Measurement of the Cross Section for Prompt Diphoton Production in p p Collisions at
p s
1:96 TeV
D. Acosta,16J. Adelman,12T. Affolder,9T. Akimoto,54M. G. Albrow,15D. Ambrose,43S. Amerio,42D. Amidei,33 A. Anastassov,50K. Anikeev,15A. Annovi,44J. Antos,1M. Aoki,54G. Apollinari,15T. Arisawa,56J.-F. Arguin,32 A. Artikov,13W. Ashmanskas,15A. Attal,7F. Azfar,41P. Azzi-Bacchetta,42N. Bacchetta,42H. Bachacou,28W. Badgett,15 A. Barbaro-Galtieri,28G. J. Barker,25V. E. Barnes,46B. A. Barnett,24S. Baroiant,6M. Barone,17G. Bauer,31F. Bedeschi,44
S. Behari,24S. Belforte,53G. Bellettini,44J. Bellinger,58E. Ben-Haim,15D. Benjamin,14A. Beretvas,15A. Bhatti,48 M. Binkley,15D. Bisello,42M. Bishai,15R. E. Blair,2C. Blocker,5K. Bloom,33B. Blumenfeld,24A. Bocci,48A. Bodek,47
G. Bolla,46A. Bolshov,31P. S. L. Booth,29D. Bortoletto,46J. Boudreau,45S. Bourov,15B. Brau,9C. Bromberg,34 E. Brubaker,12J. Budagov,13H. S. Budd,47K. Burkett,15G. Busetto,42P. Bussey,19K. L. Byrum,2S. Cabrera,14 M. Campanelli,18M. Campbell,33A. Canepa,46M. Casarsa,53D. Carlsmith,58S. Carron,14R. Carosi,44M. Cavalli-Sforza,3
A. Castro,4P. Catastini,44D. Cauz,53A. Cerri,28L. Cerrito,23J. Chapman,33C. Chen,43Y. C. Chen,1M. Chertok,6 G. Chiarelli,44G. Chlachidze,13F. Chlebana,15I. Cho,27K. Cho,27D. Chokheli,13J. P. Chou,20M. L. Chu,1S. Chuang,58
J. Y. Chung,38W.-H. Chung,58Y. S. Chung,47C. I. Ciobanu,23M. A. Ciocci,44A. G. Clark,18D. Clark,5M. Coca,47 A. Connolly,28M. Convery,48J. Conway,6B. Cooper,30M. Cordelli,17G. Cortiana,42J. Cranshaw,52J. Cuevas,10 R. Culbertson,15C. Currat,28D. Cyr,58D. Dagenhart,5S. Da Ronco,42S. D’Auria,19P. de Barbaro,47S. De Cecco,49
G. De Lentdecker,47S. Dell’Agnello,17M. Dell’Orso,44S. Demers,47L. Demortier,48M. Deninno,4D. De Pedis,49 P. F. Derwent,15C. Dionisi,49J. R. Dittmann,15C. Do¨rr,25P. Doksus,23A. Dominguez,28S. Donati,44M. Donega,18 J. Donini,42M. D’Onofrio,18T. Dorigo,42V. Drollinger,36K. Ebina,56N. Eddy,23J. Ehlers,18R. Ely,28R. Erbacher,6
M. Erdmann,25D. Errede,23S. Errede,23R. Eusebi,47H.-C. Fang,28S. Farrington,29I. Fedorko,44W. T. Fedorko,12 R. G. Feild,59M. Feindt,25J. P. Fernandez,46C. Ferretti,33R. D. Field,16G. Flanagan,34B. Flaugher,15
L. R. Flores-Castillo,45A. Foland,20S. Forrester,6G. W. Foster,15M. Franklin,20J. C. Freeman,28Y. Fujii,26I. Furic,12 A. Gajjar,29A. Gallas,37J. Galyardt,11M. Gallinaro,48M. Garcia-Sciveres,28A. F. Garfinkel,46C. Gay,59H. Gerberich,14
D. W. Gerdes,33E. Gerchtein,11S. Giagu,49P. Giannetti,44A. Gibson,28K. Gibson,11C. Ginsburg,58K. Giolo,46 M. Giordani,53M. Giunta,44G. Giurgiu,11V. Glagolev,13D. Glenzinski,15M. Gold,36N. Goldschmidt,33D. Goldstein,7
J. Goldstein,41G. Gomez,10G. Gomez-Ceballos,31M. Goncharov,51O. Gonza´lez,46I. Gorelov,36A. T. Goshaw,14 Y. Gotra,45K. Goulianos,48A. Gresele,4M. Griffiths,29C. Grosso-Pilcher,12U. Grundler,23M. Guenther,46 J. Guimaraes da Costa,20C. Haber,28K. Hahn,43S. R. Hahn,15E. Halkiadakis,47A. Hamilton,32B.-Y. Han,47R. Handler,58 F. Happacher,17K. Hara,54M. Hare,55R. F. Harr,57R. M. Harris,15F. Hartmann,25K. Hatakeyama,48J. Hauser,7C. Hays,14 H. Hayward,29E. Heider,55B. Heinemann,29J. Heinrich,43M. Hennecke,25M. Herndon,24C. Hill,9D. Hirschbuehl,25 A. Hocker,47K. D. Hoffman,12A. Holloway,20S. Hou,1M. A. Houlden,29B. T. Huffman,41Y. Huang,14R. E. Hughes,38
J. Huston,34K. Ikado,56J. Incandela,9G. Introzzi,44M. Iori,49Y. Ishizawa,54C. Issever,9A. Ivanov,47Y. Iwata,22 B. Iyutin,31E. James,15D. Jang,50J. Jarrell,36D. Jeans,49H. Jensen,15E. J. Jeon,27M. Jones,46K. K. Joo,27S. Y. Jun,11 T. Junk,23T. Kamon,51J. Kang,33M. Karagoz Unel,37P. E. Karchin,57S. Kartal,15Y. Kato,40Y. Kemp,25R. Kephart,15
U. Kerzel,25V. Khotilovich,51B. Kilminster,38D. H. Kim,27H. S. Kim,23J. E. Kim,27M. J. Kim,11M. S. Kim,27 S. B. Kim,27S. H. Kim,54T. H. Kim,31Y. K. Kim,12B. T. King,29M. Kirby,14L. Kirsch,5S. Klimenko,16B. Knuteson,31 B. R. Ko,14H. Kobayashi,54P. Koehn,38D. J. Kong,27K. Kondo,56J. Konigsberg,16K. Kordas,32A. Korn,31A. Korytov,16
K. Kotelnikov,35A. V. Kotwal,14A. Kovalev,43J. Kraus,23I. Kravchenko,31A. Kreymer,15J. Kroll,43M. Kruse,14 V. Krutelyov,51S. E. Kuhlmann,2S. Kwang,12A. T. Laasanen,46S. Lai,32S. Lami,48S. Lammel,15J. Lancaster,14 M. Lancaster,30R. Lander,6K. Lannon,38A. Lath,50G. Latino,36R. Lauhakangas,21I. Lazzizzera,42Y. Le,24C. Lecci,25 T. LeCompte,2J. Lee,27J. Lee,47S. W. Lee,51R. Lefe`vre,3N. Leonardo,31S. Leone,44S. Levy,12J. D. Lewis,15K. Li,59 C. Lin,59C. S. Lin,15M. Lindgren,15T. M. Liss,23A. Lister,18D. O. Litvintsev,15T. Liu,15Y. Liu,18N. S. Lockyer,43 A. Loginov,35M. Loreti,42P. Loverre,49R.-S. Lu,1D. Lucchesi,42P. Lujan,28P. Lukens,15G. Lungu,16L. Lyons,41J. Lys,28 R. Lysak,1D. MacQueen,32R. Madrak,15K. Maeshima,15P. Maksimovic,24L. Malferrari,4G. Manca,29R. Marginean,38
C. Marino,23A. Martin,24M. Martin,59V. Martin,37M. Martı´nez,3T. Maruyama,54H. Matsunaga,54M. Mattson,57 P. Mazzanti,4K. S. McFarland,47D. McGivern,30P. M. McIntyre,51P. McNamara,50R. NcNulty,29A. Mehta,29 S. Menzemer,31A. Menzione,44P. Merkel,15C. Mesropian,48A. Messina,49T. Miao,15N. Miladinovic,5L. Miller,20 R. Miller,34J. S. Miller,33R. Miquel,28S. Miscetti,17G. Mitselmakher,16A. Miyamoto,26Y. Miyazaki,40N. Moggi,4
B. Mohr,7R. Moore,15M. Morello,44P. A. Movilla Fernandez,28A. Mukherjee,15M. Mulhearn,31T. Muller,25
R. Mumford,24A. Munar,43P. Murat,15J. Nachtman,15S. Nahn,59I. Nakamura,43I. Nakano,39A. Napier,55R. Napora,24 D. Naumov,36V. Necula,16F. Niell,33J. Nielsen,28C. Nelson,15T. Nelson,15C. Neu,43M. S. Neubauer,8 C. Newman-Holmes,15T. Nigmanov,45L. Nodulman,2O. Norniella,3K. Oesterberg,21T. Ogawa,56S. H. Oh,14Y. D. Oh,27
T. Ohsugi,22T. Okusawa,40R. Oldeman,49R. Orava,21W. Orejudos,28C. Pagliarone,44E. Palencia,10R. Paoletti,44 V. Papadimitriou,15S. Pashapour,32J. Patrick,15G. Pauletta,53M. Paulini,11T. Pauly,41C. Paus,31D. Pellett,6A. Penzo,53 T. J. Phillips,14G. Piacentino,44J. Piedra,10K. T. Pitts,23C. Plager,7A. Pomposˇ,46L. Pondrom,58G. Pope,45X. Portell,3
O. Poukhov,13F. Prakoshyn,13T. Pratt,29A. Pronko,16J. Proudfoot,2F. Ptohos,17G. Punzi,44J. Rademacker,41 M. A. Rahaman,45A. Rakitine,31S. Rappoccio,20F. Ratnikov,50H. Ray,33B. Reisert,15V. Rekovic,36P. Renton,41
M. Rescigno,49F. Rimondi,4K. Rinnert,25L. Ristori,44W. J. Robertson,14A. Robson,41T. Rodrigo,10S. Rolli,55 L. Rosenson,31R. Roser,15R. Rossin,42C. Rott,46J. Russ,11V. Rusu,12A. Ruiz,10D. Ryan,55H. Saarikko,21S. Sabik,32
A. Safonov,6R. St. Denis,19W. K. Sakumoto,47G. Salamanna,49D. Saltzberg,7C. Sanchez,3A. Sansoni,17L. Santi,53 S. Sarkar,49K. Sato,54P. Savard,32A. Savoy-Navarro,15P. Schlabach,15E. E. Schmidt,15M. P. Schmidt,59M. Schmitt,37
L. Scodellaro,10A. Scribano,44F. Scuri,44A. Sedov,46S. Seidel,36Y. Seiya,40F. Semeria,4L. Sexton-Kennedy,15 I. Sfiligoi,17M. D. Shapiro,28T. Shears,29P. F. Shepard,45D. Sherman,20M. Shimojima,54M. Shochet,12Y. Shon,58 I. Shreyber,35A. Sidoti,44J. Siegrist,28M. Siket,1A. Sill,52P. Sinervo,32A. Sisakyan,13A. Skiba,25A. J. Slaughter,15
K. Sliwa,55D. Smirnov,36J. R. Smith,6F. D. Snider,15R. Snihur,32A. Soha,6S. V. Somalwar,50J. Spalding,15 M. Spezziga,52L. Spiegel,15F. Spinella,44M. Spiropulu,9P. Squillacioti,44H. Stadie,25B. Stelzer,32O. Stelzer-Chilton,32 J. Strologas,36D. Stuart,9A. Sukhanov,16K. Sumorok,31H. Sun,55T. Suzuki,54A. Taffard,23R. Tafirout,32S. F. Takach,57 H. Takano,54R. Takashima,22Y. Takeuchi,54K. Takikawa,54M. Tanaka,2R. Tanaka,39N. Tanimoto,39S. Tapprogge,21
M. Tecchio,33P. K. Teng,1K. Terashi,48R. J. Tesarek,15S. Tether,31J. Thom,15A. S. Thompson,19E. Thomson,43 P. Tipton,47V. Tiwari,11S. Tkaczyk,15D. Toback,51K. Tollefson,34T. Tomura,54D. Tonelli,44M. To¨nnesmann,34 S. Torre,44D. Torretta,15S. Tourneur,15W. Trischuk,32J. Tseng,41R. Tsuchiya,56S. Tsuno,39D. Tsybychev,16N. Turini,44
M. Turner,29F. Ukegawa,54T. Unverhau,19S. Uozumi,54D. Usynin,43L. Vacavant,28A. Vaiciulis,47A. Varganov,33 E. Vataga,44S. Vejcik III,15G. Velev,15V. Veszpremi,46G. Veramendi,23T. Vickey,23R. Vidal,15I. Vila,10R. Vilar,10 I. Vollrath,32I. Volobouev,28M. von der Mey,7P. Wagner,51R. G. Wagner,2R. L. Wagner,15W. Wagner,25R. Wallny,7
T. Walter,25T. Yamashita,39K. Yamamoto,40Z. Wan,50M. J. Wang,1S. M. Wang,16A. Warburton,32B. Ward,19 S. Waschke,19D. Waters,30T. Watts,50M. Weber,28W. C. Wester III,15B. Whitehouse,55A. B. Wicklund,2E. Wicklund,15
H. H. Williams,43P. Wilson,15B. L. Winer,38P. Wittich,43S. Wolbers,15M. Wolter,55M. Worcester,7S. Worm,50 T. Wright,33X. Wu,18F. Wu¨rthwein,8A. Wyatt,30A. Yagil,15C. Yang,59U. K. Yang,12W. Yao,28G. P. Yeh,15K. Yi,24 J. Yoh,15P. Yoon,47K. Yorita,56T. Yoshida,40I. Yu,27S. Yu,43Z. Yu,59J. C. Yun,15L. Zanello,49A. Zanetti,53I. Zaw,20
F. Zetti,44J. Zhou,50A. Zsenei,18and S. Zucchelli4 (CDF Collaboration)
1Institute of Physics, Academia Sinica, Taipei, Taiwan 11529, People’s 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
4Istituto Nazionale di Fisica Nucleare, University of Bologna, I-40127 Bologna, Italy
5Brandeis University, Waltham, Massachusetts 02254, USA
6University of California at Davis, Davis, California 95616, USA
7University of California at Los Angeles, Los Angeles, California 90024, USA
8University of California at San Diego, La Jolla, California 92093, USA
9University of California at Santa Barbara, Santa Barbara, California 93106, USA
10Instituto de Fisica de Cantabria, CSIC-University of Cantabria, 39005 Santander, Spain
11Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA
12Enrico Fermi Institute, University of Chicago, Chicago, Illinois 60637, USA
13Joint Institute for Nuclear Research, RU-141980 Dubna, Russia
14Duke University, Durham, North Carolina 27708, USA
15Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA
16University of Florida, Gainesville, Florida 32611, USA
17Laboratori Nazionali di Frascati, Istituto Nazionale di Fisica Nucleare, I-00044 Frascati, Italy
18University of Geneva, CH-1211 Geneva 4, Switzerland
19Glasgow University, Glasgow G12 8QQ, United Kingdom
20Harvard University, Cambridge, Massachusetts 02318, USA
21The Helsinki Group, Helsinki Institute of Physics; Division of High Energy Physics, Department of Physical Sciences, University of Helsinki, FIN-00014, Helsinki, Finland
22Hiroshima University, Higashi-Hiroshima 724, Japan
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; Seoul National University, Seoul 151-742;
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
42Istituto Nazionale di Fisica Nucleare, Sezione di Padova-Trento, University of Padova, I-35131 Padova, Italy
43University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
44Istituto Nazionale di Fisica Nucleare, University and Scuola Normale Superiore of Pisa, I-56100 Pisa, Italy
45University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
46Purdue University, West Lafayette, Indiana 47907, USA
47University of Rochester, Rochester, New York 14627, USA
48The Rockefeller University, New York, New York 10021, USA
49Istituto Nazionale di Fisica Nucleare, Sezione di Roma 1, University di Roma La Sapienza, I-00185 Roma, Italy
50Rutgers University, Piscataway, New Jersey 08855, USA
51Texas A&M University, College Station, Texas 77843, USA
52Texas Tech University, Lubbock, Texas 79409, 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 20 December 2004; published 8 July 2005)
We report a measurement of the rate of prompt diphoton production inppcollisions atps
1:96 TeV using a data sample of 207 pb1 collected with the upgraded Collider Detector at Fermilab. The background from nonprompt sources is determined using a statistical method based on differences in the electromagnetic showers. The cross section is measured as a function of the diphoton mass, the transverse momentum of the diphoton system, and the azimuthal angle between the two photons and is found to be consistent with perturbative QCD predictions.
DOI:10.1103/PhysRevLett.95.022003 PACS numbers: 13.85.Qk
Diphoton () final states are a signature of many interesting physics processes. For example, at the LHC, one of the main discovery channels for the Higgs boson search is thefinal state [1,2]. An excess ofproduc- tion at high invariant mass could be a signature of large extra dimensions [3], and in many theories involving phys- ics beyond the standard model, cascade decays of heavy new particles generate a signature [4]. However, the
QCD production rate is large compared to most new phys- ics, so an understanding of the QCD production mecha- nism is a prerequisite to searching reliably for new physics in this channel. In addition, the two-photon final state is interesting in its own right. Because of the excellent energy resolution of the CDF electromagnetic (EM) calorimeter, the 4-momenta of the two photons in the final state can be determined with good precision. This allows, for example,
a direct measurement of the transverse momentum of the system (qT), which is sensitive to initial state soft gluon radiation.
In perturbative Quantum Chromodynamics (pQCD), the leading contributions are from quark antiquark annihila- tion (qq!) and gluon-gluon scattering (gg!).
The latter subprocess involves initial state gluons coupling to the final state photons through a quark box; thus, this subprocess is suppressed by a factor of 2s with respect to theqq subprocess. However, the rate is still appreciable in kinematic regions where theggparton luminosity is high, such as at lowmass. Because the probability for a hard parton to fragment to a photon is of order em= s, pro- cesses involving the production of one (zero) prompt pho- tons and one (two) photons originating from parton fragmentation are also effectively of leading order (LO).
Next-to-leading order (NLO) contributions include real and virtual corrections to the above subprocesses.
We have compared our experimental results to three predictions: DIPHOX [5], RESBOS [6], and PYTHIA [7].
DIPHOXis a fixed-order QCD calculation that includes all of the above subprocesses at NLO (except for gg!, which is present only at LO). Recently, NLO corrections forgg!have been calculated [8] and we have added these corrections to the DIPHOX prediction. The RESBOS
program includes subprocesses where the two photons are produced at the hard scattering at NLO and fragmentation contributions at LO but also resums the effects of initial state soft gluon radiation. This is particularly important for examination of the qT distribution, which is a delta function at LO and divergent asqT !0at NLO, and thus requires a soft gluon resummation in order to provide a physical description of thedata in this region.PYTHIAis a parton shower Monte Carlo program that contains the above processes at LO.
At hadron-hadron colliders, it is difficult to measure a fully inclusive cross section due to the large back- grounds from quarks and gluons fragmenting into neutral mesons which carry most of the parent parton’s momen- tum. Isolation requirements are typically used to reduce these backgrounds. In this analysis, the isolation criterion requires that the transverse energy (ET) sum in a cone of radius R0:4 (in space) [9] about the photon direction, minus the photon energy, be less than 1 GeV.
This isolation requirement reduces the backgrounds from neutral mesons decaying into photons and photon produc- tion from fragmentation sources. The CDF isolation re- quirement effectively removes all contributions where both photons originate from fragmentation subprocesses.
However, as will be noted later, some indication of single fragmentation subprocesses can still be observed in the CDF data.
The CDF II detector is a magnetic spectrometer which is described in detail elsewhere [10]. The central detector consists of a silicon micro-strip vertex detector inside a
cylindrical drift chamber, both of which are immersed in the 1.4 T magnetic field of a superconducting solenoid.
Outside the solenoid is the central calorimeter which is divided into an electromagnetic compartment (CEM) on the inside and hadronic compartment (CHA) on the out- side. Both calorimeters are segmented into towers of gran- ularity 0:10:26. The CEM consists of a scintillator-lead calorimeter along with an embedded mul- tiwire proportional chamber (CES) located near shower maximum at 6 radiation lengths. The CES allows for a position determination of the EM shower and for a mea- surement of the lateral shower profile. The average energy resolution of the CEM isE=E13:5%=
Esin
p (with
Ein GeV) and the position resolution of the CES is 2 mm for a 50 GeV photon. Another important component for this analysis is a preshower wire chamber (CPR) mounted between the magnet coil and the CEM, at about1:2=sin radiation lengths. The CPR detects photon candidates that have converted in the magnet coil and other material in the inner detector.
This analysis [11] uses events collected with a trigger that requires two-photon candidates withET greater than 12 GeV each. A requirement of ET greater than 14 GeV (13 GeV) for the leading (softer) photon candidate in the event is imposed in the off-line analysis. The minimum transverse energy requirements for the two-photon candi- dates are different in order to avoid the kinematic region where the NLO calculation is unstable due to the imperfect cancellation of the real and virtual gluon divergences.
In identifying photons, we impose fiducial requirements to avoid uninstrumented regions at the edges of the CES; as part of this criterion we require the pseudorapidity of the photon candidate to be in the interval jj<0:9. The reconstructed z vertex for the collision is required to be less than 60 cm from the center of the detector. The ratio of the hadronic energy to EM energy (Had=EM) for the photon candidates must be less than 0:0550:00045 E, withE the EM energy in GeV. The isolation energy is required to be below 1 GeV. Although only about 1% of showers from prompt photons have more than 1 GeV of additional energy in the isolation cone, about 15% of the photon showers fail the isolation requirement because of additional energy from the underlying event [12]. Photon candidates with any tracks (pTabove 0.5 GeV) that can be extrapolated to them are rejected. The lateral profile of EM showers in the CES is compared to the profile of electrons measured in a test beam. The definition of the2from the comparison can be found in Ref. [13]. We require the2of the comparison to be less than 20 in the event selection and reject photon candidates with an additional CES cluster above 1 GeV [14]. The efficiencies for each event selection requirement, evaluated using a combination of PYTHIA
Monte Carlo simulation and data, are listed sequentially in Table I. The trigger efficiency per photon, measured using a single-photon trigger, is approximately 80% at
13 GeV and rises to greater than 99% for photons above 15 GeV. The combined selection efficiency ("tot), includ- ing acceptance and trigger efficiency, is 15.2% per dipho- ton event.
After imposing all of the requirements, 889 two-photon candidates remain in our data sample. This sample includes background from neutral mesons such as 0 and that decay to multiple photons. To estimate this background, we apply the statistical background subtraction method de- scribed in [15], which makes use of the differences on average between EM showers produced by single photons and by the multiple photons produced in neutral meson decays. The separation between single and multiple photon showers relies on the shower shape measured by the CES 2and the preshower conversion pulse height measured by the CPR. Since photons from the decay of neutral mesons with ET above 35 GeV are almost collinear in the lab frame, their shower shape in the CES is no longer distin- guishable from a single-photon shower. To estimate the background contamination in this highETregion, the CPR has been utilized. The chance for a conversion to take place in the tracking volume or magnet coil (1.1 radiation lengths) and generating a hit in the CPR is higher for the multiple photons than for a single photon. We use the CES shower shape for photon showers withET<35 GeVand the CPR pulse height forET>35 GeV. For each photon candidate, we test whether the CES2 is less than 4 (low ET) or the photon candidate produces a pulse height in the CPR greater than one minimum ionizing particle (high ET). There are four possibilities for the final state: both candidates pass the test, the first candidate passes and the second fails, the first fails and the second passes, or both candidates fail (the first candidate has the higherET). From the known efficiencies for photons and background to pass the 2 and conversion tests, we can then determine the number of true events (as well as the number of -background, background-, and background-back- ground events). Using the two background techniques dis- cussed, we determine that of the 889 candidates, 427 59statare realevents. From these events, the calcu- lated acceptance and the integrated luminosity, we deter- mine the diphoton cross sections for several kinematic variables. The mass distribution is shown in Fig. 1,
along with predictions fromDIPHOX,RESBOS, andPYTHIA. The qT distribution is shown in Fig. 2, and thedistri- bution between the two photons is shown in Fig. 3. The vertical error bars on the data indicate the combined sta- tistical and systematic uncertainties with the inner tick marks indicating the statistical uncertainty alone [16].
The PYTHIA predictions have been scaled (factor of 2) to the total measured cross section in all the figures. It should be noted that the background to the signal has been determined independently for each kinematic bin as the background fraction can vary with the kinematics.
Determining the background on a bin-by-bin basis in-
10 20 30 40 50 60 70 80 90 100
10-2
10-1
1
> 13 GeV
γ2
> 14 GeV, ET γ1
ET
| < 0.9
γ1,2
η
|
30 40 50
0 0.5 1
2) (GeV/c
γ
Mγ
))2 (pb/(GeV/cγγ/dMσd
FIG. 1 (color online). Themass distribution from the CDF Run II data, along with predictions from DIPHOX (solid line),
RESBOS(dashed line), andPYTHIA(dot-dashed line). ThePYTHIA
predictions have been scaled by a factor of 2. The inset shows, on a linear scale, the totalcross section in DIPHOXwith (solid line)/without (dashed line) theggcontribution.
TABLE I. The selection efficiencies per diphoton event.
Trigger efficiency 0.951
Reconstruction efficiency and fiducial 0.423 Isolation energy in0:4cone<1 GeV 0.727 No track pointing to the EM cluster 0.699
No extra CES cluster above 1 GeV 0.899
CES2<20 0.970
Had=EM<0:0550:00045E 0.976
jzvertexj<60 cm 0.877
Combined ("tot) 0.152
0 5 10 15 20 25 30 35 40
10-2
10-1
1
> 13 GeV
γ2
> 14 GeV, ET γ1
ET
|<0.9
γ1,2
η
|
(GeV/c) qT
(pb/(GeV/c))T/dqσd
FIG. 2 (color online). The qT distribution from the CDF Run II data, along with predictions from DIPHOX (solid line),
RESBOS(dashed line), andPYTHIA(dot-dashed line). ThePYTHIA
predictions have been scaled by a factor of 2. Also shown, at largerqT, are theDIPHOX prediction (dotted line) and the CDF Run II data (open squares: shifted to the right by 1 GeV for visibility) for the configuration where the two photons are required to have < =2.
creases the statistical uncertainty but decreases the system- atic uncertainty.
The systematic effects include uncertainties on the se- lection efficiencies (11%), uncertainties from the back- ground subtraction (20%– 30%), and from the luminosity determination (6%) [17].
We note some features of the theoretical predictions.
TheRESBOSqTcurve is smooth for the entire range, while the DIPHOXcurve is unstable at lowqT due to the singu- larity noted earlier [18]. At the highqT end,DIPHOXdis- plays a shoulder, a feature absent in theRESBOSprediction.
TheRESBOScurve lies above theDIPHOXone atvalues of the order of=2but also lies significantly below the
DIPHOXcurve at small.
The observed differences between the predictions are expected. The fragmentation contribution in RESBOS is effectively at LO. Since fragmentation to a photon is of order em= s, some2!3processes such asqg!gq, where the quark in the final state fragments to a second photon, are of order 2em sand are included in a full NLO calculation. These contributions are present inDIPHOX, but not in RESBOS, which leads to an underestimate of the production rate in the latter at highqT, low, and low mass. In particular, the shoulder atqTof approximately 30 GeV=carises from an increase in phase space for both the direct and fragmentation subprocesses [19]. It is in- structive to divide theDIPHOXpredictions into two regions:
> =2 and < =2. We do so, and plot the qT prediction for the < =2region in Fig. 2 in order to highlight this contribution. It is apparent that the bump in theDIPHOXprediction at aqT of approximately30 GeV=c is due to the ‘‘turn-on’’ of the < =2region of phase space. Atvalues above=2, the effects from soft gluon emission (included in RESBOS but not in DIPHOX) are significant.
The data are in good agreement with the predictions for the mass distribution. At low to moderate qT and
greater than=2, where the effects of soft gluon emissions are important, the data agree better with RESBOS than
DIPHOX. By contrast, in the regions where the2!3frag- mentation contribution becomes important (large qT, less than=2and low diphoton mass) the data agree better withDIPHOX.
In this Letter, we have presented results forproduc- tion in pp collisions at a center-of-mass energy of 1.96 TeV using a data sample twice that previously avail- able. Good agreement has been observed with resummed and NLO predictions in different regions of phase space.
For agreement in all areas, however, a resummed full NLO calculation will be necessary.
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 Bundesmini- sterium 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, UK;
the Russian Foundation for Basic Research; the Comision Interministerial de Ciencia y Tecnologia, Spain; and in part by the European Community’s Human Potential Programme under Contract No. HPRN-CT-2002-00292, Probe for New Physics. We would like to thank C.
Balazs, J. Ph. Guillet, E. Pilon, C. Schmidt, and C.-P.
Yuan for invaluable discussions.
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0 0.5 1 1.5 2 2.5 3
10-1
1
10 EγT1 > 14 GeV, EγT2 > 13 GeV
|<0.9
γ1,2
η
|
(rad)
γ
φγ
∆ (pb/rad)γγφ∆/dσd
FIG. 3 (color online). Theangle between the two photons from the CDF Run II data, along with predictions fromDIPHOX
(solid line),RESBOS(dashed line), andPYTHIA(dot-dashed line).
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