Measurement of the inclusive jet cross section using the <em>k_T</em> algorithm in <em>pp</em> collisions at s√=1.96  TeV with the CDF II detector

Article

Reference

Measurement of the inclusive jet cross section using the k

algorithm in pp collisions at s√=1.96  TeV with the CDF II detector

CDF Collaboration

CAMPANELLI, Mario (Collab.), et al.

Abstract

We report on measurements of the inclusive jet production cross section as a function of the jet transverse momentum in pp collisions at s√=1.96  TeV, using the kT algorithm and a data sample corresponding to 1.0  fb−1 collected with the Collider Detector at Fermilab in run II. The measurements are carried out in five different jet rapidity regions with |yjet|

CDF Collaboration, CAMPANELLI, Mario (Collab.), et al . Measurement of the inclusive jet cross section using the k

algorithm in pp collisions at s√=1.96  TeV with the CDF II detector. Physical Review. D , 2007, vol. 75, no. 09, p. 092006

DOI : 10.1103/PhysRevD.75.092006

Available at:

http://archive-ouverte.unige.ch/unige:38443

Disclaimer: layout of this document may differ from the published version.

Measurement of the inclusive jet cross section using the k

algorithm in p p collisions at p s

1:96 TeV with the CDF II detector

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J. C. Yun,¹⁷L. Zanello,⁵²A. Zanetti,⁵⁵I. Zaw,²²X. Zhang,²⁴J. Zhou,⁵³and S. Zucchelli⁵ (CDF Collaboration)

1Institute of Physics, Academia Sinica, Taipei, Taiwan 11529, Republic of China

2Argonne National Laboratory, Argonne, Illinois 60439, USA

3Institut de Fisica d’Altes Energies, Universitat Autonoma de Barcelona, E-08193, Bellaterra (Barcelona), Spain

4Baylor University, Waco, Texas 76798, USA

5Istituto Nazionale di Fisica Nucleare, University of Bologna, I-40127 Bologna, Italy

6Brandeis University, Waltham, Massachusetts 02254, USA

7University of California, Davis, Davis, California 95616, USA

8University of California, Los Angeles, Los Angeles, California 90024, USA

9University of California, San Diego, La Jolla, California 92093, USA

10University of California, Santa Barbara, Santa Barbara, California 93106, USA

11Instituto de Fisica de Cantabria, CSIC-University of Cantabria, 39005 Santander, Spain

12Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA

13Enrico Fermi Institute, University of Chicago, Chicago, Illinois 60637, USA

14Comenius University, 842 48 Bratislava, Slovakia; Institute of Experimental Physics, 040 01 Kosice, Slovakia

15Joint Institute for Nuclear Research, RU-141980 Dubna, Russia

16Duke University, Durham, North Carolina 27708, USA

17Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA

18University of Florida, Gainesville, Florida 32611, USA

19Laboratori Nazionali di Frascati, Istituto Nazionale di Fisica Nucleare, I-00044 Frascati, Italy

20University of Geneva, CH-1211 Geneva 4, Switzerland

21Glasgow University, Glasgow G12 8QQ, United Kingdom

22Harvard University, Cambridge, Massachusetts 02138, USA

23Division of High Energy Physics, Department of Physics, University of Helsinki, and Helsinki Institute of Physics, FIN-00014, Helsinki, Finland

24University of Illinois, Urbana, Illinois 61801, USA

25The Johns Hopkins University, Baltimore, Maryland 21218, USA

26Institut fu¨r Experimentelle Kernphysik, Universita¨t Karlsruhe, 76128 Karlsruhe, Germany

27High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki 305, Japan

28Center for High Energy Physics: Kyungpook National University, Taegu 702-701, Korea; Seoul National University, Seoul 151-742, Korea; and SungKyunKwan University, Suwon 440-746, Korea

29Ernest Orlando Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA

30University of Liverpool, Liverpool L69 7ZE, United Kingdom

31University College London, London WC1E 6BT, United Kingdom

32Centro de Investigaciones Energeticas Medioambientales y Tecnologicas, E-28040 Madrid, Spain

33Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

34Institute of Particle Physics: McGill University, Montre´al, Canada H3A 2T8; and University of Toronto, Toronto, Canada M5S 1A7

35University of Michigan, Ann Arbor, Michigan 48109, USA

36Michigan State University, East Lansing, Michigan 48824, USA

37Institution for Theoretical and Experimental Physics, ITEP, Moscow 117259, Russia

38University of New Mexico, Albuquerque, New Mexico 87131, USA

39Northwestern University, Evanston, Illinois 60208, USA

40The Ohio State University, Columbus, Ohio 43210, USA

41Okayama University, Okayama 700-8530, Japan

42Osaka City University, Osaka 588, Japan

43University of Oxford, Oxford OX1 3RH, United Kingdom

44University of Padova, Istituto Nazionale di Fisica Nucleare, Sezione di Padova-Trento, I-35131 Padova, Italy

45LPNHE, Universite Pierre et Marie Curie/IN2P3-CNRS, UMR7585, Paris, F-75252 France

46University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA

47Istituto Nazionale di Fisica Nucleare Pisa, Universities of Pisa, Siena and Scuola Normale Superiore, I-56127 Pisa, Italy

48University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA

49Purdue University, West Lafayette, Indiana 47907, USA

50University of Rochester, Rochester, New York 14627, USA

51The Rockefeller University, New York, New York 10021, USA

52Istituto Nazionale di Fisica Nucleare, Sezione di Roma 1, University of Rome ‘‘La Sapienza’’, I-00185 Roma, Italy

53Rutgers University, Piscataway, New Jersey 08855, USA

54Texas A&M University, College Station, Texas 77843, USA

55Istituto Nazionale di Fisica Nucleare, University of Trieste/Udine, Italy

56University of Tsukuba, Tsukuba, Ibaraki 305, Japan

57Tufts University, Medford, Massachusetts 02155, USA

58Waseda University, Tokyo 169, Japan

59Wayne State University, Detroit, Michigan 48201, USA

60University of Wisconsin, Madison, Wisconsin 53706, USA

61Yale University, New Haven, Connecticut 06520, USA

(Received 29 January 2007; published 24 May 2007; publisher error corrected 25 May 2007) We report on measurements of the inclusive jet production cross section as a function of the jet transverse momentum in pp collisions at ps

1:96 TeV, using the k_T algorithm and a data sample corresponding to1:0 fb¹ collected with the Collider Detector at Fermilab in run II. The measurements are carried out in five different jet rapidity regions withjy^jetj<2:1and transverse momentum in the range

aVisiting scientist from University of Athens, 157 84 Athens, Greece.

nVisiting scientist from Texas Tech University, Lubbock, TX 79409, USA.

mVisiting scientist from Queen Mary and Westfield College, London, E1 4NS, United Kingdom.

lVisiting scientist from Universidad de Oviedo, E-33007 Oviedo, Spain.

kVisiting scientist from Nagasaki Institute of Applied Science, Nagasaki, Japan.

jVisiting scientist from University of Manchester, Manchester M13 9PL, United Kingdom.

iVisiting scientist from University of Iberoamericana, Mexico D.F., Mexico.

hVisiting scientist from University of Heidelberg, D-69120 Heidelberg, Germany.

gVisiting scientist from University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom.

fVisiting scientist from University College Dublin, Dublin 4, Ireland.

eVisiting scientist from University of Cyprus, Nicosia CY-1678, Cyprus.

dVisiting scientist from Cornell University, Ithaca, NY 14853, USA.

cVisiting scientist from Universite Libre de Bruxelles (ULB), B-1050 Brussels, Belgium.

bVisiting scientist from University of Bristol, Bristol BS8 1TL, United Kingdom.

oVisiting scientist from Instituto de Fisica Corpuscular (IFIC), 46071 Valencia, Spain.

54< p^jet_T <700 GeV=c. Next-to-leading order perturbative QCD predictions are in good agreement with the measured cross sections.

DOI:10.1103/PhysRevD.75.092006 PACS numbers: 12.38.Aw, 13.85.t, 13.87.a

I. INTRODUCTION

The measurement of the inclusive jet cross section as a function of the jet transverse momentum,p^jet_T, inpp colli- sions at

ps

1:96 TeV constitutes a test of perturbative quantum chromodynamics (pQCD) [1]. In run II [2] of the Tevatron, measurements of the jet cross section for jets withp^jet_T up to about700 GeV=c[3,4] have extended the p^jet_T range by more than150 GeV=ccompared to run I [5–

7]. In particular, the CDF collaboration recently published results [3] on inclusive jet production using thek_T algo- rithm [8,9] for jets withp^jet_T >54 GeV=cand rapidity [10]

in the region0:1<jy^jetj<0:7, which are well described by next-to-leading order (NLO) pQCD predictions [11]. As discussed in [3], thek_Talgorithm has been widely used for precise QCD measurements at both ee and ep col- liders, and makes possible a well-defined comparison to the theoretical predictions [9]. The pQCD calculations involve matrix elements, describing the hard interaction between partons, convoluted with parton density functions (PDFs) [12,13] in the proton and antiproton that require input from experiment. The pQCD predictions are affected by the still-limited knowledge of the gluon PDF, which translates into a large uncertainty on the theoretical cross sections at highp^jet_T [3,4]. Inclusive jet cross section mea- surements from run I at the Tevatron [6], performed in different jet rapidity regions, have been used to partially constrain the gluon distribution in the proton. This article continues the studies on jet production using thek_Talgo- rithm at the Tevatron [3,7] and presents new measurements of the inclusive jet production cross section as a function of p^jet_T in five different jet rapidity regions up to jy^jetj 2:1, based on1:0 fb¹ of CDF run II data. The measurements are corrected to the hadron level [14] and compared to NLO pQCD predictions.

II. EXPERIMENTAL SETUP

The CDF II detector (see Fig.1) is described in detail in [15]. The subdetectors most relevant for this analysis are discussed briefly here. The detector has a charged particle tracking system immersed in a 1.4 T magnetic field. A silicon microstrip detector [16] provides tracking over the radial range 1.35 to 28 cm and covers the pseudorapidity rangejj<2. A 3.1-m-long open-cell drift chamber [17]

covers the radial range from 44 to 132 cm and provides tracking coverage forjj<1. Segmented sampling calo- rimeters, arranged in a projective tower geometry, surround the tracking system and measure the energy of interacting particles forjj<3:6. The central barrel calorimeter [18]

covers the region jj<1. It consists of two sections, an electromagnetic calorimeter (CEM) and a hadronic calo- rimeter (CHA), divided into 480 towers of size 0.1 inand 0.26 in. The end-wall hadronic calorimeter (WHA) [19]

is behind the central barrel calorimeter in the region0:6<

jj<1:0, providing forward coverage out tojj<1:3. In run II, new forward scintillator-plate calorimeters [20]

replaced the run I gas calorimeter system. The new plug electromagnetic calorimeter (PEM) covers the region 1:1<jj<3:6, while the new hadronic calorimeter (PHA) provides coverage in the 1:3<jj<3:6 region.

The calorimeter has gaps at jj 0 (between the two halves of the central barrel calorimeter) and at jj 1:1 (in the region between the WHA and the plug calorime- ters). The measured energy resolutions for electrons in the electromagnetic calorimeters [18,20] are 14%=

E_T p 2%

(CEM) and16%=

pE

1%(PEM), where the energies are expressed in GeV. The single-pion energy resolutions in the hadronic calorimeters, as determined in test-beam data

EQ-TARGET;temp:intralink-;da1;316;433

η=2.0 η=3.0 η=1.0

PEM CEM WHA CHA

PHA

FIG. 1. Elevation view of one-half of the CDF detector dis- playing the components of the CDF calorimeter.

[18–20], are 50%=pE_T

3% (CHA), 75%=pE_T 4%

(WHA), and 80%=

pE

5% (PHA). Cherenkov counters covering the3:7<jj<4:7region [21] measure the av- erage number of inelasticpp collisions per bunch crossing and thereby determine the beam luminosity.

III. JET RECONSTRUCTION

Thek_Talgorithm [9] is used to reconstruct jets from the energy depositions in the calorimeter towers in both data and Monte Carlo simulated events (see Sec. VI). For each calorimeter tower, the four-momenta [22] of its electro- magnetic and hadronic sections are summed to define a physics tower. First, all physics towers with transverse momentum above0:1 GeV=care considered as protojets.

The quantities

EQ-TARGET;temp:intralink-;d1;52;560

k_T;ip²_T;i; k_T;i;jminp²_T;i; p²_T;jR²_i;j=D² (1) are computed for each protojet and pair of protojets, re- spectively, wherep_T;idenotes the transverse momentum of theith protojet,R_i;jis the distance (yspace) between each pair of protojets, andDis a parameter that approxi- mately controls the size of the jet by limiting, in each iteration, the clustering of protojets according to their spacial separation. Allk_T;i andkT;i;jvalues are then col- lected into a single sorted list. In this list, if the smallest quantity is of the type k_T;i, the corresponding protojet is promoted to be a jet and removed from the list. Otherwise, if the smallest quantity is of the typek_T;i;j, the protojets are combined into a single protojet by summing up their four- vector components. The procedure is iterated over proto- jets until the list is empty. The jet transverse momentum, rapidity, and azimuthal angle are denoted asp^jet_T;cal,y^jet_cal, and ^jet_cal, respectively.

In the Monte Carlo event samples, the same jet algo- rithm is also applied to the final-state particles, considering all particles as protojets, to search for jets at the hadron level. The resulting hadron-level jet variables are denoted asp^jet_T;had,y^jet_had, and^jet_had.

IV. EVENT SELECTION

Events are selected online using a three-level trigger system [23] with unique sets of selection criteria called paths. For the different trigger paths used in this measure- ment, this selection is based on the measured energy

deposits in the calorimeter towers, with different thresh- olds on the jet E_Tand different prescale factors [24] (see TableI). In the first-level trigger, a single trigger tower [25]

withE_Tabove 5 or 10 GeV, depending on the trigger path, is required. In the second-level trigger, calorimeter clusters are formed around the selected trigger towers. The events are required to have at least one second-level trigger cluster withE_Tabove a given threshold, which varies between 15 and 90 GeV for the different trigger paths. In the third-level trigger, jets are reconstructed using the CDF run I cone algorithm [26], and the events are required to have at least one jet withE_Tabove 20 to 100 GeV.

Jets are then reconstructed using the k_T algorithm, as explained in Sec. III, withD0:7. For each trigger path, the minimump^jet_T;cal, in eachjy^jet_caljregion, is chosen in such a way that the trigger selection is more than 99% efficient.

The efficiency for a given trigger path is obtained using events from a different trigger path with lower transverse energy thresholds (see TableI). In the case of the JET 20 trigger path, the trigger efficiency is extracted from addi- tional control samples, which include a sample with only first-level trigger requirements as well as data collected using unbiased trigger paths with no requirement on the energy deposits in the calorimeter towers. As an example, for jets in the region 0:1<jy^jet_calj<0:7, Fig. 2shows the trigger efficiency as a function of p^jet_T;cal for the different samples. The following selection criteria have been im- posed:

(1) Events are required to have at least one recon- structed primary vertex with z-position within 60 cm of the nominal interaction point. This par- tially removes beam-related backgrounds and en- sures a well-understood event-by-event jet kinematics. Primary vertices are reconstructed event-by-event using the tracking system and an algorithm that identifies clusters of tracks pointing to a commonz-position along the beam line [27]. In events with more than one reconstructed primary vertex, the one with the highest jp^track_T jis used to define the kinematics, where jp^track_T j denotes the scalar sum of the transverse momentum of the tracks associated with the vertex. For the QCD event top- ologies considered in this analysis, the efficiency for the reconstruction of at least one primary vertex is essentially 100%.

(2) Events are required to have at least one jet with ra- TABLE I. Summary of trigger paths, trigger thresholds, and effective prescale factors employed to collect the data.

Trigger path Level 1 towerE_T[GeV] Level 2 clusterE_T [GeV] Level 3 jetE_T[GeV] Effective prescale

JET 20 5 15 20 775

JET 50 5 40 50 34

JET 70 10 60 70 8

JET 100 10 90 100 1

pidity in the regionjy^jet_calj<2:1and corrected p^jet_T;cal (see Sec. IX) above54 GeV=c, which constitutes the minimum jet transverse momentum considered in the analysis. The measurements are limited to jets with jy^jet_calj<2:1 to avoid contributions from the p andpremnants that would affect the measuredp^jet_T;cal in the most forward region of the calorimeter.

(3) In order to remove beam-related backgrounds and cosmic rays, the events are required to fulfill E6 _T=

E_T

p < Fp^{jet 1}_T;cal), whereE6 _Tdenotes the miss- ing transverse energy [28] in GeV andE_TP

iEⁱ_T is the total transverse energy of the event, as mea- sured using calorimeter towers with Eⁱ_T above 0.1 GeV. The threshold functionFp^{jet 1}_T;calis defined asFp^jet_T min20:0125 p^jet_T;7, wherep^{jet 1}_T;cal is the uncorrected transverse momentum of the lead- ing jet (highestp^jet_T) inGeV=c, andFis inGeV¹⁼². This criterion preserves more than 95% of the QCD events, as determined from Monte Carlo studies (see Sec. VI). A visual scan of events with p^jet_T;cal>

400 GeV=cdid not show remaining backgrounds.

Measurements are carried out in five different jet rapidity regions:jy^jet_calj<0:1,0:1<jy^jet_calj<0:7,0:7<jy^jet_calj<1:1, 1:1<jy^jet_calj<1:6, and1:6<jy^jet_calj<2:1, where the differ- ent boundaries are chosen to reduce systematic effects coming from the layout of the calorimeter system.

V. EFFECT OF MULTIPLEpp INTERACTIONS The measured p^jet_T;cal includes contributions from mul- tiplepp interactions per bunch crossing at high instanta- neous luminosity,L^inst. The data used in this measurement

were collected at L^inst between 0:2 10³¹ cm²s¹ and 16:3 10³¹ cm²s¹ with an average of 4:1 10³¹ cm²s¹. On average, 1.5 inelastic pp interactions per bunch crossing are expected. At the highest L^inst considered, an average of 5.9 interactions per bunch cross- ing are produced. This mainly affects the measured cross section at low p^jet_T where the contributions are sizable.

Multiple interactions are identified via the presence of additional primary vertices reconstructed from charged particles. The measured jet transverse momenta are cor- rected for this effect by removing a certain amount of transverse momentum,^mi_pT N_V1, whereN_Vdenotes the number of reconstructed primary vertices in the event and^mi_pTis determined from the data by requiring that, after the correction is applied, the ratio of cross sections at low and high L^inst does not show any p^jet_T dependence. The study is carried out separately in eachjy^jet_caljregion, and the results are consistent with a common value ^mi_pT 1:86 0:23 GeV=cacross the whole rapidity range.

VI. MONTE CARLO SIMULATION

Monte Carlo simulated event samples are used to deter- mine the response of the detector and the correction factors to the hadron level. The generated samples are passed through a full CDF II detector simulation (based on

GEANT3 [29], where the GFLASH [30] package is used to simulate the energy deposition in the calorimeters) and then reconstructed and analyzed using the same analysis chain as used for the data.

Samples of simulated inclusive jet events have been generated with PYTHIA 6.203 [31] and HERWIG 6.4 [32]

Monte Carlo generators, using CTEQ5L [33] PDFs. The

PYTHIAsamples have been created using a specially tuned set of parameters, denoted as PYTHIA-TUNE A [34], that includes enhanced contributions from initial-state gluon radiation and secondary parton interactions between rem- nants. The parameters were determined from dedicated studies of the underlying event using the CDF run I data [35] and has been shown to properly describe the measured jet shapes in run II [36]. In the case ofPYTHIA, fragmenta- tion into hadrons is carried out using the string model [37]

as implemented inJETSET[38], whileHERWIGimplements the cluster model [39].

VII. SIMULATION OF THE CALORIMETER RESPONSE TO JETS

Dedicated studies have been performed to validate the Monte Carlo simulation of the calorimeter response to jets for the differentjy^jet_caljregions. Previous analyses [3] for jets with 0:1<jy^jet_calj<0:7 indicate that the simulation prop- erly reproduces both the average p^jet_T and the jet momen- tum resolution,_pjet

T

, as measured in the data. The study is performed for the rest of thejy^jet_caljregions using jets in the

EQ-TARGET;temp:intralink-;d1;52;747

[GeV/c]

JET T,CAL

p

20 40 60 80 100 120 140 160 180

Trigger efficiency

0.8 0.85 0.9 0.95 1 1.05

JET 20 JET 50 JET 70 JET 100

|<0.7

JET

0.1<|yCAL

FIG. 2. Measured trigger efficiencies as a function ofp^jet_T;calfor different trigger paths and in the region0:1<jy^jet_calj<0:7. In this particular case, JET 20 trigger path is at least 99% efficient for p^jet_T;cal>32 GeV=c, JET 50 forp^jet_T;cal>60 GeV=c, JET 70 for p^jet_T;cal>84 GeV=c, and JET 100 forp^jet_T;cal>119 GeV=c.

range0:1<jy^jet_calj<0:7as a reference. An exclusive dijet sample is selected, in data and simulated events, with the following criteria:

(1) Events are required to have one and only one recon- structed primary vertex withz-position within 60 cm of the nominal interaction point.

(2) Events are required to have exactly two jets with p^jet_T;cal>10 GeV=c, where one of the jets must be in the region0:1<jy^jet_calj<0:7.

(3) E6 _T= E_T

p < Fp^{jet 1}_T;cal, as explained in Sec. IV.

The bisector method [40] is applied to data and simulated exclusive dijet events to test the accuracy of the simulated _p^jet

T

in the detector. The study indicates that the simulation systematically underestimates the measured _p^jet

T

by 6%

and 10% for jets in the regions0:7<jy^jet_calj<1:1and1:6<

jy^jet_calj<2:1, respectively, with no significantp^jet_T;cal depen- dence. An additional smearing of the reconstructedp^jet_T;calis applied to the simulated events to account for this effect. In the region1:1<jy^jet_calj<1:6,_p^jet

T is overestimated by 5% in the simulation. The effect on the final result is included via slightly modified unfolding factors (see Sec. IX). For jets with jy^jet_calj<0:1, the simulation properly describes the measured _p^jet

T

. Figure 3shows the ratio between _p^jet

T

in data and simulated events, ^data

p^jet_T =^mc

p^jet_T, in different jy^jet_calj regions as a function of the averagep^jet_T;calof the dijet event [41]. After corrections have been applied to the simulated events, data and simulation agree. In the region 1:1<

jy^jet_calj<1:6, and only for the purpose of presentation, a 5% smearing of the reconstructed p^jet_T;cal is applied to the data to show the resulting good agreement with the un- corrected simulated resolution. The relative difference be- tween data and simulated resolutions is conservatively taken to be 8% (see Fig. 3) over the whole range in p^jet_T;cal and jy^jet_calj in the evaluation of systematic uncer- tainties.

The average jet momentum calorimeter response in the simulation is then tested by comparing thep^jet_T;calbalance in data and simulated exclusive dijet events. The variable, defined as [42]

EQ-TARGET;temp:intralink-;d2;316;591

1 hi

1 hi; withp^{test jet}_T;cal p^ref:_T;cal^jet

p^{test jet}_T;cal p^ref:_T;cal^jet; (2) is computed in data and simulated events in bins of p^{test jet}_T;cal p^ref:jet_T;cal =2, where p^ref:_T;cal^jet denotes the transverse momentum of the jet in the region 0:1<jy^jet_calj<0:7, and p^ref:_T;cal^jet is the transverse momentum of the jet in thejy^jet_calj region under study. The presence of calorimeter gaps at jj 0andjj 1:1(see Sec. II) translates into a reduced average calorimeter response to jets. For jets in the regions jy^jet_calj 0 and jy^jet_calj 1:1, the value for is about 0.87.

Figure 4 presents the ratios _data=_mc as a function of p^jet_T;calp^{test jet}_T;cal in the differentjy^jet_caljbins considered in the analysis. The study indicates that small corrections are required around calorimeter gaps, jy^jet_calj<0:1 and 1:1<jy^jet_calj<1:6, as well as in the most forward region,

EQ-TARGET;temp:intralink-;d2;52;343

0.8 0.9 1 1.1 1.2 1.3

|<0.1

CAL

|yJET 0.1<|y_CAL^JET|<0.7

MC JET Tpσ/DATA JET Tpσ 0.8

0.9 1 1.1 1.2 1.3

|<1.1

CAL

0.7<|yJET

(dijet) [GeV/c]

JET T,CAL

average p

100 200 300

|<1.6

CAL

1.1<|yJET

(dijet) [GeV/c]

JET T,CAL

average p

0 100 200 300

0.7 0.8 0.9 1 1.1 1.2 1.3

|<2.1

CAL

1.6<|yJET

Ratio Data/MC before corrections Ratio Data/MC after corrections fit after corrections

8% Systematic uncertainty

FIG. 3. Ratio^data

p^jet_T =^mc

p^jet_T as a function of the averagep^jet_T;calof the dijet event, in differentjy^jet_caljregions, before (black squares) and after (open circles) corrections have been applied (see Sec. VII). The solid lines are fits to the corrected ratios. The dashed lines indicate a8%relative variation considered in the study of systematic uncertainties.

1:6<jy^jet_calj<2:1. For jets withjy^jet_calj>1:1, the correction shows a moderatep^jet_T;cal dependence, and several parame- trizations are considered to extrapolate to very highp^jet_T;cal. The difference observed in the final results, using different parametrizations, is included as part of the total systematic uncertainty.

VIII. RECONSTRUCTION OF THE JET VARIABLES

The jet reconstruction in the detector is studied using Monte Carlo event samples, with modified jet energy response in the calorimeter, as described in the previous section, and pairs of jets at the calorimeter and hadron levels matched in (y) space by requiring

y^jet_caly^jet_had^{2 jet}_cal^jet_had² q

< D. These studies indi- cate that the angular variables of a jet are reconstructed with no significant systematic shift and with a resolution better than 0.05 units inyandat lowp^jet_T;cal, improving as p^jet_T;calincreases. The measuredp^jet_T;calsystematically under- estimates that of the hadron-level jet. This is attributed mainly to the noncompensating nature of the calorimeter [18]. For jets withp^jet_T;cal around50 GeV=c, the jet trans- verse momentum is reconstructed with an average shift that varies between9%and30%and a resolution between 10% and 16%, depending on the jy^jet_calj region. The jet reconstruction improves asp^jet_T;cal increases. For jets with p^jet_T;calaround500 GeV=c, the average shift is7%and the resolution is about 7%.

IX. UNFOLDING

The measured p^jet_T;cal distributions in the different jy^jet_calj regions are unfolded back to the hadron level using simu- lated event samples (see Sec. VI), after including the modified jet energy response described in Sec. VII.

PYTHIA-TUNE A provides a reasonable description of the different jet and underlying event quantities, and is used to determine the correction factors in the unfolding proce- dure. In order to avoid any potential bias on the correction factors due to the particular PDF set used during the generation of the simulated samples, which translates into slightly different simulated p^jet_T;cal distributions, the underlying p^_t spectrum [43] in PYTHIA-TUNE A is re- weighted until the Monte Carlo samples accurately follow each of the measuredp^jet_T;caldistributions. The unfolding is carried out in two steps.

First, an average correction is computed separately in each jet rapidity region using corresponding matched pairs of jets at the calorimeter and hadron levels. The correlation hp^jet_T;hadp^jet_T;cali versus hp^jet_T;cali (see Fig. 5), computed in bins of p^jet_T;hadp^jet_T;cal=2, is used to extract correction factors which are then applied to the measured jets to obtain the corrected transverse momenta, p^jet_T;cor. In each jet rapidity region, a cross section is defined as

EQ-TARGET;temp:intralink-;d3;316;154

d²

dp^jet_T;cordy^jet_cal 1 L

Ncor^jet

p^jet_T;cory^jet_cal; (3) whereN^jetcordenotes the number of jets in a givenp^jet_T;corbin, p^jet_T;cor is the size of the bin,y^jet_caldenotes the size of the

EQ-TARGET;temp:intralink-;d3;52;747

0.95 1 1.05

|<0.1

CAL

|yJET 0.1<|y_CAL^JET|<0.7

MCβ /DATAβ 0.95 1 1.05

|<1.1

CAL

0.7<|yJET

[GeV/c]

JET T,CAL

p

100 200 300 400

|<1.6

CAL

1.1<|yJET

[GeV/c]

JET T,CAL

p

100 200 300 400

0.95 1 1.05

|<2.1

CAL

1.6<|yJET

Ratio Data/MC fit to the ratio Systematic uncertainty

FIG. 4. Ratiodata=mcas a function ofp^jet_T;calin differentjy^jet_caljregions. The solid lines show the nominal parametrizations based on fits to the ratios. In the regionjy^jet_calj>1:1, the dashed lines indicate different parametrizations used to describe the ratios at highp^jet_T;cal, and are considered in the study of systematic uncertainties.