%================================================================ % LaTeX file with prefered layout for H1 paper drafts % use: dvips -D600 file-name %================================================================ \documentclass[12pt]{article} \usepackage{epsfig} \usepackage{amsmath} \usepackage{hhline} \usepackage{amssymb} \usepackage{times} \usepackage{cite} %\usepackage{lineno} \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 %===============================title page============================= \begin{document} % The rest \newcommand{\pom}{{I\!\!P}} \newcommand{\reg}{{I\!\!R}} \newcommand{\tmod}{\ensuremath{|t|}} %\newcommand{\gevsq}{\mathrm{GeV}^2} % Results \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{\ALPHA}{1.10\pm0.03 (stat.) \pm0.04 (syst.)} \newcommand{\ALPHAZ}{1.15\pm0.04 (stat.)^{+0.04}_{-0.07} (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}{\ensuremath{x_{\PO}~}} \newcommand{\ypom}{\ensuremath{y_{\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$^{-1}$}}} % % Some useful tex commands % \newcommand{\qsq}{\ensuremath{Q^2} } \newcommand{\gevsq}{\ensuremath{~\mathrm{GeV}^2} } \newcommand{\et}{\ensuremath{E_t^*} } \newcommand{\ptgamma}{\ensuremath{P_{T}^{\gamma}} } \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^*} } %\newcommand{\alpeff}{\overline{\alpha_s}} %\newcommand{\alpeff}{\alpha_s^{eff}} \newcommand{\alpeff}{\alpha_s^{BFKL}} \newcommand{\wfitres}{\ensuremath{\delta=2.73 \pm 1.02~\mathrm{(stat.)} ^{+0.56}_{-0.78}~\mathrm{(syst.)}}} \newcommand{\tfitres}{\ensuremath{n=2.60 \pm 0.19~\mathrm{(stat.)} ^{+0.03}_{-0.08}~\mathrm{(syst.)}}} \newcommand{\alphasfitres}{\ensuremath{\alpha_S}^{Fit}=0.26 \pm 0.10 ~\mathrm{(stat.)} ^{+0.05}_{-0.07}~\mathrm{(syst.)}} \newcommand{\MYmean}{20} % Journal macro \def\Journal#1#2#3#4{{#1} {\bf #2} (#3) #4} \def\NCA{\em Nuovo Cimento} \def\NIM{\em Nucl. Instrum. Methods} \def\NIMA{{\em Nucl. Instrum. Methods} {\bf A}} \def\NPB{{\em Nucl. Phys.} {\bf B}} \def\PLB{{\em Phys. Lett.} {\bf B}} \def\PRL{\em Phys. Rev. Lett.} \def\PRD{{\em Phys. Rev.} {\bf D}} \def\ZPC{{\em Z. Phys.} {\bf C}} \def\EJC{{\em Eur. Phys. J.} {\bf C}} \def\CPC{\em Comp. Phys. Commun.} \begin{titlepage} \noindent \begin{flushleft} {DESY 08-077 \hfill ISSN 0418-9833} \\ {\tt December 2008} \\ \end{flushleft} \vspace{2cm} %\linenumbers \begin{center} \begin{Large} {\bf Measurement of Diffractive Scattering of Photons with Large Momentum Transfer at HERA} \vspace{2cm} H1 Collaboration \end{Large} \end{center} \vspace{2cm} \begin{abstract} The first measurement of diffractive scattering of quasi-real photons with large momentum transfer $\gamma p \rightarrow \gamma Y$, where $Y$ is the proton dissociative system, is made using the H1 detector at HERA. The measurement is performed for initial photon virtualities $Q^2 < 0.01\gevsq$. Single differential cross sections are measured as a function of $W$, the incident photon-proton centre of mass energy, and $t$, the square of the four-momentum transferred at the proton vertex, in the range $175 < W < 247~\mathrm{GeV}$ and $4<\tmod <36\gevsq$. The $W$ dependence is well described by a model based on perturbative QCD using a leading logarithmic approximation of the BFKL evolution. The measured $\tmod$ dependence is harder than that predicted by the model and those observed in exclusive vector meson production. \end{abstract} \vspace{1.5cm} \begin{center} Accepted by Physics Letters B \end{center} \end{titlepage} % THE PAPER DRAFTS HAVE NO AUTHORLIST % % FOR PAPER ISSUED FOR THE FINAL READING % COPY THE AUTHOR AND INSTITUTE LISTS % INTO YOUR AREA % % from /h1/iww/ipublications/h1auts.tex % AND UNCOMMENT THE NEXT THREE LINES % \begin{flushleft} %-- H1AUTS Author list by names %-- Status: Mon Mar 3 10:31:50 CET 2008 Number of authors = 273 F.D.~Aaron$^{5,49}$, %BUCH-PD 11/06 Aaron C.~Alexa$^{5}$, %BUCH-PD 06/06 Alexa V.~Andreev$^{25}$, %LPI -PD 8/88 Andreev B.~Antunovic$^{11}$, %DESY-PD 05/07 Antunovic S.~Aplin$^{11}$, %DESY-LEFT 01/08 Aplin A.~Asmone$^{33}$, %ROME-ST 07/2 Asmone A.~Astvatsatourov$^{4}$, %BRUX-LEFT 01/08 Astvatsatourov A.~Bacchetta$^{11}$, %DESY-PD 09/07 Bacchetta S.~Backovic$^{30}$, %PODG-PD 03/2 Backovic A.~Baghdasaryan$^{38}$, %YERE-PD 09/03 Baghdasaryana P.~Baranov$^{25, \dagger}$, %LPI -LEFT 05/07 Baranovp E.~Barrelet$^{29}$, %PARI-PD 11/99 Barrelet W.~Bartel$^{11}$, %DESY-PD 8/88 Bartel M.~Beckingham$^{11}$, %DESY-LEFT 08/07 Beckingham K.~Begzsuren$^{35}$, %ULBA-PD 04/06 Begzsuren O.~Behnke$^{14}$, %HDB1-LEFT 12/07 Behnke A.~Belousov$^{25}$, %LPI -PD 8/88 Belousov N.~Berger$^{40}$, %ZUTH-LEFT 10/07 Bergern J.C.~Bizot$^{27}$, %ORSA-PD 8/88 Bizot M.-O.~Boenig$^{8}$, %DORT-LEFT 10/07 Boenig V.~Boudry$^{28}$, %ECPL-PD 1/93 Boudry I.~Bozovic-Jelisavcic$^{2}$, %BEOG-PD 03/06 Bozovicjelisavcic J.~Bracinik$^{3}$, %BIRM-PD 01/2 Bracinik G.~Brandt$^{11}$, %DESY-PD 01/20 Brandt M.~Brinkmann$^{11}$, %DESY-ST 02/06 Brinkmann V.~Brisson$^{27}$, %ORSA-PD 8/88 Brisson D.~Bruncko$^{16}$, %KOSI-PD 8/88 Bruncko A.~Bunyatyan$^{13,38}$, %MPIH-PD 12/95 Bunyatyan G.~Buschhorn$^{26}$, %MPIM-PD 8/88 Buschhorn L.~Bystritskaya$^{24}$, %ITEP-PD 05/99 Bystritskaya A.J.~Campbell$^{11}$, %DESY-PD 8/88 Campbella K.B. ~Cantun~Avila$^{22}$, %MEX1-ST 04/06 Cantunavila F.~Cassol-Brunner$^{21}$, %MARS-PD 12/0 Cassolbrunner K.~Cerny$^{32}$, %PRG2-ST 09/02 Cernyk V.~Cerny$^{16,47}$, %KOSI-PD 06/04 Cernyv V.~Chekelian$^{26}$, %MPIM-PD 01/90 Chekelian A.~Cholewa$^{11}$, %DESY-ST 11/05 Cholewa J.G.~Contreras$^{22}$, %MEX1-PD 04/97 Contreras J.A.~Coughlan$^{6}$, %RAL -PD 8/88 Coughlan G.~Cozzika$^{10}$, %SACL-PD 10/07 Cozzika J.~Cvach$^{31}$, %PRAG-PD 8/88 Cvach J.B.~Dainton$^{18}$, %LIVE-PD 8/88 Dainton K.~Daum$^{37,43}$, %WUPP-PD 06/96 Daum M.~De\'{a}k$^{11}$, %DESY-ST 08/06 Deak Y.~de~Boer$^{11}$, %DESY-PD 01/08 Deboer B.~Delcourt$^{27}$, %ORSA-PD 8/88 Delcourt M.~Del~Degan$^{40}$, %ZUTH-ST 02/05 Deldegan J.~Delvax$^{4}$, %BRUX-ST 10/06 Delvax A.~De~Roeck$^{11,45}$, %DESY-PD 08/88 Deroeck E.A.~De~Wolf$^{4}$, %ANTW-PD 3/93 Dewolf C.~Diaconu$^{21}$, %MARS-PD 01/05 Diaconu V.~Dodonov$^{13}$, %MPIH-PD 04/98 Dodonov A.~Dossanov$^{26}$, %MPIM-ST 01/07 Dossanov A.~Dubak$^{30,46}$, %PODG-PD 10/03 Dubak G.~Eckerlin$^{11}$, %DESY-PD 8/88 Eckerlin V.~Efremenko$^{24}$, %ITEP-PD 8/88 Efremenko S.~Egli$^{36}$, %PSI -PD 01/01 Egli A.~Eliseev$^{25}$, %LPI -PD 01/06 Eliseev E.~Elsen$^{11}$, %DESY-PD 8/88 Elsen S.~Essenov$^{24}$, %ITEP-PD 09/03 Essenov A.~Falkiewicz$^{7}$, %CRAC-ST 07/04 Falkiewicz P.J.W.~Faulkner$^{3}$, %BIRM-PD 10/95 Faulkner L.~Favart$^{4}$, %BRUX-PD 8/88 Favart A.~Fedotov$^{24}$, %ITEP-PD 8/88 Fedotov R.~Felst$^{11}$, %DESY-PD 11/0 Felst J.~Feltesse$^{10,48}$, %SACL-PD 03/05 Feltesse J.~Ferencei$^{16}$, %KOSI-PD 01/05 Ferencei L.~Finke$^{11}$, %DESY-LEFT 04/07 Finkel M.~Fleischer$^{11}$, %DESY-PD 07/0 Fleischer A.~Fomenko$^{25}$, %LPI -PD 8/88 Fomenko E.~Gabathuler$^{18}$, %LIVE-PD 10/89 Gabathulere J.~Gayler$^{11}$, %DESY-PD 8/88 Gayler S.~Ghazaryan$^{38}$, %YERE-PD 8/88 Ghazaryan A.~Glazov$^{11}$, %DESY-PD 01/04 Glazov I.~Glushkov$^{39}$, %ZEUT-ST 11/03 Glushkov L.~Goerlich$^{7}$, %CRAC-PD 8/88 Goerlich M.~Goettlich$^{12}$, %HAM2-LEFT 11/07 Goettlich N.~Gogitidze$^{25}$, %LPI -PD 8/88 Gogitidze M.~Gouzevitch$^{28}$, %ECPL-ST 10/05 Gouzevitch C.~Grab$^{40}$, %ZUTH-PD 8/88 Grab T.~Greenshaw$^{18}$, %LIVE-PD 8/88 Greenshaw B.R.~Grell$^{11}$, %DESY-ST 09/04 Grell G.~Grindhammer$^{26}$, %MPIM-PD 8/88 Grindhammer S.~Habib$^{12,50}$, %HAM2-ST 12/05 Habib D.~Haidt$^{11}$, %DESY-PD 8/88 Haidt M.~Hansson$^{20}$, %LUND-ST 04/03 Hansson C.~Helebrant$^{11}$, %DFLC-ST 03/06 Helebrant R.C.W.~Henderson$^{17}$, %LANC-PD 8/88 Henderson H.~Henschel$^{39}$, %ZEUT-PD 06/99 Henschel G.~Herrera$^{23}$, %MEX2-PD 07/98 Herrera M.~Hildebrandt$^{36}$, %PSI -PD 10/99 Hildebrandtm K.H.~Hiller$^{39}$, %ZEUT-PD 8/88 Hiller D.~Hoffmann$^{21}$, %MARS-PD 10/0 Hoffmann R.~Horisberger$^{36}$, %PSI -PD 8/88 Horisberger A.~Hovhannisyan$^{38}$, %YERE-LEFT 09/07 Hovhannisyan T.~Hreus$^{4,44}$, %BRUX-ST 10/04 Hreus M.~Jacquet$^{27}$, %ORSA-PD 09/96 Jacquet M.E.~Janssen$^{11}$, %DFLC-ST 06/06 Janssenm X.~Janssen$^{4}$, %BRUX-PD 02/03 Janssenx V.~Jemanov$^{12}$, %HAM2-PD 07/07 Jemanov L.~J\"onsson$^{20}$, %LUND-PD 8/88 Joensson D.P.~Johnson$^{4, \dagger}$, %BRUX-LEFT 05/07 Johnsond A.W.~Jung$^{15}$, %HDB2-ST 11/04 Junga H.~Jung$^{11}$, %DESY-PD 07/00 Jungh M.~Kapichine$^{9}$, %JINR-PD 3/97 Kapichine J.~Katzy$^{11}$, %DESY-PD 09/1 Katzy I.R.~Kenyon$^{3}$, %BIRM-PD 8/88 Kenyon C.~Kiesling$^{26}$, %MPIM-PD 8/88 Kiesling M.~Klein$^{18}$, %LIVE-PD 8/88 Klein C.~Kleinwort$^{11}$, %DESY-PD 8/88 Kleinwort T.~Klimkovich$^{11}$, %DFLC-PD 06/06 Klimkovich T.~Kluge$^{18}$, %LIVE-PD 05/04 Kluge A.~Knutsson$^{11}$, %DESY-PD 04/07 Knutsson R.~Kogler$^{26}$, %MPIM-ST 01/07 Kogler V.~Korbel$^{11}$, %DESY-PD 8/88 Korbel P.~Kostka$^{39}$, %ZEUT-PD 8/88 Kostka M.~Kraemer$^{11}$, %DESY-ST 02/06 Kraemer K.~Krastev$^{11}$, %DESY-ST 02/05 Krastev J.~Kretzschmar$^{18}$, %LIVE-PD 01/08 Kretzschmar A.~Kropivnitskaya$^{24}$, %ITEP-ST 07/2 Kropivnitskaya K.~Kr\"uger$^{15}$, %HDB2-PD 01/04 Kruegerk K.~Kutak$^{11}$, %DESY-PD 01/07 Kutak M.P.J.~Landon$^{19}$, %QMWC-PD 8/88 Landon W.~Lange$^{39}$, %ZEUT-PD 8/88 Lange G.~La\v{s}tovi\v{c}ka-Medin$^{30}$, %PODG-PD 06/04 Lastovickamedin P.~Laycock$^{18}$, %LIVE-PD 11/03 Laycock A.~Lebedev$^{25}$, %LPI -PD 8/88 Lebedev G.~Leibenguth$^{40}$, %ZUTH-PD 11/04 Leibenguth V.~Lendermann$^{15}$, %HDB2-PD 01/2 Lendermann S.~Levonian$^{11}$, %DESY-PD 8/88 Levonian G.~Li$^{27}$, %ORSA-PD 09/06 Li K.~Lipka$^{12}$, %HAM2-PD 01/03 Lipka A.~Liptaj$^{26}$, %MPIM-ST 10/04 Liptaj B.~List$^{12}$, %HAM2-PD 11/99 Listb J.~List$^{11}$, %DFLC-PD 01/05 Listj N.~Loktionova$^{25}$, %LPI -PD 03/99 Loktionova R.~Lopez-Fernandez$^{23}$, %MEX2-PD 03/2 Lopezfernandez V.~Lubimov$^{24}$, %ITEP-PD 01/95 Lubimov A.-I.~Lucaci-Timoce$^{11}$, %DESY-LEFT 08/07 Lucacitimoce L.~Lytkin$^{13}$, %MPIH-PD 8/88 Lytkine A.~Makankine$^{9}$, %JINR-PD 11/02 Makankine E.~Malinovski$^{25}$, %LPI -PD 01/89 Malinovskie P.~Marage$^{4}$, %BRUX-PD 8/88 Marage Ll.~Marti$^{11}$, %DESY-ST 09/05 Marti H.-U.~Martyn$^{1}$, %AAC1-PD 8/88 Martyn S.J.~Maxfield$^{18}$, %LIVE-PD 8/88 Maxfield A.~Mehta$^{18}$, %LIVE-PD 8/88 Mehta K.~Meier$^{15}$, %HDB2-PD 8/88 Meier A.B.~Meyer$^{11}$, %DESY-PD 01/00 Meyeran H.~Meyer$^{11}$, %DFLC-ST 06/06 Meyerhe H.~Meyer$^{37}$, %WUPP-PD 8/88 Meyerhi J.~Meyer$^{11}$, %DESY-PD 8/88 Meyerj V.~Michels$^{11}$, %DESY-ST 03/05 Michels S.~Mikocki$^{7}$, %CRAC-PD 8/88 Mikocki I.~Milcewicz-Mika$^{7}$, %CRAC-ST 10/02 Milcewicz F.~Moreau$^{28}$, %ECPL-PD 01/90 Moreau A.~Morozov$^{9}$, %JINR-PD 06/99 Morozova J.V.~Morris$^{6}$, %RAL -PD 8/88 Morris M.U.~Mozer$^{4}$, %BRUX-PD 06/07 Mozer M.~Mudrinic$^{2}$, %BEOG-PD 01/07 Mudrinic K.~M\"uller$^{41}$, %ZUER-PD 8/88 Muellerk P.~Mur\'\i n$^{16,44}$, %KOSI-PD 8/88 Murin K.~Nankov$^{34}$, %SOFI-LEFT 10/07 Nankov B.~Naroska$^{12, \dagger}$, %HAM2-PD 8/88 Naroska Th.~Naumann$^{39}$, %ZEUT-PD 01/89 Naumannt P.R.~Newman$^{3}$, %BIRM-PD 10/92 Newman C.~Niebuhr$^{11}$, %DESY-PD 3/93 Niebuhr A.~Nikiforov$^{11}$, %DESY-PD 05/07 Nikiforov G.~Nowak$^{7}$, %CRAC-PD 8/88 Nowakg K.~Nowak$^{41}$, %ZUER-ST 08/05 Nowakk M.~Nozicka$^{11}$, %DESY-PD 11/06 Nozicka B.~Olivier$^{26}$, %MPIM-PD 11/04 Olivier J.E.~Olsson$^{11}$, %DESY-PD 8/88 Olsson S.~Osman$^{20}$, %LUND-ST 02/04 Osman D.~Ozerov$^{24}$, %ITEP-ST 08/98 Ozerov V.~Palichik$^{9}$, %JINR-PD 01/04 Palichik I.~Panagoulias$^{l,}$$^{11,42}$, %DESY-ST 08/04 Panagoulias M.~Pandurovic$^{2}$, %BEOG-ST 03/06 Pandurovic Th.~Papadopoulou$^{l,}$$^{11,42}$, %DESY-PD 06/04 Papadopoulou C.~Pascaud$^{27}$, %ORSA-PD 8/88 Pascaud G.D.~Patel$^{18}$, %LIVE-PD 8/88 Patel O.~Pejchal$^{32}$, %PRG2-ST 12/06 Pejchal H.~Peng$^{11}$, %DESY-LEFT 08/07 Peng E.~Perez$^{10,45}$, %SACL-PD 10/07 Perez A.~Petrukhin$^{24}$, %ITEP-ST 01/01 Petrukhin I.~Picuric$^{30}$, %PODG-PD 01/06 Picuric S.~Piec$^{39}$, %ZEUT-ST 01/06 Piec D.~Pitzl$^{11}$, %DESY-PD 8/88 Pitzl R.~Pla\v{c}akyt\.{e}$^{11}$, %DESY-PD 10/06 Placakyte R.~Polifka$^{32}$, %PRG2-ST 10/06 Polifka B.~Povh$^{13}$, %MPIH-PD 8/88 Povh T.~Preda$^{5}$, %BUCH-PD 06/06 Preda V.~Radescu$^{11}$, %DESY-PD 10/06 Radescu A.J.~Rahmat$^{18}$, %LIVE-ST 01/05 Rahmat N.~Raicevic$^{30}$, %PODG-PD 03/2 Raicevic A.~Raspiareza$^{26}$, %MPIM-PD 12/06 Raspiareza T.~Ravdandorj$^{35}$, %ULBA-PD 06/06 Ravdandorj P.~Reimer$^{31}$, %PRAG-PD 8/88 Reimer E.~Rizvi$^{19}$, %QMWC-PD 01/05 Rizvi P.~Robmann$^{41}$, %ZUER-PD 8/88 Robmann B.~Roland$^{4}$, %BRUX-ST 12/02 Roland R.~Roosen$^{4}$, %BRUX-PD 8/88 Roosen A.~Rostovtsev$^{24}$, %ITEP-PD 8/88 Rostovtsev M.~Rotaru$^{5}$, %BUCH-ST 02/07 Rotaru J.E.~Ruiz~Tabasco$^{22}$, %MEX1-ST 09/06 Ruiztabascojuliaelis Z.~Rurikova$^{11}$, %DESY-PD 05/06 Rurikova S.~Rusakov$^{25}$, %LPI -PD 8/88 Rusakov D.~Salek$^{32}$, %PRG2-ST 11/06 Salek F.~Salvaire$^{11}$, %DESY-LEFT 09/07 Salvaire D.P.C.~Sankey$^{6}$, %RAL -PD 8/88 Sankey M.~Sauter$^{40}$, %ZUTH-ST 10/05 Sauter E.~Sauvan$^{21}$, %MARS-PD 11/1 Sauvan S.~Schmidt$^{11}$, %DFLC-LEFT 09/07 Schmidts S.~Schmitt$^{11}$, %DESY-PD 09/07 Schmittst C.~Schmitz$^{41}$, %ZUER-ST 10/03 Schmitz L.~Schoeffel$^{10}$, %SACL-PD 12/98 Schoeffel A.~Sch\"oning$^{11,41}$, %ZUER-PD 02/99 Schoening H.-C.~Schultz-Coulon$^{15}$, %HDB2-PD 01/04 Schultzcoulon F.~Sefkow$^{11}$, %DFLC-PD 09/99 Sefkow R.N.~Shaw-West$^{3}$, %BIRM-ST 10/04 Shawwest I.~Sheviakov$^{25}$, %LPI -PD 01/90 Sheviakov L.N.~Shtarkov$^{25}$, %LPI -PD 8/88 Shtarkov S.~Shushkevich$^{26}$, %MPIM-ST 08/07 Shushkevich T.~Sloan$^{17}$, %LANC-PD 1/96 Sloan I.~Smiljanic$^{2}$, %BEOG-PD 03/06 Smiljanic P.~Smirnov$^{25}$, %LPI -LEFT 08/07 Smirnov Y.~Soloviev$^{25}$, %LPI -PD 8/88 Soloviev P.~Sopicki$^{7}$, %CRAC-ST 09/07 Sopicki D.~South$^{8}$, %DORT-PD 06/03 South V.~Spaskov$^{9}$, %JINR-PD 12/97 Spaskov A.~Specka$^{28}$, %ECPL-PD 3/95 Specka Z.~Staykova$^{11}$, %DESY-ST 08/06 Staykova M.~Steder$^{11}$, %DESY-ST 05/05 Steder B.~Stella$^{33}$, %ROME-PD 8/88 Stella U.~Straumann$^{41}$, %ZUER-PD 8/88 Straumann D.~Sunar$^{4}$, %ANTW-ST 03/05 Sunar T.~Sykora$^{4}$, %ANTW-PD 01/06 Sykora V.~Tchoulakov$^{9}$, %JINR-PD 05/03 Tchoulakov G.~Thompson$^{19}$, %QMWC-PD 8/88 Thompsong P.D.~Thompson$^{3}$, %BIRM-PD 08/99 Thompsonp T.~Toll$^{11}$, %DESY-ST 07/05 Toll F.~Tomasz$^{16}$, %KOSI-PD 07/05 Tomasz T.H.~Tran$^{27}$, %ORSA-ST 10/06 Tran D.~Traynor$^{19}$, %QMWC-PD 12/01 Traynor T.N.~Trinh$^{21}$, %MARS-ST 11/05 Trinh P.~Tru\"ol$^{41}$, %ZUER-PD 8/88 Truoel I.~Tsakov$^{34}$, %SOFI-PD 04/03 Tsakov B.~Tseepeldorj$^{35,51}$, %ULBA-PD 06/06 Tseepeldorj I.~Tsurin$^{39}$, %ZEUT-LEFT 09/07 Tsurin J.~Turnau$^{7}$, %CRAC-PD 8/88 Turnau E.~Tzamariudaki$^{26}$, %MPIM-LEFT 08/07 Tzamariudaki K.~Urban$^{15}$, %HDB2-ST 04/05 Urbank A.~Valk\'arov\'a$^{32}$, %PRG2-PD 8/88 Valkarova C.~Vall\'ee$^{21}$, %MARS-PD 8/88 Vallee P.~Van~Mechelen$^{4}$, %ANTW-PD 12/98 Vanmechelen A.~Vargas Trevino$^{11}$, %DFLC-PD 02/07 Vargastrevino Y.~Vazdik$^{25}$, %LPI -PD 8/88 Vazdik S.~Vinokurova$^{11}$, %DESY-ST 09/02 Vinokurova V.~Volchinski$^{38}$, %YERE-PD 12/01 Volchinski D.~Wegener$^{8}$, %DORT-PD 8/88 Wegener M.~Wessels$^{11}$, %DESY-LEFT 10/07 Wessels Ch.~Wissing$^{11}$, %DESY-PD 07/06 Wissing E.~W\"unsch$^{11}$, %DESY-PD 8/88 Wuensch V.~Yeganov$^{38}$, %YERE-LEFT 09/07 Yeganov J.~\v{Z}\'a\v{c}ek$^{32}$, %PRG2-PD 8/88 Zacek J.~Z\'ale\v{s}\'ak$^{31}$, %PRAG-PD 01/05 Zalesak Z.~Zhang$^{27}$, %ORSA-PD 10/92 Zhang A.~Zhelezov$^{24}$, %ITEP-LEFT 07/07 Zhelezov A.~Zhokin$^{24}$, %ITEP-PD 04/99 Zhokine Y.C.~Zhu$^{11}$, %DESY-LEFT 10/07 Zhu T.~Zimmermann$^{40}$, %ZUTH-ST 09/04 Zimmermannt H.~Zohrabyan$^{38}$, %YERE-PD 11/02 Zohrabyan and F.~Zomer$^{27}$ %ORSA-PD 8/88 Zomer %-- H1 Institutes \bigskip{\it $ ^{1}$ I. Physikalisches Institut der RWTH, Aachen, Germany$^{ a}$ \\ $ ^{2}$ Vinca Institute of Nuclear Sciences, Belgrade, Serbia \\ $ ^{3}$ School of Physics and Astronomy, University of Birmingham, Birmingham, UK$^{ b}$ \\ $ ^{4}$ Inter-University Institute for High Energies ULB-VUB, Brussels; Universiteit Antwerpen, Antwerpen; Belgium$^{ c}$ \\ $ ^{5}$ National Institute for Physics and Nuclear Engineering (NIPNE) , Bucharest, Romania \\ $ ^{6}$ Rutherford Appleton Laboratory, Chilton, Didcot, UK$^{ b}$ \\ $ ^{7}$ Institute for Nuclear Physics, Cracow, Poland$^{ d}$ \\ $ ^{8}$ Institut f\"ur Physik, TU Dortmund, Dortmund, Germany$^{ a}$ \\ $ ^{9}$ Joint Institute for Nuclear Research, Dubna, Russia \\ $ ^{10}$ CEA, DSM/DAPNIA, CE-Saclay, Gif-sur-Yvette, France \\ $ ^{11}$ DESY, Hamburg, Germany \\ $ ^{12}$ Institut f\"ur Experimentalphysik, Universit\"at Hamburg, Hamburg, Germany$^{ a}$ \\ $ ^{13}$ Max-Planck-Institut f\"ur Kernphysik, Heidelberg, Germany \\ $ ^{14}$ Physikalisches Institut, Universit\"at Heidelberg, Heidelberg, Germany$^{ a}$ \\ $ ^{15}$ Kirchhoff-Institut f\"ur Physik, Universit\"at Heidelberg, Heidelberg, Germany$^{ a}$ \\ $ ^{16}$ Institute of Experimental Physics, Slovak Academy of Sciences, Ko\v{s}ice, Slovak Republic$^{ f}$ \\ $ ^{17}$ Department of Physics, University of Lancaster, Lancaster, UK$^{ b}$ \\ $ ^{18}$ Department of Physics, University of Liverpool, Liverpool, UK$^{ b}$ \\ $ ^{19}$ Queen Mary and Westfield College, London, UK$^{ b}$ \\ $ ^{20}$ Physics Department, University of Lund, Lund, Sweden$^{ g}$ \\ $ ^{21}$ CPPM, CNRS/IN2P3 - Univ. Mediterranee, Marseille, France \\ $ ^{22}$ Departamento de Fisica Aplicada, CINVESTAV, M\'erida, Yucat\'an, M\'exico$^{ j}$ \\ $ ^{23}$ Departamento de Fisica, CINVESTAV, M\'exico$^{ j}$ \\ $ ^{24}$ Institute for Theoretical and Experimental Physics, Moscow, Russia \\ $ ^{25}$ Lebedev Physical Institute, Moscow, Russia$^{ e}$ \\ $ ^{26}$ Max-Planck-Institut f\"ur Physik, M\"unchen, Germany \\ $ ^{27}$ LAL, Univ Paris-Sud, CNRS/IN2P3, Orsay, France \\ $ ^{28}$ LLR, Ecole Polytechnique, IN2P3-CNRS, Palaiseau, France \\ $ ^{29}$ LPNHE, Universit\'{e}s Paris VI and VII, IN2P3-CNRS, Paris, France \\ $ ^{30}$ Faculty of Science, University of Montenegro, Podgorica, Montenegro$^{ e}$ \\ $ ^{31}$ Institute of Physics, Academy of Sciences of the Czech Republic, Praha, Czech Republic$^{ h}$ \\ $ ^{32}$ Faculty of Mathematics and Physics, Charles University, Praha, Czech Republic$^{ h}$ \\ $ ^{33}$ Dipartimento di Fisica Universit\`a di Roma Tre and INFN Roma~3, Roma, Italy \\ $ ^{34}$ Institute for Nuclear Research and Nuclear Energy, Sofia, Bulgaria$^{ e}$ \\ $ ^{35}$ Institute of Physics and Technology of the Mongolian Academy of Sciences , Ulaanbaatar, Mongolia \\ $ ^{36}$ Paul Scherrer Institut, Villigen, Switzerland \\ $ ^{37}$ Fachbereich C, Universit\"at Wuppertal, Wuppertal, Germany \\ $ ^{38}$ Yerevan Physics Institute, Yerevan, Armenia \\ $ ^{39}$ DESY, Zeuthen, Germany \\ $ ^{40}$ Institut f\"ur Teilchenphysik, ETH, Z\"urich, Switzerland$^{ i}$ \\ $ ^{41}$ Physik-Institut der Universit\"at Z\"urich, Z\"urich, Switzerland$^{ i}$ \\ \bigskip $ ^{42}$ Also at Physics Department, National Technical University, Zografou Campus, GR-15773 Athens, Greece \\ $ ^{43}$ Also at Rechenzentrum, Universit\"at Wuppertal, Wuppertal, Germany \\ $ ^{44}$ Also at University of P.J. \v{S}af\'{a}rik, Ko\v{s}ice, Slovak Republic \\ $ ^{45}$ Also at CERN, Geneva, Switzerland \\ $ ^{46}$ Also at Max-Planck-Institut f\"ur Physik, M\"unchen, Germany \\ $ ^{47}$ Also at Comenius University, Bratislava, Slovak Republic \\ $ ^{48}$ Also at DESY and University Hamburg, Helmholtz Humboldt Research Award \\ $ ^{49}$ Also at Faculty of Physics, University of Bucharest, Bucharest, Romania \\ $ ^{50}$ Supported by a scholarship of the World Laboratory Bj\"orn Wiik Research Project \\ $ ^{51}$ Also at Ulaanbaatar University, Ulaanbaatar, Mongolia \\ \smallskip $ ^{\dagger}$ Deceased \\ \bigskip $ ^a$ Supported by the Bundesministerium f\"ur Bildung und Forschung, FRG, under contract numbers 05 H1 1GUA /1, 05 H1 1PAA /1, 05 H1 1PAB /9, 05 H1 1PEA /6, 05 H1 1VHA /7 and 05 H1 1VHB /5 \\ $ ^b$ Supported by the UK Science and Technology Facilities Council, and formerly by the UK Particle Physics and Astronomy Research Council \\ $ ^c$ Supported by FNRS-FWO-Vlaanderen, IISN-IIKW and IWT and by Interuniversity Attraction Poles Programme, Belgian Science Policy \\ $ ^d$ Partially Supported by Polish Ministry of Science and Higher Education, grant PBS/DESY/70/2006 \\ $ ^e$ Supported by the Deutsche Forschungsgemeinschaft \\ $ ^f$ Supported by VEGA SR grant no. 2/7062/ 27 \\ $ ^g$ Supported by the Swedish Natural Science Research Council \\ $ ^h$ Supported by the Ministry of Education of the Czech Republic under the projects LC527 and INGO-1P05LA259 \\ $ ^i$ Supported by the Swiss National Science Foundation \\ $ ^j$ Supported by CONACYT, M\'exico, grant 48778-F \\ $ ^l$ This project is co-funded by the European Social Fund (75\%) and National Resources (25\%) - (EPEAEK II) - PYTHAGORAS II \\ } \end{flushleft} \newpage %\linenumbers %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % %% \section{Introduction} \noindent The study at the $ep$ collider HERA of exclusive diffractive processes in the presence of a hard scale has provided insight into the parton dynamics of the diffractive exchange. The four-momentum squared transferred at the proton vertex, $t$, provides a relevant scale to investigate the application of perturbative Quantum Chromodynamics (pQCD) for $\tmod \gg \Lambda^2_{\rm QCD}$ \cite{Forshaw:1997wn}. In this Letter, the first measurement at large $t$ ($\tmod>4$~GeV$^2$) of diffractive photon-proton scattering, $\gamma p \to \gamma Y$, where $Y$ is the proton dissociative system, is presented. The measurement is performed at HERA by studying the reaction $e^+ p \to e^+ \gamma Y$ in the photoproduction regime with a large rapidity gap between the final state photon and the proton dissociative system~$Y$ (as illustrated in figure \ref{fig:PhotonDiag}a). The centre of mass energy of the system formed by the exchanged photon and proton is in the range $1758~\mathrm{GeV}$ and a transverse momentum $\ptgamma>2~\mathrm{GeV}$. The hadronic final state $Y$ is reconstructed using a combination of tracking and calorimetric information. The difference between the total energy $E$ and the longitudinal component of the total momentum $P_z$, as calculated from the scattered positron, the final state photon and the hadronic system~$Y$, is restricted to $49<\Sigma(E-P_z)<61$ GeV. This requirement suppresses non-$ep$ induced background and background due to the overlap during the same bunch crossing of a Bethe-Heitler event with a DIS event. For a fully contained $ep$ event the relation \linebreak $\Sigma(E-P_z)= 2 E_e = 55$~GeV holds. In the case that charged particles from the final state are detected by the tracking detector, allowing the primary vertex to be reconstructed, the $z$ coordinate of the vertex has to satisfy $|z| < 35$~cm. For $25\%$ of the selected events, all charged particles of the final state lie outside the detector acceptance and no event vertex is reconstructed. In this case, the time averaged vertex position is used for the kinematic reconstruction. The kinematic variable $\tmod$ is reconstructed as: \begin{equation} \nonumber \tmod = (\ptgamma)^2 \, , \end{equation} %NEW with a relative resolution of $11\%$. The longitudinal momentum fraction of the diffractive exchange with respect to the proton is reconstructed using the formula: %\begin{linenomath} \begin{equation} \nonumber \xpom \simeq \frac{(E+P_z)_\gamma}{2E_{p}}, \end{equation} %\end{linenomath} where $(E+P_z)_\gamma$ is the sum of the energy and longitudinal momentum of the final state photon. The event inelasticity of the $\gamma p$ interaction is reconstructed as: %\begin{linenomath} \begin{equation} \nonumber \ypom \simeq \frac{\sum_Y(E-P_z)}{2(E_e - E_{e'})}, \end{equation} %\end{linenomath} where the summation is performed on all detected hadronic final state particles in the event, i.e. all measured particles except the scattered positron and the final state photon. This reconstruction method has the advantage that the loss of particles along the forward beam pipe only has a marginal effect on the reconstruction of $\ypom$. Diffractive events are selected by requiring that $\ypom < 0.05$. The cut value ensures a large pseudorapidity gap, $\Delta \eta$, between the photon and the proton dissociative system~$Y$, since $\ypom \simeq e^{-\Delta \eta}$. %NEW %The resolution in $W$ is $4\%$ and in $\tmod$ of $11\%$. Finally, to reduce contamination of the signal by non-diffractive background, it is required that the difference in pseudorapidity between the photon and the closest final state hadron satisfies $\Delta \eta>2$. %NEW This rapidity gap is inferred from the absence of activity in the relevant detector parts, i.e.\ absence of any track or a cluster of energy deposits above the noise threshold of $400$ MeV in the LAr calorimeter.~\footnote{ The noise level of the LAr calorimeter is about $10$ MeV per cell and the average number of cells per cluster is typically $60$.} After applying all selection criteria, 240 events remain in the data sample. \section{Monte Carlo Simulations and Comparison to Data} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \label{sec:mc} Monte Carlo (MC) simulations are used to correct the data for effects of detector acceptance and efficiency, to estimate the background and to compare model predictions to the data. All generated MC events are passed through the full GEANT\cite{Brun:1987ma} based simulation of the H1 detector and are reconstructed using the same analysis chain as is used for the data. The {\sc HERWIG} 6.4 \cite{Marchesini:1991ch} MC event generator is used to simulate the diffractive high $\tmod$ photon scattering using the LLA BFKL model \cite{Ivanov:1998jw,Evanson:1999zb,Cox:1999kv}. At leading logarithmic accuracy there are two independent free parameters in the BFKL calculation: the value of the strong coupling $\alpha_s$ and the scale, $c$, which defines the leading logarithms in the expansion of the BFKL amplitude, $\ln(W^2/(c \ \tmod))$. %NEW In exclusive production of vector mesons, the scale parameter $c$ is related to the vector meson mass. In the case of diffractive photon scattering, the unknown scale results in the absence of a prediction for the normalisation of the cross section~\cite{Cox:1999dw}. In the calculations considered here \cite{Cox:1999kv}, the running of $\alpha_s$ as a function of the scale is ignored. In order to distinguish the $\alpha_s$ parameter of the LLA BFKL model from the usual strong coupling constant this parameter will henceforth be referred to as $\alpeff$. The choice of $\alpeff=0.17$ is used for the simulation in this Letter. In the asymptotic approximation of the calculations \cite{Cox:1999kv}, the W distribution follows a power-law: \begin{equation} \nonumber \sigma(W) \sim W^{4\omega_0}, \label{eq:omega} \end{equation} where the exponent, also called the Pomeron intercept, is given directly by the choice of $\alpeff$ with $\omega_0 = (3\alpeff/{\pi})\ 4\ \ln 2$. Using the {\sc HERWIG} simulation this approximation is found to be justified given the current experimental statistical precision. The LLA BFKL model predicts an approximate power-law behaviour for the $t$ dependence of the cross section of the form ${\rm d}\sigma/{\rm d}\tmod \sim \tmod^{-n}$, where $n$, also predicted by the model, depends only on the parton density functions (PDFs) of the proton and the value of $\alpeff$. Running coupling effects, not considered here, would in principle allow $n$ to depend on $t$. The GRV94 PDFs \cite{Gluck:1994uf} are used for the proton PDFs in the {\sc HERWIG} prediction. A comparison with the CTEQ5 \cite{Lai:1999wy} and MRST PDFs \cite{Martin:2002dr} shows little dependence of the {\sc HERWIG} prediction on the input proton PDFs. In order to describe the data, the $t$ dependence of the diffractive photon scattering simulated using {\sc HERWIG} %NEW (predicting a value of $n = 3.31$ for $\alpeff = 0.17$) was weighted by a factor $|t|^{0.73}$, i.e.\ the $\tmod$ power is modified from $-3.31$ to $-2.58$. This weighted {\sc HERWIG} prediction is used to correct the data for resolution and acceptance effects. Possible sources of background are estimated using MC simulations. The background from inclusive diffractive photoproduction events ($e p \to e X Y$, where the two hadronic final states are separated by a rapidity gap) is simulated using the {\sc PHOJET} MC event generator \cite{Bopp:1998rc}. This background contributes when a single electromagnetic particle fakes the photon candidate in the SpaCal. It is estimated to amount to $3\%$ of the measured cross section. The background from electron pair production ($ep \rightarrow ee^+e^-X$) is modelled using the {\sc GRAPE} event generator \cite{Abe:2000cv}. This process contributes to the selection if one lepton is detected in the ET, a second lepton fakes the photon within the SpaCal and the remaining lepton escapes detection. This background contributes $4\%$ of the measured cross section. In order to investigate the background from high $\tmod$ diffractive exclusive $\omega$ production, where the $\omega$ decays through the $\pi^+\pi^-\pi^0$ or $\pi^0\gamma$ channel, a sample was generated using the {\sc DIFFVM} Monte Carlo generator \cite{List:1998jz}. The contribution from this background process is found to be negligible. The background from DIS events, in which the scattered positron fakes the photon candidate and an overlapping photoproduction or Bethe-Heitler event gives a positron detected in the ET, has been studied and was also found to be negligible. In figure~\ref{fig:control} the data, corrected for trigger efficiency, are compared to the Monte Carlo simulations. The background predictions from {\sc GRAPE} and {\sc PHOJET} are normalised to the integrated luminosity of the data sample. The weighted {\sc HERWIG} prediction is normalised to the number of events obtained after the subtraction of the predicted background from the data. A good description of the data by the combined Monte Carlo simulations is observed. \section{Cross Section Measurement} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% The $e p \to e \gamma Y$ differential cross sections are defined using the formula: \begin{equation} \nonumber \frac{{\rm d^2}\sigma_{ep \to e \gamma Y}}{{\rm d} W \ {\rm d}t} = \frac{N_{data} - N_{bgr}}{{\cal L} A\, \Delta W \, \Delta t}, \end{equation} where $N_{data}$ is the number of observed events corrected for trigger efficiency, $N_{bgr}$ the expected contribution from background events as estimated using the {\sc PHOJET} and {\sc GRAPE} Monte Carlos simulations, ${\cal L}$ the integrated luminosity, $A$ the signal acceptance and $\Delta W$ and $\Delta t$ the bin widths in $W$ and $t$, respectively. The acceptance, estimated using the weighted {\sc HERWIG} simulation, is the ratio of the number of events accepted after reconstruction to the number of events generated in the defined phase space on hadron level. It accounts for all detector effects, including bin-to-bin migrations, as well as geometrical acceptance and detector efficiencies. QED radiative correction effects are estimated to be less than $1$\% \cite{DESY-95-162} and are neglected. The $\gamma p \to \gamma Y$ differential cross section is then extracted from the $ep$ cross section using: \begin{equation} \frac{{\rm d^2}\sigma_{ep \to e \gamma Y}}{{\rm d} W \ {\rm d}t} = \Gamma(W) \ \frac{{\rm d}\sigma_{\gamma p \to \gamma Y}} {{\rm d}t}(W), \label{eq:flux} \end{equation} where the photon flux, $\Gamma(W)$, is integrated over the range $Q^2<0.01$ GeV$^2$ according to the modified Weizs\"acker-Williams approximation \cite{vonWeizsacker:1934sx}. The $\gamma p$ cross section is obtained by modelling $\sigma_{\gamma p \to \gamma Y}$ as a power-law in $W$, whose parameters are iteratively adjusted to reproduce the measured $W$ dependence of the $ep$ cross section. The differential $\gamma p$ cross section in $\tmod$ is then extracted from the $ep$ cross section by correcting for the effect of the photon flux over the visible $W$ range ($175 < W < 247$ GeV). The $\gamma p$ cross section as a function of $W$ is obtained by first integrating equation~(\ref{eq:flux}) over the $\tmod$ range, and then correcting for the effect of the photon flux in each bin in $W$. %NEW More details on the extraction procedure of the $\gamma p$ cross section can be found in \cite{Hreus08}. The systematic error on the measurement stems from experimental uncertainties and from model dependences. They are calculated using the weighted {\sc HERWIG} simulation of the signal process. The sources of systematic error are listed below. For each of them the typical effect on the cross section measurement is indicated. \noindent The experimental systematic errors are: \begin{itemize} \item The energy scale uncertainty of $\pm 1 \%$ for an electromagnetic cluster measured by the SpaCal gives errors in the range of $2\%$ to $4\%$. \item The uncertainty of $\pm2.5$~mrad for the measurement of the photon candidate polar angle results in an error of up to $3\%$. \item The hadronic final state energy scale uncertainty of $\pm 4 \%$ leads to an error of less than $1.5\%$. \item The energy scale uncertainty of $\pm 1.5 \%$ of the ET produces an error ranging from $1\%$ in the highest $\tmod$ bin to $10\%$ in the lowest $W$ bin. \item The uncertainty of $\pm 25\%$ on the noise threshold from the calorimeters gives an error varying from $5\%$ at low $\tmod$ to $11\%$ at the highest $\tmod$ value. \item The luminosity is measured with an accuracy of $\pm 1.5 \%$ which enters as an overall normalisation uncertainty. \end{itemize} \noindent The systematic errors due to uncertainty of model parameters are: \begin{itemize} \item The uncertainty due to the \xpom dependence, estimated by weighting the \xpom distribution by the form $(1/\xpom)^{\pm 0.4}$, yields an error varying from $3\%$ in the central $\tmod$ bin up to $9\%$ in the lowest $W$ bin. This weight would correspond to changing $\alpeff$ to the values $0.02$ and $0.31$. \item The uncertainty due to the $\tmod$ dependence, estimated by weighting the $\tmod$ distribution by the form $(1/\tmod)^{\pm 0.2}$, leads to an error ranging from $1.5\%$ to $4\%$. \item The uncertainty in the modelling of the proton remnant system~$Y$, estimated by weighting the $M_Y$ distribution by the form $(1/M_Y^2)^{\pm 0.3}$, results in a typical error of $1\%$ to $4\%$. \item The uncertainty of $100\%$ assumed on the normalisation of the subtracted inclusive diffractive background (from the {\sc PHOJET} Monte Carlo simulation) leads to an error of approximately $3\%$ in the highest $W$ bins decreasing to $1\%$ in the highest $\tmod$ bin. \item The propagation of the uncertainty on the power-law parameter $\delta$ in the $\gamma p$ cross section extraction procedure leads to an error of $4\%$ on ${\rm d}\sigma_{\gamma p \to \gamma Y}/{\rm d}\tmod$, independent of $\tmod$, and is below 1\% on $\sigma_{\gamma p \to \gamma Y}$. \end{itemize} The uncertainty on the PHOJET MC normalisation and the model uncertainties from the unknown \xpom, $\tmod$ and $M_Y$ dependences are estimated from data comparisons and defined by the range where the model describes the data. %The uncertainty on the PHOJET MC normalisation and the size of the %variation of the model dependence on \xpom, $\tmod$ %and $M_Y$, are estimated from the measured distributions %in the data. % %size of the %variation of the model dependence on \xpom, $\tmod$ %and $M_Y$, are estimated by comparison to data: %is estimated from the compatibility with the data % %The uncertainty on the PHOJET MC normalisation and the size of the %variation of the model dependence on \xpom, $\tmod$ %and $M_Y$, are estimated by comparison to data: %the variation corresponds to the range where the model %describes the data. Each source of systematic error is varied in the weighted HERWIG Monte Carlo within its uncertainty. In each measurement bin, the corresponding deviation of the normalised cross section from the central value is taken as systematic error. The total systematic error is obtained by adding the individual contributions in quadrature, on a bin-by-bin basis. The largest systematic error on the cross sections comes from the uncertainty on the \xpom and $M_Y$ dependences in the MC simulation. The total systematic error on the $W$ dependence of the cross section varies from $10\%$ in the central bins to $17\%$ in the lowest bin. The systematic error on the $\tmod$ dependence of the cross section varies from $8\%$ in the lowest bin to $14\%$ in the highest bin. An additional global uncertainty of 4\% arises from the $\gamma p$ cross section extraction procedure. The total systematic errors are comparable to or smaller than the statistical errors. \section{Results} %%%%%%%%%%%%%%%%% The cross sections measured for the domain $175 < W < 247~\mathrm{GeV}$, $4 < \tmod < 36$ GeV$^2$, $\ypom < 0.05$ and $\qsq<0.01\gevsq$ are presented in table \ref{CSvalues}. The $\gamma p \rightarrow \gamma Y$ cross section as a function of $W$ is shown in figure~\ref{fig:SigmaW}. A power-law dependence of the form $\sigma \sim W^{\delta}$ is fitted to the measured cross section. The fit yields $\wfitres$ with $\chi^2/\textrm{n.d.f.}=2.7/2$. The contributions from the systematic errors are calculated by shifting the data points according to each source of uncertainty, taking correlations into account, and repeating the fit. The errors are then added in quadrature to obtain the total systematic error. The steep rise of the cross section with $W$ is usually interpreted as an indication of the presence of a hard sub-process in the diffractive interaction and of the applicability of perturbative QCD. The present $\delta$ value, measured at an average $\tmod$ value of $6.1$~GeV$^2$, is compatible with that measured by H1 in diffractive $J/\psi$ photoproduction of $\delta=1.29 \pm0.23 (\mathrm{stat.})\pm 0.16(\mathrm{syst.})$ \cite{Aktas:2003zi} at an average $\tmod$ of $6.9$~GeV$^2$. The Pomeron intercepts associated with these $\delta$ values correspond to the strongest energy dependences measured in diffractive processes. %cross-section values \begin{table} \begin{center} \begin{tabular}{|c|c|c|c|c|} \hline \multicolumn{5}{|c|}{H1 measured $ep \rightarrow e \gamma Y$ cross sections}\\ \hline $W$ & $W$ range & ${\rm d}\sigma_{ep \rightarrow e \gamma Y}/{\rm d}W$ & $\Gamma(W)$ & $\sigma_{\gamma p \rightarrow \gamma Y}$ \\ ~[GeV] & [GeV] & $[$pb/GeV$]$ & [GeV$^{-1}$] & [nb] \\ \hline $185$ & $175-193$ & $0.414 \pm 0.069 \pm 0.072$ & $0.0565$ & $2.02 \pm 0.34 \pm 0.35$\\ $202$ & $193-211$ & $0.318 \pm 0.046 \pm 0.033$ & $0.0431$ & $1.86 \pm 0.27 \pm 0.19$\\ $220$ & $211-229$ & $0.434 \pm 0.062 \pm 0.051$ & $0.0328$ & $3.06 \pm 0.44 \pm 0.36$\\ $240$ & $229-247$ & $0.404 \pm 0.080 \pm 0.044$ & $0.0246$ & $3.48 \pm 0.69 \pm 0.38$\\ \hline \hline $|t|$ & $|t|$ range & d$\sigma_{ep \rightarrow e \gamma Y}/{\rm d}|t|$ & $\Gamma(W=219~\mathrm{GeV})$ & d$\sigma_{\gamma p \rightarrow \gamma Y}/$d$|t|$\\ ~[GeV$^2$]& [GeV$^2$]& $[$pb/GeV$^2]$ & [GeV$^{-1}$] & [pb/GeV$^2$] \\ \hline $ 6$ & $4.0-8.3 $ & $4.04 \pm 0.42 \pm 0.36$ & $0.0333$ & $401 \pm 41 \pm 36$ \\ $12$ & $8.3-17.3$ & $0.58 \pm 0.08 \pm 0.06$ & $0.0333$ & $ 57.8 \pm 8.1 \pm 6.2 $\\ $25$ & $17.3-36.0$ & $0.13 \pm 0.03 \pm 0.02$ & $0.0333$ & $ 12.5 \pm 3.1 \pm 1.8 $\\ \hline \end{tabular} \caption{The cross sections for the processes $ep \rightarrow e \gamma Y$ and the $\gamma p \rightarrow \gamma Y$, measured in the range $\ypom < 0.05$ and $\qsq<0.01\gevsq$. The upper part of the table presents the measured cross sections for different values of $W$ at an average $\langle \tmod \rangle =6.1$ GeV$^2$. The lower table presents the measured cross sections differential in $\tmod$ at $W=219$ GeV. The first errors are statistical, the second systematic. The photon flux $\Gamma$ and corresponding ranges in $W$ and $\tmod$ used for the measurements are also given.} \label{CSvalues} \end{center} \end{table} The $\gamma p$ cross section differential in $\tmod$, at $W=219$ GeV, is shown in figure~\ref{fig:Sigmat}. Figure \ref{fig:Sigmat} also shows the comparison of the cross section to a fit of the form ${\rm d}\sigma/{\rm d}t \sim \left|t\right|^{-n}$. The fit result is $\tfitres$ with $\chi^2/\textrm{n.d.f.}=1.6/1$. The $\tmod$ dependence is harder than that measured by H1 in the diffractive photoproduction of $J/\psi$ mesons at large $|t|$ \cite{Aktas:2003zi} corresponding to $n=3.78\pm0.17(\mathrm{stat.})\pm 0.06(\mathrm{syst.})$. In figures~\ref{fig:SigmaW} and \ref{fig:Sigmat} the measured cross sections are compared to predictions of the LLA BFKL model, using the {\sc HERWIG} Monte Carlo, as described in section \ref{sec:mc}, with no $\tmod$ weighting. The predictions are normalised to the integrated measured cross section, as the normalisation is not predicted by the LLA BFKL calculation \cite{Cox:1999dw}. The $W$ dependence of the cross section is well described by the LLA BFKL prediction, as shown in figure~\ref{fig:SigmaW}. The sensitivity of the measurement to the free parameter $\alpeff$ in the theoretical prediction is illustrated in figures~\ref{fig:SigmaW} and \ref{fig:Sigmat}. Using $\delta= 4\, \omega_0 = 4\ (3\alpha_S^{Fit}/{\pi})\ 4\ \ln 2$, the measured $W$ dependence leads to $\alphasfitres$. Predictions are shown in figure~\ref{fig:SigmaW} for the values $\alpeff=0.14$ and $0.37$. The LLA BFKL curve corresponding to $\alpeff=0.26$ coincides with the solid fit line. Previous measurements of diffractive scattering at HERA are well described by BFKL predictions with $\alpeff$ values similar to the value measured in this Letter. ZEUS measurements of exclusive $\rho, \phi$ and $J/\psi$ production at large $|t|$ are best described with the value of $\alpeff=0.20$ \cite{Chekanov:2002rm}. The H1 measurement of high $\tmod$ $\rho$ production \cite{Aktas:2006qs} is compatible with $\alpeff=0.20$ and the H1 measurement of high $\tmod$ $J/\psi$ production \cite{Aktas:2003zi} is described using $\alpeff=0.18$. The LLA BFKL prediction with $\alpeff =0.17$ gives a good description of the double dissociation process with a rapidity gap between jets measured by H1 \cite{Adloff:2002em}. Events with rapidity gaps between jets were also measured by ZEUS \cite{Chekanov:2006pw} and are found to be compatible with a model which uses $\alpeff =0.11$. Note, however, that for these measurements the hard scale, corresponding to the jet transverse momentum squared, is of the order of or larger than $20$ GeV$^2$. As shown in figure~\ref{fig:Sigmat}, the LLA BFKL calculation for $\alpeff=0.14, 0.26$ and $0.37$, all of which give a reasonable description of the $W$ dependence, predict steeper $\tmod$ distributions than is measured in the data. The same effect cannot be established for the exclusive $\rho$ measurement \cite{Aktas:2006qs}, where the measured $t$ range is limited to $\tmod < 8$ GeV$^2$, although an underestimate of the cross section was observed at the largest values of $\tmod$. The present situation is in contrast with the analysis of $J/\psi$ production \cite{Chekanov:2002rm,Aktas:2003zi}, where the $\tmod$ dependence was found to be well described by the LLA BFKL prediction over a similar range in $t$. %In the present discussion it is worth bearing in mind that there may %be important contributions from higher order effects beyond the LLA. %In particular considering a running $\alpeff$ could in principle modify the %predicted $\tmod$ distribution. \section{Conclusions} %%%%%%%%%%%%%%%%%%%%% Using the H1 detector, diffractive photon scattering, $\gamma p\rightarrow \gamma Y$, where the final state photon carries a large transverse momentum and is well separated from the proton dissociative system~$Y$, is measured for the first time at HERA. The measurement provides a unique test of the underlying QCD dynamics of the diffractive exchange. Cross sections are presented as a function of $W$ and differentially in $|t|$. A fit of the form $W^\delta$ performed on the cross section gives \wfitres. This strong energy dependence is compatible with that measured for the exclusive diffractive $J/\psi$ production at high $\tmod$. A fit of the form $\tmod^{-n}$ yields \tfitres, corresponding to a harder $\tmod$ dependence of the cross section than measured for high $\tmod$ diffractive $J/\psi$ production. The measured cross sections are compared to the predictions of an LLA BFKL model. A good description of the $W$ dependence of the cross section is found, whereas the LLA BFKL model predicts a $\tmod$ dependence that is too soft and hence unable to describe the data. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section*{Acknowledgements} We are grateful to the HERA machine group whose outstanding efforts have made this experiment possible. We thank the engineers and technicians for their work in constructing and maintaining the H1 detector, our funding agencies for financial support, the DESY technical staff for continual assistance and the DESY directorate for support and for the hospitality which they extend to the non DESY members of the collaboration. 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The data corrected for trigger efficiency (black points) are compared with the simulation of diffractive high $\tmod$ photons from the weighted {\sc HERWIG} based on the LLA BFKL calculation (open histogram), and the background from inclusive diffractive photoproduction simulated with {\sc PHOJET} (full histogram) and dilepton production simulated with {\sc GRAPE} (hatched histogram). The {\sc HERWIG} prediction is normalised to the number of data events after background subtraction. The total systematic uncertainty of the simulation is shown by the dark grey shaded band. } \label{fig:control} \end{figure} \begin{figure}[!p] \centering \epsfig{file=d08-077f3.eps,width=0.68\textwidth} \caption{The $\gamma p$ cross section of diffractive scattering of photons as a function of $W$ in the phase space defined by $4 < \tmod < 36$\gevsq , $\ypom < 0.05$ and $\qsq<0.01\gevsq$. The average value is $\langle \tmod \rangle =6.1$ GeV$^2$. The inner error bars show the statistical errors and the outer error bars show the statistical and systematic errors added in quadrature. The solid line shows the result of a fit to the cross section of the form $W^\delta$ with $\wfitres$. This line also corresponds to the LLA BFKL model prediction from the {\sc HERWIG} event generator with $\alpeff = 0.26$. Two additional curves show the LLA BFKL predictions for the additional choices of $\alpeff = 0.14$ and $0.37$ corresponding to one standard deviation from the fit value. } \label{fig:SigmaW} \end{figure} \begin{figure}[!p] \centering \epsfig{file=d08-077f4.eps,width=0.68\textwidth} \caption{The $\gamma p$ cross section of diffractive scattering of photons differential in $\tmod$ for $W=219$~GeV, $\ypom < 0.05$ and $\qsq<0.01\gevsq$. The inner error bars show the statistical errors and the outer error bars show the statistical and systematic errors added in quadrature. The solid line shows the result of a fit to the cross sections of the form $\tmod^{-n}$ with $\tfitres$. Three additional curves show the LLA BFKL model predictions from the {\sc HERWIG} event generator for the values $\alpeff = 0.14, 0.26$ and $0.37$. } \label{fig:Sigmat} \end{figure} \end{document}