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Observation of the Exclusive Reaction e+e

发布时间:

BABAR-PUB-06/065 SLAC-PUB-12200

Observation of the Exclusive Reaction e+ e? → φη at



s = 10.58 GeV

B. Aubert,1 M. Bona,1 D. Boutigny,1 Y. Karyotakis,1 J. P. Lees,1 V. Poireau,1 X. Prudent,1 V. Tisserand,1 A. Zghiche,1 E. Grauges,2 A. Palano,3 J. C. Chen,4 N. D. Qi,4 G. Rong,4 P. Wang,4 Y. S. Zhu,4 G. Eigen,5 I. Ofte,5 B. Stugu,5 G. S. Abrams,6 M. Battaglia,6 D. N. Brown,6 J. Button-Shafer,6 R. N. Cahn,6 Y. Groysman,6 R. G. Jacobsen,6 J. A. Kadyk,6 L. T. Kerth,6 Yu. G. Kolomensky,6 G. Kukartsev,6 D. Lopes Pegna,6 G. Lynch,6 L. M. Mir,6 T. J. Orimoto,6 M. Pripstein,6 N. A. Roe,6 M. T. Ronan,6, ? K. Tackmann,6 W. A. Wenzel,6 P. del Amo Sanchez,7 M. Barrett,7 T. J. Harrison,7 A. J. Hart,7 C. M. Hawkes,7 A. T. Watson,7 T. Held,8 H. Koch,8 B. Lewandowski,8 M. Pelizaeus,8 K. Peters,8 T. Schroeder,8 M. Steinke,8 J. T. Boyd,9 J. P. Burke,9 W. N. Cottingham,9 D. Walker,9 D. J. Asgeirsson,10 T. Cuhadar-Donszelmann,10 B. G. Fulsom,10 C. Hearty,10 N. S. Knecht,10 T. S. Mattison,10 J. A. McKenna,10 A. Khan,11 P. Kyberd,11 M. Saleem,11 D. J. Sherwood,11 L. Teodorescu,11 V. E. Blinov,12 A. D. Bukin,12 V. P. Druzhinin,12 V. B. Golubev,12 A. P. Onuchin,12 S. I. Serednyakov,12 Yu. I. Skovpen,12 E. P. Solodov,12 K. Yu Todyshev,12 M. Bondioli,13 M. Bruinsma,13 M. Chao,13 S. Curry,13 I. Eschrich,13 D. Kirkby,13 A. J. Lankford,13 P. Lund,13 M. Mandelkern,13 E. C. Martin,13 W. Roethel,13 D. P. Stoker,13 S. Abachi,14 C. Buchanan,14 S. D. Foulkes,15 J. W. Gary,15 O. Long,15 B. C. Shen,15 L. Zhang,15 E. J. Hill,16 H. P. Paar,16 S. Rahatlou,16 V. Sharma,16 J. W. Berryhill,17 C. Campagnari,17 A. Cunha,17 B. Dahmes,17 T. M. Hong,17 D. Kovalskyi,17 J. D. Richman,17 T. W. Beck,18 A. M. Eisner,18 C. J. Flacco,18 C. A. Heusch,18 J. Kroseberg,18 W. S. Lockman,18 G. Nesom,18 T. Schalk,18 B. A. Schumm,18 A. Seiden,18 D. C. Williams,18 M. G. Wilson,18 L. O. Winstrom,18 J. Albert,19 E. Chen,19 C. H. Cheng,19 A. Dvoretskii,19 F. Fang,19 D. G. Hitlin,19 I. Narsky,19 T. Piatenko,19 F. C. Porter,19 G. Mancinelli,20 B. T. Meadows,20 K. Mishra,20 M. D. Sokolo?,20 F. Blanc,21 P. C. Bloom,21 S. Chen,21 W. T. Ford,21 J. F. Hirschauer,21 A. Kreisel,21 M. Nagel,21 U. Nauenberg,21 A. Olivas,21 J. G. Smith,21 K. A. Ulmer,21 S. R. Wagner,21 J. Zhang,21 A. Chen,22 E. A. Eckhart,22 A. So?er,22 W. H. Toki,22 R. J. Wilson,22 F. Winklmeier,22 Q. Zeng,22 D. D. Altenburg,23 E. Feltresi,23 A. Hauke,23 H. Jasper,23 J. Merkel,23 A. Petzold,23 B. Spaan,23 T. Brandt,24 V. Klose,24 H. M. Lacker,24 W. F. Mader,24 R. Nogowski,24 J. Schubert,24 K. R. Schubert,24 R. Schwierz,24 J. E. Sundermann,24 A. Volk,24 D. Bernard,25 G. R. Bonneaud,25 E. Latour,25 Ch. Thiebaux,25 M. Verderi,25 P. J. Clark,26 W. Gradl,26 F. Muheim,26 S. Playfer,26 A. I. Robertson,26 Y. Xie,26 M. Andreotti,27 D. Bettoni,27 C. Bozzi,27 R. Calabrese,27 G. Cibinetto,27 E. Luppi,27 M. Negrini,27 A. Petrella,27 L. Piemontese,27 E. Prencipe,27 F. Anulli,28 R. Baldini-Ferroli,28 A. Calcaterra,28 R. de Sangro,28 G. Finocchiaro,28 S. Pacetti,28 P. Patteri,28 I. M. Peruzzi,28, ? M. Piccolo,28 M. Rama,28 A. Zallo,28 A. Buzzo,29 R. Contri,29 M. Lo Vetere,29 M. M. Macri,29 M. R. Monge,29 S. Passaggio,29 C. Patrignani,29 E. Robutti,29 A. Santroni,29 S. Tosi,29 K. S. Chaisanguanthum,30 M. Morii,30 J. Wu,30 R. S. Dubitzky,31 J. Marks,31 S. Schenk,31 U. Uwer,31 D. J. Bard,32 P. D. Dauncey,32 R. L. Flack,32 J. A. Nash,32 M. B. Nikolich,32 W. Panduro Vazquez,32 P. K. Behera,33 X. Chai,33 M. J. Charles,33 U. Mallik,33 N. T. Meyer,33 V. Ziegler,33 J. Cochran,34 H. B. Crawley,34 L. Dong,34 V. Eyges,34 W. T. Meyer,34 S. Prell,34 E. I. Rosenberg,34 A. E. Rubin,34 A. V. Gritsan,35 A. G. Denig,36 M. Fritsch,36 G. Schott,36 N. Arnaud,37 M. Davier,37 G. Grosdidier,37 A. H¨cker,37 V. Lepeltier,37 F. Le Diberder,37 o 37 37 37 37 37 A. M. Lutz, S. Pruvot, S. Rodier, P. Roudeau, M. H. Schune, J. Serrano,37 A. Stocchi,37 W. F. Wang,37 G. Wormser,37 D. J. Lange,38 D. M. Wright,38 C. A. Chavez,39 I. J. Forster,39 J. R. Fry,39 E. Gabathuler,39 R. Gamet,39 K. A. George,39 D. E. Hutchcroft,39 D. J. Payne,39 K. C. Scho?eld,39 C. Touramanis,39 A. J. Bevan,40 F. Di Lodovico,40 W. Menges,40 R. Sacco,40 G. Cowan,41 H. U. Flaecher,41 D. A. Hopkins,41 P. S. Jackson,41 T. R. McMahon,41 F. Salvatore,41 A. C. Wren,41 D. N. Brown,42 C. L. Davis,42 J. Allison,43 N. R. Barlow,43 R. J. Barlow,43 Y. M. Chia,43 C. L. Edgar,43 G. D. La?erty,43 T. J. West,43 J. C. Williams,43 J. I. Yi,43 C. Chen,44 W. D. Hulsbergen,44 A. Jawahery,44 C. K. Lae,44 D. A. Roberts,44 G. Simi,44 G. Blaylock,45 C. Dallapiccola,45 S. S. Hertzbach,45 X. Li,45 T. B. Moore,45 E. Salvati,45 S. Saremi,45 R. Cowan,46 G. Sciolla,46 S. J. Sekula,46 M. Spitznagel,46 F. Taylor,46 R. K. Yamamoto,46 H. Kim,47 S. E. Mclachlin,47 P. M. Patel,47 S. H. Robertson,47 A. Lazzaro,48 V. Lombardo,48 F. Palombo,48 J. M. Bauer,49 L. Cremaldi,49 V. Eschenburg,49 R. Godang,49 R. Kroeger,49 D. A. Sanders,49 D. J. Summers,49 H. W. Zhao,49 S. Brunet,50 D. C?t?,50 M. Simard,50 o e P. Taras,50 F. B. Viaud,50 H. Nicholson,51 N. Cavallo,52, ? G. De Nardo,52 F. Fabozzi,52, ? C. Gatto,52 L. Lista,52

arXiv:hep-ex/0611028v1 15 Nov 2006

2 D. Monorchio,52 P. Paolucci,52 D. Piccolo,52 C. Sciacca,52 M. A. Baak,53 G. Raven,53 H. L. Snoek,53 C. P. Jessop,54 J. M. LoSecco,54 G. Benelli,55 L. A. Corwin,55 K. K. Gan,55 K. Honscheid,55 D. Hufnagel,55 P. D. Jackson,55 H. Kagan,55 R. Kass,55 J. P. Morris,55 A. M. Rahimi,55 J. J. Regensburger,55 R. Ter-Antonyan,55 Q. K. Wong,55 N. L. Blount,56 J. Brau,56 R. Frey,56 O. Igonkina,56 J. A. Kolb,56 M. Lu,56 C. T. Potter,56 R. Rahmat,56 N. B. Sinev,56 D. Strom,56 J. Strube,56 E. Torrence,56 A. Gaz,57 M. Margoni,57 M. Morandin,57 A. Pompili,57 M. Posocco,57 M. Rotondo,57 F. Simonetto,57 R. Stroili,57 C. Voci,57 E. Ben-Haim,58 H. Briand,58 J. Chauveau,58 P. David,58 L. Del Buono,58 Ch. de la Vaissi`re,58 O. Hamon,58 B. L. Hart?el,58 Ph. Leruste,58 J. Malcl`s,58 e e 58 59 60 60 61 61 61 J. Ocariz, L. Gladney, M. Biasini, R. Covarelli, C. Angelini, G. Batignani, S. Bettarini, G. Calderini,61 M. Carpinelli,61 R. Cenci,61 F. Forti,61 M. A. Giorgi,61 A. Lusiani,61 G. Marchiori,61 M. A. Mazur,61 M. Morganti,61 N. Neri,61 E. Paoloni,61 G. Rizzo,61 J. J. Walsh,61 M. Haire,62 D. Judd,62 D. E. Wagoner,62 J. Biesiada,63 P. Elmer,63 Y. P. Lau,63 C. Lu,63 J. Olsen,63 A. J. S. Smith,63 A. V. Telnov,63 F. Bellini,64 G. Cavoto,64 A. D’Orazio,64 D. del Re,64 E. Di Marco,64 R. Faccini,64 F. Ferrarotto,64 F. Ferroni,64 M. Gaspero,64 L. Li Gioi,64 M. A. Mazzoni,64 S. Morganti,64 G. Piredda,64 F. Polci,64 F. Safai Tehrani,64 C. Voena,64 M. Ebert,65 H. Schr¨der,65 R. Waldi,65 T. Adye,66 B. Franek,66 E. O. Olaiya,66 S. Ricciardi,66 F. F. Wilson,66 R. Aleksan,67 o S. Emery,67 A. Gaidot,67 S. F. Ganzhur,67 G. Hamel de Monchenault,67 W. Kozanecki,67 M. Legendre,67 G. Vasseur,67 Ch. Y`che,67 M. Zito,67 X. R. Chen,68 H. Liu,68 W. Park,68 M. V. Purohit,68 J. R. Wilson,68 e M. T. Allen,69 D. Aston,69 R. Bartoldus,69 P. Bechtle,69 N. Berger,69 R. Claus,69 J. P. Coleman,69 M. R. Convery,69 J. C. Dingfelder,69 J. Dorfan,69 G. P. Dubois-Felsmann,69 D. Dujmic,69 W. Dunwoodie,69 R. C. Field,69 T. Glanzman,69 S. J. Gowdy,69 M. T. Graham,69 P. Grenier,69 V. Halyo,69 C. Hast,69 T. Hryn’ova,69 W. R. Innes,69 M. H. Kelsey,69 P. Kim,69 D. W. G. S. Leith,69 S. Li,69 S. Luitz,69 V. Luth,69 H. L. Lynch,69 D. B. MacFarlane,69 H. Marsiske,69 R. Messner,69 D. R. Muller,69 C. P. O’Grady,69 V. E. Ozcan,69 A. Perazzo,69 M. Perl,69 T. Pulliam,69 B. N. Ratcli?,69 A. Roodman,69 A. A. Salnikov,69 R. H. Schindler,69 J. Schwiening,69 A. Snyder,69 J. Stelzer,69 D. Su,69 M. K. Sullivan,69 K. Suzuki,69 S. K. Swain,69 J. M. Thompson,69 J. Va’vra,69 N. van Bakel,69 A. P. Wagner,69 M. Weaver,69 W. J. Wisniewski,69 M. Wittgen,69 D. H. Wright,69 H. W. Wulsin,69 A. K. Yarritu,69 K. Yi,69 C. C. Young,69 P. R. Burchat,70 A. J. Edwards,70 S. A. Majewski,70 B. A. Petersen,70 L. Wilden,70 S. Ahmed,71 M. S. Alam,71 R. Bula,71 J. A. Ernst,71 V. Jain,71 B. Pan,71 M. A. Saeed,71 F. R. Wappler,71 S. B. Zain,71 W. Bugg,72 M. Krishnamurthy,72 S. M. Spanier,72 R. Eckmann,73 J. L. Ritchie,73 C. J. Schilling,73 R. F. Schwitters,73 J. M. Izen,74 X. C. Lou,74 S. Ye,74 F. Bianchi,75 F. Gallo,75 D. Gamba,75 M. Pelliccioni,75 M. Bomben,76 L. Bosisio,76 C. Cartaro,76 F. Cossutti,76 G. Della Ricca,76 L. Lanceri,76 L. Vitale,76 V. Azzolini,77 N. Lopez-March,77 F. Martinez-Vidal,77 A. Oyanguren,77 Sw. Banerjee,78 B. Bhuyan,78 K. Hamano,78 R. Kowalewski,78 I. M. Nugent,78 J. M. Roney,78 R. J. Sobie,78 J. J. Back,79 P. F. Harrison,79 T. E. Latham,79 G. B. Mohanty,79 M. Pappagallo,79, § H. R. Band,80 X. Chen,80 S. Dasu,80 K. T. Flood,80 J. J. Hollar,80 P. E. Kutter,80 B. Mellado,80 Y. Pan,80 M. Pierini,80 R. Prepost,80 S. L. Wu,80 Z. Yu,80 and H. Neal81 (The BABAR Collaboration)
1

Laboratoire de Physique des Particules, IN2P3/CNRS et Universit? de Savoie, F-74941 Annecy-Le-Vieux, France e 2 Universitat de Barcelona, Facultat de Fisica, Departament ECM, E-08028 Barcelona, Spain 3 Universit` di Bari, Dipartimento di Fisica and INFN, I-70126 Bari, Italy a 4 Institute of High Energy Physics, Beijing 100039, China 5 University of Bergen, Institute of Physics, N-5007 Bergen, Norway 6 Lawrence Berkeley National Laboratory and University of California, Berkeley, California 94720, USA 7 University of Birmingham, Birmingham, B15 2TT, United Kingdom 8 Ruhr Universit¨t Bochum, Institut f¨r Experimentalphysik 1, D-44780 Bochum, Germany a u 9 University of Bristol, Bristol BS8 1TL, United Kingdom 10 University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z1 11 Brunel University, Uxbridge, Middlesex UB8 3PH, United Kingdom 12 Budker Institute of Nuclear Physics, Novosibirsk 630090, Russia 13 University of California at Irvine, Irvine, California 92697, USA 14 University of California at Los Angeles, Los Angeles, California 90024, USA 15 University of California at Riverside, Riverside, California 92521, USA 16 University of California at San Diego, La Jolla, California 92093, USA 17 University of California at Santa Barbara, Santa Barbara, California 93106, USA 18 University of California at Santa Cruz, Institute for Particle Physics, Santa Cruz, California 95064, USA 19 California Institute of Technology, Pasadena, California 91125, USA 20 University of Cincinnati, Cincinnati, Ohio 45221, USA 21 University of Colorado, Boulder, Colorado 80309, USA

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Colorado State University, Fort Collins, Colorado 80523, USA Universit¨t Dortmund, Institut f¨r Physik, D-44221 Dortmund, Germany a u 24 Technische Universit¨t Dresden, Institut f¨r Kern- und Teilchenphysik, D-01062 Dresden, Germany a u 25 Laboratoire Leprince-Ringuet, CNRS/IN2P3, Ecole Polytechnique, F-91128 Palaiseau, France 26 University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom 27 Universit` di Ferrara, Dipartimento di Fisica and INFN, I-44100 Ferrara, Italy a 28 Laboratori Nazionali di Frascati dell’INFN, I-00044 Frascati, Italy 29 Universit` di Genova, Dipartimento di Fisica and INFN, I-16146 Genova, Italy a 30 Harvard University, Cambridge, Massachusetts 02138, USA 31 Universit¨t Heidelberg, Physikalisches Institut, Philosophenweg 12, D-69120 Heidelberg, Germany a 32 Imperial College London, London, SW7 2AZ, United Kingdom 33 University of Iowa, Iowa City, Iowa 52242, USA 34 Iowa State University, Ames, Iowa 50011-3160, USA 35 Johns Hopkins University, Baltimore, Maryland 21218, USA 36 Universit¨t Karlsruhe, Institut f¨r Experimentelle Kernphysik, D-76021 Karlsruhe, Germany a u 37 Laboratoire de l’Acc?l?rateur Lin?aire, IN2P3/CNRS et Universit? Paris-Sud 11, ee e e Centre Scienti?que d’Orsay, B. P. 34, F-91898 ORSAY Cedex, France 38 Lawrence Livermore National Laboratory, Livermore, California 94550, USA 39 University of Liverpool, Liverpool L69 7ZE, United Kingdom 40 Queen Mary, University of London, E1 4NS, United Kingdom 41 University of London, Royal Holloway and Bedford New College, Egham, Surrey TW20 0EX, United Kingdom 42 University of Louisville, Louisville, Kentucky 40292, USA 43 University of Manchester, Manchester M13 9PL, United Kingdom 44 University of Maryland, College Park, Maryland 20742, USA 45 University of Massachusetts, Amherst, Massachusetts 01003, USA 46 Massachusetts Institute of Technology, Laboratory for Nuclear Science, Cambridge, Massachusetts 02139, USA 47 McGill University, Montr?al, Qu?bec, Canada H3A 2T8 e e 48 Universit` di Milano, Dipartimento di Fisica and INFN, I-20133 Milano, Italy a 49 University of Mississippi, University, Mississippi 38677, USA 50 Universit? de Montr?al, Physique des Particules, Montr?al, Qu?bec, Canada H3C 3J7 e e e e 51 Mount Holyoke College, South Hadley, Massachusetts 01075, USA 52 Universit` di Napoli Federico II, Dipartimento di Scienze Fisiche and INFN, I-80126, Napoli, Italy a 53 NIKHEF, National Institute for Nuclear Physics and High Energy Physics, NL-1009 DB Amsterdam, The Netherlands 54 University of Notre Dame, Notre Dame, Indiana 46556, USA 55 Ohio State University, Columbus, Ohio 43210, USA 56 University of Oregon, Eugene, Oregon 97403, USA 57 Universit` di Padova, Dipartimento di Fisica and INFN, I-35131 Padova, Italy a 58 Laboratoire de Physique Nucl?aire et de Hautes Energies, e IN2P3/CNRS, Universit? Pierre et Marie Curie-Paris6, e Universit? Denis Diderot-Paris7, F-75252 Paris, France e 59 University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA 60 Universit` di Perugia, Dipartimento di Fisica and INFN, I-06100 Perugia, Italy a 61 Universit` di Pisa, Dipartimento di Fisica, Scuola Normale Superiore and INFN, I-56127 Pisa, Italy a 62 Prairie View A&M University, Prairie View, Texas 77446, USA 63 Princeton University, Princeton, New Jersey 08544, USA 64 Universit` di Roma La Sapienza, Dipartimento di Fisica and INFN, I-00185 Roma, Italy a 65 Universit¨t Rostock, D-18051 Rostock, Germany a 66 Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX11 0QX, United Kingdom 67 DSM/Dapnia, CEA/Saclay, F-91191 Gif-sur-Yvette, France 68 University of South Carolina, Columbia, South Carolina 29208, USA 69 Stanford Linear Accelerator Center, Stanford, California 94309, USA 70 Stanford University, Stanford, California 94305-4060, USA 71 State University of New York, Albany, New York 12222, USA 72 University of Tennessee, Knoxville, Tennessee 37996, USA 73 University of Texas at Austin, Austin, Texas 78712, USA 74 University of Texas at Dallas, Richardson, Texas 75083, USA 75 Universit` di Torino, Dipartimento di Fisica Sperimentale and INFN, I-10125 Torino, Italy a 76 Universit` di Trieste, Dipartimento di Fisica and INFN, I-34127 Trieste, Italy a 77 IFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spain 78 University of Victoria, Victoria, British Columbia, Canada V8W 3P6 79 Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom 80 University of Wisconsin, Madison, Wisconsin 53706, USA 81 Yale University, New Haven, Connecticut 06511, USA (Dated: February 3, 2008)
23 22

4
√ We report the observation of e+ e? → φη near s = 10.58 GeV with 6.5 σ signi?cance in the K + K ? γγ ?nal state in a data sample of 224 fb?1 collected by the BABAR experiment at the PEPII e+ e? storage rings. We measure the restricted radiation-corrected cross section to be σ(e+ e?→ φη) =2.1 ± 0.4(stat) ± 0.1(syst) fb within the range | cos θ? | < 0.8, where θ? is the center-of-mass polar angle of the φ meson. The φ meson is required to be in the invariant mass range of 1.008 < mφ < 1.035 GeV/c2 . The radiation-corrected cross section in the full cos θ? range is extrapolated to be 2.9 ± 0.5(stat) ± 0.1(syst) fb.
PACS numbers: 13.66.Bc, 13.25.-k, 14.40.Ev

The large data samples of the B factories provide an opportunity to explore rare exclusive quasi-two-body processes in e+ e? annihilation, such as ?nal states produced through one virtual photon with negative C-parity (J/ψηc or other double charmonium states) [1, 2], and two-virtual-photon annihilation (TVPA) with positive Cparity (ρ0 ρ0 or φρ0 ) [3]. The process e+ e? → J/ψηc and other double charmonium processes are observed at rates approximately ten times larger than the expectation from QCD-based models [4]. Various theoretical e?orts have been made to resolve the discrepancy between experimental and theoretical results [5, 6, 7]. Another avenue to explore this puzzle is provided by the related process e+ e? → φη. A recent observation of ψ(3770) → φη at a branching fraction of (3.1 ± 0.6 ± 0.3 ± 0.1) × 10?4 [8] also stimulates a search for Υ (4S) → φη. We report the observation of e+ e? → φη, which is analogous, in the s quark sector, to the process e+ e? → J/ψηc , since the η meson has an s? quark-pair coms ponent. The Feynman diagram for the most likely production mechanism is shown in Fig. 1. However, since η is not purely s?, the cross section for this production s mechanism is determined by the projection onto the s? s component of the η meson. A calculation using the QCDbased light cone method with relativistic treatment for the light s quark is possible and therefore can provide a theoretical estimation [9]. The φη combination is a vector ? pseudoscalar (VP) ?nal state. The production rates for e+ e? → VP can be described by form factors, which are predicted in QCD-based models [10, 11, 12]. Di?erent models predict di?erent dependences on center-of-mass (CM) energy squared s. The recent measurements of e+ e? → VP (ωπ 0 , ρη and ρη ′ ) from BES [13, 14] investigated the s dependence of the cross sections and form factors in the energy range from 3.65 to 3.773 GeV. It is interesting to investigate the s dependence over a wider energy range. Since CLEO measured the cross section for e+ e? → φη √ at CM energy s = 3.67 GeV [8], a measurement of the √ same process at s = 10.58 GeV provides a meaningful test of the s dependence. This analysis uses 204 fb?1 of e+ e? colliding beam √ data collected on the Υ (4S) resonance at s = 10.58 GeV and 20 fb?1 collected 40 MeV below the Υ (4S) mass with the BABAR detector at the SLAC PEP-II asymmetric-energy B factory. The BABAR detector is

e+ e
_

s _ s

s _ s

FIG. 1: Possible Feynman diagram for e+ e? → φη.

described in detail elsewhere [15]. Charged-particle momenta and energy loss are measured in the tracking system that consists of a silicon vertex tracker (SVT) and a drift chamber (DCH). Electrons and photons are detected in a CsI(Tl) calorimeter (EMC). An internally re?ecting ring-imaging Cherenkov detector (DIRC) provides charged particle identi?cation (PID). An instrumented magnetic ?ux return (IFR) provides identi?cation of muons. Kaon and pion candidates are identi?ed using likelihoods of particle hypotheses calculated from the speci?c ionization in the DCH and SVT and the Cherenkov angle measured in the DIRC. Photons are identi?ed by shower shape and lack of associated tracks. To reconstruct φη in the K + K ? γγ mode, events with exactly two well-reconstructed, oppositely charged tracks and at least two well-identi?ed photons are selected. Charged tracks are required to have at least 12 DCH hits and a laboratory polar angle within the SVT acceptance, 0.41 < θ < 2.54 radians. The laboratory momenta of the kaon candidates are required to be greater than 800 MeV/c to reduce background. The two tracks selected must both be identi?ed as kaons. We ?t the two tracks to a common vertex, and require the χ2 probability to exceed 0.1%. The photon candidates are required to have a minimum laboratory energy of 500 MeV. The invariant mass distribution of K + K ? γγ, after requiring the invariant mass of KK to be near the φ mass (mKK < 1.1 GeV/c2 ) and that of γγ to be near the η mass (0.4 < mγγ < 0.8 GeV/c2 ) is shown in Fig. 2 (a). We accept events with a reconstructed invariant mass of K + K ? γγ within 230 MeV/c2 of the e+ e? CM energy. There is at most one entry per event in the region of interest. Figure 2(b) shows the scatter plot of invariant masses

5
events/25 MeV/c2
0.80 10 8 6 4 2 0 9.6 10.0 10.4 10.8
+ -γγ

mγ γ GeV/c2

(a)

(b)
0.70 0.60 0.50 0.40

11.2

1.00

1.02

1.04

1.06

mK K

GeV/c2

mK+K- GeV/c2

FIG. 2: (a) Distribution of the invariant mass (Υ (4S) data) for the K + K ? γγ ?nal state near the φη region. The accepted signal region is indicated by the lines. (b) Scatter plot of the invariant masses of the K + K ? and γγ pairs for those events in the accepted signal region.
Events / 14 MeV/c2
24 16 12 8 4 0 0.4 0.5 0.6 0.7

nal events is 24 ± 5 in the φ mass window, with 20±5 in the on-resonance sample and 3±2 in the o?-resonance sample. The number of background events within the φ mass window and within three standard deviations of the η mass is 7±2. The signi?cance is estimated by the log-likelihood di?erence between signal (ln(Ls )) and null (ln(Ln )) hypotheses (no φη signal component in the PDF), 2ln(Ls /Ln ), which gives 6.5 standard deviations. Given the negative C-parity of the φη ?nal state, we assume φη is produced through one-virtual-photon annihilation. The angular distributions of φη from a JP = 1? initial state, in the helicity basis [18], can be calculated to be: dN d cos θ? d cos θ
φ d?φ

Events / 2 MeV/c2

20 16 12 8 4 0 0.98

(a)

(b)

∝ sin2 θφ (1+cos2 θ? +cos 2?φ sin2 θ? ),

1.02

1.06

1.1

mK+K- GeV/c2

mγ γ GeV/c2

FIG. 3: Mass projections for (a) K + K ? pairs and (b) γγ pairs in K + K ? γγ events.

of K + K ? and γγ pairs from the accepted e+ e? → K + K ? γγ events. The concentration of events indicates φη production. We use a two-dimensional log-likelihood ?t to extract the signal for the reaction e+ e? → φη. Due to the fact that the ?nal state particle masses are far below the e+ e? collision energy, we may treat the two-body masses as uncorrelated. Justi?ed by Fig. 2 (b), the signal probability density function (PDF) is constructed as a product of two one-dimensional PDFs, one for each resonance. We use a P-wave relativistic Breit-Wigner formula to construct a PDF for the φ resonance and a Gaussian function to model the η resonance. A threshold function q 3 /(1 + q 3 Rt ) is used to model the background in the K + K ? system, where q is the daughter momentum in the φ rest frame and Rt is a shape parameter. A linear function (p0 + p1 · mγγ ) is used to model the background under the η. In the ?t to data, we ?x the mass and width of the φ and the mass of the η to the world average values [16]. The width of the η, 13.6 MeV, is ?xed to the resolution obtained from simulation. The ?oating parameters in the ?t are: Rt , p0 , p1 , and the numbers of events for all components–φη, φγγ and ηK + K ? . The mass projections in KK and γγ from the two-dimensional ?t are shown in Fig. 3 (a) and (b), respectively. We de?ne the φ mass window as 1.008 < mKK < 1.035 GeV/c2 to reduce the systematic uncertainty due to the long tail of φ masses. The extracted number of φη sig-

(1) where the production angle θ? is de?ned as the angle between the φ meson direction and incident e? beam in the CM frame. The φ helicity angle θφ is de?ned as the polar angle, measured in the φ rest frame, of the K + momentum direction with respect to an axis that is aligned with the φ momentum direction in the laboratory frame. The variable ?φ is the K + azimuthal angle around the direction of the φ measured with respect to the plane formed by the φ and the incoming electron. The helicity and azimuthal angles of the pseudoscalar η are ?at and thus not included in equation 1. Integrating over the other two angles, the distributions of the production angle, φ helicity and φ azimuthal angle are expected to be 1 + cos2 θ? , sin2 θφ and 2 + cos 2?φ , respectively. The observed angular distributions from e+ e? → φη data are consistent with the above expectation but the constraints on these angular distributions are limited by statistics. The systematic uncertainty from the two-dimensional ?t is estimated from the di?erence in yield obtained by ?oating the mean, width, and resolution parameters in the ?t. The systematic uncertainties due to PID, tracking, and photon e?ciency are estimated based on measurements from control data samples. The possible background from related modes with an extra π 0 was estimated to be small (< 1%) by using extrapolations from statistically limited four-particle mass sidebands and we ignore it. The systematic uncertainties are summarized in Table I. The radiation-corrected cross section for e+ e? → φη is calculated from: NObserved L × B(φ → KK) × B(η → γγ) × εMC × (1 + δ) (2) where NObserved is the extracted number of φη signal events from on- and o?-resonance data, L is the integrated luminosity, B(φ → KK) is the branching fraction of φ → KK, B(η → γγ) is the branching fraction of η → γγ, εMC is the signal e?ciency obtained σ=

6
TABLE I: Systematic uncertainties on the cross section of φη. Source Systematic uncertainty % Photon e?ciency 3.6 Two-dimensional ?t 1.3 Particle Identi?cation 3.0 Tracking e?ciency 2.6 Luminosity 2.0 Total 6.0
5

10

10 4

σ fb

10 3

CLEO

1/s4

10 2

1/s3
10

BABAR

from Monte Carlo simulation (MC), and δ is the radiation correction calculated according to Ref. [17]. We obtain (1 + δ) = 0.768. The uncertainties due to the theoretical model and the s dependence are negligible. The signal MC events are generated uniformly in phase space. For the determination of signal cross sections, the MC cos θ? , cos θφ and ?φ distributions are re-weighted using equation 1. The signal e?ciency in the ?ducial region of | cos θ? | < 0.8 for φη without radiative correction is estimated to be 34.3%, including corrections to MC simulation for PID and tracking. Taking the branching fraction of φ →K + K ? as 49.1%, and η → γγ as 39.4% [16], the ?nal radiation-corrected cross section for 1.008 < mφ < 1.035 GeV/c2 within | cos θ? | < 0.8 near √ s = 10.58 GeV is: σ?d (e+ e? → φη) = 2.1 ± 0.4(stat) ± 0.1(syst) fb. The cross section within cos θ? ∈ [?0.8, 0.8] can be scaled to cos θ? ∈ [?1.0, 1.0] by assuming a 1 + cos2 θ? distribution to obtain: σ(e+ e? → φη) = 2.9 ± 0.5(stat) ± 0.1(syst) fb. To study the possibility that the observed signal is due to Υ (4S) decay, we scale the o?-resonance signal to the on-resonance luminosity, and subtract it from the on-resonance signal. The resulting number of events, ?10 ± 21, is consistent with zero. The corresponding branching fraction for Υ (4S) → φη is (?0.9±1.8)×10?6. Assuming this uncertainty can be treated as Gaussian and normalizing to the physical region (≥ 0), the 90% con?dence level upper limit is 2.5 × 10?6 . There is currently no direct prediction for the cross section of this process at this energy, but the e+ e? → VP cross section is expected to have 1/s3 [12] or 1/s4 [10, 11] dependence in QCD-based models. A comparison between our result and that of CLEO, (σ = 2.1+1.9 ±0.2 pb) ?1.2 √ at s = 3.67 GeV [8], favors a 1/s3 dependence (Fig. 4). We quantify the degree to which 1/s4 scaling is disfavored by scaling our measured cross section in this fashion to √ s = 3.67 GeV, and comparing it to the CLEO measurement. Note, however, that if CLEO did have a downward statistical ?uctuation, both their central value and their uncertainty would be low. Accordingly, the uncertainty

1 10

s GeV

2

10 2

FIG. 4: Cross section extrapolations based on BABAR’s mea√ surement at s = 10.58 GeV assuming 1/s3 (black) or 1/s4 (red) energy dependence. The bands show one standard deviation uncertainties in the extrapolations. The CLEO mea√ surement at s = 3.67 GeV is also shown.

we use in this comparison is the CLEO one scaled by the square root of the ratio, 2.6, of the predicted to the observed cross sections. The resulting disagreement with 1/s4 scaling is approximately 2 standard deviations. The form of the s dependence has important theoretical implications, which may a?ect a wide range of QCD-based processes such as e+ e? → VP [10], exclusive hadronic B decays [19], and charmonium decays [20]. The large initial-state radiation sample at the B factories can provide another route to test the s dependence over a wider energy range. A direct comparison of the absolute cross section with a possible theoretical calculation [9] is also interesting. In summary, we have observed the exclusive produc√ tion of φη in e+ e? interactions at s = 10.58 GeV. Combining with CLEO’s measurement and interpreting our result as continuum production, the measured φη cross section favors 1/s3 dependence, which is in con?ict with some QCD-based predictions. The 90% con?dence level upper limit on the branching fraction B(Υ (4S) → φη) is 2.5 × 10?6 . We are grateful for the excellent luminosity and machine conditions provided by our PEP-II colleagues, and for the substantial dedicated e?ort from the computing organizations that support BABAR. We wish to thank S. Brodsky, A. Goldhaber and G. T. Bodwin for helpful discussions. The collaborating institutions wish to thank SLAC for its support and kind hospitality. This work is supported by DOE and NSF (USA), NSERC (Canada), IHEP (China), CEA and CNRS-IN2P3 (France), BMBF and DFG (Germany), INFN (Italy), FOM (The Netherlands), NFR (Norway), MIST (Russia), and PPARC

7 (United Kingdom). Individuals have received support from CONACyT (Mexico), A. P. Sloan Foundation, Research Corporation, and Alexander von Humboldt Foundation.
092001 (2006). [7] A. Vairo, hep-ph/0610251. [8] G. S. Adams et al. (CLEO Collaboration), Phys. Rev. D 73, 012002 (2006). [9] G. T. Bodwin and S. Brodsky, private communication. [10] G. P. Lepage and S. J. Brodsky, Phys. Rev. D 22, 2157 (1980); S. J. Brodsky and G. P. Lepage, Phys. Rev. D 24, 2848 (1981). [11] V. Chernyak, hep-ph/9906387; V. L. Chernyak and A. R. Zhitnitsky, Phys. Rept. 112, 173 (1984). [12] J. M. Gerard and G. Lopez Castro, Phys. Lett. B 425, 365 (1998). [13] M. Ablikim et al. (BES Collaboration), Phys. Rev. D 70, 112007 (2004), [Erratum-ibid. D 71, 019901 (2005)]. [14] P. Wang, X. H. Mo and C. Z. Yuan, Phys. Lett. B 557, 192 (2003). [15] B. Aubert et al. (BABAR Collaboration), Nucl. Instrum. Meth. A 479, 1 (2002). [16] S. Eidelman et al. (Particle Data Group), Phys. Lett. B 592, 1 (2004). [17] M. Benayoun, S. I. Eidelman, V. N. Ivanchenko and Z. K. Silagadze, Mod. Phys. Lett. A 14, 2605 (1999). [18] M. Jacob, and G. C. Wick, Ann. Phys.. (N. Y.) 7, 404 (1959); S. U. Chung, Phys. Rev. D 57, 431 (1998). [19] M. Beneke and M. Neubert, Nucl. Phys. B 675, 333 (2003). [20] S. J. Brodsky and M. Karliner, Phys. Rev. Lett. 78, 4682 (1997); C. Z. Yuan, hep-ex/0605078.

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Deceased Also with Universit` di Perugia, Dipartimento di Fisica, a Perugia, Italy Also with Universit` della Basilicata, Potenza, Italy a Also with IPPP, Physics Department, Durham University, Durham DH1 3LE, United Kingdom K. Abe et al. (Belle Collaboration), Phys. Rev. Lett. 89, 142001 (2002); K. Abe et al. (Belle Collaboration), Phys. Rev. D 70, 071102 (2004). B. Aubert et al. (BABAR Collaboration), Phys. Rev. D 72, 031101 (2005). B. Aubert et al. (BABAR Collaboration), Phys. Rev. Lett. 97, 112002 (2006). E. Braaten and J. Lee, Phys. Rev. D 67, 054007 (2003), [Erratum-ibid. D 72, 099901 (2005)]; K. Y. Liu, Z. G. He and K. T. Chao, Phys. Lett. B 557, 45 (2003). A. E. Bondar and V. L. Chernyak, Phys. Lett. B 612, 215 (2005). G. T. Bodwin, D. Kang and J. Lee, hep-ph/0603185; Y. Zhang, Y. Gao, and K. T. Chao, Phys. Rev. Lett. 96,




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