arXiv:0712.0803v2 [hep-ex] 14 Oct 2008
Measurement of the shape of the boson transverse momentum distribution in
p¯
p → Z/γ
∗→ e
+e
−+
X events produced at
√
s = 1.96 TeV
V.M. Abazov36 , B. Abbott76 , M. Abolins66 , B.S. Acharya29 , M. Adams52 , T. Adams50 , E. Aguilo6 , S.H. Ahn31 , M. Ahsan60 , G.D. Alexeev36 , G. Alkhazov40 , A. Alton65,a, G. Alverson64 , G.A. Alves2 , M. Anastasoaie35 , L.S. Ancu35 , T. Andeen54 , S. Anderson46 , B. Andrieu17 , M.S. Anzelc54 , Y. Arnoud14 , M. Arov61 , M. Arthaud18 , A. Askew50 , B. ˚Asman41
, A.C.S. Assis Jesus3
, O. Atramentov50 , C. Autermann21 , C. Avila8 , C. Ay24 , F. Badaud13 , A. Baden62 , L. Bagby53 , B. Baldin51 , D.V. Bandurin60 , S. Banerjee29 , P. Banerjee29 , E. Barberis64 , A.-F. Barfuss15 , P. Bargassa81 , P. Baringer59 , J. Barreto2 , J.F. Bartlett51 , U. Bassler18 , D. Bauer44 , S. Beale6 , A. Bean59 , M. Begalli3 , M. Begel72 , C. Belanger-Champagne41 , L. Bellantoni51 , A. Bellavance51 , J.A. Benitez66 , S.B. Beri27 , G. Bernardi17 , R. Bernhard23 , I. Bertram43 , M. Besan¸con18 , R. Beuselinck44 , V.A. Bezzubov39 , P.C. Bhat51 , V. Bhatnagar27 , C. Biscarat20 , G. Blazey53 , F. Blekman44 , S. Blessing50 , D. Bloch19 , K. Bloom68 , A. Boehnlein51 , D. Boline63 , T.A. Bolton60 , G. Borissov43 , T. Bose78 , A. Brandt79 , R. Brock66 , G. Brooijmans71 , A. Bross51 , D. Brown82 , N.J. Buchanan50 , D. Buchholz54 , M. Buehler82 , V. Buescher22 , V. Bunichev38 , S. Burdin43,b, S. Burke46 , T.H. Burnett83 , C.P. Buszello44 , J.M. Butler63 , P. Calfayan25 , S. Calvet16 , J. Cammin72 , W. Carvalho3 , B.C.K. Casey51 , N.M. Cason56 , H. Castilla-Valdez33 , S. Chakrabarti18 , D. Chakraborty53 , K.M. Chan56 , K. Chan6 , A. Chandra49 , F. Charles19,‡, E. Cheu46 , F. Chevallier14 , D.K. Cho63 , S. Choi32 , B. Choudhary28 , L. Christofek78 , T. Christoudias44,† , S. Cihangir51 , D. Claes68 , Y. Coadou6 , M. Cooke81 , W.E. Cooper51 , M. Corcoran81 , F. Couderc18 , M.-C. Cousinou15 , S. Cr´ep´e-Renaudin14 , D. Cutts78 , M. ´Cwiok30 , H. da Motta2 , A. Das46 , G. Davies44 , K. De79 , S.J. de Jong35 , E. De La Cruz-Burelo65 , C. De Oliveira Martins3 , J.D. Degenhardt65 , F. D´eliot18 , M. Demarteau51 , R. Demina72 , D. Denisov51 , S.P. Denisov39 , S. Desai51 , H.T. Diehl51 , M. Diesburg51 , A. Dominguez68 , H. Dong73 , L.V. Dudko38 , L. Duflot16 , S.R. Dugad29 , D. Duggan50 , A. Duperrin15 , J. Dyer66 , A. Dyshkant53 , M. Eads68 , D. Edmunds66 , J. Ellison49 , V.D. Elvira51 , Y. Enari78 , S. Eno62 , P. Ermolov38 , H. Evans55 , A. Evdokimov74 , V.N. Evdokimov39 , A.V. Ferapontov60 , T. Ferbel72 , F. Fiedler24 , F. Filthaut35 , W. Fisher51 , H.E. Fisk51 , M. Ford45 , M. Fortner53 , H. Fox23 , S. Fu51 , S. Fuess51 , T. Gadfort83 , C.F. Galea35 , E. Gallas51 , E. Galyaev56 , C. Garcia72 , A. Garcia-Bellido83 , V. Gavrilov37 , P. Gay13 , W. Geist19 , D. Gel´e19 , C.E. Gerber52 , Y. Gershtein50 , D. Gillberg6 , G. Ginther72 , N. Gollub41 , B. G´omez8 , A. Goussiou56 , P.D. Grannis73 , H. Greenlee51 , Z.D. Greenwood61 , E.M. Gregores4 , G. Grenier20 , Ph. Gris13 , J.-F. Grivaz16 , A. Grohsjean25 , S. Gr¨unendahl51 , M.W. Gr¨unewald30 , J. Guo73 , F. Guo73 , P. Gutierrez76 , G. Gutierrez51 , A. Haas71 , N.J. Hadley62 , P. Haefner25 , S. Hagopian50 , J. Haley69 , I. Hall66 , R.E. Hall48 , L. Han7 , K. Hanagaki51 , P. Hansson41 , K. Harder45 , A. Harel72 , R. Harrington64 , J.M. Hauptman58 , R. Hauser66 , J. Hays44 , T. Hebbeker21 , D. Hedin53 , J.G. Hegeman34 , J.M. Heinmiller52 , A.P. Heinson49 , U. Heintz63 , C. Hensel59 , K. Herner73 , G. Hesketh64 , M.D. Hildreth56 , R. Hirosky82 , J.D. Hobbs73 , B. Hoeneisen12 , H. Hoeth26 , M. Hohlfeld22 , S.J. Hong31 , S. Hossain76 , P. Houben34 , Y. Hu73 , Z. Hubacek10 , V. Hynek9 , I. Iashvili70 , R. Illingworth51 , A.S. Ito51 , S. Jabeen63 , M. Jaffr´e16 , S. Jain76 , K. Jakobs23 , C. Jarvis62 , R. Jesik44 , K. Johns46 , C. Johnson71 , M. Johnson51 , A. Jonckheere51 , P. Jonsson44 , A. Juste51 , D. K¨afer21 , E. Kajfasz15 , A.M. Kalinin36 , J.R. Kalk66 , J.M. Kalk61 , S. Kappler21 , D. Karmanov38 , P. Kasper51 , I. Katsanos71 , D. Kau50 , R. Kaur27 , V. Kaushik79 , R. Kehoe80 , S. Kermiche15 , N. Khalatyan51 , A. Khanov77 , A. Kharchilava70 , Y.M. Kharzheev36 , D. Khatidze71 , H. Kim32 , T.J. Kim31 , M.H. Kirby54 , M. Kirsch21 , B. Klima51 , J.M. Kohli27 , J.-P. Konrath23 , M. Kopal76 , V.M. Korablev39 , A.V. Kozelov39 , D. Krop55 , T. Kuhl24 , A. Kumar70 , S. Kunori62 , A. Kupco11 , T. Kurˇca20 , J. Kvita9 , F. Lacroix13 , D. Lam56 , S. Lammers71 , G. Landsberg78 , P. Lebrun20 , W.M. Lee51 , A. Leflat38 , F. Lehner42 , J. Lellouch17 , J. Leveque46 , P. Lewis44 , J. Li79 , Q.Z. Li51 , L. Li49 , S.M. Lietti5 , J.G.R. Lima53 , D. Lincoln51 , J. Linnemann66 , V.V. Lipaev39 , R. Lipton51 , Y. Liu7,† , Z. Liu6 , L. Lobo44 , A. Lobodenko40 , M. Lokajicek11 , P. Love43 , H.J. Lubatti83 , A.L. Lyon51 , A.K.A. Maciel2 , D. Mackin81 , R.J. Madaras47 , P. M¨attig26 , C. Magass21 , A. Magerkurth65 , P.K. Mal56 , H.B. Malbouisson3 , S. Malik68 , V.L. Malyshev36 , H.S. Mao51 , Y. Maravin60 , B. Martin14 , R. McCarthy73 , A. Melnitchouk67 , A. Mendes15 , L. Mendoza8 , P.G. Mercadante5 , M. Merkin38 , K.W. Merritt51 , J. Meyer22,d, A. Meyer21 , T. Millet20 , J. Mitrevski71 , J. Molina3 , R.K. Mommsen45 , N.K. Mondal29 , R.W. Moore6 , T. Moulik59 , G.S. Muanza20 , M. Mulders51 , M. Mulhearn71 , O. Mundal22 , L. Mundim3 , E. Nagy15 , M. Naimuddin51 , M. Narain78 , N.A. Naumann35 , H.A. Neal65 , J.P. Negret8 , P. Neustroev40 , H. Nilsen23 , H. Nogima3 , A. Nomerotski51 , S.F. Novaes5 , T. Nunnemann25 , V. O’Dell51 , D.C. O’Neil6 , G. Obrant40 , C. Ochando16 , D. Onoprienko60 ,
N. Oshima51 , J. Osta56 , R. Otec10 , G.J. Otero y Garz´on51 , M. Owen45 , P. Padley81 , M. Pangilinan78 , N. Parashar57 , S.-J. Park72 , S.K. Park31 , J. Parsons71 , R. Partridge78 , N. Parua55 , A. Patwa74 , G. Pawloski81 , B. Penning23 , M. Perfilov38 , K. Peters45 , Y. Peters26 , P. P´etroff16 , M. Petteni44 , R. Piegaia1 , J. Piper66 , M.-A. Pleier22 , P.L.M. Podesta-Lerma33,c, V.M. Podstavkov51 , Y. Pogorelov56 , M.-E. Pol2 , P. Polozov37 , B.G. Pope66 , A.V. Popov39 , C. Potter6 , W.L. Prado da Silva3 , H.B. Prosper50 , S. Protopopescu74 , J. Qian65 , A. Quadt22,d, B. Quinn67 , A. Rakitine43 , M.S. Rangel2 , K. Ranjan28 , P.N. Ratoff43 , P. Renkel80 , S. Reucroft64 , P. Rich45 , M. Rijssenbeek73 , I. Ripp-Baudot19 , F. Rizatdinova77 , S. Robinson44 , R.F. Rodrigues3 , M. Rominsky76 , C. Royon18 , P. Rubinov51 , R. Ruchti56 , G. Safronov37 , G. Sajot14 , A. S´anchez-Hern´andez33 , M.P. Sanders17 , A. Santoro3 , G. Savage51 , L. Sawyer61 , T. Scanlon44 , D. Schaile25 , R.D. Schamberger73 , Y. Scheglov40 , H. Schellman54 , P. Schieferdecker25 , T. Schliephake26 , C. Schwanenberger45 , A. Schwartzman69 , R. Schwienhorst66 , J. Sekaric50 , H. Severini76 , E. Shabalina52 , M. Shamim60 , V. Shary18 , A.A. Shchukin39 , R.K. Shivpuri28 , V. Siccardi19 , V. Simak10 , V. Sirotenko51 , P. Skubic76 , P. Slattery72 , D. Smirnov56 , J. Snow75 , G.R. Snow68 , S. Snyder74 , S. S¨oldner-Rembold45 , L. Sonnenschein17 , A. Sopczak43 , M. Sosebee79 , K. Soustruznik9 , M. Souza2 , B. Spurlock79 , J. Stark14 , J. Steele61 , V. Stolin37 , D.A. Stoyanova39 , J. Strandberg65 , S. Strandberg41 , M.A. Strang70 , M. Strauss76 , E. Strauss73 , R. Str¨ohmer25 , D. Strom54 , L. Stutte51 , S. Sumowidagdo50 , P. Svoisky56 , A. Sznajder3 , M. Talby15 , P. Tamburello46 , A. Tanasijczuk1 , W. Taylor6 , J. Temple46 , B. Tiller25 , F. Tissandier13 , M. Titov18 , V.V. Tokmenin36 , T. Toole62 , I. Torchiani23 , T. Trefzger24 , D. Tsybychev73 , B. Tuchming18 , C. Tully69 , P.M. Tuts71 , R. Unalan66 , S. Uvarov40 , L. Uvarov40 , S. Uzunyan53 , B. Vachon6
, P.J. van den Berg34
, R. Van Kooten55 , W.M. van Leeuwen34 , N. Varelas52 , E.W. Varnes46 , I.A. Vasilyev39 , M. Vaupel26 , P. Verdier20 , L.S. Vertogradov36 , M. Verzocchi51 , F. Villeneuve-Seguier44 , P. Vint44 , P. Vokac10 , E. Von Toerne60
, M. Voutilainen68,e, R. Wagner69
, H.D. Wahl50 , L. Wang62 , M.H.L.S Wang51 , J. Warchol56 , G. Watts83 , M. Wayne56 , M. Weber51 , G. Weber24 , A. Wenger23,f, N. Wermes22 , M. Wetstein62 , A. White79 , D. Wicke26 , G.W. Wilson59 , S.J. Wimpenny49 , M. Wobisch61 , D.R. Wood64 , T.R. Wyatt45 , Y. Xie78 , S. Yacoob54 , R. Yamada51 , M. Yan62 , T. Yasuda51 , Y.A. Yatsunenko36 , K. Yip74 , H.D. Yoo78 , S.W. Youn54 , J. Yu79 , A. Zatserklyaniy53 , C. Zeitnitz26 , T. Zhao83 , B. Zhou65 , J. Zhu73 , M. Zielinski72 , D. Zieminska55 , A. Zieminski55,‡, L. Zivkovic71 , V. Zutshi53
, and E.G. Zverev38
(The DØ Collaboration)
1Universidad de Buenos Aires, Buenos Aires, Argentina 2
LAFEX, Centro Brasileiro de Pesquisas F´ısicas, Rio de Janeiro, Brazil
3
Universidade do Estado do Rio de Janeiro, Rio de Janeiro, Brazil
4Universidade Federal do ABC, Santo Andr´e, Brazil 5
Instituto de F´ısica Te´orica, Universidade Estadual Paulista, S˜ao Paulo, Brazil
6
University of Alberta, Edmonton, Alberta, Canada, Simon Fraser University, Burnaby, British Columbia, Canada, York University, Toronto, Ontario, Canada, and McGill University, Montreal, Quebec, Canada
7University of Science and Technology of China, Hefei, People’s Republic of China 8
Universidad de los Andes, Bogot´a, Colombia
9
Center for Particle Physics, Charles University, Prague, Czech Republic
10
Czech Technical University, Prague, Czech Republic
11
Center for Particle Physics, Institute of Physics,
Academy of Sciences of the Czech Republic, Prague, Czech Republic
12
Universidad San Francisco de Quito, Quito, Ecuador
13Laboratoire de Physique Corpusculaire, IN2P3-CNRS,
Universit´e Blaise Pascal, Clermont-Ferrand, France
14
Laboratoire de Physique Subatomique et de Cosmologie, IN2P3-CNRS, Universite de Grenoble 1, Grenoble, France
15
CPPM, IN2P3-CNRS, Universit´e de la M´editerran´ee, Marseille, France
16
Laboratoire de l’Acc´el´erateur Lin´eaire, IN2P3-CNRS et Universit´e Paris-Sud, Orsay, France
17LPNHE, IN2P3-CNRS, Universit´es Paris VI and VII, Paris, France 18
DAPNIA/Service de Physique des Particules, CEA, Saclay, France
19
IPHC, Universit´e Louis Pasteur et Universit´e de Haute Alsace, CNRS, IN2P3, Strasbourg, France
20IPNL, Universit´e Lyon 1, CNRS/IN2P3, Villeurbanne, France and Universit´e de Lyon, Lyon, France 21
III. Physikalisches Institut A, RWTH Aachen, Aachen, Germany
22
Physikalisches Institut, Universit¨at Bonn, Bonn, Germany
23Physikalisches Institut, Universit¨at Freiburg, Freiburg, Germany 24Institut f¨ur Physik, Universit¨at Mainz, Mainz, Germany
25
Ludwig-Maximilians-Universit¨at M¨unchen, M¨unchen, Germany
26
Fachbereich Physik, University of Wuppertal, Wuppertal, Germany
27Panjab University, Chandigarh, India 28
Delhi University, Delhi, India
29
Tata Institute of Fundamental Research, Mumbai, India
30University College Dublin, Dublin, Ireland 31
Korea Detector Laboratory, Korea University, Seoul, Korea
32
SungKyunKwan University, Suwon, Korea
33CINVESTAV, Mexico City, Mexico
34FOM-Institute NIKHEF and University of Amsterdam/NIKHEF, Amsterdam, The Netherlands 35
Radboud University Nijmegen/NIKHEF, Nijmegen, The Netherlands
36
Joint Institute for Nuclear Research, Dubna, Russia
37Institute for Theoretical and Experimental Physics, Moscow, Russia 38
Moscow State University, Moscow, Russia
39
Institute for High Energy Physics, Protvino, Russia
40Petersburg Nuclear Physics Institute, St. Petersburg, Russia 41
Lund University, Lund, Sweden, Royal Institute of Technology and Stockholm University, Stockholm, Sweden, and Uppsala University, Uppsala, Sweden
42Physik Institut der Universit¨at Z¨urich, Z¨urich, Switzerland 43
Lancaster University, Lancaster, United Kingdom
44
Imperial College, London, United Kingdom
45
University of Manchester, Manchester, United Kingdom
46
University of Arizona, Tucson, Arizona 85721, USA
47
Lawrence Berkeley National Laboratory and University of California, Berkeley, California 94720, USA
48
California State University, Fresno, California 93740, USA
49University of California, Riverside, California 92521, USA 50
Florida State University, Tallahassee, Florida 32306, USA
51
Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA
52University of Illinois at Chicago, Chicago, Illinois 60607, USA 53
Northern Illinois University, DeKalb, Illinois 60115, USA
54
Northwestern University, Evanston, Illinois 60208, USA
55Indiana University, Bloomington, Indiana 47405, USA 56
University of Notre Dame, Notre Dame, Indiana 46556, USA
57
Purdue University Calumet, Hammond, Indiana 46323, USA
58Iowa State University, Ames, Iowa 50011, USA 59
University of Kansas, Lawrence, Kansas 66045, USA
60
Kansas State University, Manhattan, Kansas 66506, USA
61Louisiana Tech University, Ruston, Louisiana 71272, USA 62University of Maryland, College Park, Maryland 20742, USA
63
Boston University, Boston, Massachusetts 02215, USA
64
Northeastern University, Boston, Massachusetts 02115, USA
65University of Michigan, Ann Arbor, Michigan 48109, USA 66
Michigan State University, East Lansing, Michigan 48824, USA
67
University of Mississippi, University, Mississippi 38677, USA
68University of Nebraska, Lincoln, Nebraska 68588, USA 69
Princeton University, Princeton, New Jersey 08544, USA
70
State University of New York, Buffalo, New York 14260, USA
71Columbia University, New York, New York 10027, USA 72University of Rochester, Rochester, New York 14627, USA 73
State University of New York, Stony Brook, New York 11794, USA
74
Brookhaven National Laboratory, Upton, New York 11973, USA
75Langston University, Langston, Oklahoma 73050, USA 76
University of Oklahoma, Norman, Oklahoma 73019, USA
77
Oklahoma State University, Stillwater, Oklahoma 74078, USA
78Brown University, Providence, Rhode Island 02912, USA 79
University of Texas, Arlington, Texas 76019, USA
80
Southern Methodist University, Dallas, Texas 75275, USA
81Rice University, Houston, Texas 77005, USA 82
University of Virginia, Charlottesville, Virginia 22901, USA and
83
University of Washington, Seattle, Washington 98195, USA (Dated: December 5, 2007)
We present a measurement of the shape of the Z/γ∗boson transverse momentum (q
T) distribution
collected with the D0 detector at the Fermilab Tevatron collider. The data are found to be consistent with the resummation prediction at low qT, but above the perturbative QCD calculation in the
region of qT> 30 GeV/c. Using events with qT< 30 GeV/c, we extract the value of g2, one of the
non-perturbative parameters for the resummation calculation. Data at large boson rapidity y are compared with the prediction of resummation and with alternative models that employ a resummed form factor with modifications in the small Bjorken x region of the proton wave function.
PACS numbers: 13.60.Hb, 13.38.Dg, 13.85.Qk, 13.38.Bx
A complete understanding of weak vector boson pro-duction is essential for maximizing the sensitivity to new physics at hadron colliders. Studies of the Z/γ∗ boson
production play a particularly valuable role in that its kinematics can be precisely determined through measure-ment of its leptonic decays. Throughout this Letter, we use the notation “Z boson” to mean “Z/γ∗ boson”,
un-less specified otherwise.
Z boson production also serves as an ideal test-ing ground for predictions of quantum chromodynam-ics (QCD), since the boson’s transverse momentum, qT,
can be measured over a wide range of values and can be correlated with its rapidity. At large qT (approximately
greater than 30 GeV/c), the radiation of a single parton with large transverse momentum dominates the cross sec-tion, and fixed-order perturbative QCD (pQCD) calcu-lations [1, 2], should yield reliable predictions. At lower qT, multiple soft gluon emission can not be neglected,
and the fixed-order perturbation calculation no longer gives accurate results. A soft-gluon resummation tech-nique developed by Collins, Soper, and Sterman (CSS) [3] gives reliable predictions in the low-qT region. A
pre-scription has been proposed [4] for matching the low-and high-qT regions in order to provide a continuous
pre-diction for all values of qT. The CSS resummation
for-malism allows the inclusion of contributions from large logarithms of the form lnn(q2
T/Q 2
) to all orders of per-turbation theory in an effective resummed form factor, where Q2
represents the invariant mass corresponding to the four-momentum transfer. The CSS resummation can be done either in impact parameter (b) space or in transverse momentum (qT) space. In the case of b-space
resummation, this form factor can be parameterized with the following non-perturbative function first introduced by Brock, Landry, Nadolsky and Yuan (BLNY) [5]:
SN P(b, Q 2 ) = g1+ g2ln Q 2Q0 + g1g3ln(100xixj) b2 , (1) where xi and xj are the fractions of the incident hadron
momenta carried by the colliding partons, Q0 is a scale
typical of the onset of non-perturbative effects, and g1,
g2and g3are phenomenological non-perturbative
param-eters that must be obtained from fits to the data. The Z boson qT distribution at the Fermilab Tevatron is by
far most sensitive to the value of g2and quite insensitive
to the value of g3. Thus a measurement of the Z boson
qT spectrum can be used to test this formalism and to
determine the value of g2.
Recent studies of data from deep inelastic scattering (DIS) experiments [6, 7] indicate that the resummed form factor in the above equation may need to be modified for processes involving a small-x parton in the initial state. Ref. [8] indicates how such a modification would influ-ence the qT distributions of vector and Higgs bosons
pro-duced in hadronic collisions. A wider qT distribution is
predicted for Z bosons with large rapidity (called “small-x broadening”). Z bosons produced at the Tevatron in the rapidity range 2 < |y| < 3 probe processes involving a parton with 0.002 < x < 0.006, and can be used to test the modified form factor at small x.
Z boson qT distributions have been published
previ-ously by the CDF [9] and D0 [10] collaborations using about 100 pb−1 of data at√s = 1.8 TeV. In this Letter,
we report a new measurement with larger statistics and improved precision. This measurement is also the first to present a qT distribution for large-rapidity Z bosons.
The data sample used in this measurement was collected using a set of inclusive single-electron triggers with the D0 detector [11] at the Fermilab Tevatron collider, and the integrated luminosity is 980 ± 60 pb−1 [12].
Our selection criteria for Z bosons require two iso-lated electromagnetic clusters that have a shower shape consistent with that of an electron. Electron candidates are required to have transverse momentum greater than 25 GeV/c. The electron pairs must have a reconstructed invariant mass 70 < M (ee) < 110 GeV/c2
. If an event has both its candidate electrons in the central calorime-ter (CC events), each electron must be spatially matched to a reconstructed track. Because the tracking efficiency decreases with rapidity in the endcap region, events with one or two endcap calorimeter electron candidates (CE and EE events, respectively) are required to have at least one electron with a matching track. After these require-ments, 23,959 CC, 30,344 CE, and 9,598 EE events are selected; 5412 of these have a reconstructed Z boson with |y| > 2.
Electron identification efficiencies are measured using a combination of data and a geant-based [13] simulation of the D0 detector. The electron identification efficien-cies are measured from Z data. The dependence of the overall selection efficiency on the Z boson qT is
param-eterized from the geant simulation. A measurement of this shape from the data agrees well with the simulation within statistical uncertainties.
The dominant backgrounds are from photon plus jet events and di-jet events, with photons and jets misiden-tified as electrons. The kinematic properties of these events are obtained from events that satisfy most of the Z selection criteria, but fail the electron shower shape requirement. The normalization of the background is obtained by fitting to a sum of a signal shape obtained from a parameterized simulation of the detector response and the invariant mass distribution from the background sample to the invariant mass distribution of the data sample. The background fractions are (1.30±0.14)%, (8.55±0.26)%, and (4.71±0.30)% for CC, CE, and EE events respectively. Other backgrounds are negligible.
The data are corrected for acceptances within a range of generated Z masses of 40 to 200 GeV/c2
, and for se-lection efficiencies using a parameterized simulation. We use ResBos [14] as the event generator which incorpo-rates the resummation calculation in b-space using the BLNY parameterization for low qT and a NLO pQCD
calculation for high qT. We use photos [15] to simulate
the effects of final state photon radiation. The overall acceptance times efficiency falls slowly from a value of 0.27 at low qT to a minimum of 0.19 at qT = 40 GeV/c
and slowly increases for larger qT.
The measured spectrum is further corrected for de-tector resolution effects using the run (Regularized Un-folding) program [16] to obtain the true differential cross section. Its performance was verified by comparing the true and unfolded spectrum generated using pseudo-experiments. The measured Z qT resolution is about 2
GeV/c; the bin width we choose is 2.5 GeV/c for qT < 30
GeV/c. The typical correlation between adjacent bins is around 30%. Due to limited statistics, the chosen bin width is 10 GeV/c for 30 < qT < 100 GeV/c and 40
GeV/c for 100 < qT < 260 GeV/c.
Systematic uncertainties on the unfolded qT spectrum
arise from uncertainties on the electron energy calibra-tion, the electron energy resolucalibra-tion, the dependence of the overall selection efficiency on qT, and the effect of
parton distribution functions (PDFs) on the acceptance. The uncertainties on the unfolded spectrum are esti-mated from the resulting change when the smearing pa-rameters are varied within their uncertainties. CTEQ 6.1M is used as the default PDF. Uncertainties due to the PDFs are estimated using the procedure described in Ref. [17]. The uncertainty due to the choice of unfold-ing parameters in the run program is also estimated and included in the final systematic uncertainty.
The final results in the qT < 30 GeV/c range, are
shown in Fig. 1 for the inclusive sample and for the sam-ple with |y| > 2. Each data point is plotted at the average value of the expected distribution over the bin [18]. For the theoretical calculation, we use ResBos with published values of the non-perturbative parameters [5]. Good agreement between data and the prediction is ob-served for all rapidity ranges, which indicates that the
BLNY parameterization works well for the low qT region.
Z boson events produced at large rapidities (|y| > 2) are also used to test the small-x prediction. We compare data with the theoretical predictions with and without the form factor as modified from studies of small-x DIS data [8]. All curves are normalized to 1 for qT < 30
GeV/c. The default values for the parameters g1, g2,
and g3 [5] obtained from large-x data are used. The
χ2
/d.o.f. between the data and the ResBos calculation using the default parameters is 0.8/1 for qT < 5 GeV/c
and 11.1/11 for qT < 30 GeV/c, while that for the
modi-fied calculation is 5.7/1 for qT < 5 GeV/c and 31.9/11 for
qT < 30 GeV/c. It remains to be seen if retuning of the
non-perturbative parameters could improve the agree-ment for the modified calculations.
Figure 2 shows the measured differential cross sec-tion in the range qT < 260 GeV/c compared to (1) the
ResBoscalculation with its default parameters [5], (2) ResBoswith a NLO to NNLO K-factor by Arnold and Reno [19] incorporated into ResBos by its authors, (3) a pQCD calculation at NNLO [2] using the MRST 2001 NNLO PDF set [20] divided by the NNLO calculation of the total cross section [21], and (4) the NNLO calculation but rescaled to the data at qT = 30 GeV/c. The
agree-ment between data and ResBos, with or without the K-factor, is good for qT < 30 GeV/c. At higher values
of qT, the data are not in agreement with the ResBos
calculation. The data agree better with the NNLO cal-culation and ResBos prediction with the Arnold-Reno K-factor, but agrees best when the NNLO results are rescaled by a factor of 1.25 so that they match the data at qT = 30 GeV/c. This indicates that the shape from these
calculations agrees with the data, and that the source of the discrepancy is in the normalization. Table I summa-rizes the measured values for each qT bin together with
statistical and systematic uncertainties.
The CSS model parameter most sensitive to the shape at low qT (qT < 30 GeV/c) is g2. In a fit, we fix other
phenomenological parameters to the values obtained in Ref. [5] and only vary g2. A minimum χ
2
/d.o.f. of 9/11 between the model and the inclusive data for qT <
30 GeV/c is found when g2= 0.77 ± 0.06 (GeV/c) 2
. In conclusion, we have measured the normalized dif-ferential spectrum, 1
σ dσ
dqT, for Z boson events produced
in p¯p collisions at √s = 1.96 TeV with boson mass 40 < M < 200 GeV/c2
and qT < 260 GeV/c. This
rep-resents the highest center-of-mass energy measurement of this quantity over the largest phase space available to date. The overall uncertainty of this measurement has been reduced compared with the previous measurements. We find that for qT < 30 GeV/c, the CSS resummation
model used in ResBos describes the data very well at all rapidities. Our data with |y| > 2 disfavor a variant of this model that incorporates an additional small-x form factor when g1, g2, and g3from large-x data is used. Using the
(GeV/c) T * q γ Z/ 0 5 10 15 20 25 30 -1 (GeV/c) T /dq σ d × σ 1/ 0.02 0.04 0.06 0.08 ResBos DØ data DØ, 0.98 fb-1 (a) (GeV/c) T * q γ Z/ 0 5 10 15 20 25 30 -1 (GeV/c) T /dq σ d × σ 1/ 0.02 0.04 0.06 0.08 0.1 |y|>2 ResBos with small-x effect ResBos without small-x effect DØ data
DØ, 0.98 fb-1
(b)
FIG. 1: The normalized differential cross section as a function of qT for (a) the inclusive sample and (b) the sample with
Z boson |y| > 2 with qT < 30 GeV/c. The points are the data, the solid curve is the ResBos prediction, and the dashed line
in (b) is the prediction from the form factor modified after studies of small-x DIS data.
(GeV/c) T * q γ Z/ 0 50 100 150 200 250 -1 (GeV/c) T /dq σ d × σ 1/ -7 10 -6 10 -5 10 -4 10 -3 10 -2 10 -1 10 DØ 0.98 fb-1 (a) ResBos ResBos+KF NNLO Rescaled NNLO DØ data (GeV/c) T * q γ Z/ 1 10 102 (Data-Theory)/Theory -0.5 0 0.5 1 DØ 0.98 fb-1 (b) ResBos ResBos+KF NNLO Rescaled NNLO
FIG. 2: The normalized differential cross section as a function of qT compared to four theoretical calculations for (a) the
entire range measured and (b) the fractional differences between data and the theoretical predictions. The four theoretical calculations are ResBos with its default parameters, ResBos with a NLO to NNLO K-factor by Arnold and Reno, the NNLO calculation by Melnikov and Petriello, and the NNLO calculation but rescaled to data at qT= 30 GeV/c.
we obtain g2= 0.77 ± 0.06 (GeV/c)2, which is
compara-ble with the current world average value [5]. We observe a disagreement between our data and NNLO calculations in the region qT > 30 GeV/c, where our distribution is
higher than predicted by a factor of 1.25. However, the NNLO calculation agrees in shape with our data when normalized at qT = 30 GeV/c.
We thank C. Balazs, Q.H. Cao, P. Nadolsky, F. Petriello and C.P. Yuan for many useful discussions. We thank the staffs at Fermilab and collaborating in-stitutions, and acknowledge support from the DOE and NSF (USA); CEA and CNRS/IN2P3 (France); FASI, Rosatom and RFBR (Russia); CAPES, CNPq, FAPERJ, FAPESP and FUNDUNESP (Brazil); DAE and DST
(India); Colciencias (Colombia); CONACyT (Mexico); KRF and KOSEF (Korea); CONICET and UBACyT (Argentina); FOM (The Netherlands); Science and Tech-nology Facilities Council (United Kingdom); MSMT and GACR (Czech Republic); CRC Program, CFI, NSERC and WestGrid Project (Canada); BMBF and DFG (Ger-many); SFI (Ireland); The Swedish Research Council (Sweden); CAS and CNSF (China); Alexander von Hum-boldt Foundation; and the Marie Curie Program.
hqTi (GeV/c) 1/σ × dσ/dqT (GeV/c)−1 1.1 (5.32 ± 0.13 ± 0.24) × 10−2 4.0 (8.08 ± 0.12 ± 0.19) × 10−2 6.2 (6.33 ± 0.11 ± 0.14) × 10−2 8.7 (4.43 ± 0.09 ± 0.11) × 10−2 11.3 (3.15 ± 0.08 ± 0.08) × 10−2 13.7 (2.46 ± 0.07 ± 0.06) × 10−2 16.2 (1.86 ± 0.06 ± 0.05) × 10−2 18.7 (1.42 ± 0.05 ± 0.05) × 10−2 21.3 (1.09 ± 0.04 ± 0.03) × 10−2 23.7 (9.40 ± 0.40 ± 0.20) × 10−3 26.4 (6.90 ± 0.30 ± 0.20) × 10−3 28.5 (5.50 ± 0.30 ± 0.10) × 10−3 34.6 (3.90 ± 0.10 ± 0.10) × 10−3 44.6 (2.10 ± 0.07 ± 0.06) × 10−3 54.6 (1.10 ± 0.05 ± 0.03) × 10−3 64.6 (7.30 ± 0.40 ± 0.20) × 10−4 73.4 (4.20 ± 0.30 ± 0.20) × 10−4 85.4 (2.50 ± 0.20 ± 0.10) × 10−4 95.1 (1.60 ± 0.17 ± 0.08) × 10−4 117.5 (6.00 ± 0.50 ± 0.30) × 10−5 157.5 (1.10 ± 0.20 ± 0.07) × 10−5 195.5 (3.00 ± 1.00 ± 0.30) × 10−6 245.5 (7.10 ± 6.10 ± 0.60) × 10−7
TABLE I: The normalized differential cross section for Z events produced in bins of qT. The first uncertainty is
statistical and the second is systematic.
[b] Visitor from The University of Liverpool, Liverpool, UK. [c] Visitor from ICN-UNAM, Mexico City, Mexico.
[d] Visitor from II. Physikalisches Institut, Georg-August-University G¨ottingen, Germany.
[e] Visitor from Helsinki Institute of Physics, Helsinki, Fin-land.
[f] Visitor from Universit¨at Z¨urich, Z¨urich, Switzerland. [†] Fermilab International Fellow.
[‡] Deceased.
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