Article
Reference
Measurement of the Inclusive Jet Cross Section Using the k
TAlgorithm in pp Collisions at s√=1.96 TeV
CDF Collaboration
CAMPANELLI, Mario (Collab.), et al.
Abstract
We report on a measurement of the inclusive jet production cross section as a function of the jet transverse momentum in pp collisions at s√=1.96 TeV using data collected with the upgraded Collider Detector at Fermilab in run II, corresponding to an integrated luminosity of 385 pb−1. The measurement is carried out for jets with rapidity 0.1
CDF Collaboration, CAMPANELLI, Mario (Collab.), et al . Measurement of the Inclusive Jet Cross Section Using the k
TAlgorithm in pp Collisions at s√=1.96 TeV. Physical Review Letters , 2006, vol. 96, no. 12, p. 122001
DOI : 10.1103/PhysRevLett.96.122001
Available at:
http://archive-ouverte.unige.ch/unige:38322
Disclaimer: layout of this document may differ from the published version.
1 / 1
Measurement of the Inclusive Jet Cross Section Using the k
TAlgorithm in p p Collisions at
p s
1:96 TeV
A. Abulencia,23D. Acosta,17J. Adelman,13T. Affolder,10T. Akimoto,54M. G. Albrow,16D. Ambrose,16S. Amerio,42 D. Amidei,33A. Anastassov,51K. Anikeev,16A. Annovi,45J. Antos,1M. Aoki,54G. Apollinari,16J.-F. Arguin,32 T. Arisawa,56A. Artikov,14W. Ashmanskas,16A. Attal,8F. Azfar,41P. Azzi-Bacchetta,42P. Azzurri,45N. Bacchetta,42 H. Bachacou,28W. Badgett,16A. Barbaro-Galtieri,28V. E. Barnes,47B. A. Barnett,24S. Baroiant,7V. Bartsch,30G. Bauer,31
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T. Yoshida,40I. Yu,27S. S. Yu,44J. C. Yun,16L. Zanello,50A. Zanetti,53I. Zaw,21F. Zetti,45 X. Zhang,23J. Zhou,51and 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
14Joint Institute for Nuclear Research, RU-141980 Dubna, Russia
15Duke University, Durham, North Carolina 27708, USA
16Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA
17University of Florida, Gainesville, Florida 32611, USA
18Laboratori Nazionali di Frascati, Istituto Nazionale di Fisica Nucleare, I-00044 Frascati, Italy
19University of Geneva, CH-1211 Geneva 4, Switzerland
122001-2
20Glasgow University, Glasgow G12 8QQ, United Kingdom
21Harvard University, Cambridge, Massachusetts 02138, USA
22Division of High Energy Physics, Department of Physics, University of Helsinki and Helsinki Institute of Physics, FIN-00014, Helsinki, Finland
23University of Illinois, Urbana, Illinois 61801, USA
24The Johns Hopkins University, Baltimore, Maryland 21218, USA
25Institut fu¨r Experimentelle Kernphysik, Universita¨t Karlsruhe, 76128 Karlsruhe, Germany
26High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki 305, Japan
27Center 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
28Ernest Orlando Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
29University of Liverpool, Liverpool L69 7ZE, United Kingdom
30University College London, London WC1E 6BT, United Kingdom
31Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
32Institute of Particle Physics: McGill University, Montre´al, Canada H3A 2T8;
and University of Toronto, Toronto, Canada M5S 1A7
33University of Michigan, Ann Arbor, Michigan 48109, USA
34Michigan State University, East Lansing, Michigan 48824, USA
35Institution for Theoretical and Experimental Physics, ITEP, Moscow 117259, Russia
36University of New Mexico, Albuquerque, New Mexico 87131, USA
37Northwestern University, Evanston, Illinois 60208, USA
38The Ohio State University, Columbus, Ohio 43210, USA
39Okayama University, Okayama 700-8530, Japan
40Osaka City University, Osaka 588, Japan
41University of Oxford, Oxford OX1 3RH, United Kingdom
42University of Padova, Istituto Nazionale di Fisica Nucleare, Sezione di Padova-Trento, I-35131 Padova, Italy
43LPNHE-Universite de Paris 6/IN2P3-CNRS, France
44University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
45Istituto Nazionale di Fisica Nucleare Pisa, Universities of Pisa, Siena and Scuola Normale Superiore, I-56127 Pisa, Italy
46University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
47Purdue University, West Lafayette, Indiana 47907, USA
48University of Rochester, Rochester, New York 14627, USA
49The Rockefeller University, New York, New York 10021, USA
50Istituto Nazionale di Fisica Nucleare, Sezione di Roma 1, University of Rome ‘‘La Sapienza,’’ I-00185 Roma, Italy
51Rutgers University, Piscataway, New Jersey 08855, USA
52Texas A&M University, College Station, Texas 77843, USA
53Istituto Nazionale di Fisica Nucleare, University of Trieste/Udine, Italy
54University of Tsukuba, Tsukuba, Ibaraki 305, Japan
55Tufts University, Medford, Massachusetts 02155, USA
56Waseda University, Tokyo 169, Japan
57Wayne State University, Detroit, Michigan 48201, USA
58University of Wisconsin, Madison, Wisconsin 53706, USA
59Yale University, New Haven, Connecticut 06520, USA (Received 22 December 2005; published 30 March 2006)
We report on a measurement of the inclusive jet production cross section as a function of the jet transverse momentum inppcollisions at
ps
1:96 TeVusing data collected with the upgraded Collider Detector at Fermilab in run II, corresponding to an integrated luminosity of385 pb1. The measurement is carried out for jets with rapidity0:1<jyjetj<0:7and transverse momentum in the range54< pjetT <
700 GeV=c. Next-to-leading order perturbative QCD predictions are in good agreement with the measured cross section after the necessary nonperturbative parton-to-hadron corrections are included.
DOI:10.1103/PhysRevLett.96.122001 PACS numbers: 12.38.Aw, 13.85.t, 13.87.a
The measurement of inclusive jet production in pp collisions at
ps
1:96 TeVconstitutes a test of perturba- tive QCD (pQCD) [1] predictions over more than 8 orders of magnitude in cross section. The increased center-of- mass energy and integrated luminosity in run II at the Tevatron make it possible to measure the cross section for jets with transverse momentum [2] pjetT up to about
700 GeV=c, extending the pjetT range by more than 150 GeV=c compared with previous results [3]. This Letter presents a new measurement of the inclusive jet production cross section as a function ofpjetT for jets with pjetT >54 GeV=c and rapidity [2] in the region 0:1<
jyjetj<0:7, where jets are reconstructed with thekTalgo- rithm [4,5]. Similar measurements have been carried out
using cone-based jet algorithms in run II [6]. However, the kTalgorithm has been widely used for precise QCD mea- surements at both ee and ep colliders and allows a well defined comparison to the theoretical predictions, without introducing into the calculations additional pa- rameters to emulate the experimental procedure governing the merging or splitting of overlapping cones [5]. The measurements are corrected for detector effects back to the particle (hadron) level [7] and compared to pQCD next- to-leading order (NLO) predictions [8]. Previous measure- ments using thekTalgorithm at the Tevatron [9] observed a marginal agreement with NLO pQCD at lowpjetT. We find that this discrepancy is removed after nonperturbative corrections are included.
The CDF detector is described in detail elsewhere [10].
The detector has a charged particle tracking system im- mersed in a 1.4 T magnetic field, aligned coaxially with the beam line. A silicon microstrip detector provides tracking over the radial range 1.35–28 cm and covers the pseudor- apidity [2] rangejj 2. A cylindrical 3.1 m long open- cell drift chamber covers the radial range from 44 to 132 cm and provides full tracking coverage for jj 1.
Segmented sampling calorimeters, arranged in a projective tower geometry, surround the tracking system and measure the energy flow of interacting particles in jj 3:6. The central barrel calorimeter [11,12] covers the regionjj<
1. It consists of electromagnetic and hadronic calorimeters segmented into 480 towers of size 0.1 inand 15 in. The measured energy resolution for electrons is EE 13:5%=
ET GeV
p 2%. The single-pion energy reso- lution, as determined from test-beam data, is 50%=
ET GeV
p 3%. A hadronic calorimeter comple- ments the coverage of the central barrel calorimeter in the region 0:6<jj<1:0 and provides additional forward coverage out tojj<1:3. The forward region1:1<jj<
3:6 is covered by scintillator-plate electromagnetic and hadronic calorimeters. Cherenkov counters in the region 3:7<jj<4:7measure the number of inelasticpp colli- sions to compute the luminosity [13].
Monte Carlo event samples are used to determine the response of the detector and the correction factors to the hadron level. The generated samples are passed through a full CDF detector simulation (based onGEANT3[14] where the GFLASH [15] package is used to simulate the energy deposition in the calorimeters) and then reconstructed and analyzed using the same analysis chain as for the data.
Samples of simulated inclusive jet events have been gen- erated using the PYTHIA 6.203 [16] andHERWIG 6.4 [17]
Monte Carlo generators. CTEQ5L [18] parton distribution functions (PDFs) are used for the proton and antiproton.
The PYTHIA samples have been created using a special tuned set of parameters, denoted as PYTHIA-TUNE A, that includes enhanced contributions from initial-state gluon radiation and secondary parton interactions between pro- ton/antiproton beam remnants.TUNE Awas developed with
dedicated studies of the underlying event using the CDF run I data [19] and describes the measured jet shapes in run II [20].
The kT algorithm is used to reconstruct jets from the energy depositions in the calorimeter towers with trans- verse momentum above 0:1 GeV=c. First, all towers are considered as protojets. The quantities kT;i p2T;i and kTi;jminp2T;i; p2T;j R2i;j=D2 are computed for each protojet and pair of protojets, respectively, where pT;i denotes the transverse momentum of the ith protojet, Ri;j is the distance (yspace) between each pair of protojets, andDis a parameter that approximately controls the size of the jet. All kT;i and kTi;j values are then collected into a single sorted list. In this combined sorted list, if the smallest quantity is of the type kT;i, the corre- sponding protojet is promoted to be a jet and removed from the list. Otherwise, if the smallest quantity is of the type kT;i;j, the protojets are combined into a single protojet by summing up their four-vector components. The procedure is iterated over protojets until the list is empty. The jet transverse momentum, rapidity, and azimuthal angle are denoted aspjetT;CAL,yjetCAL, andjetCAL, respectively. The same jet algorithm is applied to all the final-state particles in the Monte Carlo samples to search for jets at the hadron level.
The resulting hadron-level jet variables are denoted as pjetT;HAD,yjetHAD, andjetHAD.
The measurements presented in this Letter correspond to a total integrated luminosity of38522 pb1. Events are selected on-line using three-level trigger paths [21] with different prescales. In the first-level trigger, a single trigger tower with ET above 5 or 10 GeV is required. In the second-level trigger, clusters are formed around the se- lected trigger towers, and a cluster with ET above 15–
90 GeV, depending on the trigger path, is required. In the third-level trigger, jets are reconstructed using a cone- based algorithm, and a jet with ET above 20 –100 GeV is required. Jets are then searched for using thekTalgorithm, as explained above, with D0:7. For each trigger data sample, the threshold on the minimumpjetT;CALis chosen in such a way that the trigger selection is fully efficient. The events are required to have at least one jet with rapidity in the region 0:1<jyjetCALj<0:7 and corrected transverse momentum (see below) above 54 GeV=c. The events are selected to have at least one reconstructed primary vertex with the z position within 60 cm around the nominal interaction point. In order to remove beam-related back- grounds and cosmics rays, the events are required to fulfill 6ET=
ET
p < Fpleading jet
T;CAL , where 6ETdenotes the missing transverse energy [22] andET P
iEiTis the total trans- verse energy of the event, as measured using calorimeter towers with EiT above 100 MeV. The threshold function Fpleading jet
T;CAL is defined as FpjetT min20:0125 pjetT;7, wherepleading jet
T;CAL is the uncorrected transverse mo- 122001-4
mentum of the leading jet (highestpjetT) and the units are GeV. This criterion is designed to preserve more than 95%
of the QCD events, as determined from Monte Carlo stud- ies. A visual scan for pjetT;CAL>400 GeV=c showed no remaining backgrounds.
The measured jet transverse momentum includes addi- tional contributions from multiple proton-antiproton inter- actions per bunch crossing at high instantaneous luminosity. The data were collected at instantaneous lumi- nosities varying between 0:21031 and 9:6 1031 cm2s1. At the highest instantaneous luminosities, an average of two interactions per bunch crossing are produced. This affects mainly the measured cross section at lowpjetT, where the contributions are sizable. In CDF, 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 for each additional primary ver- tex. A value1:620:700:46 GeV=cis determined from the data by requiring that, after the correction is applied, the ratio of cross sections at low and high instantaneous lumi- nosities does not show anypjetT dependence.
The reconstruction of the jet variables in the calorimeter is studied using Monte Carlo samples. These studies in- dicate that the angular variables of a jet are reconstructed with no significant systematic shift and with a resolution better than 0.05 units inyandat lowpjetT;CAL, improving aspjetT;CAL increases. The measured jet transverse momen- tum systematically underestimates that of the hadron-level jet, which is attributed mainly to the noncompensating nature of the calorimeter [23]. For jets withpjetT;CAL about 50 GeV=c, the jet transverse momentum is reconstructed with an average shift of 19%and a resolution of 14%.
The jet reconstruction improves as pjetT;CAL increases. For jets with pjetT;CAL about 500 GeV=c, the average shift is 5%and the resolution is about 7%. The bisector method [24] is employed to evaluate how well the Monte Carlo calculation reproduces the measured jet energy resolutions.
Data and Monte Carlo calculation agree within a relative uncertainty of8%over the wholepjetT;CAL range.
The measuredpjetT;CALdistribution is unfolded back to the hadron level using Monte Carlo event samples. PYTHIA- TUNE Aprovides a reasonable description of the different jet and underlying event quantities and is used to determine the correction factors in the unfolding procedure. In order to avoid any bias on the correction factors due to the particular PDF set used, which translates into slightly different simulated pjetT;CAL distributions, PYTHIA-TUNE A
is reweighted until it accurately follows the measured pjetT;CALspectrum. The unfolding is carried out in two steps.
First, an average correction is computed. The correlation
hpjetT;HADpjetT;CALivshpjetT;CALiis used to extract correction factors, which are then applied to the measured jets to obtain the corrected transverse momenta pjetT;COR. A raw cross section is defined as d2=dpjetT;CORdyjetCALL1 NCORjet =pjetT;CORyjetCAL, whereNjetCORdenotes the number of jets in a givenpjetT;CORbin,pjetT;CORis the size of the bin, yjetCALdenotes the region inyjetCALconsidered, andLis the luminosity. Second, the measurements are corrected for acceptance and smearing effects using a bin-by-bin unfold- ing procedure, which also accounts for the efficiency of the selection criteria. The unfolding factors UpjetT;COR d2=dpjetT;HADdyjetHAD=d2=dpjetT;CORdyjetCAL are extracted from Monte Carlo samples and applied to the measured pjetT;COR distribution to obtain the final result. The factor UpjetT;CORincreases with pjetT;CORand varies between 1.04 at lowpjetT;CORand 1.3 at very highpjetT;COR.
A detailed study of the different systematic uncertainties was carried out [25]. The measured jet energies were varied by2%at lowpjetT and3%at highpjetT to account for the uncertainty on the absolute energy scale in the calorimeter [26]. This introduces an uncertainty in the measured cross section which varies between 10% at low pjetT and55%40%at high pjetT. A8%uncertainty on the jet energy resolution introduces an uncertainty between 2% at low pjetT and 8% at high pjetT. The unfolding procedure was repeated usingHERWIG instead ofPYTHIA- TUNE A to account for the uncertainty on the modeling of the parton cascades and the jet fragmentation into hadrons.
This translates into an uncertainty about5%at lowpjetT. The unfolding procedure was also carried out using un- weightedPYTHIA-TUNE A, to estimate the residual depen- dence on thepjetT spectrum. This introduces an uncertainty of 4%above 400 GeV=c, which becomes negligible at lower pjetT. The quoted uncertainty on was taken into account. The effect on the measured cross section is less than 3% and negligible for jets with pjetT above 200 GeV=c. An additional 5.8% uncertainty on the total luminosity is not included.
Figure 1 shows the measured cross section as a function ofpjetT compared to NLO pQCD predictions. The data are reported in Table I. The cross section decreases by more than 8 orders of magnitude aspjetT increases from54up to about 700 GeV=c. The NLO pQCD predictions are com- puted using theJETRADprogram [8] with CTEQ6.1M PDFs [27] and the renormalization and factorization scales (R andF) set to0maxpjetT=2.
Different sources of uncertainty in the theoretical pre- dictions were considered. The main contribution comes from the uncertainty on the PDFs and was computed using the Hessian method [28]. It varies from20%10%at lowpjetT and
7%
5%forpjetT about100 GeV=cto70%30% at highpjetT, domi- nated by the limited knowledge of the gluon PDF. An increase of R and F from 0 to 20 reduces the theoretical predictions by 2% at low pjetT and 8% at high pjetT. Values significantly smaller than0 lead to unstable NLO results and were not considered.
The theoretical prediction includes a correction factor CHADpjetT that approximately accounts for nonperturba- tive contributions from the underlying event and fragmen- tation into hadrons (see Table I). CHAD was estimated, using PYTHIA-TUNE A, as the ratio between the nominal pjetT;HAD distribution and the one obtained by turning off both the interactions between proton and antiproton rem- nants and the fragmentation in the Monte Carlo samples.
The correction shows a strong pjetT dependence and de- creases as pjetT increases from about 1.2 at pjetT of 54 GeV=c and 1.1 for pjetT about 100 GeV=c to 1.02 at highpjetT. The uncertainty onCHADis about 13% at lowpjetT and decreases up to 1.6% at highpjetT, as determined using
HERWIGinstead ofPYTHIA-TUNE A.
Figure 2 shows the ratio data/theory as a function ofpjetT. Good agreement is observed in the whole range in pjetT. A 2 test, where the different sources of systematic uncer- tainty on the data are considered independent but fully correlated acrosspjetT bins and the uncertainty onCHAD is also included, gives a2 probability of 56%. In addition, Fig. 2 shows the ratio of pQCD predictions using MRST2004 [29] and CTEQ6.1M PDF sets, well inside the theoretical and experimental uncertainties.
In summary, we have presented results on inclusive jet production inpp collisions at
ps
1:96 TeVusing thekT algorithm, for jets with transverse momentum pjetT >
54 GeV=c and rapidity in the region 0:1<jyjetj<0:7,
TABLE I. Measured inclusive jet differential cross section as a function ofpjetT. An additional 5.8% uncertainty on the luminosity is not included. The parton-to-hadron correction factorsCHADpjetTare applied to the pQCD predictions.
pjetT GeV=c d2=dpjetTdyjet stat sys nb=GeV=c CHAD stat sysparton!hadron
54 – 62 14:60:21:61:6 100 1:2020:0130:158
62 –72 6:530:040:750:84 100 1:1540:0030:113
72 –83 2:810:020:300:30 100 1:1340:0050:094
83– 96 1:180:010:130:12 100 1:1130:0060:077
96 –110 5:040:040:560:54 101 1:0980:0040:066
110 –127 2:150:020:250:22 101 1:0790:0050:047
127–146 8:810:051:040:98 102 1:0640:0030:037
146 –169 3:450:020:460:41 102 1:0570:0040:030
169 –195 1:280:010:170:17 102 1:0470:0030:023
195– 224 4:670:020:740:68 103 1:0430:0030:018
224 – 259 1:630:010:300:27 103 1:0390:0040:015
259 – 298 5:080:061:020:93 104 1:0340:0030:010
298– 344 1:500:030:360:31 104 1:0300:0050:008
344 – 396 3:700:141:070:89 105 1:0160:0090:006
396 – 457 7:500:552:522:01 106 1:0170:0180:009
457–527 1:310:220:570:42 106 1:0090:0030:019
527–700 1:140:430:630:47 107 1:0180:0020:016
[GeV/c]
JET
pT
0 100 200 300 400 500 600 700 [nb/(GeV/c)]JET T dpJET / dyσ2 d
10-8
10-6
10-4
10-2
1
|<0.7 D=0.7 0.1<|yJET
KT
Data
Systematic errors NLO: JETRAD CTEQ6.1M corrected to hadron level
µ0
/ 2 =
JET
= max pT
µF R = µ
L = 385 pb-1
∫
FIG. 1 (color online). Measured inclusive jet cross section (black dots) as a function of pjetT compared to NLO pQCD predictions (histogram). The shaded band shows the total sys- tematic uncertainty on the measurement.
122001-6
based on385 pb1of CDF run II data. The measured cross section is in agreement with NLO pQCD predictions after the necessary nonperturbative parton-to-hadron correc- tions are taken into account.
We thank the Fermilab staff and the technical staffs of the participating institutions for their vital contributions.
This work was supported by the U.S. Department of Energy and National Science Foundation; the Italian Istituto Nazionale di Fisica Nucleare; the Ministry of Education, Culture, Sports, Science and Technology of Japan; the Natural Sciences and Engineering Research Council of Canada; the National Science Council of the Republic of China; the Swiss National Science Foun- dation; the A. P. Sloan Foundation; the Bundesminister- ium fuer Bildung und Forschung, Germany; the Korean Science and Engineering Foundation and the Korean Research Foundation; the Particle Physics and Astronomy Research Council and the Royal Society, United Kingdom; the Russian Foundation for Basic Research; the Comision Interministerial de Ciencia y Tecnologia, Spain; in part by the European Community’s Human Potential Programme under Contract No. HPRN- CT-2002-00292; and the Academy of Finland.
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[GeV/c]
JET
pT
0 100 200 300 400 500 600 700
Ratio to CTEQ6.1M
0 0.5 1 1.5 2 2.5 3
Data
Systematic errors PDF uncertainties
µ0
× = 2 µ
MRST2004
100 200 300
0.8 1 1.2
FIG. 2 (color online). Ratio data/theory as a function ofpjetT. The enclosed figure expands the regionpjetT <298 GeV=c. The error bars (shaded band) show the total statistical (systematic) uncertainty on the data. A 5.8% uncertainty on the luminosity is not included. The solid lines indicate the PDF uncertainty on the theoretical prediction. The dashed line presents the ratio of MRST2004 and CTEQ6.1M predictions. The dotted-dashed line shows the ratio of predictions with20 and0.
