%================================================================ % LaTeX file with prefered layout for H1 paper drafts % use: dvips -D600 file-name %================================================================ %%%%%%%%%%%%% LATEX HEADER %%%%%%%%%%%%% DO NOT DELET NOT CHANGE ANYTHING IN THE HEADER %%%%%%%%%%%%% UNLESS CLEARLY RECOMMENDED \documentclass[12pt]{article} \usepackage{multirow} \usepackage{epsfig} \usepackage{amsmath} \usepackage{hhline} \usepackage{amssymb} \usepackage{times} \usepackage{cite} \usepackage{dcolumn} %%%%%%%%%%%% Comment the next two lines to remove the line numbering %\usepackage[]{lineno} %\linenumbers %%%%%%%%%%%% %\newcolumntype{d}[1]{D{,}{,}{2}} %\newcolumntype{d}{D{.}{.}{-1}}%\newcolumntype {d}{{.}{,}{-1}}%[1]{>{\DC@{,}{,}{#1}}c<{\DC@end }}%\newcolumntype{d}{D{,}{,}{-1}} \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 %%%%%%%%%%%%%%%% END OF LATEX HEADER %===============================title page============================= \begin{document} %%%%%%%%%%%%%%%% Pre-defined commands, you can use for the most obvious notations \newcommand{\beq}{\begin{displaymath}} \newcommand{\eeq}{\end{displaymath}} \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{\mev}{\,\mbox{MeV}} \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{\mc}{MC } \newcommand{\mcs}{MCs } \newcommand{\kt}{\ensuremath{k_T}} \newcommand{\pperp}{\ensuremath{p_\perp}} \newcommand{\ptg}{\ensuremath{\vec{p}_T^{~\gamma}}} \newcommand{\ptjet}{\ensuremath{\vec{p}_T^{~jet}}} \newcommand{\Dphi}{\ensuremath{\varDelta\varPhi}} \newcommand{\Etg}{\ensuremath{E_T^\gamma}} \newcommand{\Eg}{\ensuremath{E^\gamma}} \newcommand{\etg}{\ensuremath{E_T^\gamma}} \newcommand{\etgjet}{\ensuremath{E_T^{~\gamma\mathrm{-jet}}}} \newcommand{\etag}{\ensuremath{\eta^\gamma}} \newcommand{\etj}{\ensuremath{E_T^{\rm{jet}}}} \newcommand{\Ptj}{\ensuremath{p_T^{\rm{jet}}}} \newcommand{\ptj}{\ensuremath{p_T^{\rm{jet}}}} \newcommand{\Etj}{\ensuremath{E_T^{\rm{{jet}}}}} \newcommand{\etaj}{\ensuremath{\eta^{\rm{{jet}}}}} \newcommand{\etjet}{\ensuremath{E_T^{\rm{{jet}}}}} \newcommand{\etajet}{\ensuremath{\eta^{\rm{{jet}}}}} \newcommand{\xg}{\ensuremath{x_\gamma}} \newcommand{\xp}{\ensuremath{x_{p}}} \newcommand{\xglo}{\ensuremath{x_\gamma^{LO}}} \newcommand{\xplo}{\ensuremath{x_{p}^{LO}}} \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{\ptjn}[1]{\ensuremath{p_t(\mbox{jet$_{#1}$})}} \newcommand{\detadsj}{\ensuremath{\eta(\dstar )\, \mbox{-}\, \etaj}} \newcommand{\matrixA}{\ensuremath{\textbf{A}}} % Journal macro \def\Journal#1#2#3#4{{#1} {\bf #2} (#3) #4} \def\NCA{\em Nuovo Cimento} \def\NIM{\em Nucl. Instrum. Methods} \def\NIMA{{\em Nucl. Instrum. Methods} {\bf A}} \def\NPB{{\em Nucl. Phys.} {\bf B}} \def\PLB{{\em Phys. Lett.} {\bf B}} \def\PRL{\em Phys. Rev. Lett.} \def\PRD{{\em Phys. Rev.} {\bf D}} \def\ZPC{{\em Z. Phys.} {\bf C}} \def\EJC{{\em Eur. Phys. J.} {\bf C}} \def\CPC{\em Comp. Phys. Commun.} \begin{titlepage} \noindent \begin{flushleft} {\tt DESY 09-135 \hfill ISSN 0418-9833} \\ {\tt August 2009} \\ \end{flushleft} \noindent \noindent \vspace{2cm} \begin{center} \begin{Large} {\bf Prompt Photons in Photoproduction at HERA } \vspace{2cm} H1 Collaboration \end{Large} \end{center} \vspace{2cm} \begin{abstract} \noindent The production of prompt photons is measured in the photoproduction regime of electron-proton scattering at HERA. The analysis is based on a data sample corresponding to a total integrated luminosity of $340 $~{\rm pb}$^{-1}$ collected by the H1 experiment. Cross sections are measured for photons with transverse momentum and pseudorapidity in the range $6 < \etg < 15 $\GeV{} and $-1.0 < \etag < 2.4$, respectively. Cross sections for events with an additional jet are measured as a function of the transverse energy and pseudorapidity of the jet, and as a function of the fractional momenta $\xg$ and $\xp$ carried by the partons entering the hard scattering process. The correlation between the photon and the jet is also studied. The results are compared with QCD predictions based on the collinear and on the $k_T$ factorisation approaches. \end{abstract} \vspace{1.5cm} \begin{center} Submitted to \EJC \; \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 Aug 3 17:18:57 CEST 2009 Number of authors = 243 F.D.~Aaron$^{5,49}$, %BUCH-PD 11/06 Aaron M.~Aldaya~Martin$^{11}$, %DESY-PD 10/08 Aldayamartin C.~Alexa$^{5}$, %BUCH-PD 06/06 Alexa K.~Alimujiang$^{11}$, %DESY-PD 07/08 Alimujiang V.~Andreev$^{25}$, %LPI -PD 8/88 Andreev B.~Antunovic$^{11}$, %DESY-LEFT 12/08 Antunovic S.~Backovic$^{30}$, %PODG-PD 03/2 Backovic A.~Baghdasaryan$^{38}$, %YERE-PD 09/03 Baghdasaryana E.~Barrelet$^{29}$, %PARI-PD 11/99 Barrelet W.~Bartel$^{11}$, %DESY-PD 8/88 Bartel K.~Begzsuren$^{35}$, %ULBA-PD 04/06 Begzsuren A.~Belousov$^{25}$, %LPI -PD 8/88 Belousov J.C.~Bizot$^{27}$, %ORSA-PD 8/88 Bizot V.~Boudry$^{28}$, %ECPL-PD 1/93 Boudry I.~Bozovic-Jelisavcic$^{2}$, %BEOG-PD 03/06 Bozovicjelisavcic J.~Bracinik$^{3}$, %BIRM-PD 01/2 Bracinik G.~Brandt$^{11}$, %DESY-PD 01/20 Brandt M.~Brinkmann$^{12}$, %HAM2-ST 02/09 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 K.~Cerny$^{32}$, %PRG2-PD 09/08 Cernyk V.~Cerny$^{16,47}$, %KOSI-PD 06/04 Cernyv V.~Chekelian$^{26}$, %MPIM-PD 01/90 Chekelian 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-LEFT 08/08 Deboer B.~Delcourt$^{27}$, %ORSA-PD 8/88 Delcourt M.~Del~Degan$^{40}$, %ZUTH-LEFT 09/08 Deldegan J.~Delvax$^{4}$, %BRUX-ST 10/06 Delvax 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 A.~Falkiewicz$^{7}$, %CRAC-LEFT 03/09 Falkiewicz 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 D.-J.~Fischer$^{11}$, %DESY-ST 03/08 Fischer M.~Fleischer$^{11}$, %DESY-PD 07/0 Fleischer A.~Fomenko$^{25}$, %LPI -PD 8/88 Fomenko E.~Gabathuler$^{18}$, %LIVE-PD 10/89 Gabathulere J.~Gayler$^{11}$, %DESY-PD 8/88 Gayler S.~Ghazaryan$^{38}$, %YERE-PD 8/88 Ghazaryan A.~Glazov$^{11}$, %DESY-PD 01/04 Glazov I.~Glushkov$^{39}$, %ZEUT-LEFT 11/08 Glushkov L.~Goerlich$^{7}$, %CRAC-PD 8/88 Goerlich N.~Gogitidze$^{25}$, %LPI -PD 8/88 Gogitidze M.~Gouzevitch$^{11}$, %DESY-LEFT 06/09 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$^{12}$, %HAM2-ST 12/05 Habib D.~Haidt$^{11}$, %DESY-PD 8/88 Haidt C.~Helebrant$^{11}$, %DFLC-ST 03/06 Helebrant R.C.W.~Henderson$^{17}$, %LANC-PD 8/88 Henderson E.~Hennekemper$^{15}$, %HDB2-ST 11/07 Hennekemper H.~Henschel$^{39}$, %ZEUT-PD 06/99 Henschel M.~Herbst$^{15}$, %HDB2-ST 06/08 Herbst G.~Herrera$^{23}$, %MEX2-PD 07/98 Herrera M.~Hildebrandt$^{36}$, %PSI -PD 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 T.~Hreus$^{4,44}$, %BRUX-PD 10/08 Hreus M.~Jacquet$^{27}$, %ORSA-PD 09/96 Jacquet X.~Janssen$^{4}$, %BRUX-PD 02/03 Janssenx L.~J\"onsson$^{20}$, %LUND-PD 8/88 Joensson A.W.~Jung$^{15}$, %HDB2-PD 06/09 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.~Kluge$^{18}$, %LIVE-PD 05/04 Kluge A.~Knutsson$^{11}$, %DESY-PD 04/07 Knutsson R.~Kogler$^{26}$, %MPIM-ST 01/07 Kogler P.~Kostka$^{39}$, %ZEUT-PD 8/88 Kostka M.~Kraemer$^{11}$, %HAM2-PD 07/09 Kraemer K.~Krastev$^{11}$, %DESY-LEFT 12/08 Krastev J.~Kretzschmar$^{18}$, %LIVE-PD 01/08 Kretzschmar A.~Kropivnitskaya$^{24}$, %ITEP-LEFT 08/09 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-LEFT 09/08 Leibenguth V.~Lendermann$^{15}$, %HDB2-PD 01/2 Lendermann S.~Levonian$^{11}$, %DESY-PD 8/88 Levonian G.~Li$^{27}$, %ORSA-LEFT 12/08 Li K.~Lipka$^{11}$, %DESY-PD 01/03 Lipka A.~Liptaj$^{26}$, %MPIM-LEFT 01/09 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.~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-LEFT 04/09 Marti H.-U.~Martyn$^{1}$, %DESY-PD 8/88 Martyn S.J.~Maxfield$^{18}$, %LIVE-PD 8/88 Maxfield A.~Mehta$^{18}$, %LIVE-PD 8/88 Mehta A.B.~Meyer$^{11}$, %DESY-PD 01/00 Meyeran H.~Meyer$^{11}$, %DFLC-LEFT 11/08 Meyerhe H.~Meyer$^{37}$, %WUPP-PD 8/88 Meyerhi J.~Meyer$^{11}$, %DESY-PD 8/88 Meyerj V.~Michels$^{11}$, %DESY-LEFT 08/08 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-LEFT 02/09 Murin 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-LEFT 08/09 Nikiforov D.~Nikitin$^{9}$, %JINR-PD 06/08 Nikitin G.~Nowak$^{7}$, %CRAC-PD 8/88 Nowakg K.~Nowak$^{41}$, %ZUER-ST 08/05 Nowakk M.~Nozicka$^{11}$, %DESY-LEFT 09/08 Nozicka B.~Olivier$^{26}$, %MPIM-LEFT 09/08 Olivier J.E.~Olsson$^{11}$, %DESY-PD 8/88 Olsson S.~Osman$^{20}$, %LUND-PD 06/09 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}$, %PRG2-LEFT 10/08 Pejchal E.~Perez$^{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}$, %DESY-PD 10/06 Placakyte B.~Pokorny$^{12}$, %HAM2-LEFT 04/09 Pokorny R.~Polifka$^{32}$, %PRG2-ST 10/06 Polifka B.~Povh$^{13}$, %MPIH-PD 8/88 Povh V.~Radescu$^{11}$, %DESY-PD 10/06 Radescu A.J.~Rahmat$^{18}$, %LIVE-LEFT 10/08 Rahmat N.~Raicevic$^{30}$, %PODG-PD 03/2 Raicevic A.~Raspiareza$^{26}$, %MPIM-LEFT 03/09 Raspiareza T.~Ravdandorj$^{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}$, %BRUX-LEFT 11/08 Roland R.~Roosen$^{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}$, %DESY-LEFT 09/08 Rurikova S.~Rusakov$^{25}$, %LPI -PD 8/88 Rusakov D.~\v S\'alek$^{32}$, %PRG2-ST 11/06 Salek D.P.C.~Sankey$^{6}$, %RAL -PD 8/88 Sankey M.~Sauter$^{40}$, %ZUTH-ST 10/05 Sauter E.~Sauvan$^{21}$, %MARS-PD 11/1 Sauvan S.~Schmitt$^{11}$, %DESY-PD 09/07 Schmittst L.~Schoeffel$^{10}$, %SACL-PD 12/98 Schoeffel A.~Sch\"oning$^{14}$, %HDB1-PD 04/09 Schoening H.-C.~Schultz-Coulon$^{15}$, %HDB2-PD 01/04 Schultzcoulon F.~Sefkow$^{11}$, %DFLC-PD 09/99 Sefkow R.N.~Shaw-West$^{3}$, %BIRM-ST 10/04 Shawwest L.N.~Shtarkov$^{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}$, %BEOG-PD 03/06 Smiljanic Y.~Soloviev$^{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}$, %DESY-PD 09/08 Steder B.~Stella$^{33}$, %ROME-PD 8/88 Stella G.~Stoicea$^{5}$, %BUCH-PD 02/08 Stoicea U.~Straumann$^{41}$, %ZUER-PD 8/88 Straumann D.~Sunar$^{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}$, %BIRM-PD 08/99 Thompsonp T.~Toll$^{12}$, %HAM2-ST 11/08 Toll F.~Tomasz$^{16}$, %KOSI-LEFT 12/08 Tomasz T.H.~Tran$^{27}$, %ORSA-ST 10/06 Tran D.~Traynor$^{19}$, %QMWC-PD 12/01 Traynor T.N.~Trinh$^{21}$, %MARS-LEFT 10/08 Trinh P.~Tru\"ol$^{41}$, %ZUER-PD 8/88 Truoel I.~Tsakov$^{34}$, %SOFI-PD 04/03 Tsakov B.~Tseepeldorj$^{35,50}$, %ULBA-PD 06/06 Tseepeldorj J.~Turnau$^{7}$, %CRAC-PD 8/88 Turnau K.~Urban$^{15}$, %HDB2-PD 06/09 Urbank A.~Valk\'arov\'a$^{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}$, %DESY-LEFT 10/08 Vinokurova V.~Volchinski$^{38}$, %YERE-PD 12/01 Volchinski M.~von~den~Driesch$^{11}$, %DESY-ST 06/08 Vondendriesch D.~Wegener$^{8}$, %DORT-PD 8/88 Wegener Ch.~Wissing$^{11}$, %DESY-PD 07/06 Wissing E.~W\"unsch$^{11}$, %DESY-PD 8/88 Wuensch J.~\v{Z}\'a\v{c}ek$^{32}$, %PRG2-PD 8/88 Zacek J.~Z\'ale\v{s}\'ak$^{31}$, %PRAG-PD 01/05 Zalesak Z.~Zhang$^{27}$, %ORSA-PD 10/92 Zhang A.~Zhokin$^{24}$, %ITEP-PD 04/99 Zhokine T.~Zimmermann$^{40}$, %ZUTH-LEFT 01/09 Zimmermannt H.~Zohrabyan$^{38}$, %YERE-PD 11/02 Zohrabyan F.~Zomer$^{27}$, %ORSA-PD 8/88 Zomer and R.~Zus$^{5}$ %BUCH-PD 07/08 Zus %-- H1 Institutes \bigskip{\it $ ^{1}$ I. Physikalisches Institut der RWTH, Aachen, Germany \\ $ ^{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/Irfu, CE-Saclay, Gif-sur-Yvette, France \\ $ ^{11}$ DESY, Hamburg, Germany \\ $ ^{12}$ Institut f\"ur Experimentalphysik, Universit\"at Hamburg, Hamburg, Germany$^{ a}$ \\ $ ^{13}$ Max-Planck-Institut f\"ur Kernphysik, Heidelberg, Germany \\ $ ^{14}$ Physikalisches Institut, Universit\"at Heidelberg, Heidelberg, Germany$^{ a}$ \\ $ ^{15}$ Kirchhoff-Institut f\"ur Physik, Universit\"at Heidelberg, Heidelberg, Germany$^{ a}$ \\ $ ^{16}$ Institute of Experimental Physics, Slovak Academy of Sciences, Ko\v{s}ice, Slovak Republic$^{ f}$ \\ $ ^{17}$ Department of Physics, University of Lancaster, Lancaster, UK$^{ b}$ \\ $ ^{18}$ Department of Physics, University of Liverpool, Liverpool, UK$^{ b}$ \\ $ ^{19}$ Queen Mary and Westfield College, London, UK$^{ b}$ \\ $ ^{20}$ Physics Department, University of Lund, Lund, Sweden$^{ g}$ \\ $ ^{21}$ CPPM, 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$^{ k}$ \\ $ ^{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}$ Also at Ulaanbaatar University, Ulaanbaatar, Mongolia \\ \bigskip $ ^a$ Supported by the Bundesministerium f\"ur Bildung und Forschung, FRG, under contract numbers 05H09GUF, 05H09VHC, 05H09VHF, 05H16PEA \\ $ ^b$ Supported by the UK Science and Technology Facilities Council, and formerly by the UK Particle Physics and Astronomy Research Council \\ $ ^c$ Supported by FNRS-FWO-Vlaanderen, IISN-IIKW and IWT and by Interuniversity Attraction Poles Programme, Belgian Science Policy \\ $ ^d$ Partially Supported by Polish Ministry of Science and Higher Education, grant 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, INGO-1P05LA259 and MSM0021620859 \\ $ ^i$ Supported by the Swiss National Science Foundation \\ $ ^j$ Supported by CONACYT, M\'exico, grant 48778-F \\ $ ^k$ Russian Foundation for Basic Research (RFBR), grant no 1329.2008.2 \\ $ ^l$ This project is co-funded by the European Social Fund (75\%) and National Resources (25\%) - (EPEAEK II) - PYTHAGORAS II \\ } \end{flushleft} % % Please not that the author list may need re-formatting. \newpage \section{Introduction} Isolated photons emerging from the hard subprocess $ep \rightarrow e\gamma X$, so called prompt photons, are a powerful probe of the underlying dynamics, complementary to jets. Production of isolated photons with high transverse momentum can be calculated in perturbation theory. High energy electron-proton scattering is dominated by so-called photoproduction processes, in which a beam lepton emits a quasi-real photon which either interacts directly with the proton (direct process) or fluctuates into partons which then participate in the hard scattering process (resolved process). In prompt photon production, the direct process is sensitive to the quark content of the proton through the Compton scattering of the exchanged photon with a quark ($\gamma q\rightarrow \gamma q$) as depicted in figure~\ref{fig:feynman}a). The resolved process ($q g \rightarrow \gamma q$) is sensitive to the partonic structure of both the photon and the proton. A typical diagram is shown in figure~\ref{fig:feynman}b). Figure~\ref{fig:feynman}c) and~\ref{fig:feynman}d) show typical higher order diagrams. \begin{figure}[Hhh] \begin{center} \includegraphics[height=0.19\textwidth]{d09-135f1a.eps} \hspace{0.01\textwidth} \includegraphics[height=0.19\textwidth]{d09-135f1b.eps} \hspace{0.01\textwidth} \includegraphics[height=0.19\textwidth]{d09-135f1c.eps} \hspace{0.01\textwidth} \includegraphics[height=0.19\textwidth]{d09-135f1d.eps} \end{center} \begin{picture} (0.,0.) \setlength{\unitlength}{1.0cm} \put ( 0.3, 2.2){a)} \put ( 4. ,2.2){b)} \put ( 8.6, 2.2){c)} \put (12.7, 2.2){d)} \end{picture} \caption{Examples of diagrams for the production of prompt photons in photoproduction: a) direct and b) resolved interaction with a parton from the proton, c) box diagram and d) radiation of a photon from an outgoing quark. } \label{fig:feynman} \end{figure} The H1 collaboration has previously measured prompt photon cross sections in photoproduction~\cite{H1gamma} and in deep inelastic scattering (DIS)~\cite{H1dis}. The ZEUS collaboration has also reported measurements of prompt photon production~\cite{ZEUS,ZEUS1,ZEUS2}. Both experiments found that in photoproduction the inclusive prompt photon cross section is underestimated by next-to-leading order (NLO) QCD calculations~\cite{heinrich,heinrich2,nlo1}, while there is reasonable agreement for events with a prompt photon and a jet (photon plus jet). In DIS, a leading order QCD calculation~\cite{thomas} significantly underestimates the production of isolated photons and of photons plus jets. NLO predictions~\cite{kramer} are only available for the latter and also underestimate the cross section. This paper presents results of a measurement of prompt photons in photoproduction. The data used for the measurement were collected with the H1 detector in the period from $2004$ to $2007$ and correspond to a total integrated luminosity of $340$~{\rm pb}$^{-1}$. This amounts to an increase in statistics by a factor of three compared to the previous measurement~\cite{H1gamma}. During this data taking period HERA collided positrons or electrons\footnote {Unless otherwise stated, the term electron refers to both the electron and the positron.} of energy $E_e = 27.6~{\rm GeV}$ with protons of energy $E_p = 920~{\rm GeV}$ corresponding to a centre-of-mass energy of $\sqrt{s} = 319~{\rm GeV}$. Isolated photons with transverse energy $6< E_T^\gamma < 15$~GeV and pseudorapidity $-1.0 < \eta^\gamma < 2.4$ are measured in events with the inelasticity $y$ in the range $0.15$~GeV. The combined trigger efficiency is about $85$\% at $\Etg$ of $6$~GeV rising to above $95$\% for $\Etg >$ $7$~GeV. \section{ Experimental Method} \subsection{ Event Selection and Reconstruction} \label{sect:sel} %\label{sec:sel} Events are selected with a photon candidate in the LAr calorimeter of transverse energy $6 < \etg < 15 $~GeV and pseudorapidity $-1.0 < \etag < 2.4$. Photon candidates are defined as compact clusters in the electromagnetic section of the LAr calorimeter with no matching signals in the CIP2k. The CIP2k veto rejects candidates, if there is a signal in at least two layers of the CIP2k close to the expected hit position. In addition, a track veto is applied for $\theta>45^{\circ}$. It rejects candidates, if a track in the CTD extrapolated to the LAr calorimeter front face matches the electromagnetic cluster with a distance of closest approach to the cluster's barycentre of less than $15$~cm. Photon candidates are also rejected if they are close to inactive regions between calorimeter modules. Neutral current (NC) deep-inelastic scattering (DIS) events are suppressed by rejecting events with an electron candidate not previously identified as photon candidate. Electron candidates are defined as compact electromagnetic clusters in the SpaCal or in the LAr calorimeter. In the LAr calorimeter the candidates are required to have an associated track with a distance of closest approach of less than $12$~cm. The electron suppression restricts the sample to NC events where the scattered electron escapes along the beam pipe in the negative $z$ direction. The low electron scattering angle of such events corresponds to virtualities of the exchanged photon in the range $Q^2<4$~GeV$^2$. In photoproduction the inelasticity $y$ is expressed as $y = W^2/s$, where $W$ is the $\gamma p$ centre of mass energy. In this analysis $y$ is evaluated as $y_{h}=\Sigma(E-p_z)/2E_e$, where the sum runs over all measured final state particles with energy $E$ and longitudinal momentum $p_z$. The inelasticity is restricted to $0.1 300 \mev$. \par Tracks and calorimeter energy deposits not previously identified as photon candidate are used to form combined cluster-track objects. The photon candidate and the cluster-track objects are combined into massless jets using the inclusive $k_T$ algorithm~\cite{jetalgo} with the separation parameter $R_0$ set to $1$. Jets are reconstructed in the pseudorapidity range $-2.0<\etaj<3.0$ with a transverse momentum of $\Etj > 4$~GeV. Due to the harder kinematical cuts for the photon candidate there is always a jet containing the photon candidate called the photon-jet. All other jets are classified as hadronic jets. To ensure isolation of the photon, the fraction $z=\etg/\etgjet$ of the transverse energy of the photon-jet carried by the photon candidate has to be larger than $0.9$. Here, $\etgjet$ is the transverse energy of the photon-jet. This isolation requirement largely suppresses background from photons produced in the hadron decay cascade. Only events with exactly one isolated photon candidate are accepted. For the photon plus jet sample, events are selected with a photon candidate and at least one hadronic jet with $-1.3<\etaj<2.3$. If more than one hadronic jet is selected, the one with the highest $\Etj$ is used. Four additional observables are defined for the photon plus jet sample which are sensitive to the underlying partonic process: \begin{itemize} \item The estimators $\xglo$ and $\xplo$, which in the LO approximation correspond to the longitudinal momentum fractions of the partons in the photon and the proton, respectively, are defined as \beq \xglo = \frac{\etg(e^{-\etaj} + e^{-\etag})}{(2y_hE_e)}~~~~\mbox{and}~~~~\xplo = \frac{\etg(e^{\etaj} + e^{\etag})}{(2E_p)}~\mbox{.} \eeq These definitions~\cite{heinrich3,afg94} reduce infrared sensitivity for $x_\gamma\rightarrow 1$ compared to the conventional definition of $x_\gamma = ( \etg e^{-\etag} + \etj e^{-\etaj})/(2yE_e)$. The above definitions make use of the energy of the photon only, which has a better resolution than the energy of the jet. However, $\xglo$ and $\xplo$ may become larger than unity. \item Two observables $\pperp$ and $\Dphi$ describe the transverse correlation between the photon and the jet, $\Dphi$ is the azimuthal difference between the photon and the jet, and $p_\perp$ is the photon momentum component perpendicular to the jet direction in the transverse plane \beq \pperp \equiv\frac{ \mid\ptg \times \ptjet \mid}{\mid \ptjet\mid} = \etg \cdot \sin{\Dphi}. \eeq At leading order the prompt photon and the jet are back-to-back and $\pperp$ equals zero for direct processes. The observable $\Dphi$ is strongly correlated with $\pperp$, but is less sensitive to the energies of the photon and the jet. \end{itemize} The $y_h$, $\etg$, $z$ and $\etajet$ distributions of events with an isolated photon candidate are shown in figure~\ref{fig:control} together with the MC predictions from PYTHIA for the signal and the background. The signal (background) prediction is scaled by a factor $1.45$ ($1.7$) on average. The scaling factors vary as a function of $\eta$ as suggested by the cross section measurement (section~\ref{sect:res}). In all distributions the data are described within errors by the scaled MC predictions. At this stage of the analysis there is still a significant contribution of background from the decay products of neutral mesons. \subsection{ Photon Signal Extraction} \label{sect:phot} The photon signal is extracted from the sample with photon candidates by means of a shower shape analysis based on the method described in \cite{H1dis,carsten}. It uses the following six shower shape variables calculated from the measurements of the individual cells composing the cluster: \begin{itemize} \item The transverse radius of the cluster, $R_T$. \item The transverse symmetry, which is the ratio of the spread of the transverse cell distributions along the two principal axes. Single photon clusters are expected to be more symmetric than multi-photon clusters. \item The transverse kurtosis, defined as $K_T=\mu_4/(\mu_2)^2 - 3$, with $\mu_2$ and $\mu_4$ the second and the fourth moment of the transverse energy distribution. \item The first layer fraction, defined as the fraction of the cluster's energy detected in the first calorimeter layer. \item The hot core fraction, being the fraction of the energy of the electromagnetic cluster contained in the hot core of the cluster. It is defined as the energy fraction in four to twelve contiguous cells in the first two calorimeter layers, depending on the polar angle. The cells include the most energetic cell and are chosen to maximise the energy. \item The hottest cell fraction, which is the fraction of the energy of the electromagnetic cluster contained in the cell with the largest energy deposit. \end{itemize} The distributions of the shower shape variables are shown in figure~\ref{fig:showershapes} for the prompt photon candidates with the kinematic cuts as defined above. The shaded band shows the systematic uncertainty assigned to the description of the shower shapes as described in section~\ref{sect:syst}. The data are compared with the sum of the background and the signal MC distributions, which describe the data within the systematic error. In order to discriminate between signal and background, probability density functions $p^{i}_{\gamma}$ for the signal and $p^{i}_{bg}$ for the background are defined for each of the six shower shape variables $i$. Simulated events for the signal and the background are used to determine $p^i_{\gamma}$ and $p^{i}_{bg}$. The photon and background probability densities are taken as the product of the respective shower shape densities with the method described in \cite{likeli}. For each event a discriminator $D$ is formed. It is defined as the photon probability density divided by the sum of the probability densities for photons and background. Figure~\ref{fig:discriminant} shows an example of the discriminator distribution for the range $0.94<\etag<1.42$ and four different bins in $\etg$. The discriminator has in general larger values for prompt photons than for the decay photons. The separation power is decreasing with increasing $\etg$. The sum of the MC predictions describes the data within the systematic uncertainty of the shower shapes. Additional event samples are used for the determination of systematic errors related to the cluster shapes. The first sample, containing Bethe Heitler events, $ep\rightarrow e\gamma p$, consists of events with an electron reconstructed in the LAr calorimeter, a photon in the SpaCal and nothing else in the detector. The second, complementary sample, in addition containing deeply-virtual Compton scattering \cite{DVCS} events, is selected by requiring an electron in the SpaCal, a photon in the LAr calorimeter and no other particle in the detector. These independent event selections, denoted BH and DVCS respectively, provide a clean sample of electromagnetic clusters at low transverse energies in the LAr calorimeter and are used to study the description of the shower shapes of the photons. A third sample is used to monitor the description of the shower shapes of clusters initiated by the decay of neutral hadrons. This sample, denoted BG, is background enhanced by selecting events with the inverted isolation criteria $z=\etg/\etgjet<0.9$ and no cut on the transverse radius of the photon candidate. \subsection{ Cross Section Determination} A regularised unfolding procedure~\cite{phillips,thikanov,blobel,tunfold,krzys} is used to relate distributions $\vec{y}_{\mathrm{rec}}$ of reconstructed variables (input bins) to distributions $\vec{x}_{\mathrm{true}}$ of variables on hadron level (output bins), to determine the fractions of signal and background and to correct the data for the detector acceptance. The unfolding matrix \matrixA{} relates the two vectors, $\matrixA \vec{x}_{\mathrm{true}} =\vec{y}_{\mathrm{rec}}$. Further details on the method can be found in in~\cite{krzys} and are summarised in appendix~\ref{sect:unfold}. The input is binned in three dimensions in the reconstructed quantities $\Etg$, $\etag$ and $D$; the latter allows the discrimination of signal and background. The output of the unfolding procedure contains the number of signal events $N_{sig}$ in $\Etg$-$\etag$ bins on hadron level and the amount of background events in any of the input bins. Additional underflow and overflow bins are defined for each output variable. Therefore the unfolding matrix \matrixA{} also includes migrations into or out of the phase space of the measurement. It is computed using signal and background PYTHIA simulation. For measurements including jet-related variables, both the input and the output is additionally binned in some variable $u$, where $u$ is $\etjet$, $\etajet$, $\xg$, $\xp$, $\Dphi$ or $\pperp$. The stability of the unfolding procedure is checked by varying the number of input bins and changing the bin boundaries. The results from the unfolding procedure are compared to a bin-by-bin correction method. Agreement is seen within errors for most of the analysis bins. Cross sections are presented for $Q^2<1$~GeV$^2$. The extracted number of signal events in each bin $N_{sig} $ is corrected for the contribution of DIS events with a virtuality $11.4$ the uncertainty is $4$\% on the energy scale and $4$~mrad on the scattering angle. The resulting error on the total inclusive cross section is $\pm1.5$\%. \item A $2$\% uncertainty is attributed to the measurement of the hadronic energy~\cite{krzys}. The corresponding uncertainty of the total cross section $\pm1$\%. \item An uncertainty of $\pm3$\% is attributed to the determination of the trigger efficiency. \item The uncertainty on the CIP2k and track veto efficiency results in an error of $\pm 2.5$\% on the total inclusive cross section. \item An uncertainty in the description of the dead material in the simulation is accounted for by varying the probability of photon conversion before the calorimeter by $\pm 10$\%. For polar angles $ \theta < 20^\circ$ it is varied by $\pm 30$\% because of more dead material in the forward region. This results in a $1$\% uncertainty for the cross section measurements in the central region and $3$\% in the most forward $\etag$ bin. \item The ratio of resolved to direct photoproduction events in the MC simulation is changed within limits deduced from the measured $x_\gamma$ distribution~\cite{krzys}, leading to $\pm 1$\% systematic error due to a different acceptance. \item The luminosity measurement has an error of $3.4$\%. \end{itemize} The effects of each systematic error on the cross sections are determined by evaluating an alternative unfolding matrix {\bf A$^\prime$} using the MC prediction made with the corresponding systematic variation applied. The differences to the default unfolding matrix {\bf A$^\prime$-A} are used to evaluate the contributions to the error matrices of the results using standard error propagation. The final error matrix is split into fully correlated and fully uncorrelated parts which are listed in tables~\ref{tab:inclusive} to~\ref{tab:pperp2}. The systematic uncertainty obtained on the total inclusive cross section is $\pm 13$\%. The largest contribution to this uncertainty arises from the systematic uncertainties attributed to the description of the shower shapes. \section{Results} \label{sect:res} The prompt photon cross sections presented below are given for the phase space defined in table~\ref{tab:kinem}. \renewcommand{\arraystretch}{1.2} % this increase the table in vertical direction, very useful! \begin{table}[tt] \begin{center} \begin{tabular}{|c|c|} \hline \multicolumn{2}{|c|}{\bf \boldmath{H1 Prompt Photon Phase Space} }\\ \hline \multirow{5}{30mm}{\bf ~~~~~~~Inclusive \\ ~~~~cross section} & $6 < \etg < 15$ GeV \\ & $-1.0 < \etag < 2.4$ \\ & $z=E_T^\gamma/E_T^{\gamma\mathrm{-jet}} > 0.9$ \\ & $\qsq < 1$ GeV$^2$ \\ & $0.1< y <0.7$ \\ \hline \multirow{2}{30mm}{\bf ~~~~Jet definition} & $\Etj > 4.5 $ GeV\\ & $-1.3 < \etajet < 2.3$ \\ \hline \end{tabular} \caption{ Phase space for the measurement of prompt photon cross sections. Kinematics are defined in the H1 laboratory frame.} \label{tab:kinem} \end{center} \end{table} Bin averaged differential cross sections are presented in figures~\ref{fig:xsec_incl} to~\ref{fig:xsec_pperp} and in tables~\ref{tab:inclusive} to~\ref{tab:pperp2}. For all measurements the total uncertainty is dominated by the systematic errors. The figures also show the ratio of the NLO QCD prediction (FGH)~\cite{heinrich,heinrich2} to the measured cross section $R = \sigma_{FGH}/\sigma_{meas}$ with the uncertainty of the NLO calculation. The factors $f_{corr}$ (see section~\ref{sect:theo}) for the correction of the theoretical calculations for hadronisation, multiple interaction and the definition of the isolation are given in the cross section tables with their errors. The measured inclusive prompt photon cross section in the phase space defined in table~\ref{tab:kinem} is % \begin{displaymath} \sigma(ep\rightarrow e \gamma X) = 66.9 \pm 1.8 \;\mbox{(stat)}\;\pm 8.7 \;\mbox{(syst)}\ \mbox{pb.} \end{displaymath} Both calculations predict lower cross sections of $52.1^{\,+\,5.3}_{\,-\,3.4}$~pb (FGH) and $56.7^{\,+\,2.3}_{\,-\,3.1}$~pb (LZ), while the MC expectation from PYTHIA is $46.4$~pb. Theoretical uncertainties due to missing higher orders are estimated by simultaneously varying $\mu_R$ and $\mu_F$ by a factor of $0.5$ to $2.0$. In addition, the errors on the theoretical predictions include uncertainties due to the error of $f_{corr}$ and due to the PDFs. All these error sources are added in quadrature. \par Differential inclusive prompt photon cross sections $\mbox{d}\sigma/\mbox{d}\etg$ and $\mbox{d}\sigma/\mbox{d}\etag$ are presented in table~\ref{tab:inclusive} and in figure~\ref{fig:xsec_incl}. The results are compared to a QCD calculation based on the collinear factorisation in NLO (FGH)~\cite{heinrich,heinrich2}, to a calculation based on the $k_T$ factorisation approach (LZ)~\cite{zotov}. Both calculations are below the data, most significantly at low $\etg$. The LZ calculation gives a reasonable description of the shape of $\etag$, whereas the FGH calculation is significantly below the data for central and backward photons ($\etag<0.9$). Double differential cross sections $d^2\sigma/\mbox{d}\etg \mbox{d}\etag$ are shown in figure~\ref{fig:xsec_incl2} and table~\ref{tab:incl2} for all five bins in $\etag$. The $\etag$ bins correspond to the wheel structure of the LAr calorimeter. LZ provides a reasonable description of the data with the exception of the lowest $\etg$ bin in the central $\etag$ ($0.2<\etag<0.9$) region. The FGH calculation underestimates the cross section in the central ($0.2<\etag<0.9$) and backward ($\etag<-0.6$) region. Here, it is significantly below the data. The prediction from PYTHIA is also shown. It underestimates the measured cross section by roughly $45\%$, most significantly at low $\Etg$. The prompt photon plus jet cross section is % \begin{displaymath} \sigma(ep\rightarrow e \gamma \mathrm{~jet~} X) = 50.1 \pm 1.7 \;\mbox{(stat)}\;\pm 6.5 \; \mbox{(syst)}\ \mbox{pb.} \end{displaymath} It is similar to the inclusive cross section, since the prompt photon recoils most of the time against a prominent hadronic jet. The theoretical calculations predict cross sections of $40.6^{\,+\,5.3}_{\,-\,1.9}$~pb (FGH) and $45.7^{\,+\,4.7}_{\,-\,2.1}$~pb (LZ). Both are compatible with the measurement within the errors. The PYTHIA expectation of $33.9$~pb is again too low. Cross sections for the production of a prompt photon plus jet are presented in figure~\ref{fig:xsec_excl} and tables~\ref{tab:exclusive},~\ref{tab:xgamma} as a function of the variables $\etg$, $\etag$, $\etjet$ and $\etajet$. Both calculations give a reasonable description of the $\etg$ and $\etjet$ cross sections but show deficits in the description of the $\etaj$ shape. Here, the LZ prediction is too high for jets with $\etaj<0.5$, and both calculations underestimate the rate of events with forward jets. As in the inclusive case, the FGH prediction is too low for $\etag<0.2$. Photon plus jet cross section as a function of the estimators $\xglo$ and $\xplo$ are shown in figure~\ref{fig:xsec_xg} and table~\ref{tab:exclusive}. Both distributions are described by the calculations within errors. Cross sections for the two observables describing the transverse correlation between the photon and the jet, $\pperp$ and $\Dphi$, are shown in figure~\ref{fig:xsec_pperp} and tables~\ref{tab:pperp1},~\ref{tab:pperp2}. Both variables are expected to be sensitive to higher order gluon emission. The phase-space is divided into two parts: one with $\xglo>0.8$ where the direct interaction of a photon with the proton dominates and one with $\xglo<0.8$, including significant contributions from events with a resolved photon. For $\xglo>0.8$ both predictions underestimate the tails of the distributions suggesting that there is more decorrelation in the data than predicted. For $\xglo<0.8$ the $\pperp$ distribution is harder than for $\xglo>0.8$, which reflects the increased contributions from events with a resolved photon and from photons radiated from quarks in di-jet events. The FGH calculation poorly describes the $\pperp$ distribution but gives a reasonable description of the measurement in $\Dphi$ for $\xglo<0.8$, except for the highest bin in $\Dphi$. The regions $\Dphi\rightarrow 180^\circ$ and $\pperp\rightarrow 0$ are sensitive to multiple soft gluon radiation which limits the validity of fixed order calculations~\cite{gudrun}. The LZ calculation includes multiple gluon radiation in the initial state before the hard subprocess and describes $\Dphi>170^\circ$ and $\pperp <2$~GeV, but predicts a significantly lower contribution of events in the tails of both distributions as compared to the data. The present measurement is compared to the published results of H1~\cite{H1gamma} and ZEUS~\cite{ZEUS2} in the restricted phase space $0.2 < y_h < 0.7$. For the comparison with the inclusive measurement of H1 the $\etag$ range is restricted to $-1.0 <\etag < 0.9$. For the comparison with the ZEUS results for isolated photons with a jet, the kinematic range is changed to $7< \etg< 15 $~GeV, $6 < \etj < 17$~GeV and $-1.6 < \etaj<2.4$. The results of this analysis are found in agreement with the previous measurements~\cite{krzys}. \section{Conclusions} The photoproduction of prompt photons is measured in $ep$ collisions at a centre-of-mass energy of $319~{\rm GeV}$ with the H1 detector at HERA using a data sample corresponding to an integrated luminosity of $340~{\rm pb}^{-1}$. Photons with a transverse energy in the range $6 < \etg < 15$~GeV and with pseudorapidity $-1.0 < \etag < 2.4$ are measured in the kinematic region $Q^2<1$~GeV$^2$ and $0.10.8$ and $\xglo<0.8$. More details are given in the caption of table~\ref{tab:inclusive}.} \label{tab:pperp1} \end{center} \end{table} \vspace*{\fill} %%%%%%%%%%%%%%%%%%%%%%%%%%%% dphi \clearpage \vspace*{\fill} \begin{table}[ht] \begin{center} \begin{tabular}{|r @{,} l|r @{,} l|rll||c|} \hline \multicolumn{8}{|c|}{\bf \boldmath H1 Prompt Photon plus Jet Cross Sections} \\ \hline \hline \multicolumn{2}{|c|}{\xglo} &\multicolumn{2}{|c|} {$\Dphi$} & $ \mbox{d}\sigma /\mbox{d}\Dphi$ & uncorr. & corr. & $f_{corr}$ \\ \multicolumn{2}{|c|}{}& \multicolumn{2}{|c|}{} & \multicolumn{3}{c||}{[pb]} & \\ \hline %\input{tex/tab/DPhiHiX.txt} $[0.8$&$1.1]$ & $ [ 130 $&$ 150 ] $ & $ 0.19 $ & $ \pm 0.04 $ & $ \pm 0.01 $ & $0.82^{\,+\,0.03}_{\,-\,0.04}$\\ \multicolumn{2}{|c|}{}& $ [ 150 $&$ 165 ] $ & $ 0.46 $ & $ \pm 0.06 $ & $ \pm 0.06 $ & $0.84^{\,+\,0.01}_{\,-\,0.01}$\\ \multicolumn{2}{|c|}{} & $ [ 165 $&$ 172 ] $ & $ 0.89 $ & $ \pm 0.14 $ & $ \pm 0.07 $ & $0.93^{\,+\,0.00}_{\,-\,0.01}$\\ \multicolumn{2}{|c|}{}& $ [ 172 $&$ 180 ] $ & $ 1.38 $ & $ \pm 0.04 $ & $ \pm 0.17 $ & $0.89^{\,+\,0.05}_{\,-\,0.05}$\\ \hline \hline % \input{tex/tab/DPhiLoX.txt} $[0.0$&$0.8]$ & $ [ 130 $&$ 150 ] $ & $ 0.27 $ & $ \pm 0.03 $ & $ \pm 0.04 $ & $0.94^{\,+\,0.03}_{\,-\,0.05}$\\ \multicolumn{2}{|c|}{}& $ [ 150 $&$ 165 ] $ & $ 0.52 $ & $ \pm 0.06 $ & $ \pm 0.08 $ & $0.91^{\,+\,0.04}_{\,-\,0.08}$\\ \multicolumn{2}{|c|}{} & $ [ 165 $&$ 172 ] $ & $ 0.91 $ & $ \pm 0.14 $ & $ \pm 0.18 $ & $0.83^{\,+\,0.07}_{\,-\,0.09}$\\ \multicolumn{2}{|c|}{}& $ [ 172 $&$ 180 ] $ & $ 1.21 $ & $ \pm 0.11 $ & $ \pm 0.15 $ & $0.84^{\,+\,0.08}_{\,-\,0.12}$\\ \hline \end{tabular} \caption{Bin averaged differential cross sections for prompt photon plus jet production as a function of $\Dphi$, the difference in azimuthal angle between the photon and the jet, separated into two regions with $\xglo>0.8$ and $\xglo<0.8$. More details are given in the caption of table~\ref{tab:inclusive}.} \label{tab:pperp2} \end{center} \end{table} \vspace*{\fill} \clearpage \setcounter{figure}{1} %%%%%%%%%%%%%%%%%%%%%%%%%%%%% control plots %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \vspace*{\fill} \begin{figure}[Ht] \begin{center} \includegraphics[width=1.0\textwidth]{d09-135f2.eps} \caption{ Distributions of a) the inelasticity $y_h$, b) the transverse energy $E_T^\gamma$ of the photon, c) the isolation parameter $z$ and d) $\etaj$ for events with prompt photon candidates. Data are shown as points with error bars indicating the statistical error. The signal prediction from PYTHIA for prompt photons is shown as dark full line, and the contribution of direct interactions as a dotted line. The background as simulated with PYTHIA is shown as a dashed line. The signal and background contributions are scaled on average by a factor $1.5$ and $1.7$, respectively. The sum of the scaled signal and background is shown as the light grey histogram. The vertical dashed lines indicate the kinematic region of the cross section measurement.} \begin{picture} (0.,0.) \setlength{\unitlength}{1.0cm} \put ( -6.2, 17.2){a)} \put ( 2.5 ,17.2){b)} \put ( -6.2, 10.7){c)} \put (2., 10.7){d)} \end{picture} \label{fig:control} \end{center} \end{figure}\vspace*{\fill} %%%%%%%%%%%%%%%%%%%%%%%%%%%%% shower shapes %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \vspace*{\fill}\begin{figure}[Ht] \includegraphics[width=1.0\textwidth]{d09-135f3.eps} \begin{picture} (0.,0.) \setlength{\unitlength}{1.0cm} \put (1.5, 6.8){a)} \put (6.8 ,6.8){b)} \put (15.2, 6.8){c)} \put (4.5, 1.9){d)} \put (6.8, 1.9){e)} \put (15.2, 1.9){f)} \end{picture} \begin{center} \caption{ Distributions of the shower shape variables that are used to define the discriminant for isolated photon identification: a) transverse radius, b) transverse symmetry, c) transverse kurtosis, d) the fraction of energy in the first layer, e) the fraction of energy in the hot core of the cluster and f) the fraction of energy in the hottest cell of the cluster for all the photon candidates. Data are shown as points with error bars for the statistical error. The expectation from PYTHIA for the signal (background) is shown as a full (dashed) line. The signal and background contributions are scaled on average by a factor $1.5$ and $1.7$, respectively. The shaded band shows the sum of the MC predictions. The width of the band corresponds to the systematic uncertainty assigned to the description of the shower shapes. } \label{fig:showershapes} \end{center} \end{figure}\vspace*{\fill} %%%%%%%%%%%%%%%%%%%%%%%% discriminant %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \vspace*{\fill}\begin{figure}[ht] \begin{center} \includegraphics[width=1.\textwidth]{d09-135f4.eps} \caption{ The distribution of the discriminant $D$ for $0.94<\etag<1.42$ in four different $\etg$ bins. $D$ is used in the identification of prompt photon candidates for events that have passed the event selection. Data are shown as points with error bars for the statistical error. The expectation from PYTHIA for the signal (background) is shown as a full (dashed) line. The signal and background contributions are scaled by a factor $1.5$ and $1.7$ on average, respectively. The shaded band shows the sum of the MC predictions with the systematic uncertainty from the description of the shower shapes.} %caption to figure~\ref{fig:showershapes}.} \label{fig:discriminant} \end{center} \end{figure}\vspace*{\fill} %%%%%%%%%%%%%%%%%%%%%%%% inclusive %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \vspace*{\fill}\begin{figure}[ht] \begin{center} \includegraphics[width=1.\textwidth]{d09-135f5.eps} \caption{Inclusive differential prompt photon cross sections a)~$\mathrm{d}\sigma/\mathrm{d}\etg$ and b)~$\mathrm{d}\sigma/\mathrm{d}\etag$ in the kinematic range specified in table~\ref{tab:kinem}. The inner error bars on the data points indicate the uncorrelated error including the statistical error, the full error bars contain in addition the correlated errors added in quadrature. The data are compared to a QCD calculation based on the collinear factorisation in NLO (FGH)~\cite{heinrich,heinrich2} and to a QCD calculation based on the $k_T$ factorisation approach (LZ)~\cite{zotov}. For each plot the lower figure shows the ratio of NLO QCD to the measured cross section ($R = \sigma_{\mathrm{ FGH}}/\sigma$) as a the hatched band. The width of this band shows the uncertainty from the NLO calculation only. The data points are shown at $R=1$ and their bars indicate the experimental uncorrelated uncertainty. The correlated experimental uncertainty of the data is indicated by the shaded area. } \label{fig:xsec_incl} \end{center} \begin{picture}(0,0) \setlength{\unitlength}{1.0cm} \put(7.,14.2){\textsf{a)}} \put(15.,14.2){\textsf{b)}} \end{picture} \end{figure}\vspace*{\fill} %%%%%%%%%%%%%%%%%%%%%%%% inclusive %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \vspace*{\fill}\begin{figure}[ht] \begin{center} \includegraphics[width=0.97\textwidth]{d09-135f6.eps} \caption{Inclusive double differential prompt photon cross sections $\mathrm{d}^2\sigma/\mathrm{d}\etg \mathrm{d}\etag$ for five bins in $\etag$. The errors between different $\etag$ bins are correlated. The kinematic range is specified in table~\ref{tab:kinem}. The cross sections are compared to theoretical calculations (see caption figure~\ref{fig:xsec_incl}). In addition the prediction from PYTHIA~\cite{PYTHIA} is shown as dashed line. } \label{fig:xsec_incl2} \end{center} \end{figure}\vspace*{\fill} %%%%%%%%%%%%%%%%%%%%%%%% exclusive %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \vspace*{\fill}\begin{figure}[ht] \begin{center} \includegraphics[width=1.\textwidth]{d09-135f7.eps} \caption{Differential prompt photon plus jet cross sections a)~$\mathrm{d}\sigma/\mathrm{d}\etg$, b)~$\mathrm{d}\sigma/\mathrm{d}\etag$, c)~$\mathrm{d}\sigma/\mathrm{d}\etj$ and d)~$\mathrm{d}\sigma/\mathrm{d}\etaj$ in the kinematic range specified in table~\ref{tab:kinem}. The cross sections are compared to theoretical calculations (see caption figure~\ref{fig:xsec_incl}).} \label{fig:xsec_excl} \end{center} \begin{picture}(0,0) \put(68,214.5){\textsf{a)}} \put(148,214.5){\textsf{b)}} \put(68,117){\textsf{c)}} \put(148,117){\textsf{d)}} \end{picture} \end{figure}\vspace*{\fill} %%%%%%%%%%%%%%%%%%%%%%%% xgamma %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \vspace*{\fill}\begin{figure}[ht] \begin{center} \includegraphics[width=1.\textwidth]{d09-135f8.eps} \caption{Differential prompt photon plus jet cross sections a)~$\mathrm{d}\sigma/\mathrm{d}\xglo$ and b)~$\mathrm{d}\sigma/\mathrm{d}\xplo$, in the kinematic range specified in table~\ref{tab:kinem}. The cross sections are compared to theoretical calculations (see caption figure~\ref{fig:xsec_incl}). } \label{fig:xsec_xg} \end{center} \begin{picture}(0,0) \setlength{\unitlength}{1.0cm} \put(7.,11.3){\textsf{a)}} \put(10.2,11.3){\textsf{b)}} \end{picture} \end{figure}\vspace*{\fill} %%%%%%%%%%%%%%%%%%%%%%%% xgamma %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \vspace*{\fill}\begin{figure}[ht] \begin{center} \includegraphics[width=0.97\textwidth]{d09-135f9.eps} \caption{ Differential prompt photon plus jet cross sections $\mathrm{d}\sigma/\mathrm{d}\Dphi$ and $\mathrm{d}\sigma/\mathrm{d}\pperp$ the photon momentum transverse to the jet direction, the difference in azimuthal angle between the photon and the jet. The kinematic range is specified in table~\ref{tab:kinem}. Figures a) and b) show the cross section for $\xglo>0.8$, c) and d) for $\xglo<0.8$. The cross sections are compared to theoretical calculations (see caption figure~\ref{fig:xsec_incl}).} \label{fig:xsec_pperp} \end{center} \begin{picture}(0,0) \put(70,220){\textsf{a)}} \put(100,220){\textsf{b)}} \put(65,124){\textsf{c)}} \put(100,124){\textsf{d)}} \end{picture} \end{figure}\vspace*{\fill} \end{document}