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Indirect measurement of $\sin^{2} θ_{W}$ (or $M_{W}$ ) using $μ^{+} μ^{-}$ pairs from $γ^{*} / Z$ bosons produced in $p \bar{p}$ collisions at a center-of-momentum energy of 1.96 TeV

T. Aaltonen²¹, S. Amerio^39b,39a, D. Amidei³¹, A. Anastassov^15,w, A. Annovi¹⁷, J. Antos¹², G. Apollinari¹⁵, J. A. Appel¹⁵, T. Arisawa⁵² et al.

A. Artikov¹³, J. Asaadi⁴⁷, W. Ashmanskas¹⁵, B. Auerbach², A. Aurisano⁴⁷, F. Azfar³⁸, W. Badgett¹⁵, T. Bae²⁵, A. Barbaro-Galtieri²⁶, V. E. Barnes⁴³, B. A. Barnett²³, P. Barria^41a, P. Bartos¹², M. Bauce^39b,39a, F. Bedeschi^41a, S. Behari¹⁵, G. Bellettini^41b,41a, J. Bellinger⁵⁴, D. Benjamin¹⁴, A. Beretvas¹⁵, A. Bhatti⁴⁵, K. R. Bland⁵, B. Blumenfeld²³, A. Bocci¹⁴, A. Bodek⁴⁴, D. Bortoletto⁴³, J. Boudreau⁴², A. Boveia¹¹, L. Brigliadori^6b,6a, C. Bromberg³², E. Brucken²¹, J. Budagov¹³, H. S. Budd⁴⁴, K. Burkett¹⁵, G. Busetto^39b,39a, P. Bussey¹⁹, P. Butti^41b,41a, A. Buzatu¹⁹, A. Calamba¹⁰, S. Camarda⁴, M. Campanelli²⁸, F. Canelli^11,dd, B. Carls²², D. Carlsmith⁵⁴, R. Carosi^41a, S. Carrillo^16,m, B. Casal^9,k, M. Casarsa^48a, A. Castro^6b,6a, P. Catastini²⁰, D. Cauz^48b,48c,48a, V. Cavaliere²², M. Cavalli-Sforza⁴, A. Cerri^26,f, L. Cerrito^28,r, Y. C. Chen¹, M. Chertok⁷, G. Chiarelli^41a, G. Chlachidze¹⁵, K. Cho²⁵, D. Chokheli¹³, A. Clark¹⁸, C. Clarke⁵³, M. E. Convery¹⁵, J. Conway⁷, M. Corbo^15,z, M. Cordelli¹⁷, C. A. Cox⁷, D. J. Cox⁷, M. Cremonesi^41a, D. Cruz⁴⁷, J. Cuevas^9,y, R. Culbertson¹⁵, N. d’Ascenzo^15,v, M. Datta^15,gg, P. de Barbaro⁴⁴, L. Demortier⁴⁵, M. Deninno^6a, M. D’Errico^39b,39a, F. Devoto²¹, A. Di Canto^41b,41a, B. Di Ruzza^15,q, J. R. Dittmann⁵, S. Donati^41b,41a, M. D’Onofrio²⁷, M. Dorigo^48d,48a, A. Driutti^48b,48c,48a, K. Ebina⁵², R. Edgar³¹, A. Elagin⁴⁷, R. Erbacher⁷, S. Errede²², B. Esham²², S. Farrington³⁸, J. P. Fernández Ramos²⁹, R. Field¹⁶, G. Flanagan^15,t, R. Forrest⁷, M. Franklin²⁰, J. C. Freeman¹⁵, H. Frisch¹¹, Y. Funakoshi⁵², C. Galloni^41b,41a, A. F. Garfinkel⁴³, P. Garosi^41c,41a, H. Gerberich²², E. Gerchtein¹⁵, S. Giagu^46a, V. Giakoumopoulou³, K. Gibson⁴², C. M. Ginsburg¹⁵, N. Giokaris³, P. Giromini¹⁷, G. Giurgiu²³, V. Glagolev¹³, D. Glenzinski¹⁵, M. Gold³⁴, D. Goldin⁴⁷, A. Golossanov¹⁵, G. Gomez⁹, G. Gomez-Ceballos³⁰, M. Goncharov³⁰, O. González López²⁹, I. Gorelov³⁴, A. T. Goshaw¹⁴, K. Goulianos⁴⁵, E. Gramellini^6a, S. Grinstein⁴, C. Grosso-Pilcher¹¹, R. C. Group^51,15, J. Guimaraes da Costa²⁰, S. R. Hahn¹⁵, J. Y. Han⁴⁴, F. Happacher¹⁷, K. Hara⁴⁹, M. Hare⁵⁰, R. F. Harr⁵³, T. Harrington-Taber^15,n, K. Hatakeyama⁵, C. Hays³⁸, J. Heinrich⁴⁰, M. Herndon⁵⁴, A. Hocker¹⁵, Z. Hong⁴⁷, W. Hopkins^15,g, S. Hou¹, R. E. Hughes³⁵, U. Husemann⁵⁵, M. Hussein^32,bb, J. Huston³², G. Introzzi^41e,41f,41a, M. Iori^46b,46a, A. Ivanov^7,p, E. James¹⁵, D. Jang¹⁰, B. Jayatilaka¹⁵, E. J. Jeon²⁵, S. Jindariani¹⁵, M. Jones⁴³, K. K. Joo²⁵, S. Y. Jun¹⁰, T. R. Junk¹⁵, M. Kambeitz²⁴, T. Kamon^25,47, P. E. Karchin⁵³, A. Kasmi⁵, Y. Kato^37,o, W. Ketchum^11,hh, J. Keung⁴⁰, B. Kilminster^15,dd, D. H. Kim²⁵, H. S. Kim²⁵, J. E. Kim²⁵, M. J. Kim¹⁷, S. H. Kim⁴⁹, S. B. Kim²⁵, Y. J. Kim²⁵, Y. K. Kim¹¹, N. Kimura⁵², M. Kirby¹⁵, K. Knoepfel¹⁵, K. Kondo^52,a, D. J. Kong²⁵, J. Konigsberg¹⁶, A. V. Kotwal¹⁴, M. Kreps²⁴, J. Kroll⁴⁰, M. Kruse¹⁴, T. Kuhr²⁴, M. Kurata⁴⁹, A. T. Laasanen⁴³, S. Lammel¹⁵, M. Lancaster²⁸, K. Lannon^35,x, G. Latino^41c,41a, H. S. Lee²⁵, J. S. Lee²⁵, S. Leo^41a, S. Leone^41a, J. D. Lewis¹⁵, A. Limosani^14,s, E. Lipeles⁴⁰, A. Lister^18,b, H. Liu⁵¹, Q. Liu⁴³, T. Liu¹⁵, S. Lockwitz⁵⁵, A. Loginov⁵⁵, D. Lucchesi^39b,39a, A. Lucà¹⁷, J. Lueck²⁴, P. Lujan²⁶, P. Lukens¹⁵, G. Lungu⁴⁵, J. Lys²⁶, R. Lysak^12,e, R. Madrak¹⁵, P. Maestro^41c,41a, S. Malik⁴⁵, G. Manca^27,c, A. Manousakis-Katsikakis³, L. Marchese^6a,ii, F. Margaroli^46a, P. Marino^41d,41a, M. Martínez⁴, K. Matera²², M. E. Mattson⁵³, A. Mazzacane¹⁵, P. Mazzanti^6a, R. McNulty^27,j, A. Mehta²⁷, P. Mehtala²¹, C. Mesropian⁴⁵, T. Miao¹⁵, D. Mietlicki³¹, A. Mitra¹, H. Miyake⁴⁹, S. Moed¹⁵, N. Moggi^6a, C. S. Moon^15,z, R. Moore^15,ee,ff, M. J. Morello^41d,41a, A. Mukherjee¹⁵, Th. Muller²⁴, P. Murat¹⁵, M. Mussini^6b,6a, J. Nachtman^15,n, Y. Nagai⁴⁹, J. Naganoma⁵², I. Nakano³⁶, A. Napier⁵⁰, J. Nett⁴⁷, C. Neu⁵¹, T. Nigmanov⁴², L. Nodulman², S. Y. Noh²⁵, O. Norniella²², L. Oakes³⁸, S. H. Oh¹⁴, Y. D. Oh²⁵, I. Oksuzian⁵¹, T. Okusawa³⁷, R. Orava²¹, L. Ortolan⁴, C. Pagliarone^48a, E. Palencia^9,f, P. Palni³⁴, V. Papadimitriou¹⁵, W. Parker⁵⁴, G. Pauletta^48b,48c,48a, M. Paulini¹⁰, C. Paus³⁰, T. J. Phillips¹⁴, G. Piacentino^41a, E. Pianori⁴⁰, J. Pilot⁷, K. Pitts²², C. Plager⁸, L. Pondrom⁵⁴, S. Poprocki^15,g, K. Potamianos²⁶, A. Pranko²⁶, F. Prokoshin^13,aa, F. Ptohos^17,h, G. Punzi^41b,41a, N. Ranjan⁴³, I. Redondo Fernández²⁹, P. Renton³⁸, M. Rescigno^46a, F. Rimondi^6a,a, L. Ristori^41a,15, A. Robson¹⁹, T. Rodriguez⁴⁰, S. Rolli^50,i, M. Ronzani^41b,41a, R. Roser¹⁵, J. L. Rosner¹¹, F. Ruffini^41c,41a, A. Ruiz⁹, J. Russ¹⁰, V. Rusu¹⁵, W. K. Sakumoto⁴⁴, Y. Sakurai⁵², L. Santi^48b,48c,48a, K. Sato⁴⁹, V. Saveliev^15,v, A. Savoy-Navarro^15,z, P. Schlabach¹⁵, E. E. Schmidt¹⁵, T. Schwarz³¹, L. Scodellaro⁹, F. Scuri^41a, S. Seidel³⁴, Y. Seiya³⁷, A. Semenov¹³, F. Sforza^41b,41a, S. Z. Shalhout⁷, T. Shears²⁷, P. F. Shepard⁴², M. Shimojima^49,u, M. Shochet¹¹, I. Shreyber-Tecker³³, A. Simonenko¹³, K. Sliwa⁵⁰, J. R. Smith⁷, F. D. Snider¹⁵, H. Song⁴², V. Sorin⁴, R. St. Denis¹⁹, M. Stancari¹⁵, D. Stentz^15,w, J. Strologas³⁴, Y. Sudo⁴⁹, A. Sukhanov¹⁵, I. Suslov¹³, K. Takemasa⁴⁹, Y. Takeuchi⁴⁹, J. Tang¹¹, M. Tecchio³¹, P. K. Teng¹, J. Thom^15,g, E. Thomson⁴⁰, V. Thukral⁴⁷, D. Toback⁴⁷, S. Tokar¹², K. Tollefson³², T. Tomura⁴⁹, D. Tonelli^15,f, S. Torre¹⁷, D. Torretta¹⁵, P. Totaro^39a, M. Trovato^41d,41a, F. Ukegawa⁴⁹, S. Uozumi²⁵, F. Vázquez^16,m, G. Velev¹⁵, C. Vellidis¹⁵, C. Vernieri^41d,41a, M. Vidal⁴³, R. Vilar⁹, J. Vizán^9,cc, M. Vogel³⁴, G. Volpi¹⁷, P. Wagner⁴⁰, R. Wallny^15,k, S. M. Wang¹, D. Waters²⁸, W. C. Wester III¹⁵, D. Whiteson^40,d, A. B. Wicklund², S. Wilbur⁷, H. H. Williams⁴⁰, J. S. Wilson³¹, P. Wilson¹⁵, B. L. Winer³⁵, P. Wittich^15,g, S. Wolbers¹⁵, H. Wolfe³⁵, T. Wright³¹, X. Wu¹⁸, Z. Wu⁵, K. Yamamoto³⁷, D. Yamato³⁷, T. Yang¹⁵, U. K. Yang²⁵, Y. C. Yang²⁵, W.-M. Yao²⁶, G. P. Yeh¹⁵, K. Yi^15,n, J. Yoh¹⁵, K. Yorita⁵², T. Yoshida^37,l, G. B. Yu¹⁴, I. Yu²⁵, A. M. Zanetti^48a, Y. Zeng¹⁴, C. Zhou¹⁴, and S. Zucchelli^6b,6a

¹Institute of Physics, Academia Sinica, Taipei, Taiwan 11529, Republic of China
²Argonne National Laboratory, Argonne, Illinois 60439, USA
³University of Athens, 157 71 Athens, Greece
⁴Institut de Fisica d’Altes Energies, ICREA, Universitat Autonoma de Barcelona, E-08193 Bellaterra (Barcelona), Spain
⁵Baylor University, Waco, Texas 76798, USA
^6aIstituto Nazionale di Fisica Nucleare Bologna, I-40127 Bologna, Italy
^6bUniversity of Bologna, I-40127 Bologna, Italy
⁷University of California, Davis, Davis, California 95616, USA
⁸University of California, Los Angeles, Los Angeles, California 90024, USA
⁹Instituto de Fisica de Cantabria, CSIC-University of Cantabria, 39005 Santander, Spain
¹⁰Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA
¹¹Enrico Fermi Institute, University of Chicago, Chicago, Illinois 60637, USA
¹²Institute of Experimental Physics, Comenius University, 842 48 Bratislava, Slovakia; 040 01 Kosice, Slovakia
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 02138, USA
²¹University of Helsinki, Helsinki FIN-00014, Finland and Helsinki Institute of Physics, Helsinki FIN-00014, Finland
²²University of Illinois, Urbana, Illinois 61801, USA
²³The Johns Hopkins University, Baltimore, Maryland 21218, USA
²⁴Institut für Experimentelle Kernphysik, Karlsruhe Institute of Technology, D-76131 Karlsruhe, Germany
²⁵Center for High Energy Physics, Kyungpook National University, Daegu 702-701, Korea; Seoul National University, Seoul 151-742, Korea; Sungkyunkwan University, Suwon 440-746, Korea; Korea Institute of Science and Technology Information, Daejeon 305-806, Korea; Chonnam National University, Gwangju 500-757, Korea; Chonbuk National University, Jeonju 561-756, Korea, and Ewha Womans University, Seoul 120-750, Korea
²⁶Ernest Orlando Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
²⁷University of Liverpool, Liverpool L69 7ZE, United Kingdom
²⁸University College London, London WC1E 6BT, United Kingdom
²⁹Centro de Investigaciones Energeticas Medioambientales y Tecnologicas, E-28040 Madrid, Spain
³⁰Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
³¹University of Michigan, Ann Arbor, Michigan 48109, USA
³²Michigan State University, East Lansing, Michigan 48824, USA
³³Institution for Theoretical and Experimental Physics (ITEP), Moscow 117259, Russia
³⁴University of New Mexico, Albuquerque, New Mexico 87131, USA
³⁵The Ohio State University, Columbus, Ohio 43210, USA
³⁶Okayama University, Okayama 700-8530, Japan
³⁷Osaka City University, Osaka 558-8585, Japan
³⁸University of Oxford, Oxford OX1 3RH, United Kingdom
^39aIstituto Nazionale di Fisica Nucleare, Sezione di Padova, I-35131 Padova, Italy
^39bUniversity of Padova, I-35131 Padova, Italy
⁴⁰University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
^41aIstituto Nazionale di Fisica Nucleare Pisa, I-56127 Pisa, Italy
^41bUniversity of Pisa, I-56127 Pisa, Italy
^41cUniversity of Siena, I-56127 Pisa, Italy
^41dScuola Normale Superiore, I-56127 Pisa, Italy
^41eINFN Pavia, I-27100 Pavia, Italy
^41fUniversity of Pavia, I-27100 Pavia, Italy
⁴²University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
⁴³Purdue University, West Lafayette, Indiana 47907, USA
⁴⁴University of Rochester, Rochester, New York 14627, USA
⁴⁵The Rockefeller University, New York, New York 10065, USA
^46aIstituto Nazionale di Fisica Nucleare, Sezione di Roma 1, I-00185 Roma, Italy
^46bSapienza Università di Roma, I-00185 Roma, Italy
⁴⁷Mitchell Institute for Fundamental Physics and Astronomy, Texas A&M University, College Station, Texas 77843, USA
^48aIstituto Nazionale di Fisica Nucleare Trieste, I-33100 Udine, Italy
^48bGruppo Collegato di Udine, I-33100 Udine, Italy
^48cUniversity of Udine, I-33100 Udine, Italy
^48dUniversity of Trieste, I-34127 Trieste, Italy
⁴⁹University of Tsukuba, Tsukuba, Ibaraki 305, Japan
⁵⁰Tufts University, Medford, Massachusetts 02155, USA
⁵¹University of Virginia, Charlottesville, Virginia 22906, USA
⁵²Waseda University, Tokyo 169, Japan
⁵³Wayne State University, Detroit, Michigan 48201, USA
⁵⁴University of Wisconsin, Madison, Wisconsin 53706, USA
⁵⁵Yale University, New Haven, Connecticut 06520, USA

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Phys. Rev. D 89, 072005 – Published 4 April, 2014

DOI: https://doi.org/10.1103/PhysRevD.89.072005

Abstract

Drell-Yan lepton pairs are produced in the process $p \bar{p} \to μ^{+} μ^{-} + X$ through an intermediate $γ^{*} / Z$ boson. The forward-backward asymmetry in the polar-angle distribution of the $μ^{-}$ as a function of the invariant mass of the $μ^{+} μ^{-}$ pair is used to obtain the effective leptonic determination $\sin^{2} θ_{eff}^{lept}$ of the electroweak-mixing parameter $\sin^{2} θ_{W}$ , from which the value of $\sin^{2} θ_{W}$ is derived assuming the standard model. The measurement sample, recorded by the Collider Detector at Fermilab (CDF), corresponds to $9.2 {fb}^{- 1}$ of integrated luminosity from $p \bar{p}$ collisions at a center-of-momentum energy of 1.96 TeV, and is the full CDF Run II data set. The value of $\sin^{2} θ_{eff}^{lept}$ is found to be $0.2315 \pm 0.0010$ , where statistical and systematic uncertainties are combined in quadrature. When interpreted within the context of the standard model using the on-shell renormalization scheme, where $\sin^{2} θ_{W} = 1 - M_{W}^{2} / M_{Z}^{2}$ , the measurement yields $\sin^{2} θ_{W} = 0.2233 \pm 0.0009$ , or equivalently a $W$ -boson mass of $80.365 \pm 0.047 GeV / c^{2}$ . The value of the $W$ -boson mass is in agreement with previous determinations in electron-positron collisions and at the Tevatron collider.