Study of the pion trajectory\\ in the photoproduction\\ of leading neutrons at HERA\\
Energetic neutrons produced in $ep$ collisions at HERA have been studied with the ZEUS detector in the photoproduction regime at a mean photon-proton center-of-mass energy of 220~GeV. The neutrons carry a large fraction $0.64 < x_L <0.925$ of the incoming proton energy, and the four-momentum-transfer squared at the proton-neutron vertex is small, $|t|<0.425$ GeV$^2$. The $x_L$ distribution of the neutrons is measured in bins of $t$. The $(1-x_L)$ distributions in the $t$ bins studied satisfy a power law $dN/dx_L \propto (1-x_L)^{a(t)}$, with the powers $a(t)$ following a linear function of $t$: \mbox{$a(t)=0.88\pm 0.09 ({stat.})^{+0.34}_{-0.39}({syst.})-(2.81\pm 0.42({stat.})^{+1.13}_{-0.62}({syst.})\ {GeV}^{-2})t$.} This result is consistent with the expectations of pion-exchange models, in which the incoming proton fluctuates to a neutron-pion state, and the electron interacts with the pion.
def.tex
%pomeron in text
\newcommand {\pom} {I\!\!P}
%pomeron as subscript
\newcommand {\pomsub} {{\scriptscriptstyle \pom}}
\newcommand {\reg} {I\!\!R}
\newcommand {\regsub} {{\scriptscriptstyle \reg}}
\newcommand {\ppp} {\pom\pom\pom}
\newcommand {\ppr} {\pom\pom\reg}
\newcommand {\xpom} {x_{\pomsub}}
\newcommand {\apom} {\alpha_{\pomsub}}
\newcommand {\areg} {\alpha_{\regsub}}
%
\newcommand {\qqb} {q \qbar}
\newcommand {\dstar} {D^{\ast \pm}}
\newcommand {\etam} {\eta_\smax}


piex-aut.tex
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%\topmargin-1.cm                                                                                    
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%\parindent0.cm                                                                                     
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%\def\3{\ss}                                                                                        
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\begin{center}                                                                                     
{                      \Large  The ZEUS Collaboration              }                               
\end{center}                                                                                       
                                                   %                                               
  S.~Chekanov,                                                                                     
  M.~Derrick,                                                                                      
  D.~Krakauer,                                                                                     
  J.H.~Loizides$^{   1}$,                                                                          
  S.~Magill,                                                                                       
  S.~Miglioranzi$^{   1}$,                                                                         
  B.~Musgrave,                                                                                     
  J.~Repond,                                                                                       
  R.~Yoshida\\                                                                                     
 {\it Argonne National Laboratory, Argonne, Illinois 60439-4815}, USA~$^{n}$                       
\par \filbreak                                                                                     
                                                  %                                                
  M.C.K.~Mattingly \\                                                                              
 {\it Andrews University, Berrien Springs, Michigan 49104-0380}, USA                               
\par \filbreak                                                                                     
                                                  %                                                
  P.~Antonioli,                                                                                    
  G.~Bari,                                                                                         
  M.~Basile,                                                                                       
  L.~Bellagamba,                                                                                   
  D.~Boscherini,                                                                                   
  A.~Bruni,                                                                                        
  G.~Bruni,                                                                                        
  G.~Cara~Romeo,                                                                                   
  L.~Cifarelli,                                                                                    
  F.~Cindolo,                                                                                      
  A.~Contin,                                                                                       
  M.~Corradi,                                                                                      
  S.~De~Pasquale,                                                                                  
  P.~Giusti,                                                                                       
  G.~Iacobucci,                                                                                    
  A.~Margotti,                                                                                     
  A.~Montanari,                                                                                    
  R.~Nania,                                                                                        
  F.~Palmonari,                                                                                    
  A.~Pesci,                                                                                        
  G.~Sartorelli,                                                                                   
  A.~Zichichi  \\                                                                                  
  {\it University and INFN Bologna, Bologna, Italy}~$^{e}$                                         
\par \filbreak                                                                                     
                                                    %                                              
  G.~Aghuzumtsyan,                                                                                 
  D.~Bartsch,                                                                                      
  I.~Brock,                                                                                        
  S.~Goers,                                                                                        
  H.~Hartmann,                                                                                     
  E.~Hilger,                                                                                       
  P.~Irrgang,                                                                                      
  H.-P.~Jakob,                                                                                     
  O.~Kind,                                                                                         
  U.~Meyer,                                                                                        
  E.~Paul$^{   2}$,                                                                                
  J.~Rautenberg,                                                                                   
  R.~Renner,                                                                                       
  A.~Stifutkin,                                                                                    
  J.~Tandler$^{   3}$,                                                                             
  K.C.~Voss,                                                                                       
  M.~Wang\\                                                                                        
  {\it Physikalisches Institut der Universit\"at Bonn,                                             
           Bonn, Germany}~$^{b}$                                                                   
\par \filbreak                                                                                     
                                                  %                                                
  D.S.~Bailey$^{   4}$,                                                                            
  N.H.~Brook,                                                                                      
  J.E.~Cole,                                                                                       
  G.P.~Heath,                                                                                      
  T.~Namsoo,                                                                                       
  S.~Robins,                                                                                       
  M.~Wing  \\                                                                                      
   {\it H.H.~Wills Physics Laboratory, University of Bristol,                                      
           Bristol, United Kingdom}~$^{m}$                                                         
\par \filbreak                                                                                     
  %                                                                                                
  M.~Capua,                                                                                        
  A. Mastroberardino,                                                                              
  M.~Schioppa,                                                                                     
  G.~Susinno  \\                                                                                   
  {\it Calabria University,                                                                        
           Physics Department and INFN, Cosenza, Italy}~$^{e}$                                     
\par \filbreak                                                                                     
                                      %                                                            
  J.Y.~Kim,                                                                                        
  I.T.~Lim,                                                                                        
  K.J.~Ma,                                                                                         
  M.Y.~Pac$^{   5}$ \\                                                                             
  {\it Chonnam National University, Kwangju, South Korea}~$^{g}$                                   
 \par \filbreak                                                                                    
                                                   %                                               
  A.~Caldwell$^{   6}$,                                                                            
  M.~Helbich,                                                                                      
  X.~Liu,                                                                                          
  B.~Mellado,                                                                                      
  Y.~Ning,                                                                                         
  S.~Paganis,                                                                                      
  Z.~Ren,                                                                                          
  W.B.~Schmidke,                                                                                   
  F.~Sciulli\\                                                                                     
  {\it Nevis Laboratories, Columbia University, Irvington on Hudson,                               
New York 10027}~$^{o}$                                                                             
\par \filbreak                                                                                     
                                                    %                                              
  J.~Chwastowski,                                                                                  
  A.~Eskreys,                                                                                      
  J.~Figiel,                                                                                       
  A.~Galas,                                                                                        
  K.~Olkiewicz,                                                                                    
  P.~Stopa,                                                                                        
  L.~Zawiejski  \\                                                                                 
  {\it Institute of Nuclear Physics, Cracow, Poland}~$^{i}$                                        
\par \filbreak                                                                                     
                                                           %                                       
  L.~Adamczyk,                                                                                     
  T.~Bo\l d,                                                                                       
  I.~Grabowska-Bo\l d$^{   7}$,                                                                    
  D.~Kisielewska,                                                                                  
  A.M.~Kowal,                                                                                      
  M.~Kowal,                                                                                        
  J. \L ukasik,                                                                                    
  \mbox{M.~Przybycie\'{n}},                                                                        
  L.~Suszycki,                                                                                     
  D.~Szuba,                                                                                        
  J.~Szuba$^{   8}$\\                                                                              
{\it Faculty of Physics and Nuclear Techniques,                                                    
           AGH-University of Science and Technology, Cracow, Poland}~$^{p}$                        
\par \filbreak                                                                                     
                                                           %                                       
  A.~Kota\'{n}ski$^{   9}$,                                                                        
  W.~S{\l}omi\'nski\\                                                                              
  {\it Department of Physics, Jagellonian University, Cracow, Poland}                              
\par \filbreak                                                                                     
                                                           %                                       
  V.~Adler,                                                                                        
  U.~Behrens,                                                                                      
  I.~Bloch,                                                                                        
  K.~Borras,                                                                                       
  V.~Chiochia,                                                                                     
  D.~Dannheim$^{  10}$,                                                                            
  G.~Drews,                                                                                        
  J.~Fourletova,                                                                                   
  U.~Fricke,                                                                                       
  A.~Geiser,                                                                                       
  P.~G\"ottlicher$^{  11}$,                                                                        
  O.~Gutsche,                                                                                      
  T.~Haas,                                                                                         
  W.~Hain,                                                                                         
  S.~Hillert$^{  12}$,                                                                             
  C.~Horn,                                                                                         
  B.~Kahle,                                                                                        
  U.~K\"otz,                                                                                       
  H.~Kowalski,                                                                                     
  G.~Kramberger,                                                                                   
  H.~Labes,                                                                                        
  D.~Lelas,                                                                                        
  H.~Lim,                                                                                          
  B.~L\"ohr,                                                                                       
  R.~Mankel,                                                                                       
  I.-A.~Melzer-Pellmann,                                                                           
  C.N.~Nguyen,                                                                                     
  D.~Notz,                                                                                         
  A.E.~Nuncio-Quiroz,                                                                              
  A.~Polini,                                                                                       
  A.~Raval,                                                                                        
  \mbox{L.~Rurua},                                                                                 
  \mbox{U.~Schneekloth},                                                                           
  U.~St\"osslein,                                                                                  
  G.~Wolf,                                                                                         
  C.~Youngman,                                                                                     
  \mbox{W.~Zeuner} \\                                                                              
  {\it Deutsches Elektronen-Synchrotron DESY, Hamburg, Germany}                                    
\par \filbreak                                                                                     
                                                           %                                       
  \mbox{S.~Schlenstedt}\\                                                                          
   {\it DESY Zeuthen, Zeuthen, Germany}                                                            
\par \filbreak                                                                                     
                                                           %                                       
  G.~Barbagli,                                                                                     
  E.~Gallo,                                                                                        
  C.~Genta,                                                                                        
  P.~G.~Pelfer  \\                                                                                 
  {\it University and INFN, Florence, Italy}~$^{e}$                                                
\par \filbreak                                                                                     
                                                           %                                       
                                                           %                                       
  A.~Bamberger,                                                                                    
  A.~Benen,                                                                                        
  F.~Karstens,                                                                                     
  D.~Dobur,                                                                                        
  N.N.~Vlasov\\                                                                                    
  {\it Fakult\"at f\"ur Physik der Universit\"at Freiburg i.Br.,                                   
           Freiburg i.Br., Germany}~$^{b}$                                                         
\par \filbreak                                                                                     
  M.~Bell,                                          %                                              
  P.J.~Bussey,                                                                                     
  A.T.~Doyle,                                                                                      
  J.~Ferrando,                                                                                     
  J.~Hamilton,                                                                                     
  S.~Hanlon,                                                                                       
  D.H.~Saxon,                                                                                      
  I.O.~Skillicorn\\                                                                                
  {\it Department of Physics and Astronomy, University of Glasgow,                                 
           Glasgow, United Kingdom}~$^{m}$                                                         
\par \filbreak                                                                                     
  I.~Gialas\\                                                                                      
  {\it Department of Engineering in Management and Finance, Univ. of                               
            Aegean, Greece}                                                                        
\par \filbreak                                                                                     
  T.~Carli,                                                                                        
  T.~Gosau,                                                                                        
  U.~Holm,                                                                                         
  N.~Krumnack,                                                                                     
  E.~Lohrmann,                                                                                     
  M.~Milite,                                                                                       
  H.~Salehi,                                                                                       
  P.~Schleper,                                                                                     
  \mbox{T.~Sch\"orner-Sadenius},                                                                   
  S.~Stonjek$^{  12}$,                                                                             
  K.~Wichmann,                                                                                     
  K.~Wick,                                                                                         
  A.~Ziegler,                                                                                      
  Ar.~Ziegler\\                                                                                    
  {\it Hamburg University, Institute of Exp. Physics, Hamburg,                                     
           Germany}~$^{b}$                                                                         
\par \filbreak                                                                                     
  C.~Collins-Tooth,                                                                                
  C.~Foudas,                                                                                       
  R.~Gon\c{c}alo$^{  13}$,                                                                         
  K.R.~Long,                                                                                       
  A.D.~Tapper\\                                                                                    
   {\it Imperial College London, High Energy Nuclear Physics Group,                                
           London, United Kingdom}~$^{m}$                                                          
\par \filbreak                                                                                     
                                                           %                                       
                                                           %                                       
  P.~Cloth,                                                                                        
  D.~Filges  \\                                                                                    
  {\it Forschungszentrum J\"ulich, Institut f\"ur Kernphysik,                                      
           J\"ulich, Germany}                                                                      
\par \filbreak                                                                                     
                                                           %                                       
  M.~Kataoka$^{  14}$,                                                                             
  K.~Nagano,                                                                                       
  K.~Tokushuku$^{  15}$,                                                                           
  S.~Yamada,                                                                                       
  Y.~Yamazaki\\                                                                                    
  {\it Institute of Particle and Nuclear Studies, KEK,                                             
       Tsukuba, Japan}~$^{f}$                                                                      
\par \filbreak                                                                                     
                                                    %                                              
  A.N. Barakbaev,                                                                                  
  E.G.~Boos,                                                                                       
  N.S.~Pokrovskiy,                                                                                 
  B.O.~Zhautykov \\                                                                                
  {\it Institute of Physics and Technology of Ministry of Education and                            
  Science of Kazakhstan, Almaty, \mbox{Kazakhstan}}                                                
  \par \filbreak                                                                                   
                                                      %                                            
  D.~Son \\                                                                                        
  {\it Kyungpook National University, Center for High Energy Physics, Daegu,                       
  South Korea}~$^{g}$                                                                              
  \par \filbreak                                                                                   
  K.~Piotrzkowski\\                                                                                
  {\it Institut de Physique Nucl\'{e}aire, Universit\'{e} Catholique de                            
  Louvain, Louvain-la-Neuve, Belgium}                                                              
  \par \filbreak                                                                                   
                                                         %                                         
  F.~Barreiro,                                                                                     
  C.~Glasman$^{  16}$,                                                                             
  O.~Gonz\'alez,                                                                                   
  L.~Labarga,                                                                                      
  J.~del~Peso,                                                                                     
  E.~Tassi,                                                                                        
  J.~Terr\'on,                                                                                     
  M.~Zambrana\\                                                                                    
  {\it Departamento de F\'{\i}sica Te\'orica, Universidad Aut\'onoma                               
  de Madrid, Madrid, Spain}~$^{l}$                                                                 
  \par \filbreak                                                                                   
  M.~Barbi,                                                    %                                   
  F.~Corriveau,                                                                                    
  S.~Gliga,                                                                                        
  J.~Lainesse,                                                                                     
  S.~Padhi,                                                                                        
  D.G.~Stairs,                                                                                     
  R.~Walsh\\                                                                                       
  {\it Department of Physics, McGill University,                                                   
           Montr\'eal, Qu\'ebec, Canada H3A 2T8}~$^{a}$                                            
\par \filbreak                                                                                     
                                             %                                                     
  T.~Tsurugai \\                                                                                   
  {\it Meiji Gakuin University, Faculty of General Education,                                      
           Yokohama, Japan}~$^{f}$                                                                 
\par \filbreak                                                                                     
                                                           %                                       
  A.~Antonov,                                                                                      
  P.~Danilov,                                                                                      
  B.A.~Dolgoshein,                                                                                 
  D.~Gladkov,                                                                                      
  V.~Sosnovtsev,                                                                                   
  S.~Suchkov \\                                                                                    
  {\it Moscow Engineering Physics Institute, Moscow, Russia}~$^{j}$                                
\par \filbreak                                                                                     
                                                           %                                       
  R.K.~Dementiev,                                                                                  
  P.F.~Ermolov,                                                                                    
  I.I.~Katkov,                                                                                     
  L.A.~Khein,                                                                                      
  I.A.~Korzhavina,                                                                                 
  V.A.~Kuzmin,                                                                                     
  B.B.~Levchenko,                                                                                  
  O.Yu.~Lukina,                                                                                    
  A.S.~Proskuryakov,                                                                               
  L.M.~Shcheglova,                                                                                 
  S.A.~Zotkin \\                                                                                   
  {\it Moscow State University, Institute of Nuclear Physics,                                      
           Moscow, Russia}~$^{k}$                                                                  
\par \filbreak                                                                                     
  N.~Coppola,                                                                                      
  S.~Grijpink,                                                                                     
  E.~Koffeman,                                                                                     
  P.~Kooijman,                                                                                     
  E.~Maddox,                                                                                       
  A.~Pellegrino,                                                                                   
  S.~Schagen,                                                                                      
  H.~Tiecke,                                                                                       
  M.~V\'azquez,                                                                                    
  L.~Wiggers,                                                                                      
  E.~de~Wolf \\                                                                                    
  {\it NIKHEF and University of Amsterdam, Amsterdam, Netherlands}~$^{h}$                          
\par \filbreak                                                                                     
  N.~Br\"ummer,                                                                                    
  B.~Bylsma,                                                                                       
  L.S.~Durkin,                                                                                     
  T.Y.~Ling\\                                                                                      
  {\it Physics Department, Ohio State University,                                                  
           Columbus, Ohio 43210}~$^{n}$                                                            
\par \filbreak                                                                                     
                                                           %                                       
  A.M.~Cooper-Sarkar,                                                                              
  A.~Cottrell,                                                                                     
  R.C.E.~Devenish,                                                                                 
  B.~Foster,                                                                                       
  G.~Grzelak,                                                                                      
  C.~Gwenlan$^{  17}$,                                                                             
  T.~Kohno,                                                                                        
  S.~Patel,                                                                                        
  P.B.~Straub,                                                                                     
  R.~Walczak \\                                                                                    
  {\it Department of Physics, University of Oxford,                                                
           Oxford United Kingdom}~$^{m}$                                                           
\par \filbreak                                                                                     
  A.~Bertolin,                                                         %                           
  R.~Brugnera,                                                                                     
  R.~Carlin,                                                                                       
  F.~Dal~Corso,                                                                                    
  S.~Dusini,                                                                                       
  A.~Garfagnini,                                                                                   
  S.~Limentani,                                                                                    
  A.~Longhin,                                                                                      
  A.~Parenti,                                                                                      
  M.~Posocco,                                                                                      
  L.~Stanco,                                                                                       
  M.~Turcato\\                                                                                     
  {\it Dipartimento di Fisica dell' Universit\`a and INFN,                                         
           Padova, Italy}~$^{e}$                                                                   
\par \filbreak                                                                                     
                                                           %                                       
  E.A.~Heaphy,                                                                                     
  F.~Metlica,                                                                                      
  B.Y.~Oh,                                                                                         
  J.J.~Whitmore$^{  18}$\\                                                                         
  {\it Department of Physics, Pennsylvania State University,                                       
           University Park, Pennsylvania 16802}~$^{o}$                                             
\par \filbreak                                                                                     
                                                           %                                       
  Y.~Iga \\                                                                                        
{\it Polytechnic University, Sagamihara, Japan}~$^{f}$                                             
\par \filbreak                                                                                     
                                                           %                                       
  G.~D'Agostini,                                                                                   
  G.~Marini,                                                                                       
  A.~Nigro \\                                                                                      
  {\it Dipartimento di Fisica, Universit\`a 'La Sapienza' and INFN,                                
           Rome, Italy}~$^{e}~$                                                                    
\par \filbreak                                                                                     
                                                           %                                       
  C.~Cormack$^{  19}$,                                                                             
  J.C.~Hart,                                                                                       
  N.A.~McCubbin\\                                                                                  
  {\it Rutherford Appleton Laboratory, Chilton, Didcot, Oxon,                                      
           United Kingdom}~$^{m}$                                                                  
\par \filbreak                                                                                     
  C.~Heusch\\                                                                                      
{\it University of California, Santa Cruz, California 95064}, USA~$^{n}$                           
\par \filbreak                                                                                     
  I.H.~Park\\                                                                                      
  {\it Department of Physics, Ewha Womans University, Seoul, Korea}                                
\par \filbreak                                                                                     
                          %                                                                        
  N.~Pavel \\                                                                                      
  {\it Fachbereich Physik der Universit\"at-Gesamthochschule                                       
           Siegen, Germany}                                                                        
\par \filbreak                                                                                     
                                                           %                                       
  H.~Abramowicz,                                                                                   
  A.~Gabareen,                                                                                     
  S.~Kananov,                                                                                      
  A.~Kreisel,                                                                                      
  A.~Levy\\                                                                                        
  {\it Raymond and Beverly Sackler Faculty of Exact Sciences,                                      
School of Physics, Tel-Aviv University,                                                            
 Tel-Aviv, Israel}~$^{d}$                                                                          
\par \filbreak                                                                                     
                                                           %                                       
  M.~Kuze \\                                                                                       
  {\it Department of Physics, Tokyo Institute of Technology,                                       
           Tokyo, Japan}~$^{f}$                                                                    
\par \filbreak                                                                                     
  T.~Fusayasu,                                                                                     
  S.~Kagawa,                                                                                       
  T.~Tawara,                                                                                       
  T.~Yamashita \\                                                                                  
  {\it Department of Physics, University of Tokyo,                                                 
           Tokyo, Japan}~$^{f}$                                                                    
\par \filbreak                                                                                     
                                                           %                                       
  R.~Hamatsu,                                                                                      
  T.~Hirose$^{   2}$,                                                                              
  M.~Inuzuka,                                                                                      
  H.~Kaji,                                                                                         
  S.~Kitamura$^{  20}$,                                                                            
  K.~Matsuzawa\\                                                                                   
  {\it Tokyo Metropolitan University, Department of Physics,                                       
           Tokyo, Japan}~$^{f}$                                                                    
\par \filbreak                                                                                     
                                                           %                                       
  M.~Costa,                                                                                        
  M.I.~Ferrero,                                                                                    
  V.~Monaco,                                                                                       
  R.~Sacchi,                                                                                       
  A.~Solano\\                                                                                      
  {\it Universit\`a di Torino and INFN, Torino, Italy}~$^{e}$                                      
\par \filbreak                                                                                     
  M.~Arneodo,                                                                                      
  M.~Ruspa\\                                                                                       
 {\it Universit\`a del Piemonte Orientale, Novara, and INFN, Torino,                               
Italy}~$^{e}$                                                                                      
                                                           %                                       
\par \filbreak                                                                                     
                                    %                                                              
  T.~Koop,                                                                                         
  J.F.~Martin,                                                                                     
  A.~Mirea\\                                                                                       
   {\it Department of Physics, University of Toronto, Toronto, Ontario,                            
Canada M5S 1A7}~$^{a}$                                                                             
\par \filbreak                                                                                     
  J.M.~Butterworth$^{  21}$,                                                                       
  R.~Hall-Wilton,                                                                                  
  T.W.~Jones,                                                                                      
  M.S.~Lightwood,                                                                                  
  M.R.~Sutton$^{   4}$,                                                                            
  C.~Targett-Adams\\                                                                               
  {\it Physics and Astronomy Department, University College London,                                
           London, United Kingdom}~$^{m}$                                                          
\par \filbreak                                                                                     
                                                           %                                       
  J.~Ciborowski$^{  22}$,                                                                          
  R.~Ciesielski$^{  23}$,                                                                          
  P.~{\L}u\.zniak$^{  24}$,                                                                        
  R.J.~Nowak,                                                                                      
  J.M.~Pawlak,                                                                                     
  J.~Sztuk$^{  25}$,                                                                               
  T.~Tymieniecka,                                                                                  
  A.~Ukleja,                                                                                       
  J.~Ukleja$^{  26}$,                                                                              
  A.F.~\.Zarnecki \\                                                                               
   {\it Warsaw University, Institute of Experimental Physics,                                      
           Warsaw, Poland}~$^{q}$                                                                  
\par \filbreak                                                                                     
                                                           %                                       
  M.~Adamus,                                                                                       
  P.~Plucinski\\                                                                                   
  {\it Institute for Nuclear Studies, Warsaw, Poland}~$^{q}$                                       
\par \filbreak                                                                                     
                                                           %                                       
  Y.~Eisenberg,                                                                                    
  D.~Hochman,                                                                                      
  U.~Karshon                                                                                       
  M.~Riveline\\                                                                                    
    {\it Department of Particle Physics, Weizmann Institute, Rehovot,                              
           Israel}~$^{c}$                                                                          
\par \filbreak                                                                                     
  A.~Everett,                                                                                      
  L.K.~Gladilin$^{  27}$,                                                                          
  D.~K\c{c}ira,                                                                                    
  S.~Lammers,                                                                                      
  L.~Li,                                                                                           
  D.D.~Reeder,                                                                                     
  M.~Rosin,                                                                                        
  P.~Ryan,                                                                                         
  A.A.~Savin,                                                                                      
  W.H.~Smith\\                                                                                     
  {\it Department of Physics, University of Wisconsin, Madison,                                    
Wisconsin 53706}, USA~$^{n}$                                                                       
\par \filbreak                                                                                     
                                                           %                                       
  A.~Deshpande,                                                                                    
  S.~Dhawan\\                                                                                      
  {\it Department of Physics, Yale University, New Haven, Connecticut                              
06520-8121}, USA~$^{n}$                                                                            
 \par \filbreak                                                                                    
                                                           %                                       
  S.~Bhadra,                                                                                       
  C.D.~Catterall,                                                                                  
  S.~Fourletov,                                                                                    
  G.~Hartner,                                                                                      
  S.~Menary,                                                                                       
  M.~Soares,                                                                                       
  J.~Standage\\                                                                                    
  {\it Department of Physics, York University, Ontario, Canada M3J                                 
1P3}~$^{a}$                                                                                        
                                                           %                                       
\newpage                                                                                           
                                                           %                                       
$^{\    1}$ also affiliated with University College London, London, UK \\                          
$^{\    2}$ retired \\                                                                             
$^{\    3}$ self-employed \\                                                                       
$^{\    4}$ PPARC Advanced fellow \\                                                               
$^{\    5}$ now at Dongshin University, Naju, South Korea \\                                       
$^{\    6}$ now at Max-Planck-Institut f\"ur Physik,                                               
M\"unchen, Germany\\                                                                               
$^{\    7}$ partly supported by Polish Ministry of Scientific                                      
Research and Information Technology, grant no. 2P03B 12225\\                                       
$^{\    8}$ partly supported by Polish Ministry of Scientific Research and Information             
Technology, grant no.2P03B 12625\\                                                                 
$^{\    9}$ supported by the Polish State Committee for Scientific                                 
Research, grant no. 2 P03B 09322\\                                                                 
$^{  10}$ now at Columbia University, N.Y., USA \\                                                 
$^{  11}$ now at DESY group FEB \\                                                                 
$^{  12}$ now at University of Oxford, Oxford, UK \\                                               
$^{  13}$ now at Royal Holoway University of London, London, UK \\                                 
$^{  14}$ also at Nara Women's University, Nara, Japan \\                                          
$^{  15}$ also at University of Tokyo, Tokyo, Japan \\                                             
$^{  16}$ Ram{\'o}n y Cajal Fellow \\                                                              
$^{  17}$ PPARC Postdoctoral Research Fellow \\                                                    
$^{  18}$ on leave of absence at The National Science Foundation, Arlington, VA, USA \\            
$^{  19}$ now at University of London, Queen Mary College, London, UK \\                           
$^{  20}$ present address: Tokyo Metropolitan University of                                        
Health Sciences, Tokyo 116-8551, Japan\\                                                           
$^{  21}$ also at University of Hamburg, Alexander von Humboldt                                    
Fellow\\                                                                                           
$^{  22}$ also at \L\'{o}d\'{z} University, Poland \\                                              
$^{  23}$ supported by the Polish State Committee for                                              
Scientific Research, grant no. 2P03B 07222\\                                                       
$^{  24}$ \L\'{o}d\'{z} University, Poland \\                                                      
$^{  25}$ \L\'{o}d\'{z} University, Poland, supported by the                                       
KBN grant 2P03B12925\\                                                                             
$^{  26}$ supported by the KBN grant 2P03B12725 \\                                                 
$^{  27}$ on leave from MSU, partly supported by                                                   
the Weizmann Institute via the U.S.-Israel BSF\\                                                   
                                                           %                                       
                                                           %                                       
% \par         % if index listing & table fit to 1 page, put gap here                              
\newpage   % alternatively: go to newpage, if page is too small                                    
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% \institute_references_start    % do not touch or move this line !                                
                                                           %                                       
\begin{tabular}[h]{rp{14cm}}                                                                       
                                                           %                                       
$^{a}$ &  supported by the Natural Sciences and Engineering Research                               
          Council of Canada (NSERC) \\                                                             
$^{b}$ &  supported by the German Federal Ministry for Education and                               
          Research (BMBF), under contract numbers HZ1GUA 2, HZ1GUB 0, HZ1PDA 5, HZ1VFA 5\\         
$^{c}$ &  supported by the MINERVA Gesellschaft f\"ur Forschung GmbH, the                          
          Israel Science Foundation, the U.S.-Israel Binational Science                            
          Foundation and the Benozyio Center                                                       
          for High Energy Physics\\                                                                
$^{d}$ &  supported by the German-Israeli Foundation and the Israel Science                        
          Foundation\\                                                                             
$^{e}$ &  supported by the Italian National Institute for Nuclear Physics (INFN) \\                
$^{f}$ &  supported by the Japanese Ministry of Education, Culture,                                
          Sports, Science and Technology (MEXT) and its grants for                                 
          Scientific Research\\                                                                    
$^{g}$ &  supported by the Korean Ministry of Education and Korea Science                          
          and Engineering Foundation\\                                                             
$^{h}$ &  supported by the Netherlands Foundation for Research on Matter (FOM)\\                   
$^{i}$ &  supported by the Polish State Committee for Scientific Research,                         
          grant no. 620/E-77/SPB/DESY/P-03/DZ 117/2003-2005\\                                      
$^{j}$ &  partially supported by the German Federal Ministry for Education                         
          and Research (BMBF)\\                                                                    
$^{k}$ &  supported by RF President grant N 1685.2003.2 for the leading                            
          scientific schools and by the Russian Ministry of Industry, Science                      
          and Technology through its grant for Scientific Research on High                         
          Energy Physics\\                                                                         
$^{l}$ &  supported by the Spanish Ministry of Education and Science                               
          through funds provided by CICYT\\                                                        
$^{m}$ &  supported by the Particle Physics and Astronomy Research Council, UK\\                   
$^{n}$ &  supported by the US Department of Energy\\                                               
$^{o}$ &  supported by the US National Science Foundation\\                                        
$^{p}$ &  supported by the Polish Ministry of Scientific Research and Information                  
          Technology, grant no. 112/E-356/SPUB/DESY/P-03/DZ 116/2003-2005\\                        
$^{q}$ &  supported by the Polish State Committee for Scientific Research,                         
          grant no. 115/E-343/SPUB-M/DESY/P-03/DZ 121/2001-2002, 2 P03B 07022\\                    
                                                       %                                           
\end{tabular}                                                                                      
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%\end{document}                                                                                     

piex-cit.tex
%==============================================================================
%	Some definitions of citations
%==============================================================================
%------------------------------------------------------------------------------
%	-> CTD
%------------------------------------------------------------------------------
\def\citeCTD{{\cite{%
nim:a279:290,*npps:b32:181,*nim:a338:254%
}}\xspace}
%------------------------------------------------------------------------------
%	-> CAL
%------------------------------------------------------------------------------
\def\citeCAL{{\cite{%
nim:a309:77,*nim:a309:101,*nim:a321:356,*nim:a336:23%
}}\xspace}

piex-fig.tex
%--------------------------------------------------------------------------
%       Results
%--------------------------------------------------------------------------


\begin{figure} 
\centerline{\epsfig{file=figures/detector.epsi,width=10.0cm,height=10.0cm}}
\caption{
The FNC as viewed from the rear with the tower numbers indicated on the
left-hand side.
The scintillator strips of the FNT hodoscope are shown 
superposed on towers 6-9
of the FNC.
The irregular contour shows the outline of
the geometric acceptance allowed by the proton beam-line
elements.  
The full square
%$\bullet$ 
indicates the approximate position of the projection of the zero-degree 
line.
The proton beampipe, shown as a circle, passes through a hole
in the upper part of the FNC. 
}
\label{fig-PositionFNT}
\end{figure}

\clearpage

\begin{figure}[htbp!]
\begin{center}\centerline{\epsfig{file=figures/fig2.eps,width=16cm}}
%\centerline{\epsffile{figures/tbins_feb2.eps,width=12cm}}
\end{center}\caption{
The  $x_L$ distribution
in bins of  $t$. 
The curves show the
results of fits to the data with $0.64<x_L<0.925$
to the form $(1-x_L)^{a(t)}$.
The inner error bars indicate the  statistical uncertainties
and the full bars indicate the quadratic sum of the statistical
and systematic uncertainties.
%Only statistical errors are used in the fits.
}
\label{fig-xl}
\end{figure}

\clearpage

\begin{figure}[htbp!]
\centerline{\epsfig{file=figures/fig3.eps,width=16cm}}
\caption{
The powers, $a(t)$, with statistical errors, 
as a function of $-t$.
The solid line is the result of the fit described in the text.
%The powers follow a trajectory in $t$ which
%has been fit to a straight line. 
%The error bars show the contribution of statistical error
%to the total uncertainty. 
The shaded band 
% at the bottom of the plot
shows the systematic
uncertainty.
%Only statistical errors are used in the fit.
}
\label{fig-3}
\end{figure}


piex-ref.tex
{
\def\bibname{\Large\bf References}
\def\refname{\Large\bf References}
\pagestyle{plain}
\ifzeusbst
  \bibliographystyle{./BiBTeX/bst/l4z_default}
\fi
\ifzdrftbst
  \bibliographystyle{./BiBTeX/bst/l4z_draft}
\fi
\ifzbstepj
  \bibliographystyle{./BiBTeX/bst/l4z_epj}
\fi
\ifzbstnp
  \bibliographystyle{./BiBTeX/bst/l4z_np}
\fi
\ifzbstpl
  \bibliographystyle{./BiBTeX/bst/l4z_pl}
\fi
{\raggedright
\bibliography{./BiBTeX/user/syn.bib,%
	      ./BiBTeX/user/extra.bib,%
              ./BiBTeX/bib/l4z_articles.bib,%
              ./BiBTeX/bib/l4z_books.bib,%
              ./BiBTeX/bib/l4z_conferences.bib,%
              ./BiBTeX/bib/l4z_h1.bib,%
              ./BiBTeX/bib/l4z_misc.bib,%
              ./BiBTeX/bib/l4z_old.bib,%
              ./BiBTeX/bib/l4z_preprints.bib,%
              ./BiBTeX/bib/l4z_replaced.bib,%
              ./BiBTeX/bib/l4z_temporary.bib,%
              ./BiBTeX/bib/l4z_zeus.bib}}
}
\vfill\eject

piex-tab.tex
%-------------------------------------------------------------------------------
%       tables
%-------------------------------------------------------------------------------

piex-tit.tex
\prepnum{DESY--04--037}

\title{
Study of the pion trajectory\\
in the photoproduction\\
of leading neutrons at HERA\\
}                                                       
                    
\author{ZEUS Collaboration}
\date{\today}

\abstract{
Energetic neutrons produced
in $ep$ collisions  at HERA have been studied
with the ZEUS detector in the photoproduction regime 
at a mean photon-proton center-of-mass energy of 220~GeV.
The neutrons carry a large fraction $0.64 < x_L <0.925$ of the
incoming proton energy, and the
four-momentum-transfer squared at the proton-neutron vertex  is small,
$|t|<0.425$ GeV$^2$. 
The $x_L$ distribution of the neutrons is measured 
in bins of $t$. 
The $(1-x_L)$ distributions in the $t$ bins studied satisfy a power law 
$dN/dx_L \propto (1-x_L)^{a(t)}$, 
with the powers $a(t)$ following a linear function of
$t$:
\mbox{$a(t)=0.88\pm 0.09 ({\rm stat.})^{+0.34}_{-0.39}({\rm syst.})-(2.81\pm 0.42({\rm stat.})^{+1.13}_{-0.62}({\rm syst.})\ {\rm GeV}^{-2})t$.}
This result is consistent with the expectations of 
pion-exchange models, in which the incoming proton fluctuates
to a neutron-pion state, and the electron interacts with the pion.
}

\makezeustitle


piex-txt.tex
\newcommand{\xgo}{x_{\gamma}^{\mbox{\rm\tiny OBS}}}
\newcommand{\xpo}{x_p^{\mbox{\rm\tiny OBS}}} 
\newcommand{\xpio}{x_{\pi}^{\mbox{\rm\tiny OBS}}} 
\newcommand{\ETJ}{\ensuremath{E_{\mbox{\rm\tiny T}}^{\mbox{\rm\tiny jet}}}}
\newcommand{\ETAJ}{\ensuremath{\eta^{\mbox{\rm\tiny jet}}}}
\newcommand{\ETAB}{\ensuremath{\bar{\eta}}}
\newcommand{\lap}{\ensuremath{\stackrel{_{\scriptstyle <}}{_{\scriptstyle\sim}}}}
\newcommand{\gap}{\ensuremath{\stackrel{_{\scriptstyle >}}{_{\scriptstyle\sim}}}}

\pagenumbering{arabic} 
\pagestyle{plain}
% ----------------------------------------------------------------------------
%       Introduction
% ----------------------------------------------------------------------------
\section{Introduction}
\label{sec-int}


Several studies
of leading neutron production in $ep$ interactions at HERA 
 have been  reported previously
 \cite{pl:b384:388,np:b596:3,np:b637:3,charm-with-neutron,epj:c6:587}.
Many features of the data are described by
pion exchange models, in which the incoming proton
fluctuates into a neutron-pion state and the pion interacts
with the incoming electron or positron.
The kinematic variables $t$, the square of the four-momentum
transfer at the proton-neutron vertex, and $x_L$,
the energy fraction
of the proton carried by the neutron, are 
convenient variables for studying energy-angle
correlations. 
In this 
%contribution,
% these analyses are extended to 
study of semi-inclusive photoproduction,
$\gamma p\rightarrow n X$, where the photon is quasi-real, 
the energy distribution
of leading neutrons is measured as a function of $t$, which is  
determined using a new position detector to measure 
the angle of the neutron.
The $(1-x_L)$ distribution is presented as a function of $t$
for large $x_L$ ($0.64<x_L<0.925$) and small $|t|$ ($|t|<0.425$ GeV$^2$).
The results
are interpreted in the context of pion exchange, 
in order to provide a test of the consistency of this 
picture of leading neutron production.

% ---------------------------------------------------------------------
%       Experimental set-up
% ---------------------------------------------------------------------
\section{Experimental set-up and kinematics}
\label{sec-exp}

The data used for this measurement were 
collected in the year 2000 at the $ep$ collider HERA with the 
ZEUS detector,
during a short run period in which a special trigger was implemented.
The data set corresponds to an integrated  luminosity  
of 9 pb$^{-1}$. During this period
HERA collided $27.5\gev$ positrons with $920\gev$ protons at a
center-of-mass energy of $318\gev$. 

%\Zdetdesc
%\Zctddesc{\ZcoosysfnBeta}
%\Zctddesc{}
Charged particles are tracked in the central tracking detector\citeCTD,
which operates in a magnetic field of $1.43\Tesla$ provided by a thin 
superconducting solenoid
and covers the polar-angle{\ZcoosysfnA} 
region 
\mbox{$15^\circ<\theta<164^\circ$}. 
Outside the solenoid is a hermetic, high-resolution 
uranium--scintillator calorimeter (CAL)~\citeCAL used to measure
the energies of the final-state particles.


Bremsstrahlung 
$ep \rightarrow e \gamma p$ and the photoproduction of hadrons
$ep \rightarrow e X$ are tagged using the luminosity (LUMI) detectors
\cite{desy-92-066,*zfp:c63:391,*acpp:b32:2025}. 
The bremsstrahlung photons are measured with a
lead-scintillator calorimeter 
located 107~m from the interaction point in the
positron-beam direction. 
% The energy resolution of the calorimeter is
%0.18$\sqrt{E}$ ($E$ in $\Gev$).
 A similar calorimeter at
35~m from the interaction point is used to measure positrons scattered
at very small angles in an energy range 5-20~GeV, with an
energy resolution of 0.19$\sqrt{E}$ ($E$ in $\Gev$).
%Events tagged by these electrons define a data set of
%quasi-real photoproduction, since the virtuality of the
%photon exchanged between the positron and the proton is
%almost zero.

  

ZEUS has two detectors for measuring forward particles,
a leading proton spectrometer (LPS)\cite{zfp:c73:253}, 
consisting of six stations of silicon 
strip detectors, and a forward neutron calorimeter (FNC) 
\cite{nim:a354:479,nim:a394:121,proc:calor97:295}  downstream from
the LPS, 105~m from the interaction point.
%was installed in the HERA tunnel at 
%\mbox{$\theta = 0$} degrees 
%and 106 m from the interaction point in the 
%proton-beam direction, and used for the 1995-2000 data taking.
The FNC is a
lead-scintillator sampling calorimeter, the front section of which
is divided into 14 towers,  
%with 134 layers of 1.25~cm thick 
%lead as the absorber and 0.26~cm thick scintillator as the active 
%material.
%The scintillator is 
%read out on each side with
%wavelength-shifting light-guides coupled 
%to photomultiplier tubes. 
%It is segmented longitudinally into a front section, seven 
%interaction-lengths deep, and a rear section, three interaction-lengths 
%deep.
%The front section is divided vertically into 14 towers,
as illustrated in Fig.~\ref{fig-PositionFNT}.
%,
%allowing the separation of electromagnetic and hadronic showers
%using the energy-weighted vertical width of the showers.
%(see Fig.~\ref{fig-PositionFNT}).  
The hadronic energy resolution,
as measured in a pion test beam at 120~GeV, 
is
$0.65\sqrt{E}$ ($E$ in GeV). 
%Neutrons are easily distinguished from protons,
%because the latter are deflected upwards by the beam magnets
%and deposit most of their energy in
%the top four towers of the FNC.
Three planes of veto counters, 
%each $70\times 50\times\,2$ cm$^3$, 
located 70, 78, and 199 cm 
%of the calorimeter.  
%%$50\,\mathrm{x}\,50\,\mathrm{x}\,2$ cm$^3$. 
%These counters, which completely cover the bottom front
in front of the calorimeter, are used to detect charged
particles produced by neutrons interacting in inactive material
in front of the FNC. 

Magnet apertures limit the FNC geometric acceptance to neutrons 
inside the area outlined in Fig.~\ref{fig-PositionFNT}. This
limit corresponds to 
neutron production angles less than 
%$\theta_{\mbox{\rm\tiny max}}<
0.8~mrad;
i.e., to transverse momenta $p_T = E_n\theta_n \le 0.74x_L$~GeV. 
The neutron production angle, $\theta_n$,
is measured with respect to the proton beam
direction at the interaction point.
%onto the FNC defines the
The mean value of $p_T$ of the detected neutrons is 0.22~GeV. 
The overall acceptance of the FNC
%, which includes beam-line geometry, 
%absorbing material, and the angular distribution of the neutrons,
is about 25\%
for neutrons with energy \mbox{$x_L > 0.6$}
and \mbox{$\theta_n<0.8$ mrad}.

The forward neutron tracker (FNT), designed to measure the position
of neutron showers, 
was installed in the FNC in 1998.  
It consists of two hodoscope planes of 1.2~cm-wide scintillator strips,
with 17 strips measuring the $X$ position and 15 strips measuring the
 $Y$ position.
%It is a crossed hodoscope designed to measure the position of neutron
%showers, consisting of scintillator fingers 1.2~cm wide read out by
%wavelength-shifting fibers.
% 17 for x position 
%reconstruction and 15 for y. 
Figure~\ref{fig-PositionFNT} shows the position of the FNT hodoscope in the
FNC in the plane transverse to the beam as well as the zero-degree point, the
projection of the proton beam direction at the interaction point onto the FNT.
The FNT is situated approximately one interaction length
inside the FNC. This position is deep enough that a large fraction
of the neutrons begin to shower in front of the FNT, but not so deep
as to compromise the position resolution. 
% replacing layer 16 of the FNC 
%Scans with a  radioactive $^{60}{\rm Co}$ source were performed to calibrate
%and monitor the FNT.
The position resolution of neutron showers in the FNT
 was measured to be 0.23~cm by placing an adjustable
collimator in front of 
%the most outer veto counters of 
the FNC during special test and calibration runs.

% ---------------------------------------------------------------------
%       The kinematics
% ---------------------------------------------------------------------
%\section{Kinematics}


The kinematics of inclusive photoproduction $ep\rightarrow 
e\gamma p \rightarrow eX$ at HERA
is specified by $W$, the photon-proton center-of-mass energy.
This is related to the positron-proton center-of-mass energy, 
$\sqrt{s}$, by $W^2=ys$. The inelasticity, $y$, of the scattered positron
is defined by $y=(E-E')/E$, where $E$~($E'$) is
 the energy of the incoming (scattered) positron.
%The virtuality $Q^2$ of the exchanged photon is negligible compared to $W^2$.


To describe the neutron-tagged process 
$ep \rightarrow e\gamma p \rightarrow enX$,
the variables $x_L$ and $p_T$ are also used. These are related to $t$ by 
\[
t \approx -\frac{p^2_T}{x_L}-\frac{(1-x_L)}{x_L}\left(m^2_n-x_L m^2_p\right),
\]
where
$m_p$ is the mass of the proton and $m_n$ is the mass of the
neutron.


% ---------------------------------------------------------------------
%       Event selection
% ---------------------------------------------------------------------
\section{Event selection}
\label{sec-sel}

%\subsection{Trigger}

The data sample was collected using a trigger that required at least 5 GeV 
in the LUMI electron calorimeter in coincidence with at least 0.5~GeV 
in the rear part 
\mbox{$(\theta > 127^\circ)$}
of the CAL.
%RCAL EMC.
 In addition, the trigger required an energy deposit in the FNC corresponding
to $x_L > 0.2$.
The trigger efficiency of the FNC
was close to 100\%
for the $x_L$ range under consideration in this paper
($x_L > 0.64$).


Photoproduction events were selected offline using cuts based
on the reconstructed vertex position and calorimeter energy deposits.
The events were required to have an energy in the
LUMI electron calorimeter in the range $10<E'<18$~GeV
and an energy in the LUMI photon calorimeter smaller than
%$E_{\gamma}<
$1$~GeV to eliminate bremsstrahlung overlap events.
These cuts restricted the photon virtuality, $Q^2$, to values smaller than
$\sim 0.02$~GeV$^{2}$, with a median value
of $\approx 10^{-3}$~GeV$^2$, and 
resulted in a mean value for $W$ of 220 GeV.
% peak in this region.


Events with a leading neutron were selected 
offline
by requiring  $x_L>0.64$ and by
imposing the following cleaning cuts.
%The segmentation of the FNC
%permits the identification of protons, photons, and neutrons. 
Scattered protons, bent into the top towers 11 to 14 of the FNC (Fig.~1)
by the HERA dipole magnets, 
%
%The geometric
%aperture of the FNC for neutral particles at normal incidence 
%is centered on towers 7 and 8. 
%Scattered protons 
were eliminated 
by requiring that the tower with the maximum energy deposit
be in the range 6 to 9.
% Although both photons and neutrons
%produce large energy deposits in the bottom section
%(towers 1-10), the vertical spread of electromagnetic showers is
%much less than that of hadronic showers.
Photons were removed by eliminating showers with a small energy-weighted vertical width.
%spread ($\le 3$ cm).    

Neutrons that started showering in front of the FNC were
removed by requiring that the scintillator veto counter farthest
from the FNC had an energy deposit below that of a minimum-ionizing particle.
 To minimize false vetoes due to
calorimeter albedo, only the farthest counter was used.
% Showers with spreads greater than 7.5~cm were
%also removed, since they are inconsistent with 
%having originated from a single high-energy hadron.

 Finally, only events 
with $x_L < 0.925$ were used in the analysis, since the effect of any
error in the energy scale, and the
influence of exchanges other than the pion, become significant 
 at high $x_L$ (see Sections 5 and 6, respectively).
After these selection  cuts, the data sample consisted of  31\,756
events.

Not all neutrons start to shower in front of the FNT.
To select events with useful position information, it was  required
that the energy deposited in each plane of the FNT be well above pedestal and 
that the strips with the two largest energy deposits be adjacent.
These cuts reduced the sample to 
17\,919 events.

\section{Neutron efficiencies and correction factors}
\label{sec-mc}

The efficiencies and correction factors for the 
leading neutron were calculated with a single-particle Monte Carlo (MC)
simulation. The MC program included the geometry of
the proton beam-line magnets which define the geometric acceptance, 
the details of the absorbing material as obtained from survey measurements, 
the proton beam
divergence, and the measured energy (FNC) and position (FNT) resolutions
% of the FNC and FNT
for hadronic showers.  The  MC program accounts for the different amount of 
absorbing material in front of the FNC for the two cases when the ZEUS LPS
was, or was not, in the data-taking position.
Events were generated using the observed $x_L$ spectrum and
an exponential distribution in transverse momentum,
\mbox{$e^{-b(x_L)p_T^2}$}.
%since the data have this behaviour.
The slope  $b(x_L)$ was iterated until the MC
distributions matched the
observed uncorrected distributions. The corrected
data distributions were obtained using bin-by-bin unfolding. The two samples of data, corresponding to the two cases 
 when the LPS was, or was not, in the data-taking position, were corrected independently.


The simulation of the absorbing 
material was cross-checked
by producing a material map 
from an analysis of low-energy ($x_L < 0.27$) neutron data, under the
assumption that low $x_L$ neutrons are distributed uniformly over the
geometric acceptance. This assumption is based on noting that
both the maximum $p_T$ accepted by the FNC 
as well as the slope $b$ decrease with $x_L$\cite{np:b637:3},
and hence the geometric acceptance covers
a small region of a slowly changing $p_T$ distribution. 
%and the slope in $p_T^2$ decreases with $x_L$.
%% low $x_L$ neutrons are
%distributed approximately uniformly over the aperture.
An analysis using this material map gives results consistent 
  with those obtained using the material
measurements from the survey. 



The proton beam had a transverse momentum spread of approximately
0.04 GeV horizontally and 0.1 GeV vertically, as measured
by the LPS.
The variation of
the proton beam orbit was considerably smaller than this spread.
The spread broadens the observed position distribution of the neutrons in 
the FNC, but does not change the peak position. 

\section{Results}
\label{sec-re}

The events were binned in $x_L$ and $t$. The bins were chosen to be well within
the acceptance in the $x_L$-$t$ plane and contained 12\,523 events. The 
corrected $x_L$ distributions of leading neutrons 
as a function of $t$ are shown in
Fig.~\ref{fig-xl}.
%The error bars
%show the contribution of statistical error to the 
%total uncertainty.
The distributions are consistent with a power-law dependence in
$(1-x_L)$ of the form $dN/dx_L \propto (1-x_L)^{a(t)}$.
For each $t$ bin the power $a(t)$ was obtained by a 
least-squares fit of this function to the observed distribution.
%for $x_L<0.925$. 
%At higher $x_L$ 
Only statistical errors were used in the fits because
the systematic uncertainties  are highly correlated.
The resulting fits are superposed on the measured
data points.

There are two main sources of systematic uncertainty: an uncertainty
of  $\pm 2$\% in the absolute energy scale of the 
FNC resulting from the calibration procedure
\cite{proc:calor97:295,np:b637:3,peterf}, 
and an uncertainty of
 $\pm 0.2$ cm in each of the 
$X$ and $Y$ coordinates of the zero-degree point determined from the peak
in the $X,Y$ distribution in the FNT
\cite{thoko}. 
The systematic uncertainties on $a(t)$ were obtained
by varying the energy scale and beam-spot position
within their uncertainties and then repeating the complete 
analysis. The dominant contribution comes from 
the energy-scale uncertainty.




The powers determined from the fits to the data in Fig.~2 are 
plotted as a function of $-t$ in
Fig.~\ref{fig-3}.
They are consistent with a linear function,
\[
a(t)=0.88\pm 0.09 ({\rm stat.})^{+0.34}_{-0.39}({\rm syst.})-(2.81\pm 0.42({\rm stat.})^{+1.13}_{-0.62}({\rm syst.})\ {\rm GeV}^{-2})t.
\]
The correlation between the slope and the intercept is predominantly statistical; the coefficient of  correlation is -0.9.


\section{Discussion}
\label{sec-dis}

Previous experiments ([3]
%\cite{np:b637:3} 
and references therein)
have shown that leading
neutron production in lepton-hadron and 
hadron-hadron experiments can be described by
pion-exchange models.
The consistency of this description can be tested
%It is possible to test this by
by assuming that pion exchange is the dominant mechanism and
deriving the pion Regge trajectory from the measured values
of $a(t)$.

The pion ``flux'', the 
splitting function of a proton to a neutron and pion
($p\rightarrow n \pi^+$), can be written\cite{pl:b38:510} as
%[M. Bishari, Phys. Lett. B 38 (1972) 510] 
%\[
\begin{eqnarray}
f_{\pi /p}(x_L ,t) = \frac {1}{4 \pi}\frac{g_{n \pi p}^2}{4 \pi}
\frac{-t}{(m^2_{\pi}-t)^2}(1-x_L )^{1-2 \alpha_ \pi (t)}
\left(F(x_L,t)\right)^2,
\label{eqn-flux}
\end{eqnarray}
%\]
where $g_{n \pi p}$ is the coupling at the $n \pi p$ vertex, 
$m_{\pi}$ is the mass of the pion, and
$\alpha_{\pi}(t)=\alpha_{\pi} '( t - m_{\pi}^2)$ is
the Regge trajectory 
%(with slope $\alpha_{\pi}'$
%and intercept ${\cal O} (m_{\pi}^2)$)
of the pion\cite{pitraj1}. 
The function $F(x_L,t)$ is a form-factor which accounts
for the effect of hadronic structure 
on the  $p\rightarrow \pi n$ amplitude
and  for final-state rescattering of the neutron.
As discussed elsewhere\cite{np:b596:3}, this prescription for the flux
with $F(x_L,t)$ set to 1 describes most of the $pn
\rightarrow Xp$ data and also gives a good description of
the ZEUS $x_L$ spectrum for photoproduced
neutrons\cite{np:b596:3,np:b637:3}. In this analysis it is
assumed that $F(x_L,t)$ is a function of $t$ only.


The flux is thus of the form 
$f_{\pi /p}=A(t)\; (1-x_L)^{1-2 \alpha_ \pi (t)}$.
The cross section for neutron production is
given by the product of the flux and 
the total $\gamma \pi$ cross-section 
%$\sigma_{\gamma\pi}=
$\sigma_{\gamma\pi}(s') = 
\sigma_{\gamma\pi}\left( (1-x_L)W^2 \right)  $ as
\[
\frac{d^2 \sigma}{dx_L dt} = A(t) (1-x_L)^{1-2 \alpha_ \pi (t)}
       \sigma_{\gamma\pi}\left( (1-x_L)W^2 \right),
\]
where $s'=(1-x_L)W^2$ is the square of the $\gamma\pi$ center-of-mass energy.
The total $\gamma \pi$ cross section 
%$\sigma_{\gamma\pi}$ 
is assumed to have
a power law dependence on $s'$, for large $s'$, of
the Donnachie-Landshoff form
\cite{pl:b296:227}
\[
\sigma_{\gamma\pi}(s') = {\cal A}(s')^\epsilon+{\cal B}(s')^{-\eta},
\]
where $\epsilon\approx 0.1$ and $\eta\approx 0.5$.
The two terms correspond to the exchange of the Pomeron ($\pom$)
and the Reggeon ($\reg$), respectively. 
For large $s'$ the Pomeron contribution dominates that of
the Reggeon. In this case the $(1-x_L)$ 
distribution is proportional to $(1-x_L)^{a(t)}$, where
%_{\rm{eff}}
%the power is given by 
\[
a(t)=1+\epsilon-2\alpha_{\pi} ' t .
\]
Here $m_{\pi}^2$ has been ignored, since its effect on the result
is much smaller than the systematic error.
Therefore, the measured linear function $a(t)$ discussed in Section~5
has an intercept of 
\mbox{$\alpha_{\pom}(0)=(1+\epsilon )$},
the value of the Pomeron trajectory at
\mbox{$t=0$},
and a slope of $2\alpha_{\pi} '$,
twice the slope of the pion trajectory.

It is assumed that the $\pom$ term dominates in the $x_L$ region
of this measurement. The fit\cite{pl:b296:227}
to the total $\gamma p$ cross section
suggests that the highest contribution of the $\reg$ term is
about 12\% at $x_L=0.925$. 
As $x_L$ decreases ($s'$ increases), the Reggeon contribution
falls rapidly. No correction for the Reggeon contribution is applied in
this analysis. 
% A correction for the Reggeon contribution
%is not included in the results. 

Previous measurements of the effective Regge trajectory  
in the $p\rightarrow n$ transition
in hadronic interactions\cite{pitraj1,pitraj2,pitraj3}
found it to be dominated by the pion, with 
the intercept in the range -0.1 to 0.3 and the slope
in the range 1.1 to 1.3~GeV$^{-2}$.


The values extracted from the experimental results,
\[
1+\epsilon=\alpha_{\pom}(0)=0.88\pm 0.09 ({\rm stat.})^{+0.34}_{-0.39}({\rm syst.}) 
\] 
and
\[
 \alpha'_{\pi} = 
1.40\pm 0.21({\rm stat.})^{+0.56}_{-0.31}({\rm syst.})\ {\rm GeV}^{-2},
\]
are consistent
with the expectation that
%\mbox{$\alpha_{\pom}(0)\simeq 1.1$} and 
\mbox{$\alpha_{\pom}(0)$} is about 1.1 and
%\mbox{$\alpha'_{\pi}\simeq 1$}, and
\mbox{$\alpha'_{\pi}$} is about 1~GeV$^{-2}$ 
in the range of $ 0.08 < -t < 0.425 $ 
GeV$^{2}$, and so support the hypothesis that
%give direct evidence for the 
pion exchange is the dominant process 
in this reaction. Note that the data rule out a significant
role for $\rho$ exchange. If the $\rho$ trajectory,
$\alpha_{\rho} = 0.5 + t$\cite{rhotraj1}, is substituted for the pion
trajectory in Eq.~(1), the  value for $1+\epsilon$ extracted
from the data  is 1.88 rather than 0.88, which is an inconsistent
result for $\alpha_{\pom}(0)$.


\section{Summary}

The dependence of the energy distribution of photoproduced 
leading neutrons on 
the momentum transfer at the proton-neutron vertex
has been studied  
at an average photon-proton center-of-mass energy of 220~GeV.
%Within the experimental uncertainties,
%\begin{itemize}
%\item 
The $(1-x_L)$ distributions in bins of $t$ are described by a power law,
$dN/dx_L \propto (1-x_L)^{a(t)}$, 
with the powers $a(t)$ following a linear function of
$t$:
\mbox{$a(t)= 0.88\pm 0.09 ({\rm stat.})^{+0.34}_{-0.39}({\rm syst.}) 
- (2.81\pm 0.42({\rm stat.})^{+1.13}_{-0.62}({\rm syst.})\ {\rm GeV}^{-2})t$.}



The linear function can be  interpreted in the framework of 
Regge theory.
The measured values of the intercept and slope are in
agreement with the expectations from pion exchange: i.e.,
the intercept is  the value of the
Pomeron trajectory at $t=0$, and  
the slope is twice the slope of the pion trajectory.
The data thus confirm that the production of 
leading neutrons in photon-proton collisions is well described 
by the pion-exchange model.

\section*{Acknowledgments}

We thank the DESY Directorate for their strong support and encouragement, and 
the HERA machine group for their diligent efforts.  We are grateful for the 
support of the DESY computing and network services.  The design, construction
and installation of the ZEUS detector have been made possible owing to the 
ingenuity and effort of many people who are not
listed as authors.  
This study was only made possible by the physics insight and work of
G.~Levman, to whom we are greatly indebted.
%owe a great debt of gratitude.

\vfill\eject





























piex.tex
%==============================================================================
%
%       <Insert paper title here>
%       _________________________
%
%      Please consult the WWW LaTeX4zeus documentation for explanations
%      and usage information related to this LaTeX setup:
%
%      http://www-zeus.desy.de/ZEUS_ONLY/LaTeX4zeus/WWW/html/l4z.html
%
%==============================================================================
%
%       Use 'zeus_paper' class
%       ----------------------
%
%       Options specific to zeus_paper.cls:
%
%       Paper type (mutually exclusive):
%       -> zpreprint    - DESY preprint (always 12pt)
%       -> zdraft       - draft paper (always 12pt)
%       -> zconf        - paper contributed to a conference (always 12pt)
%       -> znote        - ZEUS note (default=12pt, 10pt or 11pt can be selected)
%
%       Bibliography style (mutually exclusive):
%       ->zbstdefault   - standard ZEUS BiBTeX style file (default)    
%       ->zbstdraft     - standard ZEUS BiBTeX style file for drafts
%                         (default for drafts)   
%       ->zbstepj       - ZEUS BiBTeX style file for Eur.J.Phys papers 
%       ->zbstnp        - ZEUS BiBTeX style file for Nucl.Phys. papers 
%       ->zbstpl        - ZEUS BiBTeX style file for Phys.Lett. papers 
%
\documentclass[zpreprint,zbstdefault]{zeus_paper}
%
%       Use English language 
%       --------------------
%       <change "english" -> "american" to conform to American standards>
%
\usepackage[english]{babel}
%
%       Default auxiliary packages
%       --------------------------
%
%       The following packages are automatically loaded by zeus_paper.cls:
%       -> rotating     - to rotate boxes, pictures etc.
%       -> epsfig       - to include (encapsulated) postscript files
%       -> amsmath      - to use the AMS extended math package
%                         [centertags] -> equation numbers vertically centered
%                                         in split enevironment
%                         [intlimits]  -> integral limits on bottom and top
%                                         of integral sign
%       -> amssymb      - to obtain additional math symbols in AMS fonts
%       -> amscd        - to obtain AMS flow chart utilities
%       -> array        - to obtain additional tabular functionality
%       -> multirow     - for multirow-entries in tables
%       -> supertabular - for multi-page tables
%       -> dcolumn      - decimal-point aligned colums in tables
%       -> xspace       - to add empty space after commands
%       -> axodraw      - to draw Feynman diagrams (by J.A.M.Vermaseren)
%       -> upgreek      - provide upright greek letters
%       -> color        - color support
%       -> colors       - some color definitions
%       -> calc         - enhanced calculus in LaTeX macros
%       -> ifthen       - enhance logical structures in LaTeX macros
%       -> cite         - for multiple citations like [1-4] instead of [1,2,3,4]
%       -> mcite        - for multiple citations in one reference
%          
%       <Here you can include additional auxiliary packages:>
%       -----------------------------------------------------
%
%       use \usepackage[options]{package name}
%
%       File './LaTeX/zeus/zeus_def.tex' contains the standard set 
%                                        of TeX definitions etc.
%
\input zeus_def.tex
%
%       File './LaTeX/user/def.tex' contains additional user definitions
%
\input def.tex
%
%       File 'zdraft-cit.tex' contains citation definitions
%
\input  piex-cit.tex
%==============================================================================
%       Here comes the document.
%==============================================================================
\includeonly{piex-tit,piex-aut,piex-txt,piex-ref,piex-tab,piex-fig}
\begin{document}
%------------------------------------------------------------------------------
%       Title sheet
%------------------------------------------------------------------------------
\include{piex-tit}
%------------------------------------------------------------------------------
%       Authors
%------------------------------------------------------------------------------
\include{piex-aut}
%------------------------------------------------------------------------------
%       Text
%------------------------------------------------------------------------------
\include{piex-txt}
%------------------------------------------------------------------------------
%       Bibliography
%------------------------------------------------------------------------------
\include{piex-ref}
%------------------------------------------------------------------------------
%       Tables
%------------------------------------------------------------------------------
\include{piex-tab}
%------------------------------------------------------------------------------
%       Figures
%------------------------------------------------------------------------------
\include{piex-fig}
%
%       ... that's it
%
\end{document}

zeus_def.tex
%------------------------------------------------------------------------------
%       Standard ZEUS text fragments
%       ----------------------------
%       -> references system footnote
%------------------------------------------------------------------------------
\newcommand{\ZcoosysA}{%
The ZEUS coordinate system is a right-handed Cartesian system, with the $Z$
axis pointing in the proton beam direction, referred to as the ``forward
direction'', and the $X$ axis pointing left towards the center of HERA.
The coordinate origin is at the nominal interaction point.\xspace}
\newcommand{\ZcoosysB}{%
The ZEUS coordinate system is a right-handed Cartesian system, with the $Z$
axis pointing in the proton beam direction, referred to as the ``forward
direction'', and the $X$ axis pointing left towards the centre of HERA.
The coordinate origin is at the nominal interaction point.\xspace}
\newcommand{\Zpsrap}{%
The pseudorapidity is defined as $\eta=-\ln\left(\tan\frac{\theta}{2}\right)$,
where the polar angle, $\theta$, is measured with respect to the proton beam
direction.\xspace}
\newcommand{\ZcoosysfnA}{\footnote{\ZcoosysA}}
\newcommand{\ZcoosysfnB}{\footnote{\ZcoosysB}}
\newcommand{\ZcoosysfnAeta}{\footnote{\ZcoosysA\Zpsrap}}
\newcommand{\ZcoosysfnBeta}{\footnote{\ZcoosysB\Zpsrap}}
%------------------------------------------------------------------------------
%       -> introductory sentence for detector description
%------------------------------------------------------------------------------
\newcommand{\Zdetdesc}{%
A detailed description of the ZEUS detector can be found 
elsewhere~\cite{zeus:1993:bluebook}. A brief outline of the 
components that are most relevant for this analysis is given
below.\xspace}
%------------------------------------------------------------------------------
%       -> CTD description (coordinate system footnote is given as argument)
%------------------------------------------------------------------------------
\newcommand{\Zctddesc}[1]{%
Charged particles are tracked in the central tracking detector (CTD)~\citeCTD,
which operates in a magnetic field of $1.43\Tesla$ provided by a thin 
superconducting coil. The CTD consists of 72~cylindrical drift chamber 
layers, organized in 9~superlayers covering the polar-angle#1 region 
\mbox{$15^\circ<\theta<164^\circ$}. The transverse-momentum resolution for
full-length tracks is $\sigma(p_T)/p_T=0.0058p_T\oplus0.0065\oplus0.0014/p_T$,
with $p_T$ in $\Gev$.}
%------------------------------------------------------------------------------
%       -> CAL description
%------------------------------------------------------------------------------
\newcommand{\Zcaldesc}{%
The high-resolution uranium--scintillator calorimeter (CAL)~\citeCAL consists 
of three parts: the forward (FCAL), the barrel (BCAL) and the rear (RCAL)
calorimeters. Each part is subdivided transversely into towers and
longitudinally into one electromagnetic section (EMC) and either one (in RCAL)
or two (in BCAL and FCAL) hadronic sections (HAC). 
%The smallest subdivision of
%the calorimeter is called a cell.  
The CAL energy resolutions, as measured under
test-beam conditions, are $\sigma(E)/E=0.18/\sqrt{E}$ for electrons and
$\sigma(E)/E=0.35/\sqrt{E}$ for hadrons ($E$ in $\Gev$).}
%------------------------------------------------------------------------------
%       Handy macros, mainly for text mode:
%       -----------------------------------
%       -> unknown marker
%------------------------------------------------------------------------------
\newcommand{\xxx}{\hbox{$\qsm\qsm\qsm$}\xspace}
%------------------------------------------------------------------------------
%       -> D0 acronym
%------------------------------------------------------------------------------
\newcommand{\DO}{{D{\O}}\xspace}
%------------------------------------------------------------------------------
%       -> (anti-)something with correct hyphenation
%------------------------------------------------------------------------------
\newcommand{\Anti}[1]{\hbox{(anti-)}\discretionary{}{}{}#1}
\newcommand{\anti}[1]{(anti\discretionary{-)}{}{)}#1}
%------------------------------------------------------------------------------
%       -> characters for typewriter font (used for http addresses)
%------------------------------------------------------------------------------
\chardef\usc=95
\chardef\til=126
%------------------------------------------------------------------------------
%       -> xdotspace (like xspace, but adds period unless
%          another period follows)
%       -> "nn% C.L."
%------------------------------------------------------------------------------
\catcode`\@=11 % @ signs are now treated as letters
\DeclareRobustCommand\xdotspace{\futurelet\@let@token\@xdotspace}
\def\@xdotspace{%
  \ifx\@let@token.\else
  \ifx\@let@token\bgroup.\else
  \ifx\@let@token\egroup.\else
  \ifx\@let@token\/.\else
  \ifx\@let@token\ .\else
  \ifx\@let@token~.\else
  \ifx\@let@token!.\else
  \ifx\@let@token,.\else
  \ifx\@let@token:.\else
  \ifx\@let@token;.\else
  \ifx\@let@token?.\else
  \ifx\@let@token/.\else
  \ifx\@let@token'.\else
  \ifx\@let@token).\else
  \ifx\@let@token-.\else
  \ifx\@let@token\@xobeysp.\else
  \ifx\@let@token\space.\else
  \ifx\@let@token\@sptoken.\else
   .\space
   \fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi}
\catcode`\@=12 % @ signs are no longer letters
\newcommand{\CL}[1]{$#1\%$~C.L\xdotspace}
%------------------------------------------------------------------------------
%       -> vertical rule of width zero and variable height & depth
%------------------------------------------------------------------------------
\newcommand{\stru}[2]{%
   \relax\ifmmode\hbox{\vrule height#1 depth#2 width0pt}%
   \else\vrule height#1 depth#2 width0pt\fi}
%------------------------------------------------------------------------------
%       -> underline with resonable distance text - line
%------------------------------------------------------------------------------
\newcommand{\uline}[1]{$\underline{\hbox{#1\stru{0.pt}{.485ex}}}$}
%------------------------------------------------------------------------------
%       -> roman numbers (uppercase and lowercase)
%------------------------------------------------------------------------------
\newcommand{\Ronum}[1]{\uppercase\expandafter{\romannumeral#1}}
\newcommand{\ronum}[1]{\expandafter{\romannumeral#1}}
%------------------------------------------------------------------------------
%       -> definition for LaTeX4zeus
%------------------------------------------------------------------------------
\DeclareRobustCommand{\LaTeXZ}{%
  \LaTeX\kern-.05em4\kern-.1em
  {\raisebox{-0.2ex}{$\scriptstyle\text{ZEUS}$}}\xspace}
%------------------------------------------------------------------------------
%       -> umlaut definitions for references (needed since BiBTeX 
%          MACRO strings cannot contain quotes)
%------------------------------------------------------------------------------
\newcommand{\Auml}{\"A}
\newcommand{\Ouml}{\"O}
\newcommand{\Uuml}{\"U}
\newcommand{\auml}{\"a}
\newcommand{\ouml}{\"o}
\newcommand{\uuml}{\"u}
%------------------------------------------------------------------------------
%       -> shorthands for equation, figure, table, section references
%          (require standard use of labels: eq-... for equations, cha-...
%           for chapters, sec-... for (sub)sections, tab-... for tables
%           and fig-... for figures)
%------------------------------------------------------------------------------
\newcommand{\eq}[1]{(\ref{eq-#1})}
\newcommand{\eqsand}[2]{(\ref{eq-#1}) and~(\ref{eq-#2})}
\newcommand{\eqsto}[2]{(\ref{eq-#1})--(\ref{eq-#2})}
\newcommand{\eqstwo}[2]{(\ref{eq-#1},\ref{eq-#2})}
\newcommand{\eqsthr}[3]{(\ref{eq-#1},\ref{eq-#2},\ref{eq-#3})}
\newcommand{\eqsfou}[4]{(\ref{eq-#1},\ref{eq-#2},\ref{eq-#3},\ref{eq-#4})}
\newcommand{\Eq}[1]{Equation~(\ref{eq-#1})}
\newcommand{\Eqsto}[2]{Equations~(\ref{eq-#1})--(\ref{eq-#2})}
\newcommand{\fig}[1]{Fig.~\ref{fig-#1}}
\newcommand{\Fig}[1]{Figure~\ref{fig-#1}}
\newcommand{\figand}[2]{Figs.~\ref{fig-#1} and~\ref{fig-#2}}
\newcommand{\Figand}[2]{Figures~\ref{fig-#1} and~\ref{fig-#2}}
\newcommand{\tab}[1]{Table~\ref{tab-#1}}
\newcommand{\Tab}[1]{Table~\ref{tab-#1}}
\newcommand{\taband}[2]{Tables~\ref{tab-#1} and~\ref{tab-#2}}
\newcommand{\cha}[1]{Chap.~\ref{cha-#1}}
\newcommand{\Cha}[1]{Chapter~\ref{cha-#1}}
\newcommand{\sect}[1]{Sect.~\ref{sec-#1}}
\newcommand{\Sect}[1]{Section~\ref{sec-#1}}
\newcommand{\sectand}[2]{Sects.~\ref{sec-#1} and~\ref{sec-#2}}
\newcommand{\sectto}[2]{Sects.~\ref{sec-#1} to~\ref{sec-#2}}
\newcommand{\Sectand}[2]{Sections~\ref{sec-#1} and~\ref{sec-#2}}
\newcommand{\Sectto}[2]{Sections~\ref{sec-#1} to~\ref{sec-#2}}
%------------------------------------------------------------------------------
%       -> log file message
%------------------------------------------------------------------------------
\newcommand{\LogMess}[1]{\typeout{^^J==> #1^^J}}
%------------------------------------------------------------------------------
%       Some special symbols and settings for math mode:
%       ------------------------------------------------
%       -> redefine mathbf
%------------------------------------------------------------------------------
\DeclareMathAlphabet{\mathbf}{OT1}{cmr}{bx}{sl}
%------------------------------------------------------------------------------
%       -> physics units (eV and multiples)
%------------------------------------------------------------------------------
\newcommand{\eVdist}{\kern-0.06667em}
\newcommand{\Ev}{{\text{e}\eVdist\text{V\/}}}
\newcommand{\Kev}{{\text{ke}\eVdist\text{V\/}}}
\newcommand{\Mev}{{\text{Me}\eVdist\text{V\/}}}
\newcommand{\Gev}{{\text{Ge}\eVdist\text{V\/}}}
\newcommand{\Tev}{{\text{Te}\eVdist\text{V\/}}}
\newcommand{\ev}{{\,\text{e}\eVdist\text{V\/}}}
\newcommand{\kev}{{\,\text{ke}\eVdist\text{V\/}}}
\newcommand{\mev}{{\,\text{Me}\eVdist\text{V\/}}}
\newcommand{\gev}{{\,\text{Ge}\eVdist\text{V\/}}}
\newcommand{\tev}{{\,\text{Te}\eVdist\text{V\/}}}
%------------------------------------------------------------------------------
%       -> various other units
%------------------------------------------------------------------------------
\newcommand{\mb}{\,\text{mb}}
\newcommand{\mub}{\,\upmu\text{b}}
\newcommand{\nb}{\,\text{nb}}
\newcommand{\pb}{\,\text{pb}}
\newcommand{\fb}{\,\text{fb}}
\newcommand{\mubi}{\,\upmu\text{b}^{-1}}
\newcommand{\mbi}{\,\text{mb}^{-1}}
\newcommand{\nbi}{\,\text{nb}^{-1}}
\newcommand{\pbi}{\,\text{pb}^{-1}}
\newcommand{\fbi}{\,\text{fb}^{-1}}
\newcommand{\met}{\,\text{m}}
\newcommand{\nm}{\,\text{nm}}
\newcommand{\mum}{\,\upmu\text{m}}
\newcommand{\mm}{\,\text{mm}}
\newcommand{\cm}{\,\text{cm}}
\newcommand{\km}{\,\text{km}}
\newcommand{\Amp}{\,\text{A}}
\newcommand{\nA}{\,\text{nA}}
\newcommand{\muA}{\,\upmu\text{A}}
\newcommand{\mA}{\,\text{mA}}
\newcommand{\kA}{\,\text{kA}}
\newcommand{\Hz}{\,\text{Hz}}
\newcommand{\kHz}{\,\text{kHz}}
\newcommand{\MHz}{\,\text{MHz}}
\newcommand{\GHz}{\,\text{GHz}}
\newcommand{\ppm}{\,\text{ppm}}
\newcommand{\ppb}{\,\text{ppb}}
\newcommand{\scd}{\,\text{s}}
\newcommand{\ps}{\,\text{ps}}
\newcommand{\ns}{\,\text{ns}}
\newcommand{\mus}{\,\upmu\text{s}}
\newcommand{\ms}{\,\text{ns}}
\newcommand{\rad}{\,\text{rad}}
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\newcommand{\mrad}{\,\text{mrad}}
\newcommand{\gra}{\,\text{g}}
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\newcommand{\nang}{\,\text{ng}}
\newcommand{\mug}{\,\upmu\text{g}}
\newcommand{\mg}{\,\text{mg}}
\newcommand{\kg}{\,\text{kg}}
\newcommand{\Tesla}{\,\text{T}}
\newcommand{\Kelvin}{\,\text{K}}
%------------------------------------------------------------------------------
%       -> additional operators
%------------------------------------------------------------------------------
\newcommand{\odiv}{{\operatorname*{div}}}
\newcommand{\ograd}{{\operatorname*{grad}}}
\newcommand{\orot}{{\operatorname*{rot}}}
\newcommand{\odiag}{{\operatorname*{diag}}}
\newcommand{\ocov}{{\operatorname*{cov}}}
%------------------------------------------------------------------------------
%       -> fraction with slash instead of ratio bar
%------------------------------------------------------------------------------
\newcommand{\slashfrac}[2]{%
  \raisebox{0.5ex}{\ensuremath #1}\kern-0.12em/\kern-0.08em
  \raisebox{-.8ex}{\ensuremath #2}}
%------------------------------------------------------------------------------
%       -> shorthand for "integral limits below and above"
%------------------------------------------------------------------------------
\newcommand{\intl}{\int\limits}
\newcommand{\ointl}{\oint\limits}
%------------------------------------------------------------------------------
%       -> d'Alembert operator
%------------------------------------------------------------------------------
\newcommand{\sqr}[3]{%
    {\vcenter{\hrule height.#3ex\hbox{\vrule width.#2ex height#1ex
     \kern#1ex\vrule width.#3ex}\hrule height.#2ex}}}
\newcommand{\dalem}{\mathchoice\sqr{1.3}{08}{24}\sqr{1.4}{08}{24}
                    \sqr{1.15}{07}{21}\sqr{1.0}{06}{18}\,}
%------------------------------------------------------------------------------
%       -> vectors and matrices
%------------------------------------------------------------------------------
\newcommand{\vect}[1]{\begin{matrix}#1\end{matrix}}
\newcommand{\pvect}[1]{\begin{pmatrix}#1\end{pmatrix}}
\newcommand{\bvect}[1]{\begin{bmatrix}#1\end{bmatrix}}
\newcommand{\vvect}[1]{\begin{vmatrix}#1\end{vmatrix}}
\newcommand{\Vvect}[1]{\begin{Vmatrix}#1\end{Vmatrix}}
%------------------------------------------------------------------------------
%       -> antiparticles and particles with a bar in parentheses
%------------------------------------------------------------------------------
\newcommand{\widebar}[1]{%
   \mkern1.5mu\overline{\mkern-1.5mu#1\mkern-1.mu}\mkern1.mu}
\catcode`\@=11 % @ signs are now treated as letters
\newcommand{\parenbar}{\mathpalette\p@renb@r}
\def\p@renb@r#1#2{\vbox{%
  \ifx#1\scriptscriptstyle \dimen@.7em\dimen@ii.2em\else
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    \hbox to\dimen@{$\mathchar300\hfil\mathchar301$}\cr
    \noalign{\vskip-.3ex}%
    $#1#2$\cr}}}
\catcode`\@=12 % @ signs are no longer letters
\newcommand{\nuan}{\parenbar{\nu}}
\newcommand{\nunubar}{\parenbar{\nu}}
\newcommand{\ppbar}{\parenbar{p}}
\newcommand{\qqbar}{\parenbar{q}}
\newcommand{\pbar}{\widebar{p}}
\newcommand{\nbar}{\widebar{n}}
\newcommand{\qbar}{\widebar{q}}
\newcommand{\dbar}{\widebar{d}}
\newcommand{\ubar}{\widebar{u}}
\newcommand{\sbar}{\widebar{s}}
\newcommand{\cbar}{\widebar{c}}
\newcommand{\bbar}{\widebar{b}}
\newcommand{\tbar}{\widebar{t}}
\newcommand{\nubar}{\widebar{\nu}}
\newcommand{\Dbar}{\widebar{D}}
\newcommand{\ebar}{\widebar{e}}
\newcommand{\Ebar}{\widebar{e}}
\newcommand{\Hebar}{\widebar{\text{He}}}
\newcommand{\Cbar}{\widebar{\text{C}}}
\newcommand{\Abar}{\widebar{\text{A}}}
\newcommand{\Kbar}{\widebar{K}}
\newcommand{\chibar}{\widebar{\chi}}
\newcommand{\LQbar}{\widebar{\rm LQ}}
%------------------------------------------------------------------------------
%       -> small numbers
%------------------------------------------------------------------------------
\newcommand{\zero}{{\scriptscriptstyle 0}}
\newcommand{\sone}{{\scriptscriptstyle 1}}
\newcommand{\stwo}{{\scriptscriptstyle 2}}
\newcommand{\sthr}{{\scriptscriptstyle 3}}
\newcommand{\sfou}{{\scriptscriptstyle 4}}
\newcommand{\sfiv}{{\scriptscriptstyle 5}}
\newcommand{\ssix}{{\scriptscriptstyle 6}}
\newcommand{\ssev}{{\scriptscriptstyle 7}}
\newcommand{\seig}{{\scriptscriptstyle 8}}
\newcommand{\snin}{{\scriptscriptstyle 9}}
\newcommand{\sten}{{\scriptscriptstyle 10}}
\newcommand{\half}{{\scriptscriptstyle 1/2}}
%------------------------------------------------------------------------------
%       -> abbreviations for common math mode symbols
%------------------------------------------------------------------------------
\newcommand{\MSbar}{\hbox{$\overline{\rm MS}$}\xspace}
\newcommand{\UO}{{\rm U}(1)_\sY}
\newcommand{\SUT}{{\rm SU}(2)_\sL}
\newcommand{\SUTH}{{\rm SU}(3)_c}
\newcommand{\SUTUO}{{\rm SU}(2)_\sL\times{\rm U}(1)_\sY}
\newcommand{\SUTSUTUO}{{\rm SU}(3)_c\times{\rm SU}(2)_\sL\times{\rm U}(1)_\sY}
\newcommand{\alsmu}[1]{{\alpha_s(\mu_{#1}^2)}}
\newcommand{\alsmz}{{\alpha_s(M_Z^2)}}
\newcommand{\alsqs}{{\alpha_s(Q^2)}}
\newcommand{\als}{\alpha_s}
\newcommand{\ctwb}{\cos\theta_W}
\newcommand{\ctws}{\cos^2\theta_W}
\newcommand{\diff}{{\rm d}}
\newcommand{\gh}{{\gamma_h}}
\newcommand{\lsq}[1]{{\lambda_{#1}}}
\newcommand{\lsqp}[1]{{\lambda'_{#1}}}
\newcommand{\lsqpp}[1]{{{\lambda''}_{#1}}}
\newcommand{\rnge}{\hbox{$\,\text{--}\,$}}
\newcommand{\sihat}{{\hat\sigma}}
\newcommand{\sitil}{{\tilde\sigma}}
\newcommand{\stwb}{\sin\theta_W}
\newcommand{\stwss}{\sin^4\theta_W}
\newcommand{\stws}{\sin^2\theta_W}
\newcommand{\ta}{{\theta^\ast}}
\newcommand{\tilR}{\tilde R}
\newcommand{\tilS}{\tilde S}
\newcommand{\tilU}{\tilde U}
\newcommand{\tilV}{\tilde V}
\newcommand{\tl}{{\theta_\ell}}
\newcommand{\tw}{\theta_W}
%------------------------------------------------------------------------------
%       -> roman character combinations to be used in math mode, mainly
%          sub- or superscripts
%------------------------------------------------------------------------------
\newcommand{\Born}{{\rm Born}}
\newcommand{\BR}{{\rm BR}}
\newcommand{\CC}{{\rm CC}}
\newcommand{\CI}{{\rm CI}}
\newcommand{\CJ}{{\rm CJ}}
\newcommand{\DA}{{\rm DA}}
\newcommand{\DCA}{{\rm DCA}}
\newcommand{\GRV}{{\rm GRV}}
\newcommand{\IC}{{\rm IC}}
\newcommand{\ISR}{{\rm ISR}}
\newcommand{\IP}{{\rm I$\kern-0.01667em$P}\xspace}
\newcommand{\JB}{{\rm JB}}
\newcommand{\LL}{{\rm LL}}
\newcommand{\LQ}{{\rm LQ}}
\newcommand{\LR}{{\rm LR}}
\newcommand{\MC}{{\rm MC}}
\newcommand{\NC}{{\rm NC}}
\newcommand{\NS}{{\rm NS}}
\newcommand{\QPM}{{\rm QPM}}
\newcommand{\RL}{{\rm RL}}
\newcommand{\RPv}{{{\not R}_P}}
\newcommand{\RR}{{\rm RR}}
\newcommand{\SM}{{\rm SM}}
\newcommand{\bkg}{{\rm bkg}}
\newcommand{\cut}{{\rm cut}}
\newcommand{\data}{{\rm data}}
\newcommand{\sdet}{{\rm det}}
\newcommand{\dof}{{\rm dof}}
\newcommand{\eff}{{\rm eff}}
\newcommand{\elm}{{\rm elm}}
\newcommand{\evt}{{\rm evt}}
\newcommand{\exc}{{\rm exc}}
\newcommand{\fit}{{\rm fit}}
\newcommand{\had}{{\rm had}}
\newcommand{\jet}{{\rm jet}}
\newcommand{\meas}{{\rm meas}}
\newcommand{\miss}{{\rm miss}}
\newcommand{\obs}{{\rm obs}}
\newcommand{\pnt}{{\rm pnt}}
\newcommand{\sL}{{\rm L}}
\newcommand{\sR}{{\rm R}}
\newcommand{\sS}{{\rm S}}
\newcommand{\sT}{{\rm T}}
\newcommand{\sY}{{\rm Y}}
\newcommand{\sca}{{\rm sca}}
\newcommand{\sexp}{{\rm exp}}
\newcommand{\sint}{{\rm int}}
\newcommand{\smin}{{\rm min}}
\newcommand{\smax}{{\rm max}}
\newcommand{\srad}{{\rm rad}}
\newcommand{\sthe}{{\rm the}}
\newcommand{\sys}{{\rm sys}}
\newcommand{\tot}{{\rm tot}}
\newcommand{\true}{{\rm true}}
%------------------------------------------------------------------------------
%       -> some calligraphic symbols and applications
%------------------------------------------------------------------------------
\newcommand{\Cor}{{\cal C}}
\newcommand{\F}{{\cal F}}
\newcommand{\Lumi}{{\cal L}}
\newcommand{\Prob}{{\cal P}}
\newcommand{\ord}[1]{{\cal O}(#1)}
\newcommand{\ordlr}[1]{{\cal O}\left(#1\right)}
%------------------------------------------------------------------------------
%       -> some math symbols (+,-,...) for usage as mathchar's
%------------------------------------------------------------------------------
\mathchardef\qsm=63
\mathchardef\pls=43
\mathchardef\mns=512
\mathchardef\plm=518
\mathchardef\eql=61
\mathchardef\smallleft=300
\mathchardef\smallright=301
\mathchardef\les=316
\mathchardef\gre=318
\mathchardef\leq=532
\mathchardef\grq=533
%------------------------------------------------------------------------------
%       Additional functionality for tables and figures
%       -----------------------------------------------
%       -> alignment tools for tables
%------------------------------------------------------------------------------
\newcommand{\cA}{{\phantom{0}}}
\newcommand{\cB}{{\phantom{00}}}
\newcommand{\cC}{{\phantom{000}}}
\newcommand{\cD}{{\phantom{0000}}}
\newcommand{\cAp}{{\phantom{0.}}}
\newcommand{\cM}{{\phantom{\mns}}}
\newcommand{\cP}{{\phantom{\pls}}}
%------------------------------------------------------------------------------
%       -> comments on figures (allow to add axodraw and picture items)
%------------------------------------------------------------------------------
\catcode`\@=11 % @ signs are now treated as letters
\newcounter{pict@width}
\newcounter{pict@height}
\newlength{\pict@scale}
\setlength{\pict@scale}{0.1mm}
\newcommand{\psfigadd}[4]{%
\setcounter{pict@width}{1*\ratio{#2+\pict@scale/2}{\pict@scale}}
\setcounter{pict@height}{1*\ratio{#3+\pict@scale/2}{\pict@scale}}
\setlength{\unitlength}{\pict@scale}
\hbox to #2{\hspace{-\fill}\begin{picture}(\thepict@width,\thepict@height)
\put(0,0){\psfig{figure=#1,width=#2,height=#3,clip=}}
\SetScale{0.283466457}
\SetWidth{1.763889}
{#4}
\end{picture}}
}
\newcounter{pict@widthfst}
\newcounter{pict@widthscd}
\newcounter{pict@widthtot}
\newcommand{\psfigaddtwo}[7]{%
\setcounter{pict@widthfst}{1*\ratio{#2+\pict@scale/2}{\pict@scale}}
\setcounter{pict@widthscd}{1*\ratio{#2+#4+\pict@scale/2}{\pict@scale}}
\setcounter{pict@widthtot}{1*\ratio{#2+#4+#6+\pict@scale/2}{\pict@scale}}
\setcounter{pict@height}{1*\ratio{#3+\pict@scale/2}{\pict@scale}}
\setlength{\unitlength}{\pict@scale}
\hbox{\hspace{-\fill}\begin{picture}(\thepict@widthtot,\thepict@height)
\put(0,0){\psfig{figure=#1,width=#2,height=#3,clip=}}
\put(\thepict@widthscd,0){\psfig{figure=#5,width=#6,height=#3,clip=}}
\SetScale{0.283466457}
\SetWidth{1.763889}
{#7}
\end{picture}}
}
\newcommand{\psfigror}[4]{%
\setcounter{pict@width}{1*\ratio{#2+\pict@scale/2}{\pict@scale}}
\setcounter{pict@height}{1*\ratio{#3+\pict@scale/2}{\pict@scale}}
\setlength{\unitlength}{\pict@scale}
\hbox{\begin{picture}(\thepict@width,\thepict@height)
\put(0,\thepict@height){\psfig{figure=#1,width=#3,height=#2,clip=,angle=270}}
\SetScale{0.283466457}
\SetWidth{1.763889}
{#4}
\end{picture}}
}
\newcommand{\psfigrol}[4]{%
\setcounter{pict@width}{1*\ratio{#2+\pict@scale/2}{\pict@scale}}
\setcounter{pict@height}{1*\ratio{#3+\pict@scale/2}{\pict@scale}}
\setlength{\unitlength}{\pict@scale}
\hbox{\begin{picture}(\thepict@width,\thepict@height)
\put(0,0){\psfig{figure=#1,width=#3,height=#2,clip=,angle=90}}
\SetScale{0.283466457}
\SetWidth{1.763889}
{#4}
\end{picture}}
}
\catcode`\@=12 % @ signs are no longer letters
%------------------------------------------------------------------------------
%       -> narrow figures in list environment
%------------------------------------------------------------------------------
\newlength\listtextwidth
\newcommand{\shiftfloat}[1]{
  \setlength{\listtextwidth}{\textwidth}
  \addtolength{\listtextwidth}{-#1}}
%------------------------------------------------------------------------------
%       -> "none" marker
%------------------------------------------------------------------------------
\newcommand{\none}{\hbox{---}}
%------------------------------------------------------------------------------
%       -> protected commands in captions
%------------------------------------------------------------------------------
\newcommand{\pcite}[1]{{\protect\cite{#1}}}
\newcommand{\pnl}{\protect{\newline}}
%------------------------------------------------------------------------------
%       -> pseudo-footnotes for tables
%------------------------------------------------------------------------------
\catcode`\@=11 % @ signs are now treated as letters
\newlength{\@tabfninsert}
\newlength{\@tabfnwidth}
\newcommand{\tabfootnote}[2]{%
  \setlength{\@tabfninsert}{0.8em}
  \setlength{\@tabfnwidth}{\textwidth}
  \addtolength{\@tabfnwidth}{-\@tabfninsert}
  \addtolength{\@tabfnwidth}{-0.4em}
  \noindent\makebox[\@tabfninsert][r]{\footnotesize$^{#1}$\hfil}\hfill%
  \parbox[t]{\@tabfnwidth}{\footnotesize #2\hfill}}
\catcode`\@=12 % @ signs are no longer letters

piex.bbl
\providecommand{\etal}{et al.\xspace}
\providecommand{\coll}{Coll.\xspace}
\catcode`\@=11
\def\@bibitem#1{%
\ifmc@bstsupport
  \mc@iftail{#1}%
    {;\newline\ignorespaces}%
    {\ifmc@first\else.\fi\orig@bibitem{#1}}
  \mc@firstfalse
\else
  \mc@iftail{#1}%
    {\ignorespaces}%
    {\orig@bibitem{#1}}%
\fi}%
\catcode`\@=12
\begin{mcbibliography}{10}

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