Inclusive-jet photoproduction at HERA and determination of
Introduction
The study of jet production in ep collisions at HERA has been well established as a testing ground of perturbative QCD (pQCD). Jet cross sections provided precise determinations of the strong coupling constant, , and its scale dependence. The jet observables used to test pQCD included inclusive-jet [1], [2], [3], [4], [5], [6], [7], dijet [1], [4], [6], [7], [8], [9] and multijet [6], [7], [10], [11], [12] cross sections in neutral current (NC) deep inelastic ep scattering (DIS), inclusive-jet [13], [14], dijet [15], [16], [17], [18], [19], [20] and multijet [21], [22] cross sections in photoproduction and the internal structure of jets in NC [23], [24], [25] and charged current [26], [27] DIS. These studies also demonstrated that the cluster algorithm [28] in the longitudinally invariant inclusive mode [29] results in the smallest uncertainties in the reconstruction of jets in ep collisions. Jet cross sections in NC DIS [2] and photoproduction [16] were used by ZEUS [30] as input in a QCD analysis to extract the parton distribution functions (PDFs) of the proton; these data helped to constrain the gluon density at medium- to high-x values, where x is the fraction of the proton momentum carried by the gluon.
The algorithm is well suited for ep collisions and yields infrared- and collinear-safe cross sections at any order of pQCD. However, it might not be best suited to reconstruct jets in hadron–hadron collisions, such as those at the LHC. In order to optimise the reconstruction of jet observables in such environments, new infrared- and collinear-safe jet algorithms were recently developed, namely the anti- [31], a recombination-type jet algorithm, and the “Seedless Infrared-Safe” cone (SIScone) [32] algorithms. Measurements of jet cross sections in NC DIS using these algorithms were recently published [33] and constituted the first measurements with these new jet algorithms. The results tested the performance of these jet algorithms with data in a well understood hadron-induced reaction and it was shown that pQCD calculations with up to four partons in the final state provide a good description of the differences between jet algorithms.
Measurements of inclusive-jet cross sections in photoproduction are presented in this paper. Two types of QCD processes contribute to jet production in photoproduction; at leading order they can be separated into [34], [35] the direct process, in which the photon interacts directly with a parton in the proton, and the resolved process, in which the photon acts as a source of partons, one of which interacts with a parton in the proton. Due to the presence of the resolved processes, the analysis of jet cross sections in photoproduction with different jet algorithms provides a test of their performance in a reaction closer to hadron–hadron interactions than NC DIS.
In this paper, single-differential inclusive-jet cross sections as functions of the jet transverse energy, , and pseudorapidity, , are presented based on the , anti- and SIScone jet algorithms. The results based on the anti- and SIScone jet algorithms are compared to the measurements based on the via the ratios of cross sections. In addition, measurements of cross sections are also presented as functions of in different regions of , which have the potential to constrain further the gluon density at high x. Next-to-leading-order (NLO) QCD calculations using recent parameterisations of the proton and photon PDFs are compared to the measurements. A determination of as well as of its energy-scale dependence are also presented. The analyses presented here are based on a data sample with a more than three-fold increase in statistics with respect to the previous study [13].
Section snippets
Experimental set-up
A detailed description of the ZEUS detector can be found elsewhere [36], [37]. A brief outline of the components most relevant for this analysis is given below.
Charged particles were tracked in the central tracking detector (CTD) [38], which operated in a magnetic field of provided by a thin superconducting solenoid. The CTD consisted of 72 cylindrical drift-chamber layers, organised in nine superlayers covering the polar-angle62
Data selection
The data were collected during the running period 2005–2007, when HERA operated with protons of energy and electrons or positrons63 of energy , at an ep centre-of-mass energy of , and correspond to an integrated luminosity of .
A three-level trigger system was used to select events online [37], [43]. At the first level, events were triggered by a
Jet search
In photoproduction, jets are usually defined using the transverse-energy flow in the pseudorapidity–azimuth () plane of the laboratory frame [28], [29], [44]. The procedure to reconstruct jets with the algorithm from an initial list of objects (e.g. final-state partons, final-state hadrons or energy deposits in the calorimeter) is described below in some detail. In the following discussion, denotes the transverse energy, the pseudorapidity and the azimuthal angle of object i.
Monte Carlo simulations
Samples of events were generated to determine the response of the detector to jets of hadrons and the correction factors necessary to obtain the hadron-level jet cross sections. In addition, these samples were used to estimate hadronisation corrections to the NLO calculations (see Section 8).
The MC programs Pythia 6.146 [47] and Herwig 6.504 [48] were used to generate resolved and direct photoproduction events. In both generators, the partonic processes are simulated using leading-order matrix
Transverse-energy and acceptance corrections
The comparison of the reconstructed jet variables for the hadronic and the calorimetric jets in MC-simulated events showed that no correction was needed for the jet pseudorapidity and azimuth. However, underestimates the corresponding hadronic-jet transverse energy by with an r.m.s. of . This underestimation is mainly due to the energy lost by the particles in the inactive material in front of the CAL. The transverse-energy corrections to calorimetric jets, as functions of
Experimental uncertainties
The following sources of systematic uncertainty were considered for the measured cross sections:
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the differences in the results obtained by using either Pythia or Herwig to correct the data for detector effects. The resulting uncertainty was typically below ;
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the effect of the CAL energy-scale uncertainty on was estimated by varying by in simulated events. The uncertainty in the cross sections was below at low , increasing to at high ;
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the effect of the
Next-to-leading-order QCD calculations
The NLO QCD () calculations used in the analysis presented here were computed using the program by Klasen, Kleinwort and Kramer [59]. The calculations use the phase-space-slicing method [60] with an invariant-mass cut to isolate the singular regions of the phase space. The number of flavours was set to five and the renormalisation () and factorisation () scales were chosen to be . The strong coupling constant was calculated at two loops with , corresponding to
Results
Single- and double-differential inclusive-jet cross sections were measured in the kinematic region given by and . These cross sections include every jet of hadrons with and in each event. The jets were reconstructed using either the , the anti- or the SIScone jet algorithms. The x region covered by the measurements was determined to be .
Summary and conclusions
Measurements of differential cross sections for inclusive-jet photoproduction at a centre-of-mass energy of 318 GeV using an integrated luminosity of collected by the ZEUS detector have been presented. The cross sections refer to jets of hadrons of and identified in the laboratory frame with the , anti- or SIScone jet algorithms with jet radius . The cross sections are given in the kinematic region of and .
Measurements of
Acknowledgements
We thank the DESY Directorate for their strong support and encouragement. The remarkable achievements of the HERA machine group were essential for the successful completion of this work and are greatly appreciated. We are grateful for the support of the DESY computing and network services. The design, construction, installation and running of the ZEUS detector were made possible owing to the ingenuity and effort of many people who are not listed as authors.
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Cited by (0)
- 1
Supported by the US Department of Energy.
- 2
Supported by the Italian National Institute for Nuclear Physics (INFN).
- 3
Supported by the German Federal Ministry for Education and Research (BMBF), under contract No. 05 H09PDF.
- 4
Supported by the Science and Technology Facilities Council, UK.
- 5
Supported by an FRGS grant from the Malaysian government.
- 6
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.
- 7
Supported by the Polish Ministry of Science and Higher Education as a scientific project No. DPN/N188/DESY/2009.
- 8
Supported by the Polish Ministry of Science and Higher Education and its grants for Scientific Research.
- 9
Supported by the German Federal Ministry for Education and Research (BMBF), under contract No. 05h09GUF, and the SFB 676 of the Deutsche Forschungsgemeinschaft (DFG).
- 10
Supported by the Japanese Ministry of Education, Culture, Sports, Science and Technology (MEXT) and its grants for Scientific Research.
- 11
Supported by the Korean Ministry of Education and Korea Science and Engineering Foundation.
- 12
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.
- 13
Supported by the Spanish Ministry of Education and Science through funds provided by CICYT.
- 14
Supported by the Natural Sciences and Engineering Research Council of Canada (NSERC).
- 15
Partially supported by the German Federal Ministry for Education and Research (BMBF).
- 16
Supported by RF Presidential grant No. 4142.2010.2 for Leading Scientific Schools, by the Russian Ministry of Education and Science through its grant for Scientific Research on High Energy Physics and under contract No. 02.740.11.0244.
- 17
Supported by the Netherlands Foundation for Research on Matter (FOM).
- 18
Supported by the Israel Science Foundation.
- 19
Now at University of Salerno, Italy.
- 20
Now at Queen Mary University of London, United Kingdom.
- 21
Also funded by Max Planck Institute for Physics, Munich, Germany.
- 22
Also Senior Alexander von Humboldt Research Fellow at Hamburg University, Institute of Experimental Physics, Hamburg, Germany.
- 23
Also at Cracow University of Technology, Faculty of Physics, Mathematics and Applied Computer Science, Poland.
- 24
Supported by the research grant No. 1 P03B 04529 (2005–2008).
- 25
Supported by the Polish National Science Centre, project No. DEC-2011/01/BST2/03643.
- 26
Now at Rockefeller University, New York, NY 10065, USA.
- 27
Now at DESY group FS-CFEL-1.
- 28
Now at Institute of High Energy Physics, Beijing, China.
- 29
Now at DESY group FEB, Hamburg, Germany.
- 30
Also at Moscow State University, Russia.
- 31
Now at University of Liverpool, United Kingdom.
- 32
Now at CERN, Geneva, Switzerland.
- 33
Also affiliated with University College London, UK.
- 34
Now at Goldman Sachs, London, UK.
- 35
Also at Institute of Theoretical and Experimental Physics, Moscow, Russia.
- 36
Also at FPACS, AGH-UST, Cracow, Poland.
- 37
Partially supported by Warsaw University, Poland.
- 38
Now at Istituto Nucleare di Fisica Nazionale (INFN), Pisa, Italy.
- 39
Now at Haase Energie Technik AG, Neumünster, Germany.
- 40
Now at Department of Physics, University of Bonn, Germany.
- 41
Now at Biodiversität und Klimaforschungszentrum (BiK-F), Frankfurt, Germany.
- 42
Also affiliated with DESY, Germany.
- 43
Also at University of Tokyo, Japan.
- 44
Now at Kobe University, Japan.
- 45
Supported by DESY, Germany.
- 46
Member of National Technical University of Ukraine, Kyiv Polytechnic Institute, Kyiv, Ukraine.
- 47
Member of National University of Kyiv, Mohyla Academy, Kyiv, Ukraine.
- 48
Partly supported by the Russian Foundation for Basic Research, grant 11-02-91345-DFG_a.
- 49
Alexander von Humboldt Professor; also at DESY and University of Oxford.
- 50
STFC Advanced Fellow.
- 51
Nee Korcsak-Gorzo.
- 52
This material was based on work supported by the National Science Foundation, while working at the Foundation.
- 53
Also at Max Planck Institute for Physics, Munich, Germany, External Scientific Member.
- 54
Now at Tokyo Metropolitan University, Japan.
- 55
Now at Nihon Institute of Medical Science, Japan.
- 56
Now at Osaka University, Osaka, Japan.
- 57
Also at Łódź University, Poland.
- 58
Member of Łódź University, Poland.
- 59
Now at Department of Physics, Stockholm University, Stockholm, Sweden.
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Also at Cardinal Stefan Wyszyński University, Warsaw, Poland.
- 61
Deceased.