Measurement of Dijet Azimuthal Decorrelations at Central Rapidities
in p
p Collisions at
p
s
1:96 TeV
V. M. Abazov,33B. Abbott,70M. Abolins,61B. S. Acharya,27D. L. Adams,68M. Adams,48T. Adams,46M. Agelou,17 J.-L. Agram,18S. N. Ahmed,32S. H. Ahn,29G. D. Alexeev,33G. Alkhazov,37A. Alton,60G. Alverson,59G. A. Alves,2 M. Anastasoaie,32S. Anderson,42B. Andrieu,16Y. Arnoud,13A. Askew,73B. A˚ sman,38O. Atramentov,53C. Autermann,20
C. Avila,7L. Babukhadia,67T. C. Bacon,40F. Badaud,12A. Baden,57S. Baffioni,14B. Baldin,47P. W. Balm,31 S. Banerjee,27E. Barberis,59P. Bargassa,73P. Baringer,54C. Barnes,40J. Barreto,2J. F. Bartlett,47U. Bassler,16D. Bauer,51
A. Bean,54S. Beauceron,16F. Beaudette,15M. Begel,66A. Bellavance,63S. B. Beri,26G. Bernardi,16R. Bernhard,47,* I. Bertram,39M. Besanc¸on,17A. Besson,18R. Beuselinck,40V. A. Bezzubov,36P. C. Bhat,47V. Bhatnagar,26 M. Bhattacharjee,67M. Binder,24A. Bischoff,45K. M. Black,58I. Blackler,40G. Blazey,49F. Blekman,31S. Blessing,46
D. Bloch,18U. Blumenschein,22A. Boehnlein,47O. Boeriu,52T. A. Bolton,55P. Bonamy,17F. Borcherding,47 G. Borissov,39K. Bos,31T. Bose,65C. Boswell,45A. Brandt,72G. Briskin,71R. Brock,61G. Brooijmans,65A. Bross,47 N. J. Buchanan,46D. Buchholz,50M. Buehler,48V. Buescher,22S. Burdin,47T. H. Burnett,75E. Busato,16J. M. Butler,58
J. Bystricky,17F. Canelli,66W. Carvalho,3B. C. K. Casey,71D. Casey,61N. M. Cason,52H. Castilla-Valdez,30 S. Chakrabarti,27D. Chakraborty,49K. M. Chan,66A. Chandra,27D. Chapin,71F. Charles,18E. Cheu,42L. Chevalier,17
D. K. Cho,66S. Choi,45S. Chopra,68T. Christiansen,24L. Christofek,54D. Claes,63A. R. Clark,43B. Cle´ment,18 C. Cle´ment,38Y. Coadou,5D. J. Colling,40L. Coney,52B. Connolly,46M. Cooke,73W. E. Cooper,47D. Coppage,54 M. Corcoran,73J. Coss,19A. Cothenet,14M.-C. Cousinou,14S. Cre´pe´-Renaudin,13M. Cristetiu,45M. A. C. Cummings,49
D. Cutts,71H. da Motta,2B. Davies,39G. Davies,40G. A. Davis,50K. De,72P. de Jong,31S. J. de Jong,32 E. De La Cruz-Burelo,30C. De Oliveira Martins,3S. Dean,41K. Del Signore,60F. De´liot,17P. A. Delsart,19 M. Demarteau,47R. Demina,66P. Demine,17D. Denisov,47S. P. Denisov,36S. Desai,67H. T. Diehl,47M. Diesburg,47 M. Doidge,39H. Dong,67S. Doulas,59L. Duflot,15S. R. Dugad,27A. Duperrin,14J. Dyer,61A. Dyshkant,49M. Eads,49
D. Edmunds,61T. Edwards,41J. Ellison,45J. Elmsheuser,24J. T. Eltzroth,72V. D. Elvira,47S. Eno,57P. Ermolov,35 O. V. Eroshin,36J. Estrada,47D. Evans,40H. Evans,65A. Evdokimov,34V. N. Evdokimov,36J. Fast,47S. N. Fatakia,58
D. Fein,42L. Feligioni,58T. Ferbel,66F. Fiedler,24F. Filthaut,32W. Fisher,64H. E. Fisk,47F. Fleuret,16M. Fortner,49 H. Fox,22W. Freeman,47S. Fu,47S. Fuess,47C. F. Galea,32E. Gallas,47E. Galyaev,52M. Gao,65C. Garcia,66 A. Garcia-Bellido,75J. Gardner,54V. Gavrilov,34P. Gay,12D. Gele´,18R. Gelhaus,45K. Genser,47C. E. Gerber,48 Y. Gershtein,71G. Geurkov,71G. Ginther,66K. Goldmann,25T. Golling,21B. Go´mez,7K. Gounder,47A. Goussiou,52
G. Graham,57P. D. Grannis,67S. Greder,18J. A. Green,53H. Greenlee,47Z. D. Greenwood,56E. M. Gregores,4 S. Grinstein,1Ph. Gris,12J.-F. Grivaz,15L. Groer,65S. Gru¨nendahl,47M. W. Gru¨newald,28W. Gu,6S. N. Gurzhiev,36 G. Gutierrez,47P. Gutierrez,70A. Haas,65N. J. Hadley,57H. Haggerty,47S. Hagopian,46I. Hall,70R. E. Hall,44C. Han,60 L. Han,41K. Hanagaki,47P. Hanlet,72K. Harder,55R. Harrington,59J. M. Hauptman,53R. Hauser,61C. Hays,65J. Hays,50 T. Hebbeker,20C. Hebert,54D. Hedin,49J. M. Heinmiller,48A. P. Heinson,45U. Heintz,58C. Hensel,54G. Hesketh,59
M. D. Hildreth,52R. Hirosky,74J. D. Hobbs,67B. Hoeneisen,11M. Hohlfeld,23S. J. Hong,29R. Hooper,71S. Hou,60 P. Houben,31Y. Hu,67J. Huang,51Y. Huang,60I. Iashvili,45R. Illingworth,47A. S. Ito,47S. Jabeen,54M. Jaffre´,15S. Jain,70
V. Jain,68K. Jakobs,22A. Jenkins,40R. Jesik,40Y. Jiang,60K. Johns,42M. Johnson,47P. Johnson,42A. Jonckheere,47 P. Jonsson,40H. Jo¨stlein,47A. Juste,47M. M. Kado,43D. Ka¨fer,20W. Kahl,55S. Kahn,68E. Kajfasz,14A. M. Kalinin,33
J. Kalk,61D. Karmanov,35J. Kasper,58D. Kau,46Z. Ke,6R. Kehoe,61S. Kermiche,14S. Kesisoglou,71A. Khanov,66 A. Kharchilava,52Y. M. Kharzheev,33K. H. Kim,29B. Klima,47M. Klute,21J. M. Kohli,26M. Kopal,70V. M. Korablev,36
J. Kotcher,68B. Kothari,65A. V. Kotwal,65A. Koubarovsky,35O. Kouznetsov,13A. V. Kozelov,36J. Kozminski,61 J. Krane,53M. R. Krishnaswamy,27S. Krzywdzinski,47M. Kubantsev,55S. Kuleshov,34Y. Kulik,47S. Kunori,57 A. Kupco,17T. Kurcˇa,19V. E. Kuznetsov,45S. Lager,38N. Lahrichi,17G. Landsberg,71J. Lazoflores,46A.-C. Le Bihan,18 P. Lebrun,19S. W. Lee,29W. M. Lee,46A. Leflat,35C. Leggett,43F. Lehner,47,* C. Leonidopoulos,65P. Lewis,40J. Li,72 Q. Z. Li,47X. Li,6J. G. R. Lima,49D. Lincoln,47S. L. Linn,46J. Linnemann,61V. V. Lipaev,36R. Lipton,47L. Lobo,40 A. Lobodenko,37M. Lokajicek,10A. Lounis,18J. Lu,6H. J. Lubatti,75A. Lucotte,13L. Lueking,47C. Luo,51M. Lynker,52
A. L. Lyon,47A. K. A. Maciel,49R. J. Madaras,43P. Ma¨ttig,25A. Magerkurth,60A.-M. Magnan,13M. Maity,58 N. Makovec,15P. K. Mal,27S. Malik,56V. L. Malyshev,33V. Manankov,35H. S. Mao,6Y. Maravin,47T. Marshall,51 M. Martens,47M. I. Martin,49S. E. K. Mattingly,71A. A. Mayorov,36R. McCarthy,67R. McCroskey,42T. McMahon,69
H. Miettinen,73D. Mihalcea,49J. Mitrevski,65N. Mokhov,47J. Molina,3N. K. Mondal,27H. E. Montgomery,47 R. W. Moore,5M. Mostafa,1G. S. Muanza,19M. Mulders,47Y. D. Mutaf,67E. Nagy,14F. Nang,42M. Narain,58 V. S. Narasimham,27N. A. Naumann,32H. A. Neal,60J. P. Negret,7S. Nelson,46P. Neustroev,37C. Noeding,22 A. Nomerotski,47S. F. Novaes,4T. Nunnemann,24E. Nurse,41V. O’Dell,47D. C. O’Neil,5V. Oguri,3N. Oliveira,3 B. Olivier,16N. Oshima,47G. J. Otero y Garzo´n,48P. Padley,73K. Papageorgiou,48N. Parashar,56J. Park,29S. K. Park,29
J. Parsons,65R. Partridge,71N. Parua,67A. Patwa,68P. M. Perea,45E. Perez,17O. Peters,31P. Pe´troff,15M. Petteni,40 L. Phaf,31R. Piegaia,1P. L. M. Podesta-Lerma,30V. M. Podstavkov,47Y. Pogorelov,52B. G. Pope,61E. Popkov,58 W. L. Prado da Silva,3H. B. Prosper,46S. Protopopescu,68M. B. Przybycien,50,†J. Qian,60A. Quadt,21B. Quinn,62
K. J. Rani,27P. A. Rapidis,47P. N. Ratoff,39N. W. Reay,55J.-F. Renardy,17S. Reucroft,59J. Rha,45M. Ridel,15 M. Rijssenbeek,67I. Ripp-Baudot,18F. Rizatdinova,55C. Royon,17P. Rubinov,47R. Ruchti,52B. M. Sabirov,33G. Sajot,13
A. Sa´nchez-Herna´ndez,30M. P. Sanders,41A. Santoro,3G. Savage,47L. Sawyer,56T. Scanlon,40R. D. Schamberger,67 H. Schellman,50P. Schieferdecker,24C. Schmitt,25A. A. Schukin,36A. Schwartzman,64R. Schwienhorst,61S. Sengupta,46
H. Severini,70E. Shabalina,48V. Shary,17W. D. Shephard,52D. Shpakov,59R. A. Sidwell,55V. Simak,9V. Sirotenko,47 D. Skow,47P. Skubic,70P. Slattery,66R. P. Smith,47K. Smolek,9G. R. Snow,63J. Snow,69S. Snyder,68
S. So¨ldner-Rembold,41X. Song,49Y. Song,72L. Sonnenschein,58A. Sopczak,39V. Sorı´n,1M. Sosebee,72K. Soustruznik,8 M. Souza,2B. Spurlock,72N. R. Stanton,55J. Stark,13J. Steele,56G. Steinbru¨ck,65K. Stevenson,51V. Stolin,34A. Stone,48
D. A. Stoyanova,36J. Strandberg,38M. A. Strang,72M. Strauss,70R. Stro¨hmer,24M. Strovink,43L. Stutte,47 S. Sumowidagdo,46A. Sznajder,3M. Talby,14P. Tamburello,42W. Taylor,67P. Telford,41J. Temple,42 S. Tentindo-Repond,46E. Thomas,14B. Thooris,17M. Tomoto,47T. Toole,57J. Torborg,52S. Towers,67T. Trefzger,23 S. Trincaz-Duvoid,16T. G. Trippe,43B. Tuchming,17C. Tully,64A. S. Turcot,68P. M. Tuts,65L. Uvarov,37S. Uvarov,37
S. Uzunyan,49B. Vachon,47R. Van Kooten,51W. M. van Leeuwen,31N. Varelas,48E. W. Varnes,42I. A. Vasilyev,36 M. Vaupel,25P. Verdier,15L. S. Vertogradov,33M. Verzocchi,57F. Villeneuve-Seguier,40J.-R. Vlimant,16E. Von Toerne,55
M. Vreeswijk,31T. Vu Anh,15H. D. Wahl,46R. Walker,40N. Wallace,42Z.-M. Wang,67J. Warchol,52M. Warsinsky,21 G. Watts,75M. Wayne,52M. Weber,47H. Weerts,61M. Wegner,20N. Wermes,21A. White,72V. White,47D. Whiteson,43
D. Wicke,47D. A. Wijngaarden,32G. W. Wilson,54S. J. Wimpenny,45J. Wittlin,58T. Wlodek,72M. Wobisch,47 J. Womersley,47D. R. Wood,59Z. Wu,6T. R. Wyatt,41Q. Xu,60N. Xuan,52R. Yamada,47M. Yan,57T. Yasuda,47 Y. A. Yatsunenko,33Y. Yen,25K. Yip,68S. W. Youn,50J. Yu,72A. Yurkewicz,61A. Zabi,15A. Zatserklyaniy,49M. Zdrazil,67
C. Zeitnitz,23B. Zhang,6D. Zhang,47X. Zhang,70T. Zhao,75Z. Zhao,60H. Zheng,52B. Zhou,60Z. Zhou,53J. Zhu,57 M. Zielinski,66D. Zieminska,51A. Zieminski,51R. Zitoun,67V. Zutshi,49E. G. Zverev,35and A. Zylberstejn17
(D0 Collaboration)
1Universidad de Buenos Aires, Buenos Aires, Argentina 2LAFEX, Centro Brasileiro de Pesquisas Fı´sicas, Rio de Janeiro, Brazil
3Universidade do Estado do Rio de Janeiro, Rio de Janeiro, Brazil 4Instituto de Fı´sica Teo´rica, Universidade Estadual Paulista, Sa˜o Paulo, Brazil
5University of Alberta and Simon Fraser University, Canada 6Institute of High Energy Physics, Beijing, People’s Republic of China
7Universidad de los Andes, Bogota´, Colombia
8Charles University, Center for Particle Physics, Prague, Czech Republic 9Czech Technical University, Prague, Czech Republic
10Institute of Physics, Academy of Sciences, Center for Particle Physics, Prague, Czech Republic 11Universidad San Francisco de Quito, Quito, Ecuador
12Laboratoire de Physique Corpusculaire, IN2P3-CNRS, Universite´ Blaise Pascal, Clermont-Ferrand, France 13Laboratoire de Physique Subatomique et de Cosmologie, IN2P3-CNRS, Universite de Grenoble 1, Grenoble, France
14CPPM, IN2P3-CNRS, Universite´ de la Me´diterrane´e, Marseille, France 15Laboratoire de l’Acce´le´rateur Line´aire, IN2P3-CNRS, Orsay, France
16LPNHE, Universite´s Paris VI and VII, IN2P3-CNRS, Paris, France 17DAPNIA/Service de Physique des Particules, CEA, Saclay, France
18IReS, IN2P3-CNRS, University Louis Pasteur Strasbourg, and University de Haute Alsace, France 19Institut de Physique Nucle´aire de Lyon, IN2P3-CNRS, Universite´ Claude Bernard, Villeurbanne, France
20RWTH Aachen, III. Physikalisches Institut A, Aachen, Germany 21Universita¨t Bonn, Physikalisches Institut, Bonn, Germany 22Universita¨t Freiburg, Physikalisches Institut, Freiburg, Germany
24Ludwig-Maximilians-Universita¨t Mu¨nchen, Mu¨nchen, Germany 25Fachbereich Physik, University of Wuppertal, Wuppertal, Germany
26Punjab University, Chandigarh, India
27Tata Institute of Fundamental Research, Mumbai, India 28University College Dublin, Dublin, Ireland 29Korea Detector Laboratory, Korea University, Seoul, Korea
30CINVESTAV, Mexico City, Mexico
31FOM-Institute NIKHEF and University of Amsterdam/NIKHEF, Amsterdam, The Netherlands 32University of Nijmegen/NIKHEF, Nijmegen, The Netherlands
33Joint Institute for Nuclear Research, Dubna, Russia 34Institute for Theoretical and Experimental Physics, Moscow, Russia
35Moscow State University, Moscow, Russia 36Institute for High Energy Physics, Protvino, Russia 37Petersburg Nuclear Physics Institute, St. Petersburg, Russia
38Lund University, Royal Institute of Technology, Stockholm University, and Uppsala University, Sweden 39Lancaster University, Lancaster, United Kingdom
40Imperial College, London, United Kingdom 41University of Manchester, Manchester, United Kingdom
42University of Arizona, Tucson, Arizona 85721, USA
43Lawrence Berkeley National Laboratory and University of California, Berkeley, California 94720, USA 44California State University, Fresno, California 93740, USA
45University of California, Riverside, California 92521, USA 46Florida State University, Tallahassee, Florida 32306, USA 47Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA
48University of Illinois at Chicago, Chicago, Illinois 60607, USA 49Northern Illinois University, DeKalb, Illinois 60115, USA
50Northwestern University, Evanston, Illinois 60208, USA 51Indiana University, Bloomington, Indiana 47405, USA 52University of Notre Dame, Notre Dame, Indiana 46556, USA
53Iowa State University, Ames, Iowa 50011, USA 54University of Kansas, Lawrence, Kansas 66045, USA 55Kansas State University, Manhattan, Kansas 66506, USA 56Louisiana Tech University, Ruston, Louisiana 71272, USA 57University of Maryland, College Park, Maryland 20742, USA
58Boston University, Boston, Massachusetts 02215, USA 59Northeastern University, Boston, Massachusetts 02115, USA
60University of Michigan, Ann Arbor, Michigan 48109, USA 61Michigan State University, East Lansing, Michigan 48824, USA
62University of Mississippi, University, Mississippi 38677, USA 63University of Nebraska, Lincoln, Nebraska 68588, USA 64Princeton University, Princeton, New Jersey 08544, USA
65Columbia University, New York, New York 10027, USA 66University of Rochester, Rochester, New York 14627, USA 67State University of New York, Stony Brook, New York 11794, USA
68Brookhaven National Laboratory, Upton, New York 11973, USA 69Langston University, Langston, Oklahoma 73050, USA 70University of Oklahoma, Norman, Oklahoma 73019, USA
71Brown University, Providence, Rhode Island 02912, USA 72University of Texas, Arlington, Texas 76019, USA
73Rice University, Houston, Texas 77005, USA 74University of Virginia, Charlottesville, Virginia 22901, USA
75University of Washington, Seattle, Washington 98195, USA
(Received 16 September 2004; published 7 June 2005)
Correlations in the azimuthal angle between the two largest transverse momentum jets have been measured using the D0 detector in p pcollisions at a center-of-mass energyps 1:96 TeV. The analysis is based on an inclusive dijet event sample in the central rapidity region corresponding to an integrated luminosity of 150 pb1. Azimuthal correlations are stronger at larger transverse momenta. These are well
described in perturbative QCD at next-to-leading order in the strong coupling constant, except at large azimuthal differences where contributions with low transverse momentum are significant.
DOI: 10.1103/PhysRevLett.94.221801 PACS numbers: 13.87.Ce, 12.38.Qk
Radiation of multiple quarks and gluons is one of the more complex aspects of perturbative quantum chromody-namics (PQCD), and it is being actively studied for the physics programs at the Fermilab Tevatron Collider and the CERN LHC [1]. The proper description of radiative pro-cesses is crucial for a wide range of precision measure-ments as well as for searches for new physical phenomena where the influence of QCD radiation is unavoidable. In this Letter we study radiative processes by examining their impact on angular distributions. We investigate the azimu-thal angle between the two jets with highest transverse momenta with respect to the beam axis (pT), dijet. Dijet production in hadron-hadron collisions, in the ab-sence of radiative effects, results in two jets with equal transverse momenta and correlated azimuthal angles dijet . Additional radiation with low pT causes
small azimuthal decorrelations, whereas dijet signifi-cantly lower than is evidence of additional hard radiation with high pT. Exclusive three-jet production populates
2=3 < dijet< , while smaller values of dijet re-quire additional radiation such as a fourth jet in an event. Distributions in dijetprovide an ideal testing ground for higher-order PQCD predictions without requiring the re-construction of additional jets and offer a way to examine the transition between soft and hard QCD processes based on a single observable.
A new measurement of azimuthal decorrelations be-tween jets produced at high pT in p p collisions is pre-sented in this Letter. This is the first measurement of the differential dijet distribution in dijet production at a hadron collider. Jets are defined using a cone algorithm [2] with radius Rcone 0:7. The same jet algorithm is used for partons in the PQCD calculations, final-state particles in the Monte Carlo event generators, and recon-structed energy depositions in the experiment. The observ-able, 1= dijetd dijet=d dijet, is defined as the differential dijet cross section in dijet normalized by the dijet cross section integrated over dijet in the same phase space. (Theoretical and experimental uncertainties are reduced in this construction.) Calculations of three-jet observables at next-to-leading order (NLO) in the strong coupling constant shave recently become available [3,4]. Data were obtained with the D0 detector [5] in Run II of the Fermilab Tevatron Collider using p p collisions at
s p
1:96 TeV. The primary tool for jet detection was a compensating, finely segmented, liquid-argon and uranium calorimeter that provided nearly full solid-angle coverage. Calorimeter cells were grouped into projective towers focused on the nominal interaction point for trigger and reconstruction purposes. Events were acquired using multiple-stage inclusive-jet triggers. Four analysis regions were defined based on the jet with largest pT in an event
(pmax
T ) with the requirement that the trigger efficiency be at
least 99%. The accumulated integrated luminosities for events with pmaxT > 75, 100, 130, and 180 GeV were 1.1, 21, 90, and 150 pb16:5%, respectively. The second leading pT jet in each event was required to have pT>
40 GeV and both jets were required to have central rap-idities with jyjetj < 0:5 where yjet12 lnE pz=E
pz and E and pz are the energy and the longitudinal
momentum of the jet.
The position of the p p interaction was reconstructed using a tracking system consisting of silicon microstrip detectors and scintillating fibers located within a 2 T sole-noidal magnet. The vertex coordinate along the beam axis was required to be within 50 cm of the detector center, which preserved the projective nature of the calorimeter towers. The systematic uncertainty associated with the vertex selection efficiency is less than 3% for dijet> 2=3 and 8% for dijet =2. The missing trans-verse energy was calculated from the vector sum of the individual transverse energies in calorimeter cells. Background from cosmic rays and incorrectly vertexed events was eliminated by requiring this missing transverse energy to be below 0:7pmax
T . Background introduced by
electrons, photons, and detector noise that mimicked jets was eliminated based on characteristics of shower develop-ment expected for genuine jets. The overall efficiency for dijet< 5=6 is 82% –84%, depending on the pmax
T
re-gion. For dijet! it drops to 76%–81%.
The pT of each jet was corrected for calorimeter show-ering effects, overlaps due to multiple interactions and event pileup, calorimeter noise effects, and the energy response of the calorimeter. The calorimeter response was measured from the pT imbalance in photon jet
events. The relative uncertainty on the jet energy calibra-tion is 7% for jets with 20 < pT < 250 GeV. The
sen-sitivity of the measurement to this calibration was reduced by normalizing the dijet distribution to the integrated dijet cross section. Nevertheless, this provides the largest contribution to the systematic uncertainty ( < 7% for dijet> 5=6 but up to 23% for dijet< 2=3).
The correction for migrations between bins due to finite energy and position resolution was determined from events generated with theHERWIG [6] andPYTHIA[7] programs. The generated jets were smeared according to detector resolutions [8]. The angular jet resolution was determined from a full simulation of the D0 detector response. It was found to be better than 20 mrad for jets with energies above 80 GeV. The jet pT resolution was measured from the pT imbalance in dijet events. It decreases from 18% at pT
40 GeV to 9% for pT 200 GeV. Finite jet pTresolution
can lead to ambiguities in the selection of the two leading pT jets. This effect is large at small dijetwhere
contri-butions from higher jet multiplicities dominate. The gen-erated events were reweighted to describe the observed dijet distribution. This provided a good description of the observed pT spectra of the four leading pT jets. The correction for migrations is typically less than 8% for dijet> 2=3 and 40% for dijet =2 with a model dependence of less than 2%. Only for pmax
T <
130 GeV and at dijet =2 is the model dependence as large as 14%. The model dependence was taken into account in the evaluation of the overall systematic uncertainty.
The corrected data are presented in Fig. 1 as a function of dijet in four ranges of pmax
T . The inner error bars
represent the statistical uncertainties, and the outer error bars correspond to the quadratic sum of the statistical and systematic uncertainties. The systematic uncertainties in-clude contributions from the sources described above: event selection efficiency, jet energy calibration, and the model dependence in the correction for migrations. The spectra are strongly peaked at dijet ; the peaks are narrower at larger values of pmax
T . Overlaid on the data
points in Fig. 1 are the results of PQCD calculations ob-tained using the parton-level event generatorNLOJET++[4]
and CTEQ6.1M [9] parton distribution functions (PDFs) with sMZ 0:118. The leading order (LO) PQCD pre-diction for the observable was calculated from the ratio of the predictions for 2 ! 3 processes (d dijet=d dijet) and 2 ! 2 processes ( dijet), both at LO. The NLO prediction of the observable was analogously obtained from the NLO results of the individual pieces,
1 dijet NLO d dijet d dijet NLO :
The renormalization and factorization scales are chosen to be r f 0:5pmaxT . The ratio is insensitive to
hadro-nization corrections and the underlying event [10]. As shown in Fig. 2, data and NLO agree within 5% – 20%. The theoretical uncertainty due to the PDFs [9] is estimated to be below 20%. Also shown is the effect of renormalization and factorization scale variation (0:25pmax
T < r;f< pmaxT ). The large scale dependence
for dijet< 2=3 occurs because the NLO calculation receives contributions only from tree-level four-parton final states in this regime. Results from PQCD at large
1 2
p maxT > 180 GeV
Data / NLO Theory
DØ
1 2 130 < p maxT < 180 GeV µr, µf dependence PDF uncertainty 1 2 100 < p maxT < 130 GeV 1 2 75 < p maxT < 100 GeV ∆φ dijet (rad) NLOJET++ (CTEQ6.1M) π/2 2π/3 5π/6 πFIG. 2 (color online). Ratios of data to the NLO PQCD cal-culation for different regions of pmax
T . Theoretical uncertainties due to variation of r and f are shown as the shaded regions; the uncertainty due to the PDFs is indicated by the solid lines. The points at large dijetare excluded because the calculation
is not stable near the divergence at .
∆φ dijet (rad) 1/ σ dijet d σ dijet / d
∆φ dijet maxpT > 180 GeV (×8000) 130 < p maxT < 180 GeV (×400) 100 < p maxT < 130 GeV (×20) 75 < p maxT < 100 GeV LO NLO NLOJET++ (CTEQ6.1M) µr = µf = 0.5 pT max
DØ
10 -3 10 -2 10 -1 1 10 102 103 104 105 π/2 2π/3 5π/6 πFIG. 1 (color online). The dijetdistributions in four regions
of pmax
T . Data and predictions with pmaxT > 100 GeV are scaled by successive factors of 20 for purposes of presentation. The solid (dashed) lines show the NLO (LO) PQCD predictions.
dijetin Figs. 1 and 2 were excluded because fixed-order perturbation theory fails to describe the data in the region dijet where soft processes dominate. Overall, NLO PQCD provides a good description of the data although differences in shape can be discerned for dijet* 5=6. In this region, the observable probes the transition between two- and three-jet configurations. The cone algorithm is sensitive to the fine details of the event topology in this transition region. These details may not be adequately described by low-order PQCD, and higher-order calcula-tions may be required.
Monte Carlo event generators, such as HERWIG and
PYTHIA, use 2 ! 2 LO PQCD matrix elements with
phe-nomenological parton-shower models to simulate higher-order QCD effects. Results fromHERWIG (version 6.505) andPYTHIA(version 6.225), both using default parameters and the CTEQ6L [9] PDFs, are compared to the data in Fig. 3. HERWIG describes the data well over the entire dijetrange including dijet .PYTHIAwith default parameters describes the data poorly —the distribution is too narrowly peaked at dijet and lies significantly below the data over most of the dijet range. The maxi-mum p2
Tin the initial-state parton shower is directly related
to the maximum virtuality that can be adjusted inPYTHIA. The shaded bands in Fig. 3 indicate the range of variation when the maximum allowed virtuality is smoothly in-creased from the current default by a factor of 4 [11]. These variations result in significant changes in the low dijetregion clearly demonstrating the sensitivity of this measurement. Consequently, global efforts to tune Monte Carlo event generators should benefit from includ-ing our data.
To summarize, we have measured the dijet azimuthal decorrelation in different ranges of leading jet pT and observe an increased decorrelation towards smaller pT. NLO PQCD describes the data except for very large dijetwhere the calculation is not predictive.
We thank W. Giele, Z. Nagy, M. H. Seymour, and T. Sjo¨strand for many helpful discussions. We thank the staffs at Fermilab and collaborating institutions, and acknowl-edge support from the Department of Energy and National Science Foundation (USA), Commissariat a` l’Energie Atomique and CNRS/Institut National de Physique Nucle´aire et de Physique des Particules (France), Ministry of Education and Science, Agency for Atomic Energy and RF President Grants Program (Russia), CAPES, CNPq, FAPERJ, FAPESP, and FUNDUNESP (Brazil), Departments of Atomic Energy and Science and Technology (India), Colciencias (Colombia), CONACyT
(Mexico), KRF (Korea), CONICET and UBACyT
(Argentina), The Foundation for Fundamental Research on Matter (The Netherlands), PPARC (United Kingdom), Ministry of Education (Czech Republic), Natural Sciences and Engineering Research Council and WestGrid Project (Canada), BMBF and DFG (Germany), A. P. Sloan Foundation, Civilian Research and Development Foundation, Research Corporation, Texas Advanced Research Program, and the Alexander von Humboldt Foundation.
*Visitor from University of Zurich, Zurich, Switzerland.
†Visitor from Institute of Nuclear Physics, Krakow, Poland.
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∆φ dijet (rad) 1/ σdijet d σdijet / d ∆φ dijet p T max > 180 GeV (×8000) 130 < p maxT < 180 GeV (×400) 100 < p maxT < 130 GeV (×20) 75 < p maxT < 100 GeV HERWIG 6.505 PYTHIA 6.225 PYTHIA increased ISR (CTEQ6L)
DØ
10 -3 10 -2 10 -1 1 10 102 103 104 105 π/2 2π/3 5π/6 πFIG. 3 (color online). The dijet distributions in different
pmax
T ranges. Results fromHERWIGandPYTHIAare overlaid on the data. Data and predictions with pmax
T > 100 GeV are scaled by successive factors of 20 for purposes of presentation.
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