%)} & \multicolumn{2}{c|}{(\%)} & \multicolumn{2}{c|}{(\%)} & \multicolumn{2}{c|}{(\%)} & \multicolumn{2}{c|}{(\%)} \\ \hline 5.1 & 0.0056 & 0.0250 & 0.0120 & 3&4 & 0&3 & 5&2 & 6&2 & 2&0 & 6&6 \\ 5.1 & 0.0056 & 0.0350 & 0.0134 & 4&0 & 0&6 & 4&7 & 6&2 & 1&5 & 6&3 \\ 5.1 & 0.0056 & 0.0500 & 0.0147 & 3&9 & 0&6 & 5&4 & 6&7 & 3&4 & 7&5 \\ 5.1 & 0.0056 & 0.0750 & 0.0180 & 5&7 & 1&3 & 6&1 & 8&4 & 3&7 & 9&2 \\ 5.1 & 0.0056 & 0.0900 & 0.0224 & 12& & 3&8 & 4&9 & 14& & 3&1 & 14& \\ 5.1 & 0.0178 & 0.0085 & 0.0120 & 2&6 & 0&4 & 5&9 & 6&4 & 7&6 & 10& \\ 5.1 & 0.0178 & 0.0160 & 0.0111 & 2&6 & 0&2 & 5&2 & 5&8 & 2&8 & 6&5 \\ 5.1 & 0.0178 & 0.0250 & 0.0109 & 3&0 & 0&5 & 5&2 & 6&0 & 2&2 & 6&4 \\ 5.1 & 0.0178 & 0.0350 & 0.0101 & 4&3 & 0&6 & 5&2 & 6&8 & 2&2 & 7&2 \\ 5.1 & 0.0178 & 0.0500 & 0.0134 & 4&1 & 1&4 & 5&1 & 6&7 & 2&2 & 7&0 \\ 5.1 & 0.0178 & 0.0750 & 0.0154 & 6&4 & 2&2 & 4&8 & 8&3 & 2&9 & 8&8 \\ 5.1 & 0.0562 & 0.0025 & 0.0107 & 2&4 & 0&2 & 5&0 & 5&6 & 3&4 & 6&8 \\ 5.1 & 0.0562 & 0.0085 & 0.0088 & 2&7 & 0&3 & 5&0 & 5&7 & 3&5 & 6&7 \\ 5.1 & 0.0562 & 0.0160 & 0.0088 & 3&2 & 0&3 & 5&1 & 6&0 & 2&7 & 6&6 \\ 5.1 & 0.0562 & 0.0250 & 0.0084 & 4&5 & 0&7 & 5&0 & 6&7 & 3&1 & 7&4 \\ 5.1 & 0.0562 & 0.0500 & 0.0095 & 16& & 13& & 4&9 & 21& & 1&9 & 21& \\ 5.1 & 0.0562 & 0.0750 & 0.0153 & 23& & 14& & 5&0 & 27& & 1&9 & 27& \\ 5.1 & 0.1780 & 0.0009 & 0.0121 & 11& & 7&4 & 4&9 & 14& & 11& & 18& \\ 5.1 & 0.1780 & 0.0025 & 0.0118 & 1&6 & 0&2 & 5&9 & 6&1 & 4&2 & 7&4 \\ 5.1 & 0.1780 & 0.0085 & 0.0095 & 2&8 & 0&5 & 5&0 & 5&8 & 3&5 & 6&7 \\ 5.1 & 0.1780 & 0.0160 & 0.0075 & 14& & 12& & 4&9 & 19& & 2&3 & 19& \\ 5.1 & 0.1780 & 0.0250 & 0.0107 & 13& & 13& & 4&9 & 20& & 1&9 & 20& \\ 5.1 & 0.1780 & 0.0350 & 0.0065 & 20& & 14& & 5&0 & 25& & 2&3 & 25& \\ 5.1 & 0.5620 & 0.0003 & 0.0275 & 13& & 8&2 & 4&9 & 16& & 2&3 & 16& \\ 5.1 & 0.5620 & 0.0009 & 0.0187 & 7&0 & 8&0 & 4&6 & 12& & 1&8 & 12& \\ 5.1 & 0.5620 & 0.0025 & 0.0153 & 1&4 & 0&1 & 6&1 & 6&2 & 6&1 & 8&7 \\ 5.1 & 0.5620 & 0.0085 & 0.0137 & 19& & 19& & 4&9 & 27& & 2&3 & 27& \\ 8.8 & 0.0018 & 0.0750 & 0.0288 & 12& & 0&0 & 6&2 & 13& & 1&5 & 13& \\ 8.8 & 0.0056 & 0.0250 & 0.0152 & 5&0 & 0&8 & 5&1 & 7&2 & 2&0 & 7&5 \\ 8.8 & 0.0056 & 0.0350 & 0.0171 & 5&1 & 1&2 & 4&9 & 7&2 & 1&7 & 7&4 \\ 8.8 & 0.0056 & 0.0500 & 0.0197 & 4&1 & 1&2 & 4&6 & 6&3 & 1&6 & 6&5 \\ 8.8 & 0.0056 & 0.0750 & 0.0212 & 5&9 & 1&1 & 4&8 & 7&7 & 3&8 & 8&6 \\ 8.8 & 0.0056 & 0.0900 & 0.0281 & 9&6 & 4&4 & 5&0 & 12& & 5&7 & 13& \\ 8.8 & 0.0178 & 0.0085 & 0.0128 & 4&2 & 0&9 & 5&1 & 6&7 & 4&0 & 7&8 \\ 8.8 & 0.0178 & 0.0160 & 0.0124 & 3&1 & 0&6 & 4&9 & 5&8 & 1&5 & 6&0 \\ 8.8 & 0.0178 & 0.0250 & 0.0133 & 3&4 & 0&6 & 4&8 & 5&9 & 1&5 & 6&1 \\ \hline \end{tabular} \captcont{continued} \label{tab:xsec:b} \end{center} \end{table} \begin{table}[ht!] \begin{center} %\setlength{\extrarowheight}{1.5pt} \begin{tabular}{|c|c|c|c|r@{.}l|r@{.}l|r@{.}l|r@{.}l|r@{.}l|r@{.}l|} \hline $Q^2$ & $\beta$ & $x_{I\!\!P}$ & $x_{I\!\!P} \sigma_r^{D(3)}$ & \multicolumn{2}{c|}{$\delta_{stat}$} & \multicolumn{2}{c|}{$\delta_{uncor}$} & \multicolumn{2}{c|}{$\delta_{cor}$} & \multicolumn{2}{c|}{$\delta_{exp}$} & \multicolumn{2}{c|}{$\delta_{proc}$} & \multicolumn{2}{c|}{$\delta_{tot}$} \\ (GeV$^2$) & & & & \multicolumn{2}{c|}{(\%)} & \multicolumn{2}{c|}{(\%)} & \multicolumn{2}{c|}{(\%)} & \multicolumn{2}{c|}{(\%)} & \multicolumn{2}{c|}{(\%)} & \multicolumn{2}{c|}{(\%)} \\ \hline 8.8 & 0.0178 & 0.0350 & 0.0130 & 4&5 & 0&5 & 4&8 & 6&6 & 1&4 & 6&8 \\ 8.8 & 0.0178 & 0.0500 & 0.0159 & 3&8 & 1&0 & 4&6 & 6&1 & 1&5 & 6&3 \\ 8.8 & 0.0178 & 0.0750 & 0.0162 & 5&6 & 1&7 & 4&8 & 7&6 & 2&3 & 8&0 \\ 8.8 & 0.0178 & 0.0900 & 0.0220 & 9&5 & 5&9 & 5&0 & 12& & 2&7 & 13& \\ 8.8 & 0.0562 & 0.0025 & 0.0125 & 3&4 & 0&4 & 5&0 & 6&1 & 3&8 & 7&1 \\ 8.8 & 0.0562 & 0.0085 & 0.0106 & 3&2 & 0&6 & 5&0 & 6&0 & 2&0 & 6&3 \\ 8.8 & 0.0562 & 0.0160 & 0.0108 & 2&9 & 0&2 & 5&0 & 5&8 & 2&7 & 6&4 \\ 8.8 & 0.0562 & 0.0250 & 0.0098 & 3&6 & 0&5 & 5&0 & 6&2 & 2&5 & 6&7 \\ 8.8 & 0.0562 & 0.0350 & 0.0109 & 5&2 & 0&0 & 4&9 & 7&2 & 2&1 & 7&5 \\ 8.8 & 0.0562 & 0.0500 & 0.0144 & 5&1 & 1&1 & 5&1 & 7&3 & 2&4 & 7&7 \\ 8.8 & 0.0562 & 0.0750 & 0.0140 & 11& & 4&3 & 4&6 & 12& & 1&7 & 13& \\ 8.8 & 0.1780 & 0.0009 & 0.0177 & 7&7 & 2&7 & 5&0 & 9&6 & 1&6 & 9&7 \\ 8.8 & 0.1780 & 0.0025 & 0.0129 & 2&3 & 0&4 & 5&1 & 5&6 & 2&5 & 6&1 \\ 8.8 & 0.1780 & 0.0085 & 0.0104 & 2&6 & 0&4 & 4&6 & 5&3 & 2&7 & 5&9 \\ 8.8 & 0.1780 & 0.0160 & 0.0090 & 3&9 & 0&7 & 5&3 & 6&6 & 2&6 & 7&1 \\ 8.8 & 0.1780 & 0.0250 & 0.0098 & 14& & 14& & 4&9 & 21& & 1&9 & 21& \\ 8.8 & 0.1780 & 0.0350 & 0.0103 & 17& & 11& & 4&9 & 21& & 2&3 & 21& \\ 8.8 & 0.1780 & 0.0500 & 0.0116 & 12& & 8&3 & 4&5 & 15& & 1&8 & 16& \\ 8.8 & 0.5620 & 0.0003 & 0.0250 & 7&1 & 4&2 & 4&4 & 9&3 & 8&9 & 13& \\ 8.8 & 0.5620 & 0.0009 & 0.0207 & 5&6 & 3&5 & 4&4 & 7&9 & 6&7 & 10& \\ 8.8 & 0.5620 & 0.0025 & 0.0166 & 1&6 & 0&1 & 6&1 & 6&3 & 8&3 & 10& \\ 8.8 & 0.5620 & 0.0085 & 0.0142 & 8&5 & 4&3 & 4&3 & 10& & 8&0 & 13& \\ 8.8 & 0.5620 & 0.0160 & 0.0102 & 17& & 13& & 4&4 & 22& & 2&3 & 22& \\ 15.3 & 0.0056 & 0.0500 & 0.0245 & 6&7 & 2&2 & 4&9 & 8&6 & 1&1 & 8&7 \\ 15.3 & 0.0056 & 0.0750 & 0.0296 & 10& & 0&0 & 5&7 & 12& & 1&6 & 12& \\ 15.3 & 0.0178 & 0.0160 & 0.0176 & 4&8 & 0&7 & 5&0 & 7&0 & 2&4 & 7&4 \\ 15.3 & 0.0178 & 0.0250 & 0.0164 & 4&4 & 0&7 & 4&8 & 6&6 & 2&4 & 7&0 \\ 15.3 & 0.0178 & 0.0350 & 0.0165 & 5&7 & 1&1 & 4&7 & 7&5 & 1&4 & 7&6 \\ 15.3 & 0.0178 & 0.0500 & 0.0176 & 4&9 & 1&4 & 4&8 & 7&0 & 2&2 & 7&4 \\ 15.3 & 0.0178 & 0.0750 & 0.0211 & 6&7 & 2&1 & 4&8 & 8&5 & 2&6 & 8&9 \\ 15.3 & 0.0178 & 0.0900 & 0.0234 & 10& & 1&6 & 4&8 & 11& & 3&3 & 12& \\ 15.3 & 0.0562 & 0.0085 & 0.0134 & 4&5 & 0&0 & 6&0 & 7&5 & 6&1 & 9&7 \\ 15.3 & 0.0562 & 0.0160 & 0.0122 & 3&9 & 0&3 & 4&9 & 6&3 & 2&5 & 6&8 \\ 15.3 & 0.0562 & 0.0250 & 0.0113 & 4&5 & 0&3 & 4&8 & 6&6 & 1&0 & 6&7 \\ 15.3 & 0.0562 & 0.0350 & 0.0121 & 6&2 & 0&0 & 5&0 & 8&0 & 2&0 & 8&2 \\ 15.3 & 0.0562 & 0.0500 & 0.0140 & 5&7 & 1&1 & 4&9 & 7&6 & 2&0 & 7&8 \\ \hline \end{tabular} \captcont{continued} \label{tab:xsec:c} \end{center} \end{table} \begin{table}[ht!] \begin{center} \begin{tabular}{|c|c|c|c|r@{.}l|r@{.}l|r@{.}l|r@{.}l|r@{.}l|r@{.}l|} \hline $Q^2$ & $\beta$ & $x_{I\!\!P}$ & $x_{I\!\!P} \sigma_r^{D(3)}$ & \multicolumn{2}{c|}{$\delta_{stat}$} & \multicolumn{2}{c|}{$\delta_{uncor}$} & \multicolumn{2}{c|}{$\delta_{cor}$} & \multicolumn{2}{c|}{$\delta_{exp}$} & \multicolumn{2}{c|}{$\delta_{proc}$} & \multicolumn{2}{c|}{$\delta_{tot}$} \\ (GeV$^2$) & & & & \multicolumn{2}{c|}{(\%)} & \multicolumn{2}{c|}{(\%)} & \multicolumn{2}{c|}{(\%)} & \multicolumn{2}{c|}{(\%)} & \multicolumn{2}{c|}{(\%)} & \multicolumn{2}{c|}{(\%)} \\ \hline 15.3 & 0.0562 & 0.0750 & 0.0174 & 7&6 & 1&4 & 4&7 & 9&1 & 2&1 & 9&3 \\ 15.3 & 0.0562 & 0.0900 & 0.0162 & 10& & 3&6 & 5&1 & 12& & 2&8 & 12& \\ 15.3 & 0.1780 & 0.0025 & 0.0136 & 3&4 & 0&5 & 5&0 & 6&0 & 1&3 & 6&2 \\ 15.3 & 0.1780 & 0.0085 & 0.0111 & 3&4 & 0&5 & 4&8 & 5&9 & 2&2 & 6&2 \\ 15.3 & 0.1780 & 0.0160 & 0.0098 & 3&9 & 0&6 & 5&0 & 6&4 & 2&2 & 6&8 \\ 15.3 & 0.1780 & 0.0250 & 0.0097 & 6&1 & 0&9 & 5&2 & 8&1 & 2&4 & 8&4 \\ 15.3 & 0.1780 & 0.0350 & 0.0117 & 15& & 17& & 4&9 & 23& & 2&3 & 23& \\ 15.3 & 0.1780 & 0.0500 & 0.0134 & 12& & 15& & 4&9 & 20& & 2&3 & 20& \\ 15.3 & 0.5620 & 0.0009 & 0.0180 & 8&8 & 3&4 & 4&6 & 11& & 3&3 & 11& \\ 15.3 & 0.5620 & 0.0025 & 0.0173 & 2&5 & 0&2 & 5&8 & 6&3 & 3&5 & 7&2 \\ 15.3 & 0.5620 & 0.0085 & 0.0162 & 3&3 & 0&5 & 5&1 & 6&1 & 3&0 & 6&8 \\ 15.3 & 0.5620 & 0.0160 & 0.0151 & 17& & 14& & 4&9 & 22& & 2&3 & 22& \\ 15.3 & 0.5620 & 0.0350 & 0.0094 & 20& & 21& & 4&9 & 30& & 2&3 & 30& \\ 26.5 & 0.0056 & 0.0750 & 0.0359 & 17& & 0&0 & 5&3 & 18& & 3&2 & 18& \\ 26.5 & 0.0178 & 0.0250 & 0.0179 & 8&0 & 1&4 & 4&8 & 9&4 & 2&3 & 9&7 \\ 26.5 & 0.0178 & 0.0350 & 0.0202 & 8&6 & 0&0 & 5&3 & 10& & 1&6 & 10& \\ 26.5 & 0.0178 & 0.0500 & 0.0250 & 6&7 & 1&3 & 4&8 & 8&4 & 1&8 & 8&6 \\ 26.5 & 0.0178 & 0.0750 & 0.0249 & 10& & 2&3 & 5&2 & 12& & 2&6 & 12& \\ 26.5 & 0.0562 & 0.0085 & 0.0157 & 6&6 & 1&2 & 5&3 & 8&6 & 8&0 & 12& \\ 26.5 & 0.0562 & 0.0160 & 0.0150 & 4&9 & 0&7 & 4&8 & 7&0 & 1&8 & 7&2 \\ 26.5 & 0.0562 & 0.0250 & 0.0134 & 5&5 & 0&7 & 4&5 & 7&1 & 1&3 & 7&3 \\ 26.5 & 0.0562 & 0.0350 & 0.0157 & 7&4 & 0&0 & 4&8 & 8&8 & 1&6 & 9&0 \\ 26.5 & 0.0562 & 0.0500 & 0.0184 & 6&2 & 1&6 & 5&1 & 8&2 & 1&3 & 8&3 \\ 26.5 & 0.0562 & 0.0750 & 0.0211 & 7&4 & 1&8 & 4&5 & 8&9 & 1&5 & 9&0 \\ 26.5 & 0.0562 & 0.0900 & 0.0237 & 9&6 & 3&2 & 5&0 & 11& & 3&4 & 12& \\ 26.5 & 0.1780 & 0.0025 & 0.0138 & 5&4 & 0&4 & 5&1 & 7&5 & 1&4 & 7&6 \\ 26.5 & 0.1780 & 0.0085 & 0.0126 & 5&0 & 0&8 & 4&8 & 7&0 & 2&7 & 7&5 \\ 26.5 & 0.1780 & 0.0160 & 0.0113 & 5&5 & 0&0 & 5&1 & 7&6 & 2&2 & 7&9 \\ 26.5 & 0.1780 & 0.0250 & 0.0093 & 6&5 & 1&0 & 4&9 & 8&2 & 1&4 & 8&3 \\ 26.5 & 0.1780 & 0.0350 & 0.0100 & 9&8 & 0&0 & 5&7 & 11& & 4&0 & 12& \\ 26.5 & 0.1780 & 0.0500 & 0.0105 & 26& & 14& & 4&9 & 30& & 1&9 & 30& \\ 26.5 & 0.1780 & 0.0750 & 0.0169 & 42& & 11& & 4&9 & 44& & 1&9 & 44& \\ 26.5 & 0.5620 & 0.0009 & 0.0241 & 22& & 10& & 4&9 & 25& & 1&9 & 25& \\ 26.5 & 0.5620 & 0.0025 & 0.0189 & 3&7 & 0&2 & 6&0 & 7&0 & 9&1 & 12& \\ 26.5 & 0.5620 & 0.0085 & 0.0140 & 4&3 & 0&4 & 5&0 & 6&6 & 3&8 & 7&6 \\ 26.5 & 0.5620 & 0.0250 & 0.0136 & 31& & 15& & 4&9 & 35& & 1&9 & 35& \\ \hline \end{tabular} \captcont{continued} \label{tab:xsec:d} \end{center} \end{table} \begin{table}[ht!] \begin{center} %\setlength{\extrarowheight}{1.5pt} \begin{tabular}{|c|c|c|c|r@{.}l|r@{.}l|r@{.}l|r@{.}l|r@{.}l|r@{.}l|} \hline $Q^2$ & $\beta$ & $x_{I\!\!P}$ & $x_{I\!\!P} \sigma_r^{D(3)}$ & \multicolumn{2}{c|}{$\delta_{stat}$} & \multicolumn{2}{c|}{$\delta_{uncor}$} & \multicolumn{2}{c|}{$\delta_{cor}$} & \multicolumn{2}{c|}{$\delta_{exp}$} & \multicolumn{2}{c|}{$\delta_{proc}$} & \multicolumn{2}{c|}{$\delta_{tot}$} \\ (GeV$^2$) & & & & \multicolumn{2}{c|}{(\%)} & \multicolumn{2}{c|}{(\%)} & \multicolumn{2}{c|}{(\%)} & \multicolumn{2}{c|}{(\%)} & \multicolumn{2}{c|}{(\%)} & \multicolumn{2}{c|}{(\%)} \\ \hline 46 & 0.0178 & 0.0500 & 0.0313 & 8&6 & 4&5 & 4&7 & 11& & 1&6 & 11& \\ 46 & 0.0178 & 0.0750 & 0.0218 & 19& & 0&0 & 5&1 & 20& & 2&5 & 20& \\ 46 & 0.0562 & 0.0160 & 0.0163 & 8&8 & 0&0 & 5&2 & 10& & 2&1 & 11& \\ 46 & 0.0562 & 0.0250 & 0.0172 & 8&6 & 0&0 & 5&3 & 10& & 2&1 & 10& \\ 46 & 0.0562 & 0.0350 & 0.0158 & 8&3 & 1&8 & 4&6 & 9&6 & 2&2 & 9&8 \\ 46 & 0.0562 & 0.0500 & 0.0199 & 7&6 & 1&9 & 4&8 & 9&2 & 2&8 & 9&6 \\ 46 & 0.0562 & 0.0750 & 0.0212 & 8&4 & 1&2 & 4&9 & 9&7 & 3&2 & 10& \\ 46 & 0.0562 & 0.0900 & 0.0267 & 8&9 & 2&4 & 4&8 & 10& & 1&0 & 10& \\ 46 & 0.1780 & 0.0085 & 0.0121 & 6&6 & 1&3 & 5&4 & 8&6 & 2&1 & 8&9 \\ 46 & 0.1780 & 0.0160 & 0.0133 & 5&9 & 1&5 & 4&8 & 7&7 & 2&4 & 8&1 \\ 46 & 0.1780 & 0.0250 & 0.0135 & 8&5 & 0&0 & 4&9 & 9&8 & 2&2 & 10& \\ 46 & 0.1780 & 0.0350 & 0.0129 & 7&5 & 1&9 & 4&6 & 9&0 & 2&1 & 9&2 \\ 46 & 0.1780 & 0.0500 & 0.0148 & 7&4 & 2&9 & 4&8 & 9&3 & 2&4 & 9&6 \\ 46 & 0.1780 & 0.0750 & 0.0201 & 9&9 & 4&0 & 4&7 & 12& & 3&4 & 12& \\ 46 & 0.1780 & 0.0900 & 0.0177 & 13& & 4&2 & 5&0 & 14& & 8&6 & 17& \\ 46 & 0.5620 & 0.0025 & 0.0196 & 5&1 & 1&0 & 5&4 & 7&5 & 4&2 & 8&6 \\ 46 & 0.5620 & 0.0085 & 0.0135 & 5&1 & 1&0 & 4&9 & 7&2 & 4&6 & 8&5 \\ 46 & 0.5620 & 0.0160 & 0.0124 & 6&9 & 1&8 & 4&8 & 8&6 & 2&3 & 8&9 \\ 46 & 0.5620 & 0.0250 & 0.0106 & 13& & 0&0 & 5&9 & 14& & 1&2 & 15& \\ 46 & 0.5620 & 0.0350 & 0.0135 & 14& & 7&0 & 4&8 & 16& & 2&2 & 16& \\ 46 & 0.5620 & 0.0500 & 0.0120 & 17& & 20& & 4&9 & 26& & 2&3 & 26& \\ 46 & 0.8160 & 0.0009 & 0.0145 & 21& & 5&3 & 4&5 & 22& & 1&4 & 22& \\ 46 & 0.8160 & 0.0025 & 0.0131 & 17& & 8&1 & 5&3 & 20& & 3&0 & 20& \\ 46 & 0.8160 & 0.0085 & 0.0110 & 18& & 3&9 & 4&3 & 19& & 1&5 & 19& \\ 46 & 0.8160 & 0.0160 & 0.0092 & 27& & 3&9 & 5&4 & 28& & 4&1 & 28& \\ 80 & 0.0562 & 0.0350 & 0.0227 & 19& & 0&0 & 5&8 & 20& & 2&7 & 20& \\ 80 & 0.0562 & 0.0500 & 0.0235 & 15& & 0&0 & 5&0 & 16& & 2&0 & 16& \\ 80 & 0.0562 & 0.0750 & 0.0216 & 24& & 0&0 & 5&9 & 25& & 1&9 & 25& \\ 80 & 0.1780 & 0.0085 & 0.0206 & 15& & 0&0 & 6&0 & 16& & 2&9 & 16& \\ 80 & 0.1780 & 0.0160 & 0.0133 & 13& & 0&0 & 4&8 & 14& & 2&3 & 14& \\ 80 & 0.1780 & 0.0250 & 0.0146 & 12& & 0&0 & 5&2 & 13& & 1&6 & 13& \\ 80 & 0.1780 & 0.0350 & 0.0162 & 14& & 0&0 & 5&6 & 15& & 1&0 & 15& \\ 80 & 0.1780 & 0.0500 & 0.0146 & 15& & 0&0 & 5&5 & 16& & 2&3 & 16& \\ 80 & 0.1780 & 0.0750 & 0.0183 & 26& & 0&0 & 5&3 & 27& & 3&0 & 27& \\ 80 & 0.5620 & 0.0085 & 0.0116 & 10& & 0&0 & 6&4 & 12& & 5&1 & 13& \\ 80 & 0.5620 & 0.0160 & 0.0090 & 14& & 0&0 & 7&0 & 15& & 3&5 & 16& \\ \hline \end{tabular} \captcont{continued} \label{tab:xsec:e} \end{center} \end{table} \begin{table}[t!] \begin{center} %\setlength{\extrarowheight}{1.5pt} \begin{tabular}{|c|c|c|c|r@{.}l|r@{.}l|r@{.}l|r@{.}l|r@{.}l|r@{.}l|} \hline $Q^2$ & $\beta$ & $x_{I\!\!P}$ & $x_{I\!\!P} \sigma_r^{D(3)}$ & \multicolumn{2}{c|}{$\delta_{stat}$} & \multicolumn{2}{c|}{$\delta_{uncor}$} & \multicolumn{2}{c|}{$\delta_{cor}$} & \multicolumn{2}{c|}{$\delta_{exp}$} & \multicolumn{2}{c|}{$\delta_{proc}$} & \multicolumn{2}{c|}{$\delta_{tot}$} \\ (GeV$^2$) & & & & \multicolumn{2}{c|}{(\%)} & \multicolumn{2}{c|}{(\%)} & \multicolumn{2}{c|}{(\%)} & \multicolumn{2}{c|}{(\%)} & \multicolumn{2}{c|}{(\%)} & \multicolumn{2}{c|}{(\%)} \\ \hline 80 & 0.5620 & 0.0250 & 0.0104 & 17& & 0&0 & 6&7 & 18& & 5&3 & 19& \\ 80 & 0.5620 & 0.0350 & 0.0109 & 25& & 0&0 & 7&3 & 26& & 3&6 & 26& \\ 200 & 0.0562 & 0.0500 & 0.0162 & 28& & 0&0 & 5&0 & 28& & 1&0 & 28& \\ 200 & 0.0562 & 0.0750 & 0.0288 & 37& & 0&0 & 5&5 & 37& & 2&3 & 37& \\ 200 & 0.1780 & 0.0160 & 0.0145 & 20& & 0&0 & 5&8 & 21& & 1&3 & 21& \\ 200 & 0.1780 & 0.0250 & 0.0199 & 16& & 0&0 & 5&0 & 17& & 1&9 & 17& \\ 200 & 0.1780 & 0.0350 & 0.0169 & 22& & 0&0 & 5&2 & 23& & 2&6 & 23& \\ 200 & 0.1780 & 0.0500 & 0.0235 & 20& & 0&0 & 5&5 & 21& & 2&6 & 21& \\ 200 & 0.1780 & 0.0750 & 0.0209 & 35& & 0&0 & 5&6 & 35& & 2&5 & 36& \\ 200 & 0.5620 & 0.0085 & 0.0109 & 19& & 0&0 & 6&6 & 21& & 3&9 & 21& \\ 200 & 0.5620 & 0.0160 & 0.0093 & 23& & 0&0 & 6&4 & 24& & 1&9 & 24& \\ 200 & 0.5620 & 0.0250 & 0.0074 & 27& & 0&0 & 6&7 & 28& & 4&9 & 29& \\ 200 & 0.5620 & 0.0350 & 0.0158 & 33& & 0&0 & 6&7 & 34& & 2&4 & 34& \\ 200 & 0.5620 & 0.0500 & 0.0151 & 29& & 0&0 & 5&4 & 29& & 1&8 & 29& \\ 200 & 0.5620 & 0.0750 & 0.0228 & 50& & 0&0 & 5&9 & 50& & 3&2 & 50& \\ \hline \end{tabular} \captcont{continued} \label{tab:xsec:f} \end{center} \end{table} %%%%%%%%%%%%%%%%%%%%%%%%%%% FIGURES %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{figure}[hb] \begin{center} \includegraphics[scale=0.8]{d12-100f2.eps} \caption{Reduced diffractive cross section $x_{\pom} \, \sigma_r^{D(3)}(\beta,Q^2,x_{\pom})$ for $0.09 < |t| < 0.55 \ {\rm GeV^2}$ as a function of $Q^2$ for different values of $\beta$ and $\xip$. The H1 `FPS~HERA II'~\cite{h1-fps2}, H1 `FPS~HERA I'~\cite{h1-fps1}, ZEUS `LPS~2'~\cite{zeus-lrglps} and ZEUS `LPS~1'~\cite{zeus-lps1} data are presented. The inner error bars indicate the statistical uncertainties, the outer error bars show the statistical and systematic uncertainties added in quadrature. Normalisation uncertainties are not included in the error bars of the individual measurements. } \label{fig-q2dep-allinputs} \end{center} \end{figure} \begin{figure}[hb] \begin{center} \includegraphics[scale=0.8]{d12-100f3.eps} \caption{Pull distributions %of pulls for the individual data sets. % ~There are no entries outside the histogram range. The root mean square gives the root mean square of the distributions. % The curves show the result of a Gaussian fit to the distributions. } \label{fig-pulls} \end{center} \end{figure} \begin{figure}[hb] \begin{center} \includegraphics[scale=0.8]{d12-100f4.eps} \caption{Reduced diffractive cross section $x_{\pom} \, \sigma_r^{D(3)}(\beta,Q^2,x_{\pom})$ for $0.09 < |t| < 0.55 \ {\rm GeV^2}$ as a function of $Q^2$ for different values of $\beta$ at $\xip = 0.05$. The combined data are compared to the H1 and ZEUS data input to the averaging procedure. % the H1 `FPS~HERA II'~\cite{h1-fps2}, % H1 `FPS~HERA I'~\cite{h1-fps1}, ZEUS `LPS~2'~\cite{zeus-lrglps} and ZEUS `LPS~1'~\cite{zeus-lps1} data. The points for % which only one data set contributes are also shown. The error bars indicate the statistical and systematic uncertainties added in quadrature for the input measurements and the statistical, systematic and procedural uncertainties added in quadrature for the combined points. Normalisation uncertainties are not included in the error bars of the individual measurements, whereas they are included in the error bars of the combined points.} \label{fig-q2sel-all} \end{center} \end{figure} \begin{figure}[hb] \begin{center} \includegraphics[scale=0.8]{d12-100f5.eps} \caption{HERA combined reduced diffractive cross section $x_{\pom} \, \sigma_r^{D(3)}(\beta,Q^2,x_{\pom})$ for $0.09 < |t| < 0.55 \ {\rm GeV^2}$ as a function of $Q^2$ for different values of $\beta$ and $\xip$. The error bars indicate the statistical, systematic and procedural uncertainties added in quadrature. The normalisation uncertainty is included.} \label{fig-q2dep-comb} \end{center} \end{figure} \begin{figure}[hb] \begin{center} \includegraphics[scale=0.8]{d12-100f6.eps} \caption{HERA combined reduced diffractive cross section $x_{\pom} \, \sigma_r^{D(3)}(\beta,Q^2,x_{\pom})$ for $0.09 < |t| < 0.55 \ {\rm GeV^2}$ as a function of $\xip$ for different values of $\beta$ and $Q^2$. The error bars indicate the statistical, systematic and procedural uncertainties added in quadrature. The normalisation uncertainty is included.} \label{fig-xpdep-comb} \end{center} \end{figure} \end{document}