1 Introduction

DESY 09-158 ISSN 0418-9833
January 2010

Combined Measurement and QCD Analysis of the Inclusive Scattering Cross Sections at HERA

H1 and ZEUS Collaborations

A combination is presented of the inclusive deep inelastic cross sections measured by the H1 and ZEUS Collaborations in neutral and charged current unpolarised scattering at HERA during the period -. The data span six orders of magnitude in negative four-momentum-transfer squared, , and in Bjorken . The combination method used takes the correlations of systematic uncertainties into account, resulting in an improved accuracy. The combined data are the sole input in a NLO QCD analysis which determines a new set of parton distributions, HERAPDF1.0, with small experimental uncertainties. This set includes an estimate of the model and parametrisation uncertainties of the fit result.

The H1 and ZEUS Collaborations

F.D. Aaron, H. Abramowicz, I. Abt, L. Adamczyk, M. Adamus, M. Aldaya Martin, C. Alexa, V. Andreev, S. Antonelli, P. Antonioli, A. Antonov, B. Antunovic, M. Arneodo, V. Aushev, O. Bachynska, S. Backovic, A. Baghdasaryan, A. Bamberger, A.N. Barakbaev, G. Barbagli, G. Bari, F. Barreiro, E. Barrelet, W. Bartel, D. Bartsch, M. Basile, K. Begzsuren, O. Behnke, J. Behr, U. Behrens, L. Bellagamba, A. Belousov, A. Bertolin, S. Bhadra, M. Bindi, J.C. Bizot, C. Blohm, T. Bołd, E.G. Boos, M. Borodin, K. Borras, D. Boscherini, D. Bot, V. Boudry, S.K. Boutle, I. Bozovic-Jelisavcic, J. Bracinik, G. Brandt, M. Brinkmann, V. Brisson, I. Brock, E. Brownson, R. Brugnera, N. Brümmer, D. Bruncko, A. Bruni, G. Bruni, B. Brzozowska, A. Bunyatyan, G. Buschhorn, P.J. Bussey, J.M. Butterworth, B. Bylsma, L. Bystritskaya, A. Caldwell, A.J. Campbell, K.B. Cantun Avila, M. Capua, R. Carlin, C.D. Catterall, K. Cerny, V. Cerny, S. Chekanov, V. Chekelian, A. Cholewa, J. Chwastowski, J. Ciborowski, R. Ciesielski, L. Cifarelli, F. Cindolo, A. Contin, J.G. Contreras, A.M. Cooper-Sarkar, N. Coppola, M. Corradi, F. Corriveau, M. Costa, J.A. Coughlan, G. Cozzika, J. Cvach, G. D’Agostini, J.B. Dainton, F. Dal Corso, K. Daum, M. Deák, J. de Favereau, B. Delcourt, J. del Peso, J. Delvax, R.K. Dementiev, S. De Pasquale, M. Derrick, R.C.E. Devenish, E.A. De Wolf, C. Diaconu, D. Dobur, V. Dodonov, B.A. Dolgoshein, A. Dossanov, A.T. Doyle, V. Drugakov, A. Dubak, L.S. Durkin, S. Dusini, G. Eckerlin, V. Efremenko, S. Egli, Y. Eisenberg, A. Eliseev, E. Elsen, P.F. Ermolov , A. Eskreys, A. Falkiewicz, S. Fang, L. Favart, S. Fazio, A. Fedotov, R. Felst, J. Feltesse, J. Ferencei, J. Ferrando, M.I. Ferrero, J. Figiel, D.-J. Fischer, M. Fleischer, A. Fomenko, M. Forrest, B. Foster, S. Fourletov, E. Gabathuler, A. Galas, E. Gallo, A. Garfagnini, J. Gayler, A. Geiser, S. Ghazaryan, I. Gialas, L.K. Gladilin, D. Gladkov, C. Glasman, A. Glazov, I. Glushkov, L. Goerlich, N. Gogitidze, Yu.A. Golubkov, P. Göttlicher, M. Gouzevitch, C. Grab, I. Grabowska-Bołd, J. Grebenyuk, T. Greenshaw, I. Gregor, B.R. Grell, G. Grigorescu, G. Grindhammer, G. Grzelak, C. Gwenlan, T. Haas, S. Habib, D. Haidt, W. Hain, R. Hamatsu, J.C. Hart, H. Hartmann, G. Hartner, C. Helebrant, R.C.W. Henderson, E. Hennekemper, H. Henschel, M. Herbst, G. Herrera, M. Hildebrandt, E. Hilger, K.H. Hiller, D. Hochman, D. Hoffmann, U. Holm, R. Hori, R. Horisberger, K. Horton, T. Hreus, A. Hüttmann, G. Iacobucci, Z.A. Ibrahim, Y. Iga, R. Ingbir, M. Ishitsuka, M. Jacquet, H.-P. Jakob, X. Janssen, F. Januschek, M. Jimenez, T.W. Jones, L. Jönsson, A.W. Jung, H. Jung, M. Jüngst, I. Kadenko, B. Kahle, B. Kamaluddin, S. Kananov, T. Kanno, M. Kapichine, U. Karshon, F. Karstens, I.I. Katkov, J. Katzy, M. Kaur, P. Kaur, I.R. Kenyon, A. Keramidas, L.A. Khein, C. Kiesling, J.Y. Kim, D. Kisielewska, S. Kitamura, R. Klanner, M. Klein, U. Klein, C. Kleinwort, T. Kluge, A. Knutsson, E. Koffeman, R. Kogler, D. Kollar, P. Kooijman, Ie. Korol, I.A. Korzhavina, P. Kostka, A. Kotański, U. Kötz, H. Kowalski, M. Kraemer, K. Krastev, J. Kretzschmar, A. Kropivnitskaya, K. Krüger, P. Kulinski, O. Kuprash, K. Kutak, M. Kuze, V.A. Kuzmin, M.P.J. Landon, W. Lange, G. Laštovička-Medin, P. Laycock, A. Lebedev, A. Lee, V. Lendermann, B.B. Levchenko, S. Levonian, A. Levy, G. Li, V. Libov, S. Limentani, T.Y. Ling, K. Lipka, A. Liptaj, M. Lisovyi, B. List, J. List, E. Lobodzinska, W. Lohmann, B. Löhr, E. Lohrmann, J.H. Loizides, N. Loktionova, K.R. Long, A. Longhin, D. Lontkovskyi, R. Lopez-Fernandez, V. Lubimov, J. Łukasik, O.Yu. Lukina, P. Łużniak, J. Maeda, S. Magill, A. Makankine, I. Makarenko, E. Malinovski, J. Malka, R. Mankel, P. Marage, A. Margotti, G. Marini, Ll. Marti, J.F. Martin, H.-U. Martyn, A. Mastroberardino, T. Matsumoto, M.C.K. Mattingly, S.J. Maxfield, A. Mehta, I.-A. Melzer-Pellmann, A.B. Meyer, H. Meyer, H. Meyer, J. Meyer, S. Miglioranzi, S. Mikocki, I. Milcewicz-Mika, F. Mohamad Idris, V. Monaco, A. Montanari, F. Moreau, A. Morozov, J.D. Morris, J.V. Morris, M.U. Mozer, M. Mudrinic, K. Müller, P. Murín, B. Musgrave, K. Nagano, T. Namsoo, R. Nania, Th. Naumann, P.R. Newman, D. Nicholass, C. Niebuhr, A. Nigro, A. Nikiforov, D. Nikitin, Y. Ning, U. Noor, D. Notz, G. Nowak, K. Nowak, R.J. Nowak, A.E. Nuncio-Quiroz, B.Y. Oh, N. Okazaki, K. Oliver, K. Olkiewicz, J.E. Olsson, Yu. Onishchuk, S. Osman, O. Ota, D. Ozerov, V. Palichik, I. Panagoulias, M. Pandurovic, Th. Papadopoulou, K. Papageorgiu, A. Parenti, C. Pascaud, G.D. Patel, E. Paul, J.M. Pawlak, B. Pawlik, O. Pejchal, P.G. Pelfer, A. Pellegrino, E. Perez, W. Perlanski, H. Perrey, A. Petrukhin, I. Picuric, S. Piec, K. Piotrzkowski, D. Pitzl, R. Plačakytė, P. Plucinski, B. Pokorny, N.S. Pokrovskiy, R. Polifka, A. Polini, B. Povh, A.S. Proskuryakov, M. Przybycień, V. Radescu, A.J. Rahmat, N. Raicevic, A. Raspiareza, A. Raval, T. Ravdandorj, D.D. Reeder, P. Reimer, B. Reisert, Z. Ren, J. Repond, Y.D. Ri, E. Rizvi, A. Robertson, P. Robmann, B. Roland, P. Roloff, E. Ron, R. Roosen, A. Rostovtsev, M. Rotaru, I. Rubinsky, J.E. Ruiz Tabasco, S. Rusakov, M. Ruspa, R. Sacchi, D. Sálek, A. Salii, U. Samson, D.P.C. Sankey, G. Sartorelli, M. Sauter, E. Sauvan, A.A. Savin, D.H. Saxon, M. Schioppa, S. Schlenstedt, P. Schleper, W.B. Schmidke, S. Schmitt, U. Schneekloth, L. Schoeffel, V. Schönberg, A. Schöning, T. Schörner-Sadenius, H.-C. Schultz-Coulon, J. Schwartz, F. Sciulli, F. Sefkow, R.N. Shaw-West, L.M. Shcheglova, R. Shehzadi, S. Shimizu, L.N. Shtarkov, S. Shushkevich, I. Singh, I.O. Skillicorn, T. Sloan, W. Słomiński, I. Smiljanic, W.H. Smith, V. Sola, A. Solano, Y. Soloviev, D. Son, P. Sopicki, Iu. Sorokin, V. Sosnovtsev, D. South, V. Spaskov, A. Specka, A. Spiridonov, H. Stadie, L. Stanco, Z. Staykova, M. Steder, B. Stella, A. Stern, T.P. Stewart, A. Stifutkin, G. Stoicea, P. Stopa, U. Straumann, S. Suchkov, D. Sunar, G. Susinno, L. Suszycki, T. Sykora, J. Sztuk, D. Szuba, J. Szuba, A.D. Tapper, E. Tassi, V. Tchoulakov, J. Terrón, T. Theedt, G. Thompson, P.D. Thompson, H. Tiecke, K. Tokushuku, T. Toll, F. Tomasz, J. Tomaszewska, T.H. Tran, D. Traynor, T.N. Trinh, P. Truöl, I. Tsakov, B. Tseepeldorj, T. Tsurugai, M. Turcato, J. Turnau, T. Tymieniecka, K. Urban, C. Uribe-Estrada, A. Valkárová, C. Vallée, P. Van Mechelen, A. Vargas Trevino, Y. Vazdik, M. Vázquez, A. Verbytskyi, V. Viazlo, S. Vinokurova, N.N. Vlasov, V. Volchinski, O. Volynets, M. von den Driesch, R. Walczak, W.A.T. Wan Abdullah, D. Wegener, J.J. Whitmore, J. Whyte, L. Wiggers, M. Wing, Ch. Wissing, M. Wlasenko, G. Wolf, H. Wolfe, K. Wrona, E. Wünsch, A.G. Yagües-Molina, S. Yamada, Y. Yamazaki, R. Yoshida, C. Youngman, J. Žáček, J. Zálešák, A.F. Żarnecki, L. Zawiejski, O. Zeniaev, W. Zeuner, Z. Zhang, B.O. Zhautykov, A. Zhokin, C. Zhou, A. Zichichi, T. Zimmermann, H. Zohrabyan, M. Zolko, F. Zomer, D.S. Zotkin


I. Physikalisches Institut der RWTH, Aachen, Germany

Institute of Physics and Technology of Ministry of Education and Science of Kazakhstan, Almaty, Kazakhstan

NIKHEF and University of Amsterdam, Amsterdam, Netherlands 

Argonne National Laboratory, Argonne, Illinois 60439-4815, USA 

Vinca Institute of Nuclear Sciences, Belgrade, Serbia

Andrews University, Berrien Springs, Michigan 49104-0380, USA

School of Physics and Astronomy, University of Birmingham, Birmingham, United Kingdom 

INFN Bologna, Bologna, Italy 

University and INFN Bologna, Bologna, Italy 

Physikalisches Institut der Universität Bonn, Bonn, Germany 

H.H. Wills Physics Laboratory, University of Bristol, Bristol, United Kingdom 

Inter-University Institute for High Energies ULB-VUB, Brussels; Universiteit Antwerpen, Antwerpen; Belgium 

National Institute for Physics and Nuclear Engineering (NIPNE), Bucharest, Romania

Panjab University, Department of Physics, Chandigarh, India

Department of Engineering in Management and Finance, Univ. of the Aegean, Chios, Greece

Physics Department, Ohio State University, Columbus, Ohio 43210, USA 

Calabria University, Physics Department and INFN, Cosenza, Italy 

The Henryk Niewodniczanski Institute of Nuclear Physics, Polish Academy of Sciences, Cracow, Poland 

Faculty of Physics and Applied Computer Science, AGH-University of Science and Technology, Cracow, Poland 

Department of Physics, Jagellonian University, Cracow, Poland

Kyungpook National University, Center for High Energy Physics, Daegu, South Korea 

Rutherford Appleton Laboratory, Chilton, Didcot, United Kingdom 

Institut für Physik, TU Dortmund, Dortmund, Germany 

Joint Institute for Nuclear Research, Dubna, Russia

INFN Florence, Florence, Italy 

University and INFN Florence, Florence, Italy 

Fakultät für Physik der Universität Freiburg i.Br., Freiburg i.Br., Germany 

CEA, DSM/Irfu, CE-Saclay, Gif-sur-Yvette, France

Department of Physics and Astronomy, University of Glasgow, Glasgow, United Kingdom 

Institut für Experimentalphysik, Universität Hamburg, Hamburg, Germany 

Deutsches Elektronen-Synchrotron DESY, Hamburg, Germany

Max-Planck-Institut für Kernphysik, Heidelberg, Germany

Physikalisches Institut, Universität Heidelberg, Heidelberg, Germany 

Kirchhoff-Institut für Physik, Universität Heidelberg, Heidelberg, Germany 

Nevis Laboratories, Columbia University, Irvington on Hudson, New York 10027, USA 

Institute for Nuclear Research, National Academy of Sciences, and Kiev National University, Kiev, Ukraine

Institute of Experimental Physics, Slovak Academy of Sciences, Košice, Slovak Republic 

Jabatan Fizik, Universiti Malaya, 50603 Kuala Lumpur, Malaysia 

Chonnam National University, Kwangju, South Korea

Department of Physics, University of Lancaster, Lancaster, United Kingdom 

Department of Physics, University of Liverpool, Liverpool, United Kingdom 

Physics and Astronomy Department, University College London, London, United Kingdom 

Queen Mary and Westfield College, London, United Kingdom 

Imperial College London, High Energy Nuclear Physics Group, London, United Kingdom 

Institut de Physique Nucléaire, Université Catholique de Louvain, Louvain-la-Neuve, Belgium 

Physics Department, University of Lund, Lund, Sweden 

Departamento de Fisica Aplicada, CINVESTAV, Mérida, Yucatán, Mexico 

Departamento de Fisica, CINVESTAV, México City, Mexico 

Department of Physics, University of Wisconsin, Madison, Wisconsin 53706, USA 

Departamento de Física Teórica, Universidad Autónoma de Madrid, Madrid, Spain 

CPPM, CNRS/IN2P3 - Univ. Mediterranee, Marseille, France

Department of Physics, McGill University, Montréal, Québec, Canada H3A 2T8 

Institute for Theoretical and Experimental Physics, Moscow, Russia 

Lebedev Physical Institute, Moscow, Russia 

Moscow Engineering Physics Institute, Moscow, Russia 

Moscow State University, Institute of Nuclear Physics, Moscow, Russia 

Max-Planck-Institut für Physik, München, Germany

LAL, Univ. Paris-Sud, CNRS/IN2P3, Orsay, France

Department of Physics, University of Oxford, Oxford, United Kingdom 

INFN Padova, Padova, Italy 

Dipartimento di Fisica dell’Università and INFN, Padova, Italy 

LLR, Ecole Polytechnique, CNRS/IN2P3, Palaiseau, France

LPNHE, Universités Paris VI and VII, CNRS/IN2P3, Paris, France

Faculty of Science, University of Montenegro, Podgorica, Montenegro 

Institute of Physics, Academy of Sciences of the Czech Republic, Praha, Czech Republic 

Faculty of Mathematics and Physics, Charles University, Praha, Czech Republic 

Department of Particle Physics, Weizmann Institute, Rehovot, Israel 

Dipartimento di Fisica Università di Roma Tre and INFN Roma 3, Roma, Italy

Dipartimento di Fisica, Università ’La Sapienza’ and INFN, Rome, Italy 

Polytechnic University, Sagamihara, Japan 

Institute for Nuclear Research and Nuclear Energy, Sofia, Bulgaria 

Raymond and Beverly Sackler Faculty of Exact Sciences, School of Physics, Tel Aviv University, Tel Aviv, Israel 

Department of Physics, Tokyo Institute of Technology, Tokyo, Japan 

Department of Physics, University of Tokyo, Tokyo, Japan 

Tokyo Metropolitan University, Department of Physics, Tokyo, Japan 

Università di Torino and INFN, Torino, Italy 

Università del Piemonte Orientale, Novara, and INFN, Torino, Italy 

Department of Physics, University of Toronto, Toronto, Ontario, Canada M5S 1A7 

Institute of Particle and Nuclear Studies, KEK, Tsukuba, Japan 

Institute of Physics and Technology of the Mongolian Academy of Sciences, Ulaanbaatar, Mongolia

Department of Physics, Pennsylvania State University, University Park, Pennsylvania 16802, USA 

Paul Scherrer Institut, Villigen, Switzerland

Warsaw University, Institute of Experimental Physics, Warsaw, Poland

Institute for Nuclear Studies, Warsaw, Poland

Fachbereich C, Universität Wuppertal, Wuppertal, Germany

Yerevan Physics Institute, Yerevan, Armenia

Meiji Gakuin University, Faculty of General Education, Yokohama, Japan 

Department of Physics, York University, Ontario, Canada M3J1P3 

Deutsches Elektronen-Synchrotron DESY, Zeuthen, Germany

Institut für Teilchenphysik, ETH, Zürich, Switzerland 

Physik-Institut der Universität Zürich, Zürich, Switzerland 




Also at Physics Department, National Technical University, Zografou Campus, GR-15773 Athens, Greece

Also at Rechenzentrum, Universität Wuppertal, Wuppertal, Germany

Also at University of P.J. Šafárik, Košice, Slovak Republic

Also at CERN, Geneva, Switzerland

Also at Max-Planck-Institut für Physik, München, Germany

Also at Comenius University, Bratislava, Slovak Republic

Also at DESY and University Hamburg, Helmholtz Humboldt Research Award

Also at Faculty of Physics, University of Bucharest, Bucharest, Romania

Also at Ulaanbaatar University, Ulaanbaatar, Mongolia



Also affiliated with University College London, United Kingdom

Now at University of Salerno, Italy

Now at Queen Mary University of London, United Kingdom

Also working at Max Planck Institute, Munich, Germany

Now at Institute of Aviation, Warsaw, Poland

Supported by the research grant No. 1 P03B 04529 (2005-2008)

This work was supported in part by the Marie Curie Actions Transfer of Knowledge project COCOS (contract MTKD-CT-2004-517186)

Now at DESY group FEB, Hamburg, Germany

Also at Moscow State University, Russia

Now at University of Liverpool, United Kingdom

On leave of absence at CERN, Geneva, Switzerland

Now at CERN, Geneva, Switzerland

Also at Institut of Theoretical and Experimental Physics, Moscow, Russia

Also at INP, Cracow, Poland

Also at FPACS, AGH-UST, Cracow, Poland

Partially supported by Warsaw University, Poland

Partially supported by Moscow State University, Russia

Also affiliated with DESY, Germany

Now at Japan Synchrotron Radiation Research Institute (JASRI), Hyogo, Japan

Also at University of Tokyo, Japan

Now at Kobe University, Japan

Supported by DESY, Germany

Partially supported by Russian Foundation for Basic Research grant No. 05-02-39028-NSFC-a

STFC Advanced Fellow

Nee Korcsak-Gorzo

This material was based on work supported by the National Science Foundation, while working at the Foundation.

Also at Max Planck Institute, Munich, Germany, Alexander von Humboldt Research Award

Now at Nihon Institute of Medical Science, Japan

Now at SunMelx Co. Ltd., Tokyo, Japan

Now at Osaka University, Osaka, Japan

Now at University of Bonn, Germany

also Senior Alexander von Humboldt Research Fellow at Hamburg University

Also at Łódź University, Poland

Member of Łódź University, Poland

Now at Lund University, Lund, Sweden

Supported by Chonnam National University, South Korea, in 2009

Also at University of Podlasie, Siedlce, Poland




Supported by the German Federal Ministry for Education and Research (BMBF), under contract numbers 05H09GUF, 05H09VHC, 05H09VHF and 05H16PEA


Supported by the German Federal Ministry for Education and Research (BMBF), under contract numbers 05 HZ6PDA, 05 HZ6GUA, 05 HZ6VFA and 05 HZ4KHA


Supported by FNRS-FWO-Vlaanderen, IISN-IIKW and IWT and by Interuniversity Attraction Poles Programme, Belgian Science Policy


Supported by the Polish State Committee for Scientific Research, project No. DESY/256/2006 - 154/DES/2006/03


Partially Supported by Polish Ministry of Science and Higher Education, grant PBS/DESY/70/2006

Supported by the Deutsche Forschungsgemeinschaft

Supported by VEGA SR grant no. 2/7062/ 27

Supported by the Swedish Natural Science Research Council

Supported by the Ministry of Education of the Czech Republic under the projects LC527, INGO-1P05LA259 and MSM0021620859

Supported by the Swiss National Science Foundation

Supported by CONACYT, México, grant 48778-F

Russian Foundation for Basic Research (RFBR), grant no 1329.2008.2

This project is co-funded by the European Social Fund (75% and National Resources (25%) - (EPEAEK II) - PYTHAGORAS II


Supported by the Natural Sciences and Engineering Research Council of Canada (NSERC)


Supported in part by the MINERVA Gesellschaft für Forschung GmbH, the Israel Science Foundation (grant No. 293/02-11.2) and the US-Israel Binational Science Foundation

Supported by the Israel Science Foundation

Supported by the Italian National Institute for Nuclear Physics (INFN)

Supported by the Japanese Ministry of Education, Culture, Sports, Science and Technology (MEXT) and its grants for Scientific Research

Supported by the Korean Ministry of Education and Korea Science and Engineering Foundation

Supported by the Netherlands Foundation for Research on Matter (FOM)


Partially supported by the German Federal Ministry for Education and Research (BMBF)

Supported by RF Presidential grant N 1456.2008.2 for the leading scientific schools and by the Russian Ministry of Education and Science through its grant for Scientific Research on High Energy Physics

Supported by the Spanish Ministry of Education and Science through funds provided by CICYT

Supported by the UK Science and Technology Facilities Council

Supported by the US Department of Energy

Supported by the US National Science Foundation. Any opinion, findings and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.

Supported by the Polish Ministry of Science and Higher Education as a scientific project (2009-2010)

Supported by FNRS and its associated funds (IISN and FRIA) and by an Inter-University Attraction Poles Programme subsidised by the Belgian Federal Science Policy Office

Supported by an FRGS grant from the Malaysian government


deceased



1 Introduction

Deep inelastic scattering (DIS) at HERA has been central to the exploration of proton structure and quark-gluon interaction dynamics as prescribed in perturbative Quantum Chromodynamics (QCD). HERA allowed inelastic interactions to be studied at high centre-of-mass energy, GeV, where , the lepton beam energy  GeV and the proton beam energy  GeV for most of the running period. Operation of HERA proceeded in two phases, HERA I, from 1992-2000, and HERA II, from 2002-2007. The luminosity collected by each of the collider experiments, H1 and ZEUS, in unpolarised and scattering during the first phase was approximately  pband  pb, respectively.

The paper presents the combination of the published H1 [1, 2, 3, 4, 5] and ZEUS [6, 7, 8, 9, 10, 11, 12, 13, 14] measurements from HERA I on inclusive DIS in neutral (NC) and charged current (CC) reactions which cover a wide range of negative four-momentum-transfer squared, , and Bjorken . The combination is performed using a method introduced in [15] and extended in [1]. This also provides a model-independent check of the data consistency. The correlated systematic uncertainties and global normalisations are fitted such that one coherent data set is obtained. Since H1 and ZEUS have employed different experimental techniques, using different detectors and methods of kinematic reconstruction, the combination leads to a significantly reduced uncertainty.

The combined data set contains complete information on inclusive DIS cross sections published by the H1 and ZEUS collaborations based on data collected in the years -. The kinematic range of the NC data is and  GeV, for values of inelasticity between and , where . The kinematic range of the CC data is and  GeV, for values of between and . An extensive overview of the results on HERA I data from both H1 and ZEUS is given in [16].

Analyses of the and dependences of the NC and CC DIS cross sections measured at HERA have determined sets of quark and gluon momentum distributions in the proton, both from H1 [2] and ZEUS [17]. In such analyses, the lower NC data determine the low- sea quark and gluon distributions. The high- CC data, together with the difference between NC and cross sections at high , constrain the valence quark distributions. The use of the HERA CC data allows the down quark distribution in the proton to be determined without assuming isospin symmetry. In addition, the use of HERA data alone for the determination of parton distribution functions (PDFs) eliminates the need for heavy target corrections, which must be applied to DIS data from nuclear targets. In this paper the combined HERA data are used to determine a new set of parton distributions termed HERAPDF1.0. Consistency of the input data ensures that the experimental uncertainty of the HERAPDF1.0 set can be determined using rigorous statistical methods. Uncertainties resulting from model assumptions and from the choice of PDF parametrisation are also considered, similarly to [2].

The paper is organised as follows. In section 2 the measurements by H1 and ZEUS and the input data are described. In section 3 the combination of the NC and CC data sets from H1 and ZEUS is discussed. The QCD analysis is described in section 4. A summary is given in section 5.

2 Measurements of Inclusive DIS Cross Sections

2.1 Cross Sections and Parton Distributions

The neutral current deep inelastic scattering cross section, at tree level, is given by a linear combination of generalised structure functions. For unpolarised beams it can be expressed as

(1)

where the electromagnetic coupling constant , the photon propagator and a helicity factor are absorbed in the definition of the reduced cross section , and . The functions , and depend on the electroweak parameters as [18]

(2)

Here and are the vector and axial-vector weak couplings of the electron to the boson and . The effective values for the electroweak mixing angle, , and the boson mass,  GeV, are used [19]. At low , the contribution of exchange is negligible and . The contribution of the term containing the structure function is only significant for large values of .

In the Quark Parton Model (QPM), [20] and the other functions in equation 2.1 are given as

(3)

where denote the electric charge of up- or down-type quarks while and are the vector and axial-vector weak couplings of the up- or down-type quarks to the boson. Here , , and denote the sums of up-type, of down-type and of their anti-quark distributions, respectively. Below the quark mass threshold, these sums are related to the quark distributions as follows

(4)

where and are the strange and charm quark distributions. Assuming symmetry between sea quarks and anti-quarks, the valence quark distributions result from

(5)

Defining a reduced cross section for the inclusive unpolarised charged current scattering as

(6)

gives a sum of charged current structure functions, analogous to equation 1, as

(7)

For the Fermi constant, an effective value  GeV is used, the boson mass is  GeV [19]. In the QPM and the CC structure functions represent sums and differences of quark and anti-quark-type distributions depending on the charge of the lepton beam as

(8)

From these equations it follows that

(9)

Therefore the NC and CC measurements may be used to determine the combined sea quark distribution functions, and , and the valence quark distributions, and . A QCD analysis in the DGLAP formalism [21, 22, 23, 24, 25] also allows the gluon momentum distribution, , in the proton to be determined from scaling violations.

2.2 Reconstruction of Kinematics

The deep inelastic scattering cross section of the inclusive neutral and charged current reactions depends on the centre-of-mass energy and on two kinematic variables, and . Usually is obtained from the measurement of the inelasticity and from and through the relationship . The salient feature of the HERA collider experiments is the possibility to determine the NC event kinematics from the scattered electron111In this paper, the term electron is used for both electrons and positrons, unless otherwise stated. , or from the hadronic final state , or using a combination of the two. The choice of the most appropriate kinematic reconstruction method for a given phase space region is based on resolution, measurement accuracy and radiative correction effects and has been optimised differently for the two experiments. The use of different reconstruction techniques by the two experiments contributes to the improved accuracy of the combined data set.

For NC scattering, in the “electron method”, the inelasticity and the negative four-momentum-transfer squared can be calculated using the electron kinematics as

(10)

Here , where is the angle between the scattered electron direction and the proton beam direction222In the right-handed H1 and ZEUS coordinate systems, the axis points along the proton beam direction, termed the forward direction. The () axis is directed horizontally (vertically). , is the scattered electron energy, and is its transverse momentum. Similar relations are obtained from the hadronic final state reconstruction [26], and are used for CC scattering,

(11)

where is the hadronic variable with the sum extending over the reconstructed hadronic final state particles , and is the total transverse momentum of the hadronic final state with being the transverse momentum vector of the particle . The combination of and defines the hadronic scattering angle

(12)

which, within the QPM, corresponds to the direction of the struck quark. In the “sigma method” [27] the total variable

(13)

is introduced. For non-radiative events this variable equals such that equations 10 and 11 can be modified as

(14)

A hybrid “e-sigma method”  [27, 3, 7] uses and to reconstruct the event kinematics

(15)

An extension of the sigma method [1, 2] is

(16)

This modification takes radiative effects at the lepton vertex into account by replacing the electron beam energy in the calculation of , in a similar manner to .

The “double angle method” [28, 29] is used to reconstruct and from the electron and hadronic scattering angles as

(17)

The method is largely insensitive to hadronization and, to first order, is independent of the detector energy scales. However, the hadronic angle is less well-determined than the electron angle due to particle loss in the beampipe. In the “PT method” of reconstruction [30] the well-measured electron kinematics is used to obtain a good event-by-event estimate of the hadronic energy loss, by employing . This improves both the resolution and uncertainties of the reconstructed and . The PT method uses all measured variables to optimise the resolution over the entire kinematic range measured, namely,

(18)

The variable is then substituted for in the formulae for the double angle method to determine ,