Measurement of the forward-backward asymmetries in the production of Ξ and Ω baryons in p p ¯ collisions
aa r X i v : . [ h e p - e x ] M a y FERMILAB-PUB-16-168-E
Measurement of the forward-backward asymmetries in the production of Ξ and Ω baryons in p ¯ p collisions V.M. Abazov, B. Abbott, B.S. Acharya, M. Adams, T. Adams, J.P. Agnew, G.D. Alexeev, G. Alkhazov, A. Alton a , A. Askew, S. Atkins, K. Augsten, V. Aushev, Y. Aushev, C. Avila, F. Badaud, L. Bagby, B. Baldin, D.V. Bandurin, S. Banerjee, E. Barberis, P. Baringer, J.F. Bartlett, U. Bassler, V. Bazterra, A. Bean, M. Begalli, L. Bellantoni, S.B. Beri, G. Bernardi, R. Bernhard, I. Bertram, M. Besan¸con, R. Beuselinck, P.C. Bhat, S. Bhatia, V. Bhatnagar, G. Blazey, S. Blessing, K. Bloom, A. Boehnlein, D. Boline, E.E. Boos, G. Borissov, M. Borysova l , A. Brandt, O. Brandt, M. Brochmann, R. Brock, A. Bross, D. Brown, X.B. Bu, M. Buehler, V. Buescher, V. Bunichev, S. Burdin b , C.P. Buszello, E. Camacho-P´erez, B.C.K. Casey, H. Castilla-Valdez, S. Caughron, S. Chakrabarti, K.M. Chan, A. Chandra, E. Chapon, G. Chen, S.W. Cho, S. Choi, B. Choudhary, S. Cihangir ‡ , D. Claes, J. Clutter, M. Cooke k , W.E. Cooper, M. Corcoran, F. Couderc, M.-C. Cousinou, J. Cuth, D. Cutts, A. Das, G. Davies, S.J. de Jong,
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E. De La Cruz-Burelo, F. D´eliot, R. Demina, D. Denisov, S.P. Denisov, S. Desai, C. Deterre c , K. DeVaughan, H.T. Diehl, M. Diesburg, P.F. Ding, A. Dominguez, A. Dubey, L.V. Dudko, A. Duperrin, S. Dutt, M. Eads, D. Edmunds, J. Ellison, V.D. Elvira, Y. Enari, H. Evans, A. Evdokimov, V.N. Evdokimov, A. Faur´e, L. Feng, T. Ferbel, F. Fiedler, F. Filthaut,
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W. Fisher, H.E. Fisk, M. Fortner, H. Fox, J. Franc, S. Fuess, P.H. Garbincius, A. Garcia-Bellido, J.A. Garc´ıa-Gonz´alez, V. Gavrilov, W. Geng,
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C.E. Gerber, Y. Gershtein, G. Ginther, O. Gogota, G. Golovanov, P.D. Grannis, S. Greder, H. Greenlee, G. Grenier, Ph. Gris, J.-F. Grivaz, A. Grohsjean c , S. Gr¨unendahl, M.W. Gr¨unewald, T. Guillemin, G. Gutierrez, P. Gutierrez, J. Haley, L. Han, K. Harder, A. Harel, J.M. Hauptman, J. Hays, T. Head, T. Hebbeker, D. Hedin, H. Hegab, A.P. Heinson, U. Heintz, C. Hensel, I. Heredia-De La Cruz d , K. Herner, G. Hesketh f , M.D. Hildreth, R. Hirosky, T. Hoang, J.D. Hobbs, B. Hoeneisen, J. Hogan, M. Hohlfeld, J.L. Holzbauer, I. Howley, Z. Hubacek,
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V. Hynek, I. Iashvili, Y. Ilchenko, R. Illingworth, A.S. Ito, S. Jabeen m , M. Jaffr´e, A. Jayasinghe, M.S. Jeong, R. Jesik, P. Jiang ‡ , K. Johns, E. Johnson, M. Johnson, A. Jonckheere, P. Jonsson, J. Joshi, A.W. Jung o , A. Juste, E. Kajfasz, D. Karmanov, I. Katsanos, M. Kaur, R. Kehoe, S. Kermiche, N. Khalatyan, A. Khanov, A. Kharchilava, Y.N. Kharzheev, I. Kiselevich, J.M. Kohli, A.V. Kozelov, J. Kraus, A. Kumar, A. Kupco, T. Kurˇca, V.A. Kuzmin, S. Lammers, P. Lebrun, H.S. Lee, S.W. Lee, W.M. Lee, X. Lei, J. Lellouch, D. Li, H. Li, L. Li, Q.Z. Li, J.K. Lim, D. Lincoln, J. Linnemann, V.V. Lipaev ‡ , R. Lipton, H. Liu, Y. Liu, A. Lobodenko, M. Lokajicek, R. Lopes de Sa, R. Luna-Garcia g , A.L. Lyon, A.K.A. Maciel, R. Madar, R. Maga˜na-Villalba, S. Malik, V.L. Malyshev, J. Mansour, J. Mart´ınez-Ortega, R. McCarthy, C.L. McGivern, M.M. Meijer,
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A. Melnitchouk, D. Menezes, P.G. Mercadante, M. Merkin, A. Meyer, J. Meyer i , F. Miconi, N.K. Mondal, M. Mulhearn, E. Nagy, M. Narain, R. Nayyar, H.A. Neal, J.P. Negret, P. Neustroev, H.T. Nguyen, T. Nunnemann, J. Orduna, N. Osman, A. Pal, N. Parashar, V. Parihar, S.K. Park, R. Partridge e , N. Parua, A. Patwa j , B. Penning, M. Perfilov, Y. Peters, K. Petridis, G. Petrillo, P. P´etroff, M.-A. Pleier, V.M. Podstavkov, A.V. Popov, M. Prewitt, D. Price, N. Prokopenko, J. Qian, A. Quadt, B. Quinn, P.N. Ratoff, I. Razumov, I. Ripp-Baudot, F. Rizatdinova, M. Rominsky, A. Ross, C. Royon, P. Rubinov, R. Ruchti, G. Sajot, A. S´anchez-Hern´andez, M.P. Sanders, A.S. Santos h , G. Savage, M. Savitskyi, L. Sawyer, T. Scanlon, R.D. Schamberger, Y. Scheglov, H. Schellman,
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M. Schott, C. Schwanenberger, R. Schwienhorst, J. Sekaric, H. Severini, E. Shabalina, V. Shary, S. Shaw, A.A. Shchukin, V. Simak, P. Skubic, P. Slattery, G.R. Snow, J. Snow, S. Snyder, S. S¨oldner-Rembold, L. Sonnenschein, K. Soustruznik, J. Stark, N. Stefaniuk, D.A. Stoyanova, M. Strauss, L. Suter, P. Svoisky, M. Titov, V.V. Tokmenin, Y.-T. Tsai, D. Tsybychev, B. Tuchming, C. Tully, L. Uvarov, S. Uvarov, S. Uzunyan, R. Van Kooten, W.M. van Leeuwen, N. Varelas, E.W. Varnes, I.A. Vasilyev, A.Y. Verkheev, L.S. Vertogradov, M. Verzocchi, M. Vesterinen, D. Vilanova, P. Vokac, H.D. Wahl, M.H.L.S. Wang, J. Warchol, G. Watts, M. Wayne, J. Weichert, L. Welty-Rieger, M.R.J. Williams n , G.W. Wilson, M. Wobisch, D.R. Wood, T.R. Wyatt, Y. Xie, R. Yamada, S. Yang, T. Yasuda, Y.A. Yatsunenko, W. Ye, Z. Ye, H. Yin, K. Yip, S.W. Youn, J.M. Yu, J. Zennamo, T.G. Zhao, B. Zhou, J. Zhu, M. Zielinski, D. Zieminska, and L. Zivkovic (The D0 Collaboration ∗ ) LAFEX, Centro Brasileiro de Pesquisas F´ısicas, Rio de Janeiro, RJ 22290, Brazil Universidade do Estado do Rio de Janeiro, Rio de Janeiro, RJ 20550, Brazil Universidade Federal do ABC, Santo Andr´e, SP 09210, Brazil University of Science and Technology of China, Hefei 230026, People’s Republic of China Universidad de los Andes, Bogot´a, 111711, Colombia Charles University, Faculty of Mathematics and Physics,Center for Particle Physics, 116 36 Prague 1, Czech Republic Czech Technical University in Prague, 116 36 Prague 6, Czech Republic Institute of Physics, Academy of Sciences of the Czech Republic, 182 21 Prague, Czech Republic Universidad San Francisco de Quito, Quito, Ecuador LPC, Universit´e Blaise Pascal, CNRS/IN2P3, Clermont, F-63178 Aubi`ere Cedex, France LPSC, Universit´e Joseph Fourier Grenoble 1, CNRS/IN2P3,Institut National Polytechnique de Grenoble, F-38026 Grenoble Cedex, France CPPM, Aix-Marseille Universit´e, CNRS/IN2P3, F-13288 Marseille Cedex 09, France LAL, Univ. Paris-Sud, CNRS/IN2P3, Universit´e Paris-Saclay, F-91898 Orsay Cedex, France LPNHE, Universit´es Paris VI and VII, CNRS/IN2P3, F-75005 Paris, France CEA Saclay, Irfu, SPP, F-91191 Gif-Sur-Yvette Cedex, France IPHC, Universit´e de Strasbourg, CNRS/IN2P3, F-67037 Strasbourg, France IPNL, Universit´e Lyon 1, CNRS/IN2P3, F-69622 Villeurbanne Cedex,France and Universit´e de Lyon, F-69361 Lyon CEDEX 07, France III. Physikalisches Institut A, RWTH Aachen University, 52056 Aachen, Germany Physikalisches Institut, Universit¨at Freiburg, 79085 Freiburg, Germany II. Physikalisches Institut, Georg-August-Universit¨at G¨ottingen, 37073 G¨ottingen, Germany Institut f¨ur Physik, Universit¨at Mainz, 55099 Mainz, Germany Ludwig-Maximilians-Universit¨at M¨unchen, 80539 M¨unchen, Germany Panjab University, Chandigarh 160014, India Delhi University, Delhi-110 007, India Tata Institute of Fundamental Research, Mumbai-400 005, India University College Dublin, Dublin 4, Ireland Korea Detector Laboratory, Korea University, Seoul, 02841, Korea CINVESTAV, Mexico City 07360, Mexico Nikhef, Science Park, 1098 XG Amsterdam, the Netherlands Radboud University Nijmegen, 6525 AJ Nijmegen, the Netherlands Joint Institute for Nuclear Research, Dubna 141980, Russia Institute for Theoretical and Experimental Physics, Moscow 117259, Russia Moscow State University, Moscow 119991, Russia Institute for High Energy Physics, Protvino, Moscow region 142281, Russia Petersburg Nuclear Physics Institute, St. Petersburg 188300, Russia Instituci´o Catalana de Recerca i Estudis Avan¸cats (ICREA) and Institutde F´ısica d’Altes Energies (IFAE), 08193 Bellaterra (Barcelona), Spain Uppsala University, 751 05 Uppsala, Sweden Taras Shevchenko National University of Kyiv, Kiev, 01601, Ukaine Lancaster University, Lancaster LA1 4YB, United Kingdom Imperial College London, London SW7 2AZ, United Kingdom The University of Manchester, Manchester M13 9PL, United Kingdom University of Arizona, Tucson, Arizona 85721, USA University of California Riverside, Riverside, California 92521, USA Florida State University, Tallahassee, Florida 32306, USA Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA University of Illinois at Chicago, Chicago, Illinois 60607, USA Northern Illinois University, DeKalb, Illinois 60115, USA Northwestern University, Evanston, Illinois 60208, USA Indiana University, Bloomington, Indiana 47405, USA Purdue University Calumet, Hammond, Indiana 46323, USA University of Notre Dame, Notre Dame, Indiana 46556, USA Iowa State University, Ames, Iowa 50011, USA University of Kansas, Lawrence, Kansas 66045, USA Louisiana Tech University, Ruston, Louisiana 71272, USA Northeastern University, Boston, Massachusetts 02115, USA University of Michigan, Ann Arbor, Michigan 48109, USA Michigan State University, East Lansing, Michigan 48824, USA University of Mississippi, University, Mississippi 38677, USA University of Nebraska, Lincoln, Nebraska 68588, USA Rutgers University, Piscataway, New Jersey 08855, USA Princeton University, Princeton, New Jersey 08544, USA State University of New York, Buffalo, New York 14260, USA University of Rochester, Rochester, New York 14627, USA State University of New York, Stony Brook, New York 11794, USA Brookhaven National Laboratory, Upton, New York 11973, USA Langston University, Langston, Oklahoma 73050, USA University of Oklahoma, Norman, Oklahoma 73019, USA Oklahoma State University, Stillwater, Oklahoma 74078, USA Oregon State University, Corvallis, Oregon 97331, USA Brown University, Providence, Rhode Island 02912, USA University of Texas, Arlington, Texas 76019, USA Southern Methodist University, Dallas, Texas 75275, USA Rice University, Houston, Texas 77005, USA University of Virginia, Charlottesville, Virginia 22904, USA University of Washington, Seattle, Washington 98195, USA (Dated: May 11, 2016)We measure the forward-backward asymmetries A FB of charged Ξ and Ω baryons produced in p ¯ p collisions recorded by the D0 detector at the Fermilab Tevatron collider at √ s = 1 .
96 TeV as afunction of the baryon rapidity y . We find that the asymmetries A FB for charged Ξ and Ω baryonsare consistent with zero within statistical uncertainties. INTRODUCTION
We present a study of the forward-backward asymme-tries A FB for the production of charged Ξ and Ω baryonsin p ¯ p collisions at a center of mass energy √ s = 1 .
96 TeV,recorded by the D0 detector at the Fermilab Tevatroncollider.We previously performed a study of A FB for Λ and ¯Λproduction [1], where A FB is defined as the relative excessof Λ (¯Λ) baryons produced with longitudinal momentum p z in the p (¯ p ) direction. These results are in agreementwith the observations in a wide range of proton colli-sion experiments that the ¯Λ / Λ production ratio followsa universal function of the “rapidity loss” y p − y betweenthe beam proton and the produced ¯Λ or Λ baryon which ∗ with visitors from a Augustana College, Sioux Falls, SD 57197,USA, b The University of Liverpool, Liverpool L69 3BX, UK, c Deutshes Elektronen-Synchrotron (DESY), Notkestrasse 85, Ger-many, d CONACyT, M-03940 Mexico City, Mexico, e SLAC, MenloPark, CA 94025, USA, f University College London, London WC1E6BT, UK, g Centro de Investigacion en Computacion - IPN, CP07738 Mexico City, Mexico, h Universidade Estadual Paulista, S˜aoPaulo, SP 01140, Brazil, i Karlsruher Institut f¨ur Technologie (KIT)- Steinbuch Centre for Computing (SCC), D-76128 Karlsruhe, Ger-many, j Office of Science, U.S. Department of Energy, Washing-ton, D.C. 20585, USA, k American Association for the Advance-ment of Science, Washington, D.C. 20005, USA, l Kiev Institute forNuclear Research (KINR), Kyiv 03680, Ukraine, m University ofMaryland, College Park, MD 20742, USA, n European Orgnaizationfor Nuclear Research (CERN), CH-1211 Geneva, Switzerland and o Purdue University, West Lafayette, IN 47907, USA. ‡ Deceased. does not depend significantly on √ s or on the nature ofthe target p , ¯ p , Be, or Pb (see Ref. [1] and referencestherein). These results support the view that a strangequark produced directly in the hard scattering of point-like partons, or indirectly in the subsequent showering,can coalesce with a diquark remnant of the beam particleto produce a Λ baryon with a probability that increasesas the rapidity difference between the incoming protonand outgoing Λ baryon decreases.If this hypothesis is correct, we also expect A FB > c (¯Λ c ), and Λ b (¯Λ b ) production in which a c or b quarkcan coalesce with a diquark form the proton. For the B mesons and Ξ and Ω baryons, we expect A F B ≈ A FB ( B − , B + ) [2] and A FB (Λ b , ¯Λ b ) [3].In this article, we present measurements of theforward-backward asymmetries of Ξ ∓ and Ω ∓ produc-tion, where we use the notation Ξ + ≡ Ξ − and Ω + ≡ Ω − .The Ξ − and Ξ + baryons are defined as “forward” if their p z points in the p or ¯ p direction, respectively. The asym-metry A FB is defined as A FB ≡ σ F (Ξ − ) − σ B (Ξ − ) + σ F (Ξ + ) − σ B (Ξ + ) σ F (Ξ − ) + σ B (Ξ − ) + σ F (Ξ + ) + σ B (Ξ + ) , (1)where σ F and σ B are the forward and backward crosssections of Ξ − or Ξ + production, and similarly for Ω ∓ baryons. The measurements include Ξ ∓ and Ω ∓ baryonsthat are either directly produced or decay products ofheavier hadrons. The measurement strategy for theasymmetry A FB of Ξ ∓ and Ω ∓ baryons presented hereclosely follows the analysis method used to determine A FB for Λ and ¯Λ baryons in Ref. [1]. DETECTOR AND DATA
The D0 detector is described in detail in Refs. [4–7].The collision region is surrounded by a central trackingsystem that comprises a silicon microstrip vertex detec-tor and a central fiber tracker, both located within a1 . . M [ GeV ] E n t r i e s / . G e V DØ, 10.4 fb -1 X - X + FIG. 1: Invariant mass distributions of reconstructed Ξ − → Λ π − (circles) and Ξ + → ¯Λ π + (triangles) for p ¯ p → µ Ξ ∓ X data. M [ GeV ] E n t r i e s / . G e V DØ, 10.4 fb -1 W - W + FIG. 2: Invariant mass distributions of reconstructed Ω − → Λ K − (circles) and Ω + → ¯Λ K + (triangles) for p ¯ p → µ Ω ∓ X data. The longitudinal momentum p z and the rapidity y ≡ ln [( E + p z ) / ( E − p z )] / p ¯ p center of massframe where E is the energy of the baryon. We presentresults for the full integrated luminosity of 10 . − ,collected from 2002 to 2011, using two data sets (i) p ¯ p → Ξ ∓ X , and (ii) p ¯ p → µ Ξ ∓ X . The first data set is unbiasedsince it is collected using a pre-scaled trigger on beamcrossing (“zero bias events”) or with a pre-scaled triggeron energy deposited in the forward counters (“minimumbias events”). The second data set is selected with a suiteof single muon triggers which implies that most eventscontain heavy-quark ( b or c ) decays. This data set isdefined using the same muon triggers and muon selectionsas in Ref. [8, 9]. The muon data provides a sizable dataset that adds additional statistics for the analysis. ForΩ’s there are fewer events, so we only present results forthe set p ¯ p → µ Ω ∓ X .We observe Ξ baryons through their decays Ξ − → Λ π − and Ξ + → ¯Λ π + , and Ω baryons through their decaysΩ − → Λ K − and Ω + → ¯Λ K + , with Λ → pπ − and¯Λ → ¯ pπ + in both cases. The Λ and ¯Λ candidates arereconstructed from pairs of oppositely curved tracks witha common vertex ( V ). Each track is required to havea non-zero impact parameter in the transverse plane(IP) with respect to the p ¯ p interaction vertex with asignificance of at least two standard deviations. Theproton (pion) mass is assigned to the daughter trackwith larger (smaller) total momentum since the decayΛ → pπ is just above threshold. The invariant mass ofthe ( p, π − ) or (¯ p, π + ) pair is required to be in the interval1 . < M ( pπ ) < .
125 GeV [1]. We require Λ and ¯Λcandidates with 1 . < p T <
25 GeV and pseudorapid-ity | η | < . ∓ orΩ ∓ candidates are required to have an IP consistent withzero within three standard deviations. The observed de-cay lengths in the transverse plane of the Λ and Ξ − orΩ − (or ¯Λ and Ξ + or Ω + ) are required to be greater than4 mm. The invariant mass for the Ξ ∓ candidate is re-quired to be in the interval 1 . < M (Λ π ) < . . < M (Λ K ) < .
85 GeV for Ω ∓ candidates. Thekinematic selections for the Ξ ∓ and Ω ∓ candidates are p T > . | η | < .
2. The pion or kaon track andthe two daughter tracks of the Λ baryon are required tobe different from any track associated to a muon. Theinvariant mass distributions for the decays Ξ − → Λ π − and Ξ + → ¯Λ π + are shown in Fig. 1 and for the decaysΩ − → Λ K − and Ω + → ¯Λ K + in Fig. 2. RAW ASYMMETRIES AND DETECTOREFFECTS
We obtain the numbers N F (Ξ ∓ ) and N B (Ξ ∓ ) of re-constructed Ξ ∓ baryons in the forward and backwardcategories in each bin of | y | by counting Ξ ∓ candidatesin the signal region, 1 . < M (Λ π ) < .
335 GeV,and subtracting the counts in two sideband regions, de-fined by 1 . < M (Λ π ) < . . 645 GeV and1 . < M (Λ K ) < . 715 GeV.The normalization factor N and the three raw asym-metries A ′ FB , A ′ NS , and A ′ Ξ are defined by N F (Ξ − ) ≡ N (1 + A ′ FB )(1 − A ′ NS )(1 + A ′ Ξ ) ,N B (Ξ − ) ≡ N (1 − A ′ FB )(1 + A ′ NS )(1 + A ′ Ξ ) ,N F (Ξ + ) ≡ N (1 + A ′ FB )(1 + A ′ NS )(1 − A ′ Ξ ) ,N B (Ξ + ) ≡ N (1 − A ′ FB )(1 − A ′ NS )(1 − A ′ Ξ ) , (2)and similarly for Ω. The raw asymmetries A ′ FB , A ′ NS ,and A ′ Ξ have contributions from the physical asymme-tries A FB , A NS , and A Ξ , and from detector effects. Theforward-backward asymmetry A FB measures the relativeexcess of Ξ − (Ξ + ) baryons with p z in the p (¯ p ) direction.The asymmetry A NS is given by the relative excess ofthe sum of Ξ − and Ξ + baryons with p z in the ¯ p beamdirection (north) with respect to the p beam direction(south). The asymmetry A Ξ is the relative excess of neg-atively charged over positively charged baryons.The initial p ¯ p state is invariant with respect to CPconjugation, which changes the sign of A NS and A Ξ , while A FB remains unchanged. A non-zero value of A NS or A Ξ would indicate CP violation.The asymmetry A ′ NS is mainly due to differences inthe product of the acceptance and efficiency between thenorthern hemisphere of the DØ detector with respect tothe southern hemisphere. The difference in reconstruc-tion efficiencies of Ξ − and Ξ + baryons caused by the dif-ferent inelastic interaction cross-sections of p and ¯ p withthe detector material creates the additional asymmetry A ′ Ξ [1].The raw asymmetries including terms up to second-order in the asymmetries are given by A ′ FB = A ′ NS A ′ Ξ + N F (Ξ − ) − N B (Ξ − ) + N F (Ξ + ) − N B (Ξ + ) N F (Ξ − ) + N B (Ξ − ) + N F (Ξ + ) + N B (Ξ + ) , (3) A ′ NS = A ′ FB A ′ Ξ + − N F (Ξ − ) + N B (Ξ − ) + N F (Ξ + ) − N B (Ξ + ) N F (Ξ − ) + N B (Ξ − ) + N F (Ξ + ) + N B (Ξ + ) , (4) A ′ Ξ = A ′ FB A ′ NS + N F (Ξ − ) + N B (Ξ − ) − N F (Ξ + ) − N B (Ξ + ) N F (Ξ − ) + N B (Ξ − ) + N F (Ξ + ) + N B (Ξ + ) . (5) p T [ GeV ] E v e n t s / . G e V -1 (a) X - X + p z [ GeV ] E v e n t s / . G e V -1 (b) y E v e n t s / . -1 (c) FIG. 3: Distributions of p T , p z , and y of reconstructed Ξ − (circles) and Ξ + candidates (triangles) with p T > p ¯ p → Ξ ∓ X . The polarities of the solenoid and toroid magnets werereversed about once every two weeks during data-takingto collect approximately the same number of events foreach of the four solenoid-toroid polarity combinations.We apply weights to equalize the sums of Ξ − and Ξ + can-didates reconstructed for each of the four polarity com-binations. This averaging over magnet polarities cancelscontributions from the detector geometry to A ′ FB and A ′ Ξ ,but not to A ′ NS [1].The raw asymmetry A ′ FB has negligible contributionsfrom detector effects after averaging over solenoid andtoroid magnet polarities. The raw asymmetries A ′ NS and A ′ Ξ are dominated by detector effects [1]. The quadraticterm A ′ NS A ′ Ξ in Eq. (3) corrects A ′ FB for the detectoreffects A ′ NS and A ′ Ξ on the particle counts N F (Ξ ∓ ) and N B (Ξ ∓ ). We can therefore set A ′ FB = A FB where A FB isdefined in Eq. (1). TABLE I: Forward-backward asymmetry A FB of Ξ ∓ baryons with p T > p ¯ p → Ξ ∓ X , and muonevents p ¯ p → µ Ξ ∓ X , and A FB of Ω − and Ω + baryons with p T > p ¯ p → µ Ω ∓ X . The first uncertainty isstatistical, the second is systematic due to the detector asymmetry A ′ NS A ′ Ξ . | y | A FB × 100 (Ξ ∓ , min. bias) A FB × 100 (Ξ ∓ , with µ ) A FB × 100 (Ω ∓ , with µ )0.0 to 0.5 − . ± . ± . − . ± . ± . − . ± . ± . . ± . ± . − . ± . ± . 03 3 . ± . ± . . ± . ± . 45 1 . ± . ± . 05 0 . ± . ± . . ± . ± . − . ± . ± . 27 5 . ± . ± . |y| A F B -1 (a) |y| A ¢ N S -0.1500.150 0.5 1 1.5 2DØ, 10.4 fb -1 (b) |y| A ¢X -0.200 0.5 1 1.5 2DØ, 10.4 fb -1 (c) FIG. 4: Asymmetries A ′ FB = A FB , A ′ NS and A ′ Ξ of recon-structed Ξ − and Ξ + candidates with p T > | y | , for the minimum bias data sample p ¯ p → Ξ ∓ X .The uncertainties are statistical. MINIMUM BIAS SAMPLE EVENTS p ¯ p → Ξ ∓ X The minimum bias sample contains 3 . × recon-structed Ξ ∓ candidates with p T > p T , p z , and y for the Ξ ∓ candidates are shown in Fig.3 and the corresponding raw asymmetries A ′ FB = A FB , A ′ NS and A ′ Ξ in Fig. 4. These asymmetries are calculatedusing Eqs. 3-5, neglecting the quadratic terms since theyare small compared to the statistical uncertainties. Thecorrection A ′ NS A ′ Ξ needed to obtain A ′ FB = A FB is mea-sured to be consistent with zero within statistical uncer-tainties, see Figs. 4 (b) and (c). Thus, we choose notto apply this correction, but rather take the full mea- y E v e n t s / . -1 (a) m + data X - X + y E v e n t s / . -1 (b) m - data FIG. 5: Distributions of rapidity y for reconstructed Ξ − (circles) and Ξ + candidates (triangles) in events with a (a)positively or (b) negatively charged muon for Ξ ∓ candidateswith p T > sured detector asymmetry A ′ NS A ′ Ξ as the systematic un-certainty on the measurement of A FB . The results aresummarized in Table I. MUON SAMPLE EVENTS p ¯ p → µ Ξ ∓ X AND p ¯ p → µ Ω ∓ X To study the asymmetries using a larger data set, weconsider p ¯ p → µ Ξ ∓ X and p ¯ p → µ Ω ∓ X events takenfrom the single muon trigger sample. Charged particleswith transverse momentum in the range 1 . < p T < | η | < . p T > . | p z | > . . × |y| A F B -0.0300.030 0.5 1 1.5 2DØ, 10.4 fb -1 (a) |y| A ¢ N S -0.0500 0.5 1 1.5 2DØ, 10.4 fb -1 (b) |y| A ¢X -1 (c) FIG. 6: Asymmetries A ′ FB = A FB , A ′ NS and A ′ Ξ of recon-structed Ξ − and Ξ + candidates with p T > | y | , for p ¯ p → µ Ξ ∓ X events. The uncertainties arestatistical. reconstructed muons and 7 . × reconstructed Ξ − andΞ + candidates with p T > . × reconstructed Ω − and Ω + candidates.Rapidity distributions for reconstructed Ξ − and Ξ + candidates are shown in Fig. 5. From these distribu-tions we observe that (i) the detection efficiency for Ξ − baryons is larger than for Ξ + baryons as explained above,and (ii) there are more Ξ ∓ µ ± than Ξ ∓ µ ∓ events. An ex-ample of a process with a correlated Ξ − µ + pair is thedecay Ξ c → Ξ − µ + X . We find that the asymmetry A ′ FB obtained with events containing a µ + is consistent withthe corresponding asymmetry with µ − within statisticaluncertainties. We therefore combine the µ + and µ − sam-ples to obtain the asymmetries presented in Figs. 6 and7. The p T , p z , and y distributions for p ¯ p → µ Ω ∓ X eventsare shown in Fig. 8, and the corresponding asymmetry A FB is presented in Fig. 9. The Ξ ∓ and Ω ∓ asymmetriesare summarized in Table I. |y| A F B -0.0500.050 0.5 1 1.5 22.0 < p T < -1 (a) |y| A F B -0.0500.050 0.5 1 1.5 24.0 < p T < -1 (b) |y| A F B -0.0800.080 0.5 1 1.5 2p T > -1 (c) FIG. 7: Asymmetry A ′ FB = A FB as a function of | y | for p ¯ p → µ Ξ ∓ X events with (a) 2 . < p T < . . . CONCLUSIONS We have measured the forward-backward asymmetries A FB in p ¯ p → Ξ ∓ X , p ¯ p → µ Ξ ∓ X , and p ¯ p → µ Ω ∓ X events using 10 . − of integrated luminosity recordedwith the D0 detector. We find that A FB for Ξ ∓ and Ω ∓ are consistent with zero within uncertainties.We thank the staffs at Fermilab and collaborating in-stitutions, and acknowledge support from the Depart-ment of Energy and National Science Foundation (UnitedStates of America); Alternative Energies and Atomic En-ergy Commission and National Center for Scientific Re-search/National Institute of Nuclear and Particle Physics(France); Ministry of Education and Science of the Rus-sian Federation, National Research Center “KurchatovInstitute” of the Russian Federation, and Russian Foun-dation for Basic Research (Russia); National Council forthe Development of Science and Technology and CarlosChagas Filho Foundation for the Support of Researchin the State of Rio de Janeiro (Brazil); Department of p T [ GeV ] E v e n t s / . G e V -1 (a) W - W + p z [ GeV ] E v e n t s / . G e V -1 (b) y E v e n t s / . -1 (c) FIG. 8: Distributions of p T , p z , and y of reconstructed Ω − (circles) and Ω + (triangles) with p T > p ¯ p → µ Ω ∓ X . Atomic Energy and Department of Science and Tech-nology (India); Administrative Department of Science,Technology and Innovation (Colombia); National Councilof Science and Technology (Mexico); National ResearchFoundation of Korea (Korea); Foundation for Funda-mental Research on Matter (The Netherlands); Scienceand Technology Facilities Council and The Royal Soci-ety (United Kingdom); Ministry of Education, Youth andSports (Czech Republic); Bundesministerium f¨ur Bildungund Forschung (Federal Ministry of Education and Re-search) and Deutsche Forschungsgemeinschaft (GermanResearch Foundation) (Germany); Science FoundationIreland (Ireland); Swedish Research Council (Sweden);China Academy of Sciences and National Natural ScienceFoundation of China (China); and Ministry of Educationand Science of Ukraine (Ukraine). [1] V.M. 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