Article
Reference
Measurement of the forward-backward charge asymmetry of electron-positron pairs in pp collisions at s√=1.96 TeV
CDF Collaboration
CAMPANELLI, Mario (Collab.), et al.
Abstract
We present a measurement of the mass dependence of the forward-backward charge asymmetry (AFB) for e+e− pairs produced via an intermediate Z/γ∗ with mass Mee>40 GeV/c2. We study the constraints on the Z-quark couplings imposed by our measurement.
We analyze an integrated luminosity of 72 pb−1 collected by the CDF-II detector in pp collisions at s√=1.96 TeV at the Fermilab Tevatron. A comparison of the uncorrected AFB between data and standard model Monte Carlo gives good agreement with a χ2/DOF of 15.7/15. The couplings measurements are also consistent with standard model predictions.
CDF Collaboration, CAMPANELLI, Mario (Collab.), et al . Measurement of the forward-backward charge asymmetry of electron-positron pairs in pp collisions at s√=1.96 TeV. Physical Review.
D , 2005, vol. 71, no. 05, p. 052002
DOI : 10.1103/PhysRevD.71.052002
Available at:
http://archive-ouverte.unige.ch/unige:38303
Disclaimer: layout of this document may differ from the published version.
Measurement of the forward-backward charge asymmetry of electron-positron pairs in pp collisions at
p s
1:96 TeV
D. Acosta,16T. Affolder,9T. Akimoto,54M. G. Albrow,15D. Ambrose,43S. Amerio,42D. Amidei,33A. Anastassov,50 K. Anikeev,31A. Annovi,44J. Antos,1M. Aoki,54G. Apollinari,15T. Arisawa,56J-F. Arguin,32A. Artikov,13
W. 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,58D. Benjamin,14A. Beretvas,15A. Bhatti,48M. Binkley,15 D. Bisello,42M. Bishai,15R. E. Blair,2C. Blocker,5K. Bloom,33B. Blumenfeld,24A. Bocci,48A. Bodek,47G. Bolla,46 A. Bolshov,31P. S. L. Booth,29D. Bortoletto,46J. Boudreau,45S. Bourov,15C. Bromberg,34E. Brubaker,12J. Budagov,13 H. S. Budd,47K. Burkett,15G. Busetto,42P. Bussey,19K. L. Byrum,2S. Cabrera,14P. Calafiura,28M. Campanelli,18 M. Campbell,33A. Canepa,46M. Casarsa,53D. Carlsmith,58S. Carron,14R. Carosi,44M. Cavalli-Sforza,3A. Castro,4
P. Catastini,44D. Cauz,53A. Cerri,28C. Cerri,44L. Cerrito,23J. Chapman,33C. Chen,43Y. C. Chen,1M. Chertok,6 G. Chiarelli,44G. Chlachidze,13F. Chlebana,15I. Cho,27K. Cho,27D. Chokheli,13M. L. Chu,1S. Chuang,58J. Y. Chung,38
W-H. Chung,58Y. S. Chung,47C. I. Ciobanu,23M. A. Ciocci,44A. G. Clark,18D. Clark,5M. Coca,47A. Connolly,28 M. Convery,48J. Conway,50B. Cooper,30M. Cordelli,17G. Cortiana,42J. Cranshaw,52J. Cuevas,10R. Culbertson,15 C. Currat,28D. Cyr,58D. Dagenhart,5S. Da Ronco,42S. D’Auria,19P. de Barbaro,47S. De Cecco,49G. De Lentdecker,47
S. Dell’Agnello,17M. Dell’Orso,44S. Demers,47L. Demortier,48M. Deninno,4D. De Pedis,49P. F. Derwent,15 C. Dionisi,49J. R. Dittmann,15P. Doksus,23A. Dominguez,28S. Donati,44M. Donega,18J. Donini,42M. D’Onofrio,18 T. Dorigo,42V. Drollinger,36K. Ebina,56N. Eddy,23R. Ely,28R. Erbacher,15M. Erdmann,25D. Errede,23S. Errede,23 R. Eusebi,47H-C. Fang,28S. Farrington,29I. Fedorko,44R. G. Feild,59M. Feindt,25J. P. Fernandez,46C. Ferretti,33 R. D. Field,16I. Fiori,44G. Flanagan,34B. Flaugher,15L. R. Flores-Castillo,45A. Foland,20S. Forrester,6G. W. Foster,15
M. Franklin,20J. Freeman,28H. Frisch,12Y. Fujii,26I. Furic,12A. Gajjar,29A. Gallas,37J. Galyardt,11M. Gallinaro,48 M. Garcia-Sciveres,28A. F. Garfinkel,46C. Gay,59H. Gerberich,14D. W. Gerdes,33E. Gerchtein,11S. Giagu,49 P. Giannetti,44A. Gibson,28K. Gibson,11C. Ginsburg,58K. Giolo,46M. Giordani,53G. Giurgiu,11V. Glagolev,13 D. Glenzinski,15M. Gold,36N. Goldschmidt,33D. Goldstein,7J. Goldstein,41G. Gomez,10G. Gomez-Ceballos,31 M. Goncharov,51O. Gonza´lez,46I. Gorelov,36A. T. Goshaw,14Y. Gotra,45K. Goulianos,48A. Gresele,4M. Griffiths,29
C. Grosso-Pilcher,12M. Guenther,46J. Guimaraes da Costa,20C. Haber,28K. Hahn,43S. R. Hahn,15E. Halkiadakis,47 R. Handler,58F. Happacher,17K. Hara,54M. Hare,55R. F. Harr,57R. M. Harris,15F. Hartmann,25K. Hatakeyama,48 J. Hauser,7C. Hays,14H. Hayward,29E. Heider,55B. Heinemann,29J. Heinrich,43M. Hennecke,25M. Herndon,24C. Hill,9 D. Hirschbuehl,25A. Hocker,47K. D. Hoffman,12A. Holloway,20S. Hou,1M. A. Houlden,29B. T. Huffman,41Y. Huang,14 R. E. Hughes,38J. Huston,34K. Ikado,56J. Incandela,9G. Introzzi,44M. Iori,49Y. Ishizawa,54C. Issever,9A. Ivanov,47 Y. Iwata,22B. Iyutin,31E. James,15D. Jang,50J. Jarrell,36D. Jeans,49H. Jensen,15E. J. Jeon,27M. Jones,46K. K. Joo,27 S. Jun,11T. Junk,23T. Kamon,51J. Kang,33M. Karagoz Unel,37P. E. Karchin,57S. Kartal,15Y. Kato,40Y. Kemp,25
R. Kephart,15U. Kerzel,25V. Khotilovich,51B. Kilminster,38D. H. Kim,27H. S. Kim,23J. E. Kim,27M. J. Kim,11 M. S. Kim,27S. B. Kim,27S. H. Kim,54T. H. Kim,31Y. K. Kim,12B. T. King,29M. Kirby,14L. Kirsch,5S. Klimenko,16 B. Knuteson,31B. R. Ko,14H. Kobayashi,54P. Koehn,38D. J. Kong,27K. Kondo,56J. Konigsberg,16K. Kordas,32A. Korn,31
A. Korytov,16K. Kotelnikov,35A. V. Kotwal,14A. Kovalev,43J. Kraus,23I. Kravchenko,31A. Kreymer,15J. Kroll,43 M. Kruse,14V. Krutelyov,51S. E. Kuhlmann,2N. Kuznetsova,15A. T. Laasanen,46S. Lai,32S. Lami,48S. Lammel,15 J. Lancaster,14M. Lancaster,30R. Lander,6K. Lannon,38A. Lath,50G. Latino,36R. Lauhakangas,21I. Lazzizzera,42 Y. Le,24C. Lecci,25T. LeCompte,2J. Lee,27J. Lee,47S. W. Lee,51N. Leonardo,31S. Leone,44J. D. Lewis,15K. Li,59 C. Lin,59C. S. Lin,15M. Lindgren,15T. M. Liss,23D. O. Litvintsev,15T. Liu,15Y. Liu,18N. S. Lockyer,43A. Loginov,35
M. Loreti,42P. Loverre,49R-S. Lu,1D. Lucchesi,42P. Lujan,28P. Lukens,15L. Lyons,41J. Lys,28R. Lysak,1 D. MacQueen,32R. Madrak,20K. Maeshima,15P. Maksimovic,24L. Malferrari,4G. Manca,29R. Marginean,38M. Martin,24 A. Martin,59V. Martin,37M. Martı´nez,3T. Maruyama,54H. Matsunaga,54M. Mattson,57P. Mazzanti,4K. S. McFarland,47
D. McGivern,30P. M. McIntyre,51P. McNamara,50R. NcNulty,29S. Menzemer,31A. Menzione,44P. Merkel,15 C. Mesropian,48A. Messina,49T. Miao,15N. Miladinovic,5L. Miller,20R. Miller,34J. S. Miller,33R. Miquel,28 S. Miscetti,17G. Mitselmakher,16A. Miyamoto,26Y. Miyazaki,40N. Moggi,4B. Mohr,7R. Moore,15M. Morello,44
A. Mukherjee,15M. Mulhearn,31T. Muller,25R. Mumford,24A. Munar,43P. Murat,15J. Nachtman,15S. Nahn,59 I. Nakamura,43I. Nakano,39A. Napier,55R. Napora,24D. Naumov,36V. Necula,16F. Niell,33J. Nielsen,28C. Nelson,15
T. Nelson,15C. Neu,43M. S. Neubauer,8C. Newman-Holmes,15A-S. Nicollerat,18T. Nigmanov,45L. Nodulman,2
O. Norniella,3K. Oesterberg,21T. Ogawa,56S. H. Oh,14Y. D. Oh,27T. Ohsugi,22T. Okusawa,40R. Oldeman,49R. Orava,21 W. Orejudos,28C. Pagliarone,44F. Palmonari,44R. Paoletti,44V. Papadimitriou,15S. Pashapour,32J. Patrick,15 G. Pauletta,53M. Paulini,11T. Pauly,41C. Paus,31D. Pellett,6A. Penzo,53T. J. Phillips,14G. Piacentino,44J. Piedra,10 K. T. Pitts,23C. Plager,7A. Pomposˇ,46L. Pondrom,58G. Pope,45O. Poukhov,13F. Prakoshyn,13T. Pratt,29A. Pronko,16
J. Proudfoot,2F. Ptohos,17G. Punzi,44J. Rademacker,41A. Rakitine,31S. Rappoccio,20F. Ratnikov,50H. Ray,33 A. Reichold,41B. Reisert,15V. Rekovic,36P. Renton,41M. Rescigno,49F. Rimondi,4K. Rinnert,25L. Ristori,44 W. J. Robertson,14A. Robson,41T. Rodrigo,10S. Rolli,55L. Rosenson,31R. Roser,15R. Rossin,42C. Rott,46J. Russ,11
A. Ruiz,10D. Ryan,55H. Saarikko,21A. Safonov,6R. St. Denis,19W. K. Sakumoto,47G. Salamanna,49D. Saltzberg,7 C. Sanchez,3A. Sansoni,17L. Santi,53S. Sarkar,49K. Sato,54P. Savard,32A. Savoy-Navarro,15P. Schemitz,25 P. Schlabach,15E. E. Schmidt,15M. P. Schmidt,59M. Schmitt,37L. Scodellaro,42A. Scribano,44F. Scuri,44A. Sedov,46
S. Seidel,36Y. Seiya,40F. Semeria,4L. Sexton-Kennedy,15I. Sfiligoi,17M. D. Shapiro,28T. Shears,29P. F. Shepard,45 M. Shimojima,54M. Shochet,12Y. Shon,58I. Shreyber,35A. Sidoti,44J. Siegrist,28M. Siket,1A. Sill,52P. Sinervo,32
A. Sisakyan,13A. Skiba,25A. J. Slaughter,15K. Sliwa,55D. Smirnov,36J. R. Smith,6F. D. Snider,15R. Snihur,32 S. V. Somalwar,50J. Spalding,15M. Spezziga,52L. Spiegel,15F. Spinella,44M. Spiropulu,9P. Squillacioti,44H. Stadie,25
A. Stefanini,44B. Stelzer,32O. Stelzer-Chilton,32J. Strologas,36D. Stuart,9A. Sukhanov,16K. Sumorok,31H. Sun,55 T. Suzuki,54A. Taffard,23R. Tafirout,32S. F. Takach,57H. Takano,54R. Takashima,22Y. Takeuchi,54K. Takikawa,54 M. Tanaka,2R. Tanaka,39N. Tanimoto,39S. Tapprogge,21M. Tecchio,33P. K. Teng,1K. Terashi,48R. J. Tesarek,15
S. Tether,31J. Thom,15A. S. Thompson,19E. Thomson,43P. Tipton,47V. Tiwari,11S. Tkaczyk,15D. Toback,51 K. Tollefson,34T. Tomura,54D. Tonelli,44M. To¨nnesmann,34S. Torre,44D. Torretta,15W. Trischuk,32J. Tseng,41 R. Tsuchiya,56S. Tsuno,39D. Tsybychev,16N. Turini,44M. Turner,29F. Ukegawa,54T. Unverhau,19S. Uozumi,54 D. Usynin,43L. Vacavant,28A. Vaiciulis,47A. Varganov,33E. Vataga,44S. Vejcik III,15G. Velev,15G. Veramendi,23 T. Vickey,23R. Vidal,15I. Vila,10R. Vilar,10I. Volobouev,28M. von der Mey,7P. Wagner,51R. G. Wagner,2R. L. Wagner,15 W. Wagner,25R. Wallny,7T. Walter,25Z. Wan,50M. J. Wang,1S. M. Wang,16A. Warburton,32B. Ward,19S. Waschke,19
D. Waters,30T. Watts,50M. Weber,28W. C. Wester III,15B. Whitehouse,55A. B. Wicklund,2E. Wicklund,2 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,15T. Yamashita,39K. Yamamoto,40U. K. Yang,12W. Yao,28
G. P. Yeh,15K. Yi,24J. Yoh,15P. Yoon,47K. Yorita,56T. Yoshida,40I. Yu,27S. Yu,43Z. Yu,59J. C. Yun,15L. Zanello,49 A. Zanetti,53I. Zaw,20F. Zetti,44J. Zhou,50A. Zsenei,18and S. Zucchelli4
(CDF Collaboration)
1Institute of Physics, Academia Sinica, Taipei, Taiwan 11529, Republic of China
2Argonne National Laboratory, Argonne, Illinois 60439, USA
3Institut de Fisica d’Altes Energies, Universitat Autonoma de Barcelona, E-08193, Bellaterra (Barcelona), Spain
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
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 02138, USA
21The Helsinki Group: Helsinki Institute of Physics; and Division of High Energy Physics, Department of Physical Sciences, University of Helsinki, FIN-00044, 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;
and SungKyunKwan University, Suwon 440-746; Korea
28Ernest Orlando Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
29University of Liverpool, Liverpool L69 7ZE, United Kingdom
30University College London, London WC1E 6BT, United Kingdom
31Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
32Institute of Particle Physics, McGill University, Montre´al, Canada H3A 2T8;
and University of Toronto, Toronto, Canada M5S 1A7
33University of Michigan, Ann Arbor, Michigan 48109, USA
34Michigan State University, East Lansing, Michigan 48824, USA
35Institution for Theoretical and Experimental Physics, ITEP, Moscow 117259, Russia
36University of New Mexico, Albuquerque, New Mexico 87131, USA
37Northwestern University, Evanston, Illinois 60208, USA
38The Ohio State University, Columbus, Ohio 43210, USA
39Okayama University, Okayama 700-8530, Japan
40Osaka City University, Osaka 588, Japan
41University of Oxford, Oxford OX1 3RH, United Kingdom
42University of Padova, Istituto Nazionale di Fisica Nucleare, Sezione di Padova-Trento, I-35131 Padova, Italy
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 29 October 2004; published 25 March 2005)
We present a measurement of the mass dependence of the forward-backward charge asymmetry (AFB) foreepairs produced via an intermediateZ=with massMee>40 GeV=c2. We study the constraints on theZ-quark couplings imposed by our measurement. We analyze an integrated luminosity of72 pb1 collected by the CDF-II detector in pp collisions at
ps
1:96 TeV at the Fermilab Tevatron. A comparison of the uncorrectedAFBbetween data and standard model Monte Carlo gives good agreement with a 2=DOF of 15.7/15. The couplings measurements are also consistent with standard model predictions.
DOI: 10.1103/PhysRevD.71.052002 PACS numbers: 13.85.Qk, 12.15.Ji, 12.15.Mm, 12.38.Qk
I. INTRODUCTION
The reaction pp!‘‘, where ‘ is an isolated high-pT lepton, is mediated primarily by virtual photons at low values of dilepton invariant mass (M‘‘) [1,2], primarily by theZat M‘‘MZ, and by a combination of photons andZbosons outside these regions. The pres- ence of both vector and axial-vector couplings of electro-
weak bosons to fermions in the process qq! Z= !‘‘ gives rise to an asymmetry in the polar angle of the lepton momentum relative to the incoming quark momentum in the rest frame of the lepton pair.
At tree level, the process qq!‘‘ proceeds via an s-channel exchange of either a virtual photon or aZboson.
The neutral-current coupling of a fermionfto theZboson . . .
has vector and axial-vector components: JZffg fV gfA5 f, wheregfV andgfA are the vector and axial-vector couplings of the fermion to theZ respectively. The cou- pling of the same fermion to the photon is purely a vector coupling and its strength is proportional to the charge of the fermion Qf. The differential cross section for qq!
‘‘is obtained by squaring the matrix-element, integrat- ing over the azimuthal angle, averaging over the polariza- tion of the incoming particles, and summing over the spin and polarization of the final-state particles:
dqq !‘‘
dcos C2
2s fQ2‘Q2q1cos2
Q‘QqRes 2gqVg‘V1cos2 4gqAg‘Acos js j2gq2V gq2A g‘2V g‘2A 1cos2
8gqVgqAg‘Vg‘Acosg (1) whereCis the color factor,is the emission angle of the lepton (antilepton) relative to the quark (antiquark) in the rest frame of the lepton pair, and
s 1
cos2Wsin2W
s
sM2ZiZMZ: (2) The first and the third terms in Eq. (1) correspond to the pure and Z exchange, respectively, while the second term corresponds to the Z= interference. The angular dependence of the various terms is either cos or 1 cos2 . Thecosterms integrate to zero in the total cross section but induce the forward-backward asymmetry.
Let
RVV Q2‘Q2q2Q‘QqgqVg‘VRes g‘2Vgq2V gq2A js j2 (3)
RAAg‘2Agq2V gq2A js j2 (4) RVA32gqAg‘AQ‘QqRes 2gqVg‘Vjs j2: (5) Then the differential cross section is reduced to the follow- ing simple expression:
d
dcos C4 3
2 s Rf
3
81cos2 AFBcos
(6) where RfRVVRAA andAFBRRVA
f . The meaning of the quantitiesRfandAFBcan be clearly seen. Integrating Eq. (6) over cos, the first term in the square brackets integrates to unity, the second integrates to 0. Therefore totalCRfQED0 , where QED0 is the total QED cross section (the cross section if the Z0 exchange amplitude were absent). The quantityAFBcan be written as
AFB R1
0 d
dcosdcosR1
0 d
dcosdcos R1
1 d
dcosdcos FB
FB NFNB
NFNB (7)
and is identified as the forward-backward asymmetry, where NF is the number of forward (cos >0) events andNBis the number of backward (cos <0) events.
A measurement of AFB can constrain the properties of any additional non-standard model amplitudes contribut- ing to qq !‘‘ [3], and is complementary to direct searches for non-standard model amplitudes that look for an excess in the total cross section. This is particularly interesting for Mee above LEP II energies, where the measurement is unique to the Tevatron.
In addition, Eq. (1) shows that depending on the invari- ant mass, a different combination of vector and axial- vector couplings contribute to the differential cross section.
Consequently,AFBis a direct probe of the relative strengths of the coupling constants between the Z boson and the quarks. The invariant-mass dependence of AFB is also sensitive touanddquarks separately, unlike other precise measurements of light-quarkZcouplings in'Nscattering [4] and atomic parity violation [5] on heavy nuclei.
In this paper, a number of different comparisons be- tween the data and standard model expectations are pre- sented. The uncorrected Mee, cos, and AFB data distributions are compared with the output of our Monte Carlo and detector simulation. The first principal result is a measurement of AFB in 15 Mee bins using an unfolding analysis that does not assume a prior standard model AFB distribution. The second principal result is a measurement of three sets of parameters: the Z-quark couplings, the Z-electron couplings, andsin2W. In making each of these three measurements, the other parameters are held fixed with the values given by the standard model. The measured Z-quark couplings are then used to determine experimental correction factors for acceptance and efficiency of dielec- tron events. The correction factors are used for the mea- surement ofAFBwith standard model assumptions.
The previous measurement from the collider detector at Fermilab (CDF) [6] was made with the data taken between 1992 and 1995 using the Run I detector. The Run I mea- surement assumed a standard model AFB distribution for calculating efficiency and acceptance experimental correc- tion factors. The present measurement uses the dielectron data taken between March 2002 and January 2003 with the CDF-II detector, corresponding to an integrated luminosity of72 pb1.
The paper is structured as follows. A description of the detector and an overview of the analysis are given in Sec. II. Event selection and candidate events are discussed in Sec. III. The estimation and characteristics of the back-
grounds are described in Sec. IV. The acceptance and corrections for detector effects are described in Sec. V.
The systematic uncertainties are summarized in Sec. VI.
Finally, the results of the forward-backward asymmetry and coupling measurements are presented in Sec. VII.
II. OVERVIEW
This section begins with a discussion of aspects of the detector, triggers and data samples that are relevant to this measurement. The nature of Z= !eeevents in a hadron collider and the overall strategy of the analysis are presented. This paper uses a cylindrical coordinate system, with the positivezaxis oriented along the beamline in the direction of the proton’s momentum.
A. Detector and triggers
The collider detector at Fermilab (CDF-II) is a general- purpose detector designed to study the physics of pp collisions at
ps
1:96 TeV at the Fermilab Tevatron collider. Like most detectors used at high-energy colliders, it has a cylindrical geometry with axial and forward- backward symmetry. A diagram of the inner part of the CDF-II detector is shown in Fig. 1. The innermost part of the detector contains an integrated tracking system with a silicon detector and an open-cell drift chamber. A solenoi- dal magnet surrounding the tracking chambers provides a 1.4 T field aligned with the proton-beam axis. The inte- grated tracking system is surrounded by calorimeters which cover 2 in azimuth and from 3:6 to 3.6 in pseudorapidity, )det (see Fig. 1). Outside of the calorim- eters is a muon system with coverage from1:5to 1.5 in )det. The CDF-II detector is a major upgrade to the detec- tor that took data until 1996. The entire tracking system subtendingj)detj<2and the plug calorimeter subtending 1:1<j)detj<3:6have been replaced to handle the higher rate of collisions and increase the capabilities for physics analyses in Run II. This analysis uses the open-cell drift chamber called the central outer tracker (COT) and the calorimeters. A more detailed detector description can be found in Refs. [7,8], and a description of the upgraded detector can be found in Ref. [9].
The COT detector [10] is a 96 layer, 3.2 m long open-cell drift chamber which, combined with the solenoid, is used to measure the momenta of charged particles withj)detj<
1. The detector extends from a radius of 40 cm to a radius of 137 cm. The 96 layers are divided into eight ‘‘super- layers,’’ which alternate between superlayers where the wires are axial (i.e., parallel to thezaxis) and superlayers where the wires have a2stereo angle, providing three- dimensional tracking. The calorimeter consists of a lead- scintillator electromagnetic (EM) compartment with shower position detection backed by an iron-scintillator hadronic compartment. The calorimeters are segmented in projective )det*towers pointing to the nominal inter- action point, at z0. While the central calorimeter
(j)detj<1:1) is retained mostly unchanged from Run I [11–15], the plug calorimeter [16] with1:1<j)detj<3:6 is a major component of the Run II upgrade (Fig. 2), and largely follows the design of the central detector. Since the calorimeter segmentation is coarse compared to the dimen- sions of an electron shower, position detectors (shower maximum detectors, CES in the central region and PES in the plug region) are placed at a depth of approximately six radiation lengths, roughly the position of the shower maximum, inside the EM calorimeters. These detectors measure the position and profile of the showers and help differentiate electrons from hadrons.
The trigger system has undergone a complete redesign as a result of the accelerator and detector upgrades. The CDF trigger is a three-level system that selects events out of a 2.5 MHz crossing rate to be written to magnetic tape at a rate of75 Hz. The first two levels [17] are composed of custom electronics with data paths separate from the data acquisition system. The third level [18] receives the com- plete detector information from the data acquisition system and runs a version of the reconstruction software optimized for speed on a farm of commercial computers. TheZ=
FIG. 1 (color online). One quadrant of the CDF-II tracking and calorimetric detectors. The detectors have axial and reflective symmetry about z0. CDF uses a cylindrical coordinate sys- tem with thez(longitudinal) axis along the proton-beam direc- tion;ris the transverse coordinate, and*is the azimuthal angle.
The detector pseudorapidity is defined as )det lntandet2 , wheredetis the polar angle relative to the proton-beam direc- tion measured fromz0. The event pseudorapidity is defined as)evt lntanevt2 , whereevt is the polar angle measured from the nominal pp collision point inz. The transverse mo- mentum (pT) and energy (ET) are the components projected onto the plane perpendicular to the beam axis (pTpsin;ET Esin). The missing transverse energy, E6 T, is defined as the magnitude of$iEiTn^i, wheren^iis a unit vector in the perpen- dicular plane that points from the beamline to theith calorimeter tower.
. . .
events used in this measurement are selected by high-ET central electron triggers. At Level 1, electrons are selected by the presence of an energy deposition ofET>8 GeVin an EM calorimeter tower and a matching two-dimensional (r–*plane) track withpT >8 GeV=creconstructed in the COT by trigger electronics called the eXtremely Fast Tracker (XFT) [19]. At Level 2, the electron energy is reconstructed in a cluster of EM towers and is required to haveET>16 GeV. At Level 3, a reconstructed EM cluster with ET>18 GeV and a matching three-dimensional track withpT>9 GeV=care required. At each level, the energy in the hadronic towers just behind the EM tower or cluster is required to be less than 12.5% of the EM energy.
Another trigger path that does not require a hadronic energy fraction is added to this measurement in order to
improve the trigger efficiency for central electrons with very highET. The second trigger path has not added any events to the current sample, but will be important if events are found with very high masses. The integrated luminosity of the data sample for this analysis is 724 pb1.
B. Data samples
Four data samples are employed in this analysis. These are described briefly below and in more detail in subse- quent sections.
(a) Z=!ee sample: —A sample of 5200 dielec- tron candidates is used to measureAFB, calibrate the energy scale and resolution of the EM calorimeter, and study the material in the tracking volume.
(b) W !e' sample: —A sample of 38 000 W !e' candidates, where the electron is reconstructed in the central calorimeter, is used to study the material in the tracking volume, to calibrate the relative calorimeter response within a central tower, and to check charge biases in measuring electrons.
(c) Inclusive electron sample: —A sample of 3 million central electron candidates with ET>8 GeV is used to calibrate the relative response of the central EM calorimeter towers.
(d) Dijet samples: —A sample of one million dijet events (events with at least two jets, each withET>
20 GeV) is used to measure the rate at which jets fake an electron signature and to estimate the dijet background. A jet is defined as a cluster of energy reconstructed in the calorimeter. Triggers for the sample require a calorimeter tower with ET>
5 GeVat Level 1, a calorimeter cluster withET>
15 GeV at Level 2, and a reconstructed jet with ET>20 GeVat Level 3. Because of the high cross section, only one in roughly 400 events on average were randomly selected to be recorded for this trigger. Jet samples with higher trigger thresholds (50 GeV, 70 GeV, and 100 GeV at Level 3) are also used to cross-check the fake rate for a trigger bias.
C. Monte Carlo samples
Monte Carlo generation and detector simulation are used to measure the acceptance for the Drell-Yan process, model the effect of radiation and detector resolution, de- termine the characteristics and amount of background in the data sample, and understand systematic uncertainties on theAFBmeasurement. PYTHIA [20] and HERWIG [21]
generators with CTEQ5L PDFs [22] are used for most of the samples. These generate processes at leading-order and incorporate initial- and final-state QCD and QED radiation via their parton-shower algorithms (HERWIG does not include final-state QED radiation). PYTHIA is tuned so that the underlying event (the remaining pp fragments FIG. 2. Cross section of upper part of plug calorimeter (top),
and transverse segmentation, showing physical and trigger tow- ers in a 30* section (bottom). The logical segmentation for clustering purposes is the same except in the outer two rings ( >30), where two neighboring (in azimuth) 7.5 towers are merged to match the 15 segmentation of the central and wall calorimeters behind them.
from the collision) and thepT spectrum ofZbosons agree with the CDF data [23]. Two matrix-element generators, WGAMMA [24] and ALPGEN [25], are used to check the WX!e'X background estimate from PYTHIA, where X is a photon or hadronic jet. The generator WGAMMA calculates the cross section of thepp!W process. It uses electroweak helicity amplitudes for W production and radiative W boson decays, including all interference terms. ALPGEN performs the calculation of the matrix-element for the production of Wquark and Wgluon final states. The detector simulation models the decay of generated particles and their interactions with the various elements of the CDF detector. A full GEANT3 [26]
simulation is used to simulate the tracking volume. A parameterized simulation is used for the calorimeters and muon chambers. Comparisons between the data and Monte Carlo simulation are discussed in Sec. III D.
There are nine Monte Carlo samples used in this analy- sis, which are briefly described below.
(a) Z= !ee sample: A sample generated with PYTHIA is used to calculate corrections due to acceptance, bremsstrahlung, and energy resolution, and to estimate the systematic uncertainties due to the energy scale and resolution. A quarter of the sample was generated withMZ=>105 GeV=c2to reduce the statistical uncertainties associated with the Monte Carlo sample in the high-mass region.
(b) Z= !ee sample for material systematics:
Three PYTHIA samples are used to estimate the change in the measured AFB between the default simulation and a modified simulation which adds or subtracts 1.5% radiation length (X0) of copper in a cylinder in the central region and16X0 of iron on the face of the plug calorimeter. QCD fragmentation is turned off for these samples in order to save CPU time.
(c) Z= !00 sample:A PYTHIA sample is used to estimate the background due toZ=!00. TAUOLA [27] is used to decay0’s.
(d) Dijet sample: —A PYTHIA sample with all2!2 processes is used to understand the characteristics of the dijet background. A lower limit ofpT >18 GeV on the transverse momentum in the rest frame of the hard interaction is applied.
(e) ttsample: A HERWIG sample is used to estimate the background due tottproduction.
(f ) Diboson samples: A sample with WW production and a sample with WZ production are generated using PYTHIA and used to estimate the diboson backgrounds.
(g) W!e' sample: A PYTHIA sample is used to estimate the background due to the inclusive W production.
(h) W!e'sample:A WGAMMA sample is used to cross-check the background due to W production.
(i) Wq=g!e'q=gsample:An ALPGEN sam- ple is used to estimate the background due to W quark or gluon production.
D. Strategy of analysis
This analysis focuses on ee pair production via an intermediate Z=. The goal of this analysis is to measure AFB as a function of the invariant mass of the dielectron pair. The dielectron sample is chosen because of the low backgrounds and the good polar angle coverage of elec- trons in the CDF-II detector.
When the incoming quarks participating in the Drell- Yan process have no transverse momentum relative to their parent baryons,in Eq. (6) is determined unambiguously from the four-momenta of the electrons by calculating the angle that the electron makes with the proton-beam in the center-of-mass frame of the electron-positron pair. When either of the incoming quarks has significant transverse momentum, however, there exists an ambiguity in the four- momenta of the incoming quarks in the frame of the electron-positron pair, since one cannot determine the four-momenta of the quark and antiquark individually (see Fig. 3). The Collins-Soper formalism [28] is adopted to minimize the effects of the transverse momentum of the incoming quarks in Eq. (6). (The magnitude of the effect in the Collins-Soper frame is discussed in Sec. VII B.) In this formalism, the polar axis is defined as the bisector of the proton-beam momentum and the negative of the anti-pro- ton-beam momentum when they are boosted into the center-of-mass frame of the electron-positron pair. The variable is defined as the angle between the electron
p
p − q
− q
γ, g
* Z γ,
FIG. 3. Diagram of pp!Z=, where one of the quarks radiates a gluon or photon imparting transverse momentum to the quark. Once the quarks annihilate toZ=, the source of the transverse momentum is ambiguous.
. . .
and the polar axis. Let Q (QT) be the four-momentum (transverse momentum) of the electron-positron pair, P1 be the four-momentum of the electron, andP2be the four- momentum of the positron, all measured in the lab frame.
Thencos is given by
cos 2
Q2Q2Q2T
q P1P2 P1P2 ; (8) where Pi p12P0iP3i , and P0 and P3 represent the energy and the longitudinal component of the momentum, respectively. Forward events are defined as havingcos>
0and backward events are defined as havingcos<0.
The AFB measurement is made in 15 bins of Mee be- tween 40 GeV=c2 and 600 GeV=c2. The bin sizes are chosen based on the detectorMeeresolution and the rela- tive Drell-Yan cross sections in each bin. Once the event selection has been made, the estimated number of forward and backward background events are subtracted from the candidate sample in each Mee bin. The raw forward- backward asymmetry (ArawFB) is calculated by applying Eq. (7) to the background-subtracted sample.
The goal is to connect what we measure in the detector after background subtraction (ArawFB) to theoretical calcula- tions (AphysFB ). If the detector simulation is available, a direct comparison can be made between the uncorrected data and a model prediction. These comparisons are made in Sec.
VII A. If the simulation is not available, the trueAphysFB must be unfolded fromArawFB.ArawFB must be corrected for detector acceptances and efficiencies (which sculpt the cos dis- tribution) and for smearing effects (which move events betweenMeebins) to obtainAphysFB , which can be compared directly to theoretical calculations. TheMeebin migration near theZpole is not negligible, which makes it difficult to unfold AphysFB in those bins. Performing an unconstrained unfolding analysis in those bins results in large uncertain- ties, while applying standard model or other constraints can bias the result. Two different unfolding analyses are performed to reconstruct AphysFB with different constraints.
Both unfolding analyses assume the standard modeldMd
eeto be able to calculate the event migration effects. The un- certainties associated with systematic effects are estimated by varying the magnitude of these effects in the Monte Carlo simulation and recalculating the results for each analysis.
The first and least constrained analysis is performed by fitting for AphysFB with a smoothing constraint. The accep- tance and event migration are parameterized (Sec. V D) to transformAphysFB intoArawFB,
ArawFB igA; i ; (9) where A fAphysFB 1;AphysFB 2;. . .;AphysFB 15g: (10) The probability, for a given AFB, to find a number of
forward and backward events is the binomial probability (PAFB; NF; NB). The maximum likelihood method is used to obtain the 15 values of AphysFB or A (Sec. VII C), where the negative log likelihood with a smoothing con- straint for bins near theZpole is defined as
X15
i1
logPgA; i ; NFi; NiB 6X9
i2
SAi; (11)
where Ai fAphysFB i1;AphysFB i;AphysFB i1g; (12) SAiis a regularization function, and6is the regulariza- tion parameter. This analysis makes no assumptions about the shape of AFB (aside from it being smooth near theZ pole), but it has the largest uncertainties.
In a second analysis, the parameterized acceptance and event migration are also used for the measurement of the Z-quark and Z-electron coupling constants, andsin2effW . We vary the couplings at generator-level and perform a2 fit between the smeared theoretical calculations and ArawFB to extract the couplings. This analysis is described in detail in Sec. VII D.
Continuing with the second analysis, AFBcan be mea- sured by assuming the standard modelAFBshape with the measured Z-quark couplings. In this method, acceptance correction factors (acor) are used to correct the number of forward and backward events in eachMeebin. The correc- tion factor accounts for the effects of detector acceptance and efficiency, and bin migration (Sec. V E). These correc- tion factors depend on the input AphysFB that is used to calculate them. To constrain the standard model bias, the inputAphysFB is constrained to the prediction with uncertain- ties from theZ-quark coupling analysis. ThenAphysFB can be calculated directly using the correction factors (Sec.
VII E). Equation (7) can be rewritten:
AiFBdMd i dMd i
dMd i dMd i ; (13) where
d dM
i
NiBi
'MiLacor i: (14) In Eq. (14),'Miis the size of thei-th mass bin, andLis the integrated luminosity. NN andBB are the num- ber of candidate and estimated background events in the forward (backward) region, respectively. Canceling com- mon factors, the forward-backward asymmetry can be written as
AiFB
NiBi
acori NaiBi cori
NiBi
acori NaiBi cori
: (15)
The analysis using correction factors has smaller uncer- tainties than the unconstrained method, but it assumes no
