Ratio of isolated photon cross sections in $p\bar p$ collisions at $\sqrt s$ = 630 and 1800 GeV

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Ratio of isolated photon cross sections in p¯

p collisions at

√

s = 630 and 1800 GeV

V.M. Abazov, B. Abbott, Abdelmalek Abdesselam, M. Abolins, V. Abramov,

B.S. Acharya, D.L. Adams, M. Adams, S.N. Ahmed, G.D. Alexeev, et al.

To cite this version:

arXiv:hep-ex/0106026 v5 30 Nov 2001

Ratio of Isolated Photon Cross Sections at

√

s = 630 GeV and 1800 GeV

V.M. Abazov,23 _{B. Abbott,}57 _{A. Abdesselam,}11 _{M. Abolins,}50_{V. Abramov,}26_{B.S. Acharya,}17 _{D.L. Adams,}59

M. Adams,37_{S.N. Ahmed,}21 _{G.D. Alexeev,}23 _{A. Alton,}49_{G.A. Alves,}2_{N. Amos,}49 _{E.W. Anderson,}42 _{Y. Arnoud,}9

C. Avila,5_{M.M. Baarmand,}54_{V.V. Babintsev,}26 _{L. Babukhadia,}54_{T.C. Bacon,}28_{A. Baden,}46_{B. Baldin,}36

P.W. Balm,20_{S. Banerjee,}17 _{E. Barberis,}30 _{P. Baringer,}43_{J. Barreto,}2 _{J.F. Bartlett,}36_{U. Bassler,}12 _{D. Bauer,}28

A. Bean,43 _{F. Beaudette,}11 _{M. Begel,}53 _{A. Belyaev,}35_{S.B. Beri,}15 _{G. Bernardi,}12 _{I. Bertram,}27 _{A. Besson,}9

R. Beuselinck,28 _{V.A. Bezzubov,}26 _{P.C. Bhat,}36 _{V. Bhatnagar,}11_{M. Bhattacharjee,}54 _{G. Blazey,}38_{F. Blekman,}20

S. Blessing,35 _{A. Boehnlein,}36 _{N.I. Bojko,}26 _{F. Borcherding,}36 _{K. Bos,}20_{T. Bose,}52 _{A. Brandt,}59 _{R. Breedon,}31

G. Briskin,58_{R. Brock,}50_{G. Brooijmans,}36_{A. Bross,}36_{D. Buchholz,}39 _{M. Buehler,}37 _{V. Buescher,}14_{V.S. Burtovoi,}26

J.M. Butler,47 _{F. Canelli,}53_{W. Carvalho,}3_{D. Casey,}50_{Z. Casilum,}54 _{H. Castilla-Valdez,}19_{D. Chakraborty,}38

K.M. Chan,53_{S.V. Chekulaev,}26 _{D.K. Cho,}53_{S. Choi,}34_{S. Chopra,}55_{J.H. Christenson,}36 _{M. Chung,}37_{D. Claes,}51

A.R. Clark,30_{J. Cochran,}34 _{L. Coney,}41_{B. Connolly,}35_{W.E. Cooper,}36_{D. Coppage,}43_{S. Cr´ep´e-Renaudin,}9

M.A.C. Cummings,38 _{D. Cutts,}58 _{G.A. Davis,}53_{K. Davis,}29_{K. De,}59 _{S.J. de Jong,}21_{K. Del Signore,}49

M. Demarteau,36 _{R. Demina,}44_{P. Demine,}9 _{D. Denisov,}36_{S.P. Denisov,}26_{S. Desai,}54 _{H.T. Diehl,}36 _{M. Diesburg,}36

S. Doulas,48_{Y. Ducros,}13_{L.V. Dudko,}25_{S. Duensing,}21 _{L. Duflot,}11_{S.R. Dugad,}17_{A. Duperrin,}10 _{A. Dyshkant,}38

D. Edmunds,50_{J. Ellison,}34_{V.D. Elvira,}36 _{R. Engelmann,}54 _{S. Eno,}46 _{G. Eppley,}61 _{P. Ermolov,}25 _{O.V. Eroshin,}26

J. Estrada,53_{H. Evans,}52_{V.N. Evdokimov,}26_{T. Fahland,}33_{S. Feher,}36 _{D. Fein,}29 _{T. Ferbel,}53 _{F. Filthaut,}21

H.E. Fisk,36_{Y. Fisyak,}55_{E. Flattum,}36_{F. Fleuret,}12_{M. Fortner,}38 _{H. Fox,}39_{K.C. Frame,}50 _{S. Fu,}52 _{S. Fuess,}36

E. Gallas,36_{A.N. Galyaev,}26_{M. Gao,}52_{V. Gavrilov,}24_{R.J. Genik II,}27 _{K. Genser,}36 _{C.E. Gerber,}37 _{Y. Gershtein,}58

R. Gilmartin,35_{G. Ginther,}53 _{B. G´omez,}5 _{G. G´omez,}46_{P.I. Goncharov,}26_{J.L. Gonz´alez Sol´ıs,}19_{H. Gordon,}55

L.T. Goss,60_{K. Gounder,}36_{A. Goussiou,}28_{N. Graf,}55_{G. Graham,}46_{P.D. Grannis,}54_{J.A. Green,}42 _{H. Greenlee,}36

Z.D. Greenwood,45_{S. Grinstein,}1 _{L. Groer,}52 _{S. Gr¨unendahl,}36_{A. Gupta,}17_{S.N. Gurzhiev,}26_{G. Gutierrez,}36

P. Gutierrez,57_{N.J. Hadley,}46_{H. Haggerty,}36_{S. Hagopian,}35_{V. Hagopian,}35_{R.E. Hall,}32 _{P. Hanlet,}48 _{S. Hansen,}36

J.M. Hauptman,42 _{C. Hays,}52 _{C. Hebert,}43 _{D. Hedin,}38_{J.M. Heinmiller,}37 _{A.P. Heinson,}34_{U. Heintz,}47

T. Heuring,35 _{M.D. Hildreth,}41_{R. Hirosky,}62_{J.D. Hobbs,}54 _{B. Hoeneisen,}8 _{Y. Huang,}49 _{R. Illingworth,}28_{A.S. Ito,}36

M. Jaffr´e,11_{S. Jain,}17_{R. Jesik,}28_{K. Johns,}29 _{M. Johnson,}36 _{A. Jonckheere,}36 _{H. J¨ostlein,}36_{A. Juste,}36 _{W. Kahl,}44

S. Kahn,55_{E. Kajfasz,}10 _{A.M. Kalinin,}23_{D. Karmanov,}25_{D. Karmgard,}41_{R. Kehoe,}50 _{A. Khanov,}44

A. Kharchilava,41_{S.K. Kim,}18_{B. Klima,}36_{B. Knuteson,}30 _{W. Ko,}31_{J.M. Kohli,}15_{A.V. Kostritskiy,}26_{J. Kotcher,}55

B. Kothari,52 _{A.V. Kotwal,}52_{A.V. Kozelov,}26_{E.A. Kozlovsky,}26 _{J. Krane,}42 _{M.R. Krishnaswamy,}17_{P. Krivkova,}6

S. Krzywdzinski,36 _{M. Kubantsev,}44_{S. Kuleshov,}24 _{Y. Kulik,}54_{S. Kunori,}46 _{A. Kupco,}7 _{V.E. Kuznetsov,}34

G. Landsberg,58 _{W.M. Lee,}35 _{A. Leflat,}25 _{C. Leggett,}30 _{F. Lehner,}36,∗ _{J. Li,}59_{Q.Z. Li,}36 _{X. Li,}4_{J.G.R. Lima,}3

D. Lincoln,36_{S.L. Linn,}35 _{J. Linnemann,}50 _{R. Lipton,}36_{A. Lucotte,}9 _{L. Lueking,}36 _{C. Lundstedt,}51 _{C. Luo,}40

A.K.A. Maciel,38_{R.J. Madaras,}30_{V.L. Malyshev,}23 _{V. Manankov,}25_{H.S. Mao,}4_{T. Marshall,}40_{M.I. Martin,}38

K.M. Mauritz,42 _{B. May,}39_{A.A. Mayorov,}40_{R. McCarthy,}54 _{T. McMahon,}56 _{H.L. Melanson,}36_{M. Merkin,}25

K.W. Merritt,36_{C. Miao,}58_{H. Miettinen,}61 _{D. Mihalcea,}38_{C.S. Mishra,}36 _{N. Mokhov,}36_{N.K. Mondal,}17

H.E. Montgomery,36_{R.W. Moore,}50 _{M. Mostafa,}1 _{H. da Motta,}2_{E. Nagy,}10_{F. Nang,}29_{M. Narain,}47

V.S. Narasimham,17_{N.A. Naumann,}21_{H.A. Neal,}49 _{J.P. Negret,}5 _{S. Negroni,}10_{T. Nunnemann,}36 _{D. O’Neil,}50

V. Oguri,3_{B. Olivier,}12_{N. Oshima,}36 _{P. Padley,}61_{L.J. Pan,}39 _{K. Papageorgiou,}37_{A. Para,}36_{N. Parashar,}48

R. Partridge,58_{N. Parua,}54_{M. Paterno,}53 _{A. Patwa,}54_{B. Pawlik,}22_{J. Perkins,}59_{O. Peters,}20 _{P. P´etroff,}11

R. Piegaia,1_{B.G. Pope,}50 _{E. Popkov,}47_{H.B. Prosper,}35 _{S. Protopopescu,}55 _{M.B. Przybycien,}39 _{J. Qian,}49

R. Raja,36_{S. Rajagopalan,}55_{E. Ramberg,}36_{P.A. Rapidis,}36 _{N.W. Reay,}44 _{S. Reucroft,}48 _{M. Ridel,}11

M. Rijssenbeek,54 _{F. Rizatdinova,}44_{T. Rockwell,}50 _{M. Roco,}36_{C. Royon,}13_{P. Rubinov,}36_{R. Ruchti,}41

J. Rutherfoord,29_{B.M. Sabirov,}23 _{G. Sajot,}9_{A. Santoro,}2_{L. Sawyer,}45 _{R.D. Schamberger,}54_{H. Schellman,}39

A. Schwartzman,1 _{N. Sen,}61_{E. Shabalina,}37_{R.K. Shivpuri,}16_{D. Shpakov,}48_{M. Shupe,}29 _{R.A. Sidwell,}44_{V. Simak,}7

H. Singh,34_{J.B. Singh,}15_{V. Sirotenko,}36_{P. Slattery,}53 _{E. Smith,}57_{R.P. Smith,}36_{R. Snihur,}39_{G.R. Snow,}51

J. Snow,56_{S. Snyder,}55 _{J. Solomon,}37_{Y. Song,}59_{V. Sor´ın,}1_{M. Sosebee,}59 _{N. Sotnikova,}25_{K. Soustruznik,}6

M. Souza,2 _{N.R. Stanton,}44_{G. Steinbr¨uck,}52 _{R.W. Stephens,}59 _{F. Stichelbaut,}55 _{D. Stoker,}33 _{V. Stolin,}24

A. Stone,45_{D.A. Stoyanova,}26_{M.A. Strang,}59_{M. Strauss,}57 _{M. Strovink,}30_{L. Stutte,}36 _{A. Sznajder,}3 _{M. Talby,}10

W. Taylor,54_{S. Tentindo-Repond,}35_{S.M. Tripathi,}31_{T.G. Trippe,}30 _{A.S. Turcot,}55 _{P.M. Tuts,}52_{V. Vaniev,}26

R. Van Kooten,40 _{N. Varelas,}37 _{L.S. Vertogradov,}23_{F. Villeneuve-Seguier,}10 _{A.A. Volkov,}26_{A.P. Vorobiev,}26

H.D. Wahl,35_{H. Wang,}39_{Z.-M. Wang,}54_{J. Warchol,}41 _{G. Watts,}63_{M. Wayne,}41_{H. Weerts,}50 _{A. White,}59

J.T. White,60 _{D. Whiteson,}30_{J.A. Wightman,}42_{D.A. Wijngaarden,}21_{S. Willis,}38_{S.J. Wimpenny,}34_{J. Womersley,}36

D.R. Wood,48_{Q. Xu,}49_{R. Yamada,}36_{P. Yamin,}55_{T. Yasuda,}36_{Y.A. Yatsunenko,}23 _{K. Yip,}55_{S. Youssef,}35_{J. Yu,}36

(DØ Collaboration)

1_{Universidad 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} 4_{Institute of High Energy Physics, Beijing, People’s Republic of China}

5_{Universidad de los Andes, Bogot´a, Colombia}

6_{Charles University, Center for Particle Physics, Prague, Czech Republic}

7_{Institute of Physics, Academy of Sciences, Center for Particle Physics, Prague, Czech Republic} 8_{Universidad San Francisco de Quito, Quito, Ecuador}

9_{Institut des Sciences Nucl´eaires, IN2P3-CNRS, Universite de Grenoble 1, Grenoble, France} 10_{CPPM, IN2P3-CNRS, Universit´e de la M´editerran´ee, Marseille, France}

11_{Laboratoire de l’Acc´el´erateur Lin´eaire, IN2P3-CNRS, Orsay, France} 12_{LPNHE, Universit´es Paris VI and VII, IN2P3-CNRS, Paris, France} 13_{DAPNIA/Service de Physique des Particules, CEA, Saclay, France}

14_{Universit¨at Mainz, Institut f¨ur Physik, Mainz, Germany} 15_{Panjab University, Chandigarh, India}

16_{Delhi University, Delhi, India}

17_{Tata Institute of Fundamental Research, Mumbai, India} 18_{Seoul National University, Seoul, Korea}

19_{CINVESTAV, Mexico City, Mexico}

20_{FOM-Institute NIKHEF and University of Amsterdam/NIKHEF, Amsterdam, The Netherlands} 21_{University of Nijmegen/NIKHEF, Nijmegen, The Netherlands}

22_{Institute of Nuclear Physics, Krak´ow, Poland} 23_{Joint Institute for Nuclear Research, Dubna, Russia} 24_{Institute for Theoretical and Experimental Physics, Moscow, Russia}

25_{Moscow State University, Moscow, Russia} 26_{Institute for High Energy Physics, Protvino, Russia}

27_{Lancaster University, Lancaster, United Kingdom} 28_{Imperial College, London, United Kingdom} 29_{University of Arizona, Tucson, Arizona 85721}

30_{Lawrence Berkeley National Laboratory and University of California, Berkeley, California 94720} 31_{University of California, Davis, California 95616}

32_{California State University, Fresno, California 93740} 33_{University of California, Irvine, California 92697} 34_{University of California, Riverside, California 92521} 35_{Florida State University, Tallahassee, Florida 32306} 36_{Fermi National Accelerator Laboratory, Batavia, Illinois 60510}

37_{University of Illinois at Chicago, Chicago, Illinois 60607} 38_{Northern Illinois University, DeKalb, Illinois 60115}

39_{Northwestern University, Evanston, Illinois 60208} 40_{Indiana University, Bloomington, Indiana 47405} 41_{University of Notre Dame, Notre Dame, Indiana 46556}

42_{Iowa State University, Ames, Iowa 50011} 43_{University of Kansas, Lawrence, Kansas 66045} 44_{Kansas State University, Manhattan, Kansas 66506} 45_{Louisiana Tech University, Ruston, Louisiana 71272} 46_{University of Maryland, College Park, Maryland 20742}

47_{Boston University, Boston, Massachusetts 02215} 48_{Northeastern University, Boston, Massachusetts 02115}

49_{University of Michigan, Ann Arbor, Michigan 48109} 50_{Michigan State University, East Lansing, Michigan 48824}

51_{University of Nebraska, Lincoln, Nebraska 68588} 52_{Columbia University, New York, New York 10027} 53_{University of Rochester, Rochester, New York 14627} 54_{State University of New York, Stony Brook, New York 11794}

58_{Brown University, Providence, Rhode Island 02912} 59_{University of Texas, Arlington, Texas 76019} 60_{Texas A&M University, College Station, Texas 77843}

61_{Rice University, Houston, Texas 77005} 62_{University of Virginia, Charlottesville, Virginia 22901} 63_{University of Washington, Seattle, Washington 98195}

(16 Aug 2001)

(QCD), isolated single photons are direct photons: pro-duced from the primary parton-parton interactions. Be-cause the dominant production mechanism for photons of modest transverse energy (ET) at the Fermilab

Teva-tron is gluon Compton scattering (qg → γq), the cross section for direct-photon production is sensitive to the gluon distribution in the proton [1]. A measurement of the final state photons provides a probe of QCD with-out additional complications from fragmentation and jet identification, providing a powerful and effective means for studying the constituents of hadronic matter.

Previous experiments, at center-of-mass energies of both 630 GeV [2] and 1800 GeV [3,4], have reported pho-ton production in excess of next-to-leading-order (NLO) QCD predictions at low transverse energies (E_Tγ <_{∼ 30} GeV). This disagreement with data could result from gluon radiation not included in NLO calculations [5] or because the parton distributions are not well known [6]. In this Letter, we present a measurement of the iso-lated photon cross section in p¯p collisions for photons in two pseudorapidity regions,|η| < 0.9 and 1.6 < |η| < 2.5, where η =_{− ln tan}θ

2and θ is the polar angle with respect

to the proton beam. We compare the production cross section at√s = 630 GeV with the previously published DØ results at √s = 1800 GeV [3]. A ratio of the cross sections at different energies reduces systematic uncer-tainties and minimizes the sensitivity to the choice of parton distribution functions (PDF) because the mea-surements at both energies use the same detector and the same analysis method.

The cross section measurement at 630 GeV uses a sam-ple of 520 nb−1 of data recorded in 1995 [7] with the DØ detector at the Fermilab Tevatron [8]. The analysis uses the uranium/liquid argon calorimeter to identify electro-magnetic (EM) showers, and the drift chambers in front of the calorimeter to differentiate photon showers from electron showers. The EM calorimeter provides full az-imuthal (φ) coverage, and consists of a central cryostat (CC) with_{|η| <∼ 1.1, and two forward cryostats (EC) with} 1.4 <_{∼ |η|}<_{∼ 4.0. The EM calorimeter is divided into four} longitudinal layers, EM1–EM4, of approximately 2, 2, 7, and 10 radiation lengths, respectively. The EM energy resolution in the central and forward calorimeter is given by σE/E ={15%/pE(GeV)} ⊕ 0.3%.

Photons interacting in the calorimeter are detected us-ing a three-level triggerus-ing system. The first level con-sists of scintillation counters near the beam pipe, which detect inelastic p¯p collisions. The second level requires a minimum energy deposition in a ∆φ_{× ∆η = 0.2 × 0.2} trigger tower, with thresholds of 2.0, 3.0, and 7.0 GeV. In the final step, calorimeter clusters are formed with corresponding thresholds of 4.5, 8.0, and 14.0 GeV. The trigger efficiency is determined for the 14.0 and 8.0 GeV thresholds by taking the ratio of events passing each trig-ger criteria to those passing the 8.0 and 4.5 GeV criteria,

old trigger is 100% efficient. Monte Carlo studies of the trigger algorithms show agreement with the data for the two higher energy triggers, and are used to determine the trigger efficiency for the 4.5 GeV trigger. Trigger ef-ficiencies are typically about 20% at the nominal energy threshold and rise to almost 100% a few GeV above the threshold value. Consequently, photon candidates are accepted only for transverse energies of at least 7.35, 10, and 16 GeV for the three triggers, respectively.

Photon candidates are identified as energy clusters lo-cated well within the pseudorapidity boundaries of the central calorimeter or the forward calorimeter, and, in the central calorimeter, located at least 1.6 cm from the az-imuthal section boundaries. The event vertex position is required to be within 50 cm of the center of the detector. The resulting geometric acceptance is A = 0.622_{± 0.007} (0.787± 0.007) in the central (forward) region. Candi-dates must pass a series of selection criteria [3], that iden-tify the energy cluster as an electromagnetic shower. The total transverse energy near any candidate cluster must satisfy an isolation requirement ETR≤0.4− ER≤0.2T < 2.0

GeV, where _{R =}p(∆η)2_{+ (∆φ)}2 _{is the distance from}

the cluster center. The combined selection and isolation efficiency, s, is estimated as a function of ETγ from a

geant-based Monte Carlo simulation of the DØ detec-tor. We find s∼ 60% (75%) in the CC (EC) at 8.0 GeV

and s∼ 88% (90%) above 20 GeV. To minimize

back-ground from electrons, photon candidates are rejected if any tracks in the drift chamber extrapolate to within a road of width ∆φ× ∆θ = 0.2 × 0.2 defined by the angle subtended by the candidate photon cluster and the initial interaction vertex. The total charged tracking efficiency is estimated from Z → e+_e− _{events to be 0.858± 0.013}

(0.593_{± 0.079) in the central (forward) region.}

The predominant background to direct photon pro-duction arises from the decay of π0 _{or η mesons to two}

photons. The fraction of direct photons is determined from the energy (E1) deposited in the innermost

longi-tudinal section of the calorimeter, EM1. Photons have a small probability of showering in the material in front of the calorimeter and, thus, tend to deposit little ergy in EM1. Sensitivity to the amount of EM1 en-ergy can be used to distinguish multiple photon back-ground from a single photon signal. We use the function f(E1) = log10[1 + log10{1 + E1(GeV)}] as our

background samples are generated so that charged and neutral background fractions can be separately fit to the data, thus minimizing uncertainties from the tracking ef-ficiency and from the model used for jet fragmentation. A systematic uncertainty in modeling jet fragmentation is estimated by varying the multiplicity of neutral mesons in the core of pythia jets by_{±10%. The detector response} is modeled using a detailed geant simulation with the energy response in EM1 calibrated to match the data from W _{→ eν events.}

The same criteria used to select photon candidates in the data are applied to the Monte Carlo events. The dis-tribution of f from the data is fitted to a normalized lin-ear combination of Monte Carlo photons and background with and without charged tracks in the road pointing back to the interaction vertex. The fit is performed in different Eγ_T regions using the cernlib fitting package hmcmll [10], with the fractions of signal and background constrained to be between 0.0 and 1.0. The purity is de-fined as the fraction of Monte Carlo photons in the nor-malized fitted distribution. A representative fit is shown in Fig. 1 and the photon purity as a function of ETγ is

plotted in Fig. 2. 0 5 10 15 20 25 30 35 40 45 -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 log(1+log(1+E₁)) Events _|η|<0.9 19 < ETγ< 26 GeV (a) (b) (c)

FIG. 1. Distribution of the discriminant, f , for determining photon purity, where E1is in units of GeV. Points with error bars indicate data. Broken lines indicate simulated distribu-tions of (a) single photons, and jet background (b) without and (c) with charged tracks. The solid line depicts a fit sum of all three distributions.

The final cross sections d2_σ/dEγ

Tdη, after applying

ef-ficiency and purity corrections, are shown in Fig. 3 and tabulated in Table I. The error bars show all uncorre-lated uncertainties, which include the statistical uncer-tainty, and uncertainties from selection criteria, trigger efficiency, and the fitted photon purity. The contribu-tion from the fit to photon purity is the largest source of uncorrelated uncertainty. The correlated uncertainty consists of the uncertainties in luminosity, tracking ef-ficiency, geometric acceptance, calorimeter energy scale, and the largest contribution, that from the fragmentation model. 0 0.2 0.4 0.6 0.8 1 Purity |η|<0.9 0 0.2 0.4 0.6 0.8 0 5 10 15 20 25 30 35 40 45 50 ETγ (GeV) 1.6<|η|<2.5

FIG. 2. The photon purity as a function of E_Tγ for central and forward photons. The error bars indicate the uncertainty in the fit purity and are larger than errors derived from sta-tistical analysis alone.

10 -1 1 10 102 103 104 105 0 5 10 15 20 25 30 35 40 45 50 E_Tγ(GeV) d 2 σ /dE T γ dη (pb/GeV)

NLO QCD, CTEQ5M, µ=Emax_T

1.6<|η|<2.5 |η|<0.9

FIG. 3. The cross section for production of isolated pho-tons in central and forward regions at√s = 630 GeV. The error bars show the total uncorrelated error, and the curves show cross sections predicted from NLO QCD.

Eγ T Range Plotted E γ T d 2_σ/dEγ Tdη (pb/GeV) δσU δσC (GeV) (GeV) Measured NLO QCD (%) (%)

using CTEQ5M parton distributions [11], with renormal-ization and factorrenormal-ization scales µR= µF = EmaxT , where

Emax

T is the maximum photon transverse energy in the

event. Figure 4 compares the data and theory. A co-variance matrix χ2provides a measure of the probability that the theory describes the data. A complete covari-ance matrix, composed of correlated and uncorrelated uncertainties, is determined and the theoretical cross sec-tion is compared to the data with a χ2 _{value of 11 (4.6)}

for 7 degrees of freedom in the CC (EC) region. This gives a standard χ2 _{probability that the theory is}

con-sistent with the data at 12% (71%) probability in the CC (EC) regions. Deviations between theory and data are largest at low E_Tγ in the central region. These re-sults are in qualitative agreement with those previously published at√s = 1800 GeV, where the theory is lower than the data at low Eγ_T (≈10–40 GeV) in the CC, but is consistent with the data over all ETγ in the EC [3].

Using different PDFs changed the cross section by less than 5% [13]. Setting scales to µR = µF = 2.0ETmax or

µR= µF = 0.5ETmax changed the cross section by about

20%, as shown in Fig. 4. -1 0 1 2 3 4 5 (Data-Theory)/Theory µ=0.5 E_T µ=2.0 E_T µ=E_T |η|<0.9 -1 0 1 2 3 4 0 5 10 15 20 25 30 35 40 45 50 ETγ (GeV) 1.6<|η|<2.5

FIG. 4. Comparison of the measured cross section for pro-duction of isolated photons at√s = 630 GeV with NLO QCD using CTEQ5M parton distribution functions. The error bars indicate the uncorrelated uncertainty and the shaded bands indicate the correlated uncertainty

In the simple parton model, the dimensionless cross section E4

T · Ed

3_σ

dp3, as a function of xT = 2E√_sT, is

in-dependent of √s. Although deviations from such naive scaling are expected, the dimensionless framework pro-vides a useful context for comparison with QCD. The experimental dimensionless cross section, averaged over azimuth, becomes σD = E 3 T 2π · d 2_σ/dE Tdη. The ratio

σD(√s = 630 GeV)/σD(√s = 1800 GeV) is determined

by combining the cross section reported in this Letter with the DØ measurement at √s = 1800 GeV [3,14].

Table II together with the NLO QCD prediction.

0 1 2 3 4 5 µ=0.5 E_T µ=2.0 E_T NLO QCD (CTEQ5M) µ=E_T |η|<0.9 σD (630 GeV)/ σD (1800 GeV) 0 1 2 3 4 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 x_T 1.6<|η|<2.5

FIG. 5. The ratio of the dimensionless cross sections, σD(√s = 630 GeV)/σD(√s = 1800 GeV). The error bars indicate the uncorrelated uncertainty and the shaded bands indicate the correlated uncertainty.

Comparison of the theoretical cross section ratio to the data, using the complete covariance matrix, gives a χ2 _{value of 6.5 (3.0) for 7 degrees of freedom in the CC}

(EC), which corresponds to a standard χ2 _{probability of}

49% (89%) in the CC (EC) region. Although the low-est xT points are systematically higher than NLO QCD

predictions in both the CC and EC regions, the devia-tions are not significant in light of our combined statis-tical and systematic uncertainties, and there exists good agreement between the measured ratio and theory.

We have measured the production cross section for iso-lated photons in pp collisions at√s = 630 GeV and com-pared this cross section with that measured at√s = 1800 GeV. The measurement is higher than the theoretical prediction at low ET in the central rapidity region but

agrees at all other ET and in the forward rapidity region.

The difference between data and theory is less significant for the ratio of cross sections, and the theory is consistent with the data over all ET.

Nether-xT Range Plotted xT Ratio Theory δσU(%) δσC (%) |η| < 0.9 0.023–0.029 0.026 3.36 1.32 46 39 0.029–0.040 0.034 2.00 1.34 31 27 0.040–0.047 0.043 2.24 1.40 35 18 0.047–0.060 0.053 1.01 1.39 25 13 0.060–0.083 0.070 1.47 1.44 15 9 0.083–0.094 0.089 1.37 1.45 27 8 0.094–0.156 0.118 1.59 1.42 23 7 1.6 <_{|η| < 2.5} 0.023–0.029 0.026 2.84 1.39 56 22 0.029–0.040 0.034 1.31 1.41 45 17 0.040–0.047 0.043 2.05 1.47 52 14 0.047–0.060 0.052 1.86 1.48 24 13 0.060–0.083 0.070 1.51 1.54 24 11 0.083–0.094 0.088 1.81 1.57 47 11 0.094–0.156 0.116 0.563 1.55 160 10

TABLE II. The measured ratio and NLO QCD prediction for the dimensionless cross section at√s = 630 GeV to that at √s = 1800 GeV. The columns labeled δσU and δσC are the uncorrelated and correlated uncertainties, respectively.

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