Study of radiative bottomonium transitions using converted photons
J. P. Lees,1V. Poireau,1E. Prencipe,1V. Tisserand,1J. Garra Tico,2E. Grauges,2M. Martinelli,3a,3bD. A. Milanes,3a A. Palano,3a,3bM. Pappagallo,3a,3bG. Eigen,4B. Stugu,4L. Sun,4D. N. Brown,5L. T. Kerth,5Yu. G. Kolomensky,5
G. Lynch,5H. Koch,6T. Schroeder,6D. J. Asgeirsson,7C. Hearty,7T. S. Mattison,7J. A. McKenna,7A. Khan,8 V. E. Blinov,9A. R. Buzykaev,9V. P. Druzhinin,9V. B. Golubev,9E. A. Kravchenko,9A. P. Onuchin,9S. I. Serednyakov,9
Yu. I. Skovpen,9E. P. Solodov,9K. Yu. Todyshev,9A. N. Yushkov,9M. Bondioli,10S. Curry,10D. Kirkby,10 A. J. Lankford,10M. Mandelkern,10D. P. Stoker,10H. Atmacan,11J. W. Gary,11F. Liu,11O. Long,11G. M. Vitug,11
C. Campagnari,12T. M. Hong,12D. Kovalskyi,12J. D. Richman,12C. A. West,12A. M. Eisner,13J. Kroseberg,13 W. S. Lockman,13A. J. Martinez,13T. Schalk,13B. A. Schumm,13A. Seiden,13C. H. Cheng,14D. A. Doll,14B. Echenard,14
K. T. Flood,14D. G. Hitlin,14P. Ongmongkolkul,14F. C. Porter,14A. Y. Rakitin,14R. Andreassen,15M. S. Dubrovin,15 B. T. Meadows,15M. D. Sokoloff,15P. C. Bloom,16W. T. Ford,16A. Gaz,16M. Nagel,16U. Nauenberg,16J. G. Smith,16
S. R. Wagner,16R. Ayad,17,*W. H. Toki,17B. Spaan,18M. J. Kobel,19K. R. Schubert,19R. Schwierz,19D. Bernard,20 M. Verderi,20P. J. Clark,21S. Playfer,21J. E. Watson,21D. Bettoni,22aC. Bozzi,22aR. Calabrese,22a,22bG. Cibinetto,22a,22b
E. Fioravanti,22a,22bI. Garzia,22a,22bE. Luppi,22a,22bM. Munerato,22a,22bM. Negrini,22a,22bL. Piemontese,22a R. Baldini-Ferroli,23A. Calcaterra,23R. de Sangro,23G. Finocchiaro,23M. Nicolaci,23S. Pacetti,23P. Patteri,23
I. M. Peruzzi,23,†M. Piccolo,23M. Rama,23A. Zallo,23R. Contri,24a,24bE. Guido,24a,24bM. Lo Vetere,24a,24b M. R. Monge,24a,24bS. Passaggio,24aC. Patrignani,24a,24bE. Robutti,24aB. Bhuyan,25V. Prasad,25C. L. Lee,26M. Morii,26
A. J. Edwards,27A. Adametz,28J. Marks,28U. Uwer,28F. U. Bernlochner,29M. Ebert,29H. M. Lacker,29T. Lueck,29 P. D. Dauncey,30M. Tibbetts,30P. K. Behera,31U. Mallik,31C. Chen,32J. Cochran,32H. B. Crawley,32W. T. Meyer,32
S. Prell,32E. I. Rosenberg,32A. E. Rubin,32A. V. Gritsan,33Z. J. Guo,33N. Arnaud,34M. Davier,34D. Derkach,34 G. Grosdidier,34F. Le Diberder,34A. M. Lutz,34B. Malaescu,34P. Roudeau,34M. H. Schune,34A. Stocchi,34G. Wormser,34
D. J. Lange,35D. M. Wright,35I. Bingham,36C. A. Chavez,36J. P. Coleman,36J. R. Fry,36E. Gabathuler,36 D. E. Hutchcroft,36D. J. Payne,36C. Touramanis,36A. J. Bevan,37F. Di Lodovico,37R. Sacco,37M. Sigamani,37 G. Cowan,38S. Paramesvaran,38D. N. Brown,39C. L. Davis,39A. G. Denig,40M. Fritsch,40W. Gradl,40A. Hafner,40 K. E. Alwyn,41D. Bailey,41R. J. Barlow,41G. Jackson,41G. D. Lafferty,41R. Cenci,42B. Hamilton,42A. Jawahery,42 D. A. Roberts,42G. Simi,42C. Dallapiccola,43E. Salvati,43R. Cowan,44D. Dujmic,44G. Sciolla,44D. Lindemann,45 P. M. Patel,45S. H. Robertson,45M. Schram,45P. Biassoni,46a,46bA. Lazzaro,46a,46bV. Lombardo,46aF. Palombo,46a,46b
S. Stracka,46a,46bL. Cremaldi,47R. Godang,47,‡R. Kroeger,47P. Sonnek,47D. J. Summers,47X. Nguyen,48P. Taras,48 G. De Nardo,49a,49bD. Monorchio,49a,49bG. Onorato,49a,49bC. Sciacca,49a,49bG. Raven,50H. L. Snoek,50C. P. Jessop,51
K. J. Knoepfel,51J. M. LoSecco,51W. F. Wang,51K. Honscheid,52R. Kass,52J. Brau,53R. Frey,53N. B. Sinev,53 D. Strom,53E. Torrence,53E. Feltresi,54a,54bN. Gagliardi,54a,54bM. Margoni,54a,54bM. Morandin,54aM. Posocco,54a
M. Rotondo,54aF. Simonetto,54a,54bR. Stroili,54a,54bE. Ben-Haim,55M. Bomben,55G. R. Bonneaud,55H. Briand,55 G. Calderini,55J. Chauveau,55O. Hamon,55Ph. Leruste,55G. Marchiori,55J. Ocariz,55S. Sitt,55M. Biasini,56a,56b
E. Manoni,56a,56bA. Rossi,56a,56bC. Angelini,57a,57bG. Batignani,57a,57bS. Bettarini,57a,57bM. Carpinelli,57a,57b,§ G. Casarosa,57a,57bA. Cervelli,57a,57bF. Forti,57a,57bM. A. Giorgi,57a,57bA. Lusiani,57a,57cN. Neri,57a,57bB. Oberhof,57a,57b
E. Paoloni,57a,57bA. Perez,57aG. Rizzo,57a,57bJ. J. Walsh,57aD. Lopes Pegna,58C. Lu,58J. Olsen,58A. J. S. Smith,58 A. V. Telnov,58F. Anulli,59aG. Cavoto,59aR. Faccini,59a,59bF. Ferrarotto,59aF. Ferroni,59a,59bM. Gaspero,59a,59b L. Li Gioi,59aM. A. Mazzoni,59aG. Piredda,59aC. Bu¨nger,60T. Hartmann,60T. Leddig,60H. Schro¨der,60R. Waldi,60 T. Adye,61E. O. Olaiya,61F. F. Wilson,61S. Emery,62G. Hamel de Monchenault,62G. Vasseur,62Ch. Ye`che,62D. Aston,63
D. J. Bard,63R. Bartoldus,63J. F. Benitez,63C. Cartaro,63M. R. Convery,63J. Dorfan,63G. P. Dubois-Felsmann,63 W. Dunwoodie,63R. C. Field,63M. Franco Sevilla,63B. G. Fulsom,63A. M. Gabareen,63M. T. Graham,63P. Grenier,63
C. Hast,63W. R. Innes,63M. H. Kelsey,63H. Kim,63P. Kim,63M. L. Kocian,63D. W. G. S. Leith,63P. Lewis,63S. Li,63 B. Lindquist,63S. Luitz,63V. Luth,63H. L. Lynch,63D. B. MacFarlane,63D. R. Muller,63H. Neal,63S. Nelson,63I. Ofte,63
M. Perl,63T. Pulliam,63B. N. Ratcliff,63A. Roodman,63A. A. Salnikov,63V. Santoro,63R. H. Schindler,63A. Snyder,63 D. Su,63M. K. Sullivan,63J. Va’vra,63A. P. Wagner,63M. Weaver,63W. J. Wisniewski,63M. Wittgen,63D. H. Wright,63 H. W. Wulsin,63A. K. Yarritu,63C. C. Young,63V. Ziegler,63W. Park,64M. V. Purohit,64R. M. White,64J. R. Wilson,64
A. Randle-Conde,65S. J. Sekula,65M. Bellis,66P. R. Burchat,66T. S. Miyashita,66M. S. Alam,67J. A. Ernst,67 R. Gorodeisky,68N. Guttman,68D. R. Peimer,68A. Soffer,68P. Lund,69S. M. Spanier,69R. Eckmann,70J. L. Ritchie,70
A. M. Ruland,70C. J. Schilling,70R. F. Schwitters,70B. C. Wray,70J. M. Izen,71X. C. Lou,71F. Bianchi,72a,72b D. Gamba,72a,72bL. Lanceri,73a,73bL. Vitale,73a,73bN. Lopez-March,74F. Martinez-Vidal,74A. Oyanguren,74H. Ahmed,75
J. Albert,75Sw. Banerjee,75H. H. F. Choi,75G. J. King,75R. Kowalewski,75M. J. Lewczuk,75C. Lindsay,75I. M. Nugent,75 J. M. Roney,75R. J. Sobie,75T. J. Gershon,76P. F. Harrison,76T. E. Latham,76E. M. T. Puccio,76H. R. Band,77S. Dasu,77
Y. Pan,77R. Prepost,77C. O. Vuosalo,77and S. L. Wu77
(BABARCollaboration)
1Laboratoire d’Annecy-le-Vieux de Physique des Particules (LAPP), Universite´ de Savoie, CNRS/IN2P3,
F-74941 Annecy-Le-Vieux, France
2Universitat de Barcelona, Facultat de Fisica, Departament ECM, E-08028 Barcelona, Spain 3aINFN Sezione di Bari, I-70126 Bari, Italy
3bDipartimento di Fisica, Universita` di Bari, I-70126 Bari, Italy 4University of Bergen, Institute of Physics, N-5007 Bergen, Norway 5Lawrence Berkeley National Laboratory and University of California,
Berkeley, California 94720, USA
6Ruhr Universita¨t Bochum, Institut fu¨r Experimentalphysik 1, D-44780 Bochum, Germany 7University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z1
8Brunel University, Uxbridge, Middlesex UB8 3PH, United Kingdom 9Budker Institute of Nuclear Physics, Novosibirsk 630090, Russia 10University of California at Irvine, Irvine, California 92697, USA 11University of California at Riverside, Riverside, California 92521, USA 12University of California at Santa Barbara, Santa Barbara, California 93106, USA 13
University of California at Santa Cruz, Institute for Particle Physics, Santa Cruz, California 95064, USA
14California Institute of Technology, Pasadena, California 91125, USA 15University of Cincinnati, Cincinnati, Ohio 45221, USA 16University of Colorado, Boulder, Colorado 80309, USA 17Colorado State University, Fort Collins, Colorado 80523, USA
18Technische Universita¨t Dortmund, Fakulta¨t Physik, D-44221 Dortmund, Germany
19Technische Universita¨t Dresden, Institut fu¨r Kern- und Teilchenphysik, D-01062 Dresden, Germany 20Laboratoire Leprince-Ringuet, CNRS/IN2P3, Ecole Polytechnique, F-91128 Palaiseau, France
21University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom 22a
INFN Sezione di Ferrara, I-44100 Ferrara, Italy
22bDipartimento di Fisica, Universita` di Ferrara, I-44100 Ferrara, Italy 23INFN, Laboratori Nazionali di Frascati, I-00044 Frascati, Italy
24aINFN Sezione di Genova, I-16146 Genova, Italy
24bDipartimento di Fisica, Universita` di Genova, I-16146 Genova, Italy 25Indian Institute of Technology Guwahati, Guwahati, Assam, 781 039, India
26Harvard University, Cambridge, Massachusetts 02138, USA 27Harvey Mudd College, Claremont, California 91711
28Universita¨t Heidelberg, Physikalisches Institut, Philosophenweg 12, D-69120 Heidelberg, Germany 29Humboldt-Universita¨t zu Berlin, Institut fu¨r Physik, Newtonstr. 15, D-12489 Berlin, Germany
30Imperial College London, London, SW7 2AZ, United Kingdom 31University of Iowa, Iowa City, Iowa 52242, USA 32Iowa State University, Ames, Iowa 50011-3160, USA 33Johns Hopkins University, Baltimore, Maryland 21218, USA
34Laboratoire de l’Acce´le´rateur Line´aire, IN2P3/CNRS et Universite´ Paris-Sud 11,
Centre Scientifique d’Orsay, B. P. 34, F-91898 Orsay Cedex, France
35
Lawrence Livermore National Laboratory, Livermore, California 94550, USA
36University of Liverpool, Liverpool L69 7ZE, United Kingdom 37Queen Mary, University of London, London, E1 4NS, United Kingdom
38University of London, Royal Holloway and Bedford New College,
Egham, Surrey TW20 0EX, United Kingdom
39University of Louisville, Louisville, Kentucky 40292, USA
40Johannes Gutenberg-Universita¨t Mainz, Institut fu¨r Kernphysik, D-55099 Mainz, Germany 41University of Manchester, Manchester M13 9PL, United Kingdom
42University of Maryland, College Park, Maryland 20742, USA 43University of Massachusetts, Amherst, Massachusetts 01003, USA 44Massachusetts Institute of Technology, Laboratory for Nuclear Science,
45McGill University, Montre´al, Que´bec, Canada H3A 2T8 46aINFN Sezione di Milano, I-20133 Milano, Italy
46bDipartimento di Fisica, Universita` di Milano, I-20133 Milano, Italy 47University of Mississippi, University, Mississippi 38677, USA
48Universite´ de Montre´al, Physique des Particules, Montre´al, Que´bec, Canada H3C 3J7 49aINFN Sezione di Napoli, I-80126 Napoli, Italy
49bDipartimento di Scienze Fisiche, Universita` di Napoli Federico II, I-80126 Napoli, Italy 50NIKHEF, National Institute for Nuclear Physics and High Energy Physics,
NL-1009 DB Amsterdam, The Netherlands
51University of Notre Dame, Notre Dame, Indiana 46556, USA 52Ohio State University, Columbus, Ohio 43210, USA
53University of Oregon, Eugene, Oregon 97403, USA 54aINFN Sezione di Padova, I-35131 Padova, Italy
54bDipartimento di Fisica, Universita` di Padova, I-35131 Padova, Italy
55Laboratoire de Physique Nucle´aire et de Hautes Energies, IN2P3/CNRS, Universite´ Pierre et Marie Curie-Paris6,
Universite´ Denis Diderot-Paris7, F-75252 Paris, France
56aINFN Sezione di Perugia, I-06100 Perugia, Italy
56bDipartimento di Fisica, Universita` di Perugia, I-06100 Perugia, Italy 57aINFN Sezione di Pisa, I-56127 Pisa, Italy
57bDipartimento di Fisica, Universita` di Pisa, I-56127 Pisa, Italy 57cScuola Normale Superiore di Pisa, I-56127 Pisa, Italy 58Princeton University, Princeton, New Jersey 08544, USA
59aINFN Sezione di Roma, I-00185 Roma, Italy
59bDipartimento di Fisica, Universita` di Roma La Sapienza, I-00185 Roma, Italy 60
Universita¨t Rostock, D-18051 Rostock, Germany
61Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX11 0QX, United Kingdom 62CEA, Irfu, SPP, Centre de Saclay, F-91191 Gif-sur-Yvette, France
63SLAC National Accelerator Laboratory, Stanford, California 94309 USA 64University of South Carolina, Columbia, South Carolina 29208, USA
65Southern Methodist University, Dallas, Texas 75275, USA 66Stanford University, Stanford, California 94305-4060, USA 67State University of New York, Albany, New York 12222, USA 68Tel Aviv University, School of Physics and Astronomy, Tel Aviv, 69978, Israel
69University of Tennessee, Knoxville, Tennessee 37996, USA 70University of Texas at Austin, Austin, Texas 78712, USA 71University of Texas at Dallas, Richardson, Texas 75083, USA
72aINFN Sezione di Torino, I-10125 Torino, Italy
72bDipartimento di Fisica Sperimentale, Universita` di Torino, I-10125 Torino, Italy 73aINFN Sezione di Trieste, I-34127 Trieste, Italy
73bDipartimento di Fisica, Universita` di Trieste, I-34127 Trieste, Italy 74IFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spain 75University of Victoria, Victoria, British Columbia, Canada V8W 3P6 76Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
77University of Wisconsin, Madison, Wisconsin 53706, USA
(Received 27 April 2011; published 10 October 2011; corrected 18 October 2011)
We use (111 1) million ð3SÞ and (89 1) million ð2SÞ events recorded by the BABAR detector at the PEP-II B-factory at SLAC to perform a study of radiative transitions between bottomonium states using photons that have been converted to eþe pairs by the detector material. We observe ð3SÞ ! b0;2ð1PÞ decay, make precise measurements of the branching fractions for b1;2ð1P; 2PÞ ! ð1SÞ and
b1;2ð2PÞ ! ð2SÞ decays, and search for radiative decay to the bð1SÞ and bð2SÞ states.
DOI:10.1103/PhysRevD.84.072002 PACS numbers: 13.20.Gd, 14.40.Pq
*Now at Temple University, Philadelphia, Pennsylvania 19122, USA
†Also at Universita` di Perugia, Dipartimento di Fisica, Perugia, Italy ‡Now at University of South Alabama, Mobile, Alabama 36688, USA §Also at Universita` di Sassari, Sassari, Italy
I. INTRODUCTION
Bottomonium spectroscopy and radiative transitions between b b states can be well-described by effective po-tential models [1]. To leading order, radiative decays are expected to be dominantly electric (E1) or magnetic (M1) dipole transitions. In the nonrelativistic limit, theoretical predictions for these decays are straightforward and well-understood. However, there are a few notable cases where the nonrelativistic decay rates are small or zero, e.g. in ‘‘hindered’’ M1 transitions between S-wave bottomonium such as ðnSÞ ! bðn0SÞ (n > n0), and as a consequence
of small initial- and final-state wave-function overlap in the case of ð3SÞ ! bJð1PÞ decays [2]; higher-order
rela-tivistic and model-dependent corrections then play a sub-stantial role. Measurements of these and other E1 transition rates can lead to a better understanding of the relativistic contributions to, and model dependencies of, interquark potentials. Furthermore, because radiative transitions have a distinct photon energy signature associated with the mass difference between the relevant b b states, they are useful in spectroscopic studies for mass measurements, and in the search for and identification of undiscovered resonances.
Radiative transitions within the bottomonium system have been studied previously in several experiments, such as Crystal Ball [3,4], ARGUS with converted photons [5], and iterations of CUSB [6–10] and CLEO [11–15] (including an analysis of photon-pair conversions in a lead radiator inserted specifically for that purpose [16]). These analyses have focused mainly on bJðnPÞ-related
measure-ments, such as the determination of the masses and the E1 transition rates to and from ðmSÞ states. More recently, the BABAR experiment finished its operation by collecting large samples of data at the ð3SÞ and ð2SÞ center-of-mass (CM) energies. These data are useful for studies of bottomonium spectroscopy and decay and have already led to the discovery of the long-sought bð1SÞ bottomonium
ground state [17,18], an observation later confirmed by CLEO [19].
In this paper, we present a study of radiative transitions in the bottomonium system using the inclusive converted photon energy spectrum from ð3SÞ and ð2SÞ decays. The rate of photon conversion and the reconstruction of the resulting eþepairs has a much lower detection efficiency than that for photons in the BABAR electromagnetic calo-rimeter, a disadvantage offset by a substantial improve-ment in the photon energy resolution. This improveimprove-ment in resolution is well-suited for performing precise transition energy (hence, particle mass, and, potentially, width) mea-surements, and to disentangle overlapping photon energy lines in the inclusive photon energy spectrum. This analy-sis has different techniques, data selection, and systematic uncertainties than the previous studies [17–19], and it is relatively free from complications due to overlapping transition peaks, and calorimeter energy scale and mea-surement uncertainties. We report meamea-surements of
bJð2PÞ ! ð2SÞ, bJð1P; 2PÞ ! ð1SÞ, observation
of ð3SÞ ! b0;2ð1PÞ, and searches for the bð1S; 2SÞ
states.
In Sec.IIwe describe the BABAR detector and the data samples used in this analysis. Section III describes the photon conversion reconstruction procedure and the event selection criteria. Each of the following sections (IV,V,VI, andVII) individually describes the analysis of a particular region of interest in the inclusive photon energy spectrum. Section VIII summarizes the results obtained. Appendix provides specific details of some systematic uncertainties related to this analysis.
II. THEBABAR DETECTOR AND DATA SAMPLES
The BABAR detector is described in detail elsewhere [20]; a brief summary is provided here. Moving outwards from the collision axis, the detector consists of a double-sided five-layer silicon vertex tracker (SVT) for measuring decay vertices close to the interaction point, a 40-layer drift chamber (DCH) for charged-particle tracking and momen-tum measurement, a ring-imaging Cherenkov detector for particle identification, and a CsI(Tl) crystal electromag-netic calorimeter (EMC) for measuring the energy depos-ited by electrons and photons. These detector subsystems are contained within a large solenoidal magnet which generates a 1.5 T field. The steel magnetic flux return is instrumented with a muon detection system consisting of resistive plate chambers and limited streamer tubes [21].
The inner tracking region also contains noninstrumented support structure elements. Interior to the SVT, the inter-action region is surrounded by a water-cooled, gold-coated beryllium beam pipe. The SVT support structure consists primarily of carbon fiber and KevlarÒ. The SVT, beam pipe and vacuum chamber, and the near-interaction-point magnetic elements are mounted inside a cylindrical, carbon-fiber support tube. The inner wall of the DCH is a cylindrical tube of beryllium coated with anticorrosion paint. A photon at normal incidence traverses approxi-mately 0.01 radiation lengths (X0) of material before
reach-ing the SVT, and an additional 0:03X0 before the DCH.
Because of the asymmetric energy of the incoming eþe beams, the photons in this analysis tend to be boosted in the direction of the ebeam, increasing the typical number of radiation lengths up to 0:02X0 and 0:08X0 to reach the
previously noted detector subsystems. While this extra material is usually considered detrimental to detector per-formance, it is essential for ! eþe conversions in the present analysis.
The BABAR detector collected data samples of (121 1) million ð3SÞ and (98 1) million ð2SÞ de-cays [22] produced by the PEP-II asymmetric energy eþe collider. This corresponds to an integrated luminosity of 27:9 0:2 fb1 (13:6 0:1 fb1) taken at the ð3SÞ (ð2SÞ) resonance. Approximately 10% of these data
(referred to here as the ‘‘test sample’’) were used for feasibility studies and event selection optimization; they are excluded in the final analysis. The results presented in this analysis are based on data samples of (111 1) million ð3SÞ and (89 1) million ð2SÞ de-cays. An additional 2:60 0:02 ð1:42 0:01Þ fb1of data were taken at a CM energy approximately 30 MeV below the nominal ð3SÞ (ð2SÞ) resonance energy, to be used for efficiency-related studies.
Large Monte Carlo (MC) datasets simulating the signal and expected background decay modes are used for the determination of efficiencies and the parametrization of line shapes for signal extraction. The particle production and decays are simulated using a combination ofEVTGEN [23] and JETSET [24]. The radiative decays involving bJðnPÞ states are assumed to be dominantly E1 radiative
transitions, and the MC events are generated with theoreti-cally predicted helicity amplitudes [25]. The interactions of the decay products traversing the detector are modeled by Geant4 [26].
III. EVENT RECONSTRUCTION AND SELECTION
Photon conversions are reconstructed with a dedicated fitting algorithm that pairs oppositely charged particle tracks to form secondary vertices away from the interaction point. The algorithm minimizes a 2 value (2
fit) based on
the difference between the measured helical track parame-ters and those expected for the hypothesis that the second-ary vertex had originated from two nearly parallel tracks emitted from a ! eþe conversion. The 2
fit value
in-cludes a term to account for an observed finite opening angle between the converted tracks. Requiring 2
fit< 34 is
found to be the optimal value to select a high-purity con-verted photon sample. The reconstructed concon-verted pho-tons are also required to have an eþe invariant mass of meþe< 30 MeV=c2(although, in practice, meþeis
typi-cally less than 10 MeV=c2). To remove internal conver-sions and Dalitz decays, and to improve signal purity, the conversion vertex radius () is required to satisfy
1:7 < < 27 cm. This restricts the photon conversions
to the beam pipe, SVT, support tube, and the inner wall of the DCH, as seen in the plot of conversion vertex position for a portion of the test sample in Fig.1. The efficiency for photon conversion and reconstruction versus energy in the CM frame (E), as determined from a generic ð3SÞ MC
sample, is shown in Fig.2.
Figure3shows the inclusive distributions of the result-ing reconstructed converted photon energy. The data are divided into four energy ranges, as indicated by the shaded regions in Fig.3. These ranges, and the corre-sponding bottomonium transitions of interest listed in parentheses, are, in ð3SÞ data: 180 E
300 MeV (bJð2PÞ ! ð2SÞ); 300 E 600 MeV
(ð3SÞ ! bJð1PÞ and ð3SÞ ! bð2SÞ); 600
E 1100 MeV (bJð2PÞ ! ð1SÞ and ð3SÞ !
bð1SÞ); and, in ð2SÞ data: 300 E 800 MeV
(bJð1PÞ ! ð1SÞ and ð2SÞ ! bð1SÞ). Figure4
summarizes these energy ranges and the radiative transi-tions of interest in a pictorial form. Peaks related to some of these transitions are already clearly visible in Fig. 3, where the photon energy in the CM frame of the initial particle for the radiative transition from an initial (i) to final (f) state is given in terms of their respective masses by
Eði ! fÞ ¼ m2 i m2f 2mi c2: (1) x (cm) -30 -20 -10 0 10 20 30 y (cm) -30 -20 -10 0 10 20 30 0 20 40 60 80 100 120 140 160
FIG. 1 (color online). End view of the BABAR inner detector along the beam axis as seen by converted photons. Points indicate the number of converted photon vertices per cross-sectional area, as measured in a subset of the test sample data. From the center outward, features of note include the beam pipe, the SVT (the hexagonal inner layers) and its support structure rods, the support tube, and the inner wall of the DCH.
(GeV)
* γ
E
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Photon Efficiency / (10 MeV)
0 0.005 0.01 0.015 0.02 0.025
FIG. 2. Efficiency for the conversion and reconstruction of a photon versus photon energy as derived from a sample of generic ð3SÞ MC events before the optimal selection criteria have been applied.
Because we analyze the photon energy in the CM frame of the initial ðmSÞ system (E), the photon spectra from
subsequent boosted decays (e.g. bJðnPÞ ! ð1SÞ) are
affected by Doppler broadening due to the motion of the parent state in the CM frame.
To best enhance the number of signal (S) to background (B) events, the event selection criteria are chosen by optimizing the figure of merit F ¼ ffiffiffiffiffiffiffiffiS
SþB
p . This is done separately for each energy region. The 180 E
300 MeV energy region in ð3SÞ uses the same criteria as determined for the similarly low-energy 300 E
600 MeV range. We determine S from MC samples of ðmSÞ ! bð1SÞ weighted to match the measured
branching fractions [27], and ð3SÞ ! bð2SÞ, assuming
the same branching fraction as for the decay to bð1SÞ.
Because the generic decay processes of ð3SÞ are not well-known (i.e. a large percentage of the exclusive branching fractions have not been measured), the test sample data are used to estimate B. The optimization is performed by varying the selection criteria for the total number of tracks in the event (nTRK), the absolute value of the cosine of the angle in the CM frame between the photon momentum and
the thrust axis (j cosTj) [28], and a 0 veto excluding
converted photons producing an invariant mass (m)
con-sistent with m0 when paired with any other photon (con-verted or calorimeter-detected) above a minimum energy (E2) in the event. A requirement on the ratio of the second
and zeroth Fox-Wolfram moments [29] of each event, R2,
is also applied. The reason for using these particular var-iables (indicated in parentheses) is to preferentially select bottomonium decays to hadronic final states (nTRK), and to remove photons from continuum background events (j cosTj and R2) and 0 decays (m
0 veto). TableI sum-marizes the values for the optimized selection criteria.
The efficiency for reconstruction and selection of signal events () is determined from MC simulation. A dedicated eþe! þ sample is used to study our detector model and converted photon efficiency (discussed in Appendix ), and the correspondence between simulation and data is found to be in very good agreement. Once the (GeV) * γ E 0 0.2 0.4 0.6 0.8 1 1.2 Events / (4 MeV) 0 10000 20000 30000 40000 50000 60000 70000 (a) IV V VII (GeV) * γ E 0 0.2 0.4 0.6 0.8 1 1.2 Events / (4 MeV) 0 10000 20000 30000 40000 50000 (b) VI
FIG. 3. Raw inclusive converted photon energy spectrum from (a) ð3SÞ and (b) ð2SÞ decays. The shaded areas indicate different regions of interest considered in detail in this analysis. Each Roman numeral indicates the corresponding section of this article in which each energy region is discussed.
(1S) b η Υ(1S) (1P) bJ χ ) J (1D Υ (2S) b η Υ(2S) (2P) bJ χ (3S) Υ V VI VII V VI VII IV IV
FIG. 4. Pictorial representation of energy levels in the botto-monium system and the radiative transitions studied here. Each Roman numeral indicates the corresponding section of this article in which the labeled transition is discussed.
TABLE I. Acceptance criteria for converted photon events.
Variable E range (MeV)
ð3SÞ ð3SÞ ð2SÞ [180, 600] [600, 1100] [300, 800] nTRK 8 8 8 j cosTj <0:85 <0:75 <0:85 jm m0j (MeV=c2) >10 >20 >20 E2(MeV) >90 >75 >70 R2 <0:98 <0:98 <0:98
optimal selection criteria have been applied, & 1:5% for conversions compared to40% for photons in the EMC for the energy range of interest in this analysis. Conversely, a large improvement is gained in photon energy resolution, e.g. from25 MeV in the calorimeter to 4 MeV or better with converted photons. Figure 3 demonstrates both of these features. The sharply peaking structures correspond to bottomonium transitions, and are narrow and well-resolved in this analysis. Unlike in the photon energy spectrum expected from the EMC [17,18], the distribution for converted photons drops with energy. The efficiency decreases (also seen in Fig. 2) due to the inability to fully reconstruct the conversion pair as at least one of the individual track momenta approaches the limit of detector sensitivity. We are unable to contribute useful new information on transitions expected below E ¼
180ð300Þ MeV for the ð3SÞ (ð2SÞ) analysis, which is why those energy ranges are not considered here.
The number of signal events for a given bottomonium transition is extracted from the data by performing a 2 fit to the Edistribution in 1 MeV bins. The functional form
and parametrization for each photon signal is determined from MC samples, as described below. In general, the line shape is related to the Crystal Ball function [30], i.e. a Gaussian function with a power-law tail. This functional form is used to account for bremsstrahlung losses of the eþe pair. Comparisons between simulation and data made on eþe ! eþe events used for the standard luminosity measurement in BABAR demonstrate that the bremsstrahlung tails of these distributions are found to be well-described. The underlying smooth inclusive photon background is described by a fourth-order polynomial multiplied by an exponential function. This functional form adequately describes the background in each separate energy range.
IV.ð3SÞ: 180 E 300 MeV
The main purpose of the fit to the 180 E
300 MeV region of the ð3SÞ photon energy spectrum, shown in detail in Fig. 5, is to measure the bJð2PÞ !
ð2SÞ transitions. The only previous measurements of these transitions were made by CUSB [10] and CLEO [12] nearly two decades ago. Those analyses examined the low-energy photon spectrum from exclusive ð3SÞ ! ð2SÞð‘þ‘Þ decays to derive the branching fractions forBðb1;2ð2PÞ ! ð2SÞÞ, and, in the case of the CUSB result, to obtain evidence for b0ð2PÞ ! ð2SÞ. We
present the first fit to E to measure the photon from
bJð2PÞ ! ð2SÞ directly. Although this analysis is
potentially sensitive to all six ð1DJÞ ! bJð1PÞ decays,
we treat these decays as a small systematic effect to the bJð2PÞ ! ð2SÞ measurement.
The bJð2PÞ transition line shapes are parametrized by a
Gaussian with power-law tails on both the high and low side. This is best understood as a ‘‘double-sided’’ Crystal
Ball function with different transition points and exponents for the high and low tails, but with a common Gaussian mean and standard deviation in the central region. The effects of Doppler broadening, due to the motion of the bJð2PÞ in the CM frame, are small (2 MeV width) for
these transitions. The ð1DJÞ-related line shapes are
indi-vidually parametrized in terms of a single Crystal Ball function. Parametrization of these transitions presents a complication because only the mass of the J ¼ 2 state has been measured reliably [31,32], the value mð1D2Þ¼ ð10 163:7 1:4Þ MeV=c2being obtained when the
experi-mental results are averaged. Marginal evidence for the J ¼ 1 and 3 states was also seen at 10 152 MeV=c2
and10 173 MeV=c2, respectively [31,32]. These values are consistent with several theoretical predictions [33], given a shift to bring the theoretical value for mð1D2Þ into agreement with experiment. We therefore assume the
(GeV) * γ E 0.18 0.2 0.22 0.24 0.26 0.28 0.3 Events / (1 MeV) 0 500 1000 1500 2000 2500 3000 3500 4000 4500 (a) (GeV) * γ E 0.18 0.2 0.22 0.24 0.26 0.28 0.3 Events / (2 MeV) -200 0 200 400 600 800 1000 1200 (b) (2P) b0 χ (2P) b1 χ (2P) b2 χ ) J (1D Υ
FIG. 5. Fit to the 180 E 300 MeV region of the ð3SÞ
data (a) for all of the data, and (b) after subtraction of the fitted background contribution. The 2=ndof (where ndof stands for
number of degrees of freedom) for the fit is 119:1=110. The thin gray lines indicate the individual signal components in the fit, as labeled.
mð1D1;3Þmass values stated above to compute the expected energy for transitions from those states. The event yields for these transitions are fixed to the branching fractions expected when Bðð3SÞ ! bJð2PÞÞ [27] is combined with the predictions for BðbJð2PÞ ! bJð1PÞÞ via ð1DJÞ [34]. The efficiencies for the ð1DJÞ transition
signals range from approximately 0.17 to 0.30%, mono-tonically rising with E.
Figure 5 shows the measured photon spectrum and results of the fit, before and after subtraction of the inclu-sive background. In this fit, the parameters describing the background and any systematic offset in the E scale are
free parameters, together with the signal yields for bJð2PÞ ! ð2SÞ decays. Table II summarizes the fit
results. Considering both statistical and systematic uncer-tainties, we find significant b1;2ð2PÞ ! ð2SÞ signals
( >12 and >8 , respectively, where represents stan-dard deviation), but we do not find evidence for b0ð2PÞ !
ð2SÞ decay. The overall energy offset, determined pre-dominantly by the position of the b1;2ð2PÞ transition
peaks compared to the nominal [27] values, is found to be inconsequential ( 0:3 0:2 MeV).
The systematic uncertainties on these measurements (with their approximate sizes given in parentheses below and throughout) include the uncertainty in the fit parame-ters fixed from MC, uncertainty in the converted photon efficiency, assumptions related to the ð1DJÞ
contribu-tions, uncertainty on masses used to calculate the expected E values, the ðmSÞ counting uncertainty, effects of the
fit mechanics, and the effect of the choice for the back-ground shape. For each fit component, all of the parameters fixed to MC-determined values are varied individually by 1 of the statistical uncertainty from the MC determi-nation, and the fit repeated. The maximal variation of the fit result for each component is taken as the systematic un-certainty, and summed in quadrature (4%). The system-atic uncertainty on the converted photon efficiency (4.7%) is estimated using an off-peak control sample and varied selection criteria, as described for all energy regions in Appendix . The fits are repeated with the ð1DJÞ masses
individually varied by their approximate experimental un-certainties ( 1:8, 1:4, and 1:5 MeV=c2 for J ¼ 1, 2,
and 3, respectively) [32], and the fixed yields by50% of the theoretical values [34]. To make a theory-independent determination of the impact due to ð1DJÞ, the fit is also
repeated with four of the ð1DJÞ ! bJð1PÞ yields free
to vary. (The ð1D1Þ ! b1ð1PÞ and ð1D3Þ !
b2ð1PÞ yields are fit as a single component because
their E values are nearly identical, and the ð1D1Þ !
b2ð1PÞ transition is overwhelmed by the main
b1;2ð2PÞ ! ð2SÞ peaks and remains fixed.) Under
this scenario, none of the ð1DJÞ-related transitions is
found to be significant, and the yields are consistent with the theoretical predictions within statistical uncertainty. The bJð2PÞ ! ð2SÞ yields are not significantly
affected. The changes in the fit yields for all of these alternative cases are added in quadrature and taken as the systematic uncertainty due to ð1DJÞ decays ( 2%). It is
worth reiterating that the excellent resolution obtained by using converted photons separates the ð1DJÞ- and
bJð2PÞ-related components in E, which is why the
im-pact of the ð1DJÞ states does not dominate the
measure-ment uncertainty. The fit is repeated with the bottomonium masses (hence, Evalues) varied according to the Particle
Data Group (PDG) uncertainties [27], and the change in the yield added in quadrature (2%). The number of ðmSÞ mesons and its uncertainty (1.0%) were calculated separately, based on visible cross sections computed from dedicated eþe! eþeðÞ and eþe ! þðÞ con-trol samples. Systematic effects due to the fit mechanics were tested by repeating the fit separately with an ex-panded Erange and a bin width of 0.5 MeV, the difference
in results defining a small systematic uncertainty (1.5%). As a cross-check, the fit was repeated with the b0ð2PÞ
component restricted to a physical range. The effect on the other signal yields was found to be small ( < 2%). Finally, the background shape was replaced by a fifth-order polynomial and half of the resulting change in the yield (< 1%) was taken as the symmetric error due to this assumed parametrization.
We findBðð3SÞ ! bJð2PÞÞ BðbJ! ð2SÞÞ ¼ ð0:3 0:2þ0:5
0:4Þ%, ð2:4 0:1 0:2Þ%, and ð1:1 0:1
0:1Þ% for J ¼ 0, 1, and 2, respectively. Using Bðð3SÞ ! bJð2PÞÞ from [27], we deriveBðbJð2PÞ ! ð2SÞÞ ¼
ð4:7 2:8þ0:7
0:8 0:5Þ%, ð18:9 1:1 1:2 1:8Þ%, and
ð8:3 0:8 0:6 1:0Þ%, where the errors are statistical, systematic, and from the uncertainty on Bðð3SÞ ! bJð2PÞÞ, respectively. From these values, we calculate
a 90% confidence-level upper limit of Bðb0ð2PÞ ! ð2SÞÞ < 2:8% [35]. Past experimental results [10,12] averaged by the PDG [27] rely on assumptions for the branching fractions of ð2SÞ ! ‘þ‘ and ð3SÞ ! bJð2PÞ and their uncertainties that are no longer valid.
In TableII, we have rescaled these previous results using the current values in order to make a useful comparison. We find our results to be in good agreement with the previous results and to be the most precise values to date for the J ¼ 1 and 2 decays.
V.ð3SÞ: 300 E 600 MeV
The 300 E 600 MeV range in the inclusive ð3SÞ
photon energy spectrum, shown in Fig. 6, is complicated by many radiative bottomonium transitions. A principal feature is the photon lines from the three direct ð3SÞ ! bJð1PÞ decays. Photons from the secondary decays,
bJð1PÞ ! ð1SÞ, have energies that overlap with
these initial transitions. There are several ways to produce bJð1PÞ from ð3SÞ, each with unique Doppler
broadening and relative rate. These decays ‘‘feed down’’ to produce many extraneous bJð1PÞ mesons that contribute
substantially to the background level through subsequent bJð1PÞ ! ð1SÞ decay. At the lower edge of this
energy range, there are potential contributions from ð3SÞ ! bð2SÞ and ð2SÞ production from initial state
radiation (ISR).
The best known of the ð3SÞ ! bJð1PÞ branching
fractions comes from the CLEO experiment, which was able to isolate the ð3SÞ ! b0ð1PÞ signal [14]. A
sepa-rate analysis of bJð1PÞ decays to multihadronic final
states further set upper limits on Bðð3SÞ ! bJð1PÞÞ [36]. A recent analysis of ð3SÞ ! b1;2ð1PÞ !
ð1SÞ transitions with exclusive ð1SÞ ! ‘þ‘decays has resulted in a measurement of ð3SÞ ! b1;2ð1PÞ
branching fractions [15]. Our improved E resolution
with the converted photon sample allows us to disentangle the overlapping photon lines to make a direct measurement of these radiative transitions as well. We also search for a signal for ð3SÞ ! bð2SÞ.
The direct ð3SÞ ! bJð1PÞ line shapes are
parame-trized using the double-sided Crystal Ball function de-scribed in Sec. IV plus an independent Gaussian to account for broadening from nonlinearities in the E
reso-lution due to low momentum tracks encountered in this energy range. The ð3SÞ ! bð2SÞ line shape is
mod-eled with the convolution of a relativistic Breit-Wigner function (natural line shape for the bð2SÞ) and a Crystal
Ball function (experimental resolution function), where the Breit-Wigner function has been modified by a transforma-tion of variables to E using Eq. (1). The ISR-produced
ð2SÞ signal is parametrized with a Crystal Ball function, for which the width is dominated by the spread in the eþe beam energy.
The line shapes for the decays bJð1PÞ ! ð1SÞ
de-pend on the initial decays that produced the bJð1PÞ states.
We consider six main production pathways: ð3SÞ ! bJð1PÞ;
ð3SÞ ! ð2SÞ ! bJð1PÞ;
ð3SÞ ! ð1DJÞ ! bJð1PÞ;
TABLE II. Summary of the analysis of the 180 E 300 MeV region of the ð3SÞ data. The E column lists the transition
energy assumed in this analysis. Errors on the yield are statistical only. Regarding the derived branching fractions BðbJð2PÞ ! ð2SÞÞ: the BABAR values are from this paper, while the CUSB and CLEO columns are derivations based on [10,12] using up-to-date secondary branching fractions from [27]. For the BABAR result, the listed uncertainties are statistical, systematic, and from the uncertainties on secondary branching fractions, respectively. For the other results, the total uncertainty (all sources combined in quadrature) is given. Upper limits are given at the 90% confidence level.
Transition E Yield Derived branching fraction (%)
(MeV) (%) BABAR CUSB CLEO
b0ð2PÞ ! ð2SÞ 205.0 347 209 0.105 4:7 2:8þ0:70:8 0:5ð<2:8Þ 3:6 1:6 <5:2 b1ð2PÞ ! ð2SÞ 229.7 4294 251 0.152 18:9 1:1 1:2 1:8 13:6 2:4 21:1 4:5 b2ð2PÞ ! ð2SÞ 242.3 2462 243 0.190 8:3 0:8 0:6 1:0 10:9 2:2 9:9 2:7 (GeV) * γ E 0.3 0.35 0.4 0.45 0.5 0.55 0.6 Events / (1 MeV) 0 1000 2000 3000 4000 5000 6000 (a) (GeV) * γ E 0.3 0.35 0.4 0.45 0.5 0.55 0.6 Events / (3 MeV) 0 1000 2000 3000 4000 (b) (1P) b0 χ (1P) b1 χ (1P) b2 χ (1P) b0 χ χb1(1P)χb2(1P) hb(1P)
FIG. 6. Fit to the 300 E 600 MeV region of the ð3SÞ
data (a) for all of the data, and (b) after subtraction of the fitted background contribution. The 2=ndof for the fit is 316=290.
The thick solid lines indicate the total fit; the thin solid lines indicate the ð3SÞ ! bJð1PÞ components; and the dashed
lines indicate the contributions from bJð1PÞ ! ð1SÞ and
hbð1PÞ ! bð1SÞ, as labeled above the data points for the
ð3SÞ ! bJð1PÞ components, and below the points for all
others.
ð3SÞ ! ð2SÞ ! bJð1PÞ;
ð3SÞ ! bJð2PÞ ! bJð1PÞ;
eþe ! ISRð2SÞ ! ISRbJð1PÞ:
The feed-down contribution from ð3SÞ ! bJð1PÞ is
determined directly from the fit to the data. The line shapes for the subsequent bJð1PÞ ! ð1SÞ decays are
distorted by Doppler-broadening effects. We parametrize the bJð1PÞ transition line shape with the convolution of a
rectangular function and a Crystal Ball function. Because of the large Doppler width (20 MeV), the resulting shape is relatively broad and nonpeaking. In the fit, the relative yields of the direct to the secondary transitions are fixed according to the ratios of the expected efficiencies for each mode and the branching fractions for the bJð1PÞ ! ð1SÞ decays (to be discussed below).
There are two 3 pathways from ð3SÞ to bJð1PÞ.
Decays via ð2SÞ are fairly well understood, and the precision branching-fraction results from Sec.IVare used to determine the expected yields and uncertainties. In contrast, the decays via ð1DJÞ have not been measured
in detail. We rely on theoretical predictions [34], found to be consistent with an experimental measurement of the 4 cascade to ð1SÞ [31], to estimate the total feed-down component. We take the uncertainties on Bðð3SÞ ! bJð2PÞÞ [27] and introduce a 30%
uncer-tainty on each theoretically calculated branching fraction in the decay chain. Doppler effects introduce a smooth 5 MeV broadening in these (and other) multistep decay processes, so the line shapes for the individual 3 path-ways are adequately parametrized using a standard Crystal Ball function.
There are two di-pion decay chains leading to bJð1PÞ:
via either ð3SÞ ! ð2SÞ or bJð2PÞ ! bJð1PÞ.
The former has been precisely measured by BABAR in a recent analysis of the recoil against þ to search for the hbð1PÞ state [37]. We combine the branching fraction
from that analysis with the PDG average [27] to obtain Bðð3SÞ ! þð2SÞ ¼ ð2:7 0:2Þ%. For the 00
transition, we use the current world-average branching-fraction value [27]. The relevant MC samples are generated with the experimentally determined mþ distribution
[38]. Di-pion transitions between bJð2PÞ and bJð1PÞ
for J ¼ 1 and 2 have been measured experimentally by CLEO [39]. The above-mentioned BABAR di-pion analysis [37] also measured these quantities, which are averaged with the CLEO results to derive BðbJð2PÞ ! þbJð1PÞÞ equal to ð9:1 1:0Þ 103 and ð5:0
0:6Þ 103 for J ¼ 1 and 2, respectively. Decays to the J ¼ 0 state, with different initial and final J values, and via 00 have thus far been below the level of experimental
sensitivity. To calculate the expected feed down, we as-sume isospin conservation such that 00 ¼1
2þ, and
estimateBðb0ð2PÞ ! b0ð1PÞÞ to be about one-fifth
of that of the other J states [40]. We assume a 30% uncertainty on all theoretically estimated branching fractions.
Radiative decay of ISR-produced ð2SÞ mesons can yield bJð1PÞ signals. The estimated production cross
section for ð2SÞ is ð28:6 1:4Þ pb [41], where we have assigned a 5% uncertainty to this theoretical calculation. We combine this with the ð2SÞ ! bJð1PÞ branching
fraction [27] to determine the size of this contribution to the background. From MC simulation, we conclude that the line shape may be parametrized with a Crystal Ball function.
Except for feed down from ð3SÞ ! bJð1PÞ, which
is determined from the data, the yields of these components are fixed in the fit. The branching fractions for the final step of the decay chain, BðbJð1PÞ ! ð1SÞÞ, are measured precisely for J ¼ 1 and 2 in Sec.VI. Our values for these decays are averaged with results from CLEO [15]. For decays with J ¼ 0, the CLEO [15] Collaboration has recently presented observations. Since we do not observe this decay in Sec. VI, we use the measured branching-fraction value from CLEO [15].
In the fit, we include two components related to hbð1PÞ ! bð1SÞ decays. The hbð1PÞ decay is assumed
to decay with a large branching fraction via hbð1PÞ !
bð1SÞ [42]. The two relevant hbð1PÞ production
mechanisms are ð3SÞ ! þhbð1PÞ and ð3SÞ !
0hbð1PÞ. BABAR has studied both of these modes,
finding Bðð3SÞ ! þhbð1PÞÞ < 2:5 104 [37]
and Bðð3SÞ ! 0h
bð1PÞÞ Bðhbð1PÞ ! bð1SÞÞ ¼
ð4:7 1:5 0:6Þ 104 [43]. Because of the effects of
Doppler broadening, we parametrize the decay via 0 using the Doppler-broadened Crystal Ball function as de-scribed for bJð1PÞ ! ð1SÞ transitions from ð3SÞ !
bJð1PÞ, and via þ using a standard Crystal Ball
function. The yields for these components are fixed in the fit and are nearly negligible.
In the fit, all of the line-shape parameters are fixed to the MC-determined values except for the yield of the ð3SÞ ! bJð1PÞ (and its related bJð1PÞ ! ð1SÞ
components), an overall E scale offset, and the
back-ground line-shape parameters. The feed-down yields are fixed using the branching fractions as described above. Repeated trials of the signal extraction on simulated data sets determine that, given the low efficiency and expected number of events and the high level of background, obtain-ing a reliable yield for bð2SÞ and ISR-produced ð2SÞ is
not possible. These components are therefore not included in the fit. The measured photon energy spectrum and the fitted yields are presented in Fig. 6, before and after the subtraction of the inclusive background. There is a clear separation of the ð3SÞ ! bJð1PÞ transitions, enabling
us to observe the transitions to J ¼ 0, 2 and to find only a very small indication for J ¼ 1. Table IIIsummarizes the fit results.
We consider systematic uncertainties due to the choice of background shape (1–2%), fit range, and binning (1.5%), the effect of fixing parameters to the MC-determined values (3–6%), uncertainty in the photon conversion efficiency (3.6%), uncertainty in the ðmSÞ counting (1.0%), uncertainty in the bottomonium masses (1–3%), and the impact of fixed feed-down yields (2%). The values in parentheses are representative of the ð3SÞ ! b0;2ð1PÞ decays; for the b1-related results,
the effects of the feed-down line shapes and the yields and the background shape dominate (about 20% each) due the marginal signal size. The evaluation of these un-certainties is done as described in Sec. IV, with the ex-ception of the feed-down-related uncertainty that is unique to this energy region. To assess the uncertainty related to the assumed branching fractions, we repeat the analysis many times with the value of each input branching fraction varied randomly within its total uncertainty. We adopt the standard deviation of the change in the results as a system-atic error. As a cross-check, we repeat the fit with the yields of the ð1DJÞ-related feed-down components allowed to
vary as a free parameter. We find only a small change (< 2%) in the overall branching fraction results and con-sider this to be sufficiently accounted for by the systematic uncertainty determined from our procedure of varying the branching fractions. Including ISR and bð2SÞ
compo-nents in the fit produces an effect of less than 1%, due to their slight impact on determining the overall back-ground shape.
We measure Bðð3SÞ ! bJð1PÞÞ ¼ ð2:7 0:4 0:2Þ 103, ð0:5 0:3þ0:20:1Þ 103, and ð10:5 0:3þ0:70:6Þ 103 for J ¼ 0, 1 and 2, respectively. We ob-serve evidence for the ð3SÞ ! b0;2ð1PÞ transitions,
with total significances greater than 6:8 and 16 , respec-tively. We do not find evidence for the suppressed ð3SÞ ! b1ð1PÞ decay, and set the 90% confidence-level upper
limit of Bðð3SÞ ! b1ð1PÞÞ < 1:0 103. These re-sults are consistent with previous limits [36] and improve upon the only measured value for the J ¼ 0 transition [14]. Our measurements of the ð3SÞ ! b1;2ð1PÞ branching
fractions both differ from the recent CLEO observations [15] by nearly 2 . Forcing the b1;2ð1PÞ yields in our fit to
match the CLEO results gives a poor 2=ndof (where ndof
stands for number of degrees of freedom) of 399=293.
However, using the Bðb1;2ð1PÞ ! ð1SÞÞ results from Sec. VI to derive a total ð3SÞ ! ð1SÞ branching fraction via b1;2ð1PÞ (comparable to ‘‘J ¼ 1 and 2’’
[15]), we find the results of the two experiments to be in close agreement.
Adopting these results, we search for the ð3SÞ ! bð2SÞ transition in the range 335 E 375 MeV
and find no evidence. Taking into account the dominant statistical uncertainty, we derive an upper limit of Bðð3SÞ ! bð2SÞÞ < 1:9 103 at the 90%
confi-dence level. This limit is a factor of 2 larger than the limit set by CLEO [14].
VI.ð2SÞ: 300 E 800 MeV
We study five possible signals in the 300 E
800 MeV range in ð2SÞ data: three bJð1PÞ ! ð1SÞ
transitions, ISR ð1SÞ production, and ð2SÞ ! bð1SÞ.
This energy region, shown in Fig. 7, has been analyzed using calorimeter-detected photons by both BABAR [18] and CLEO [19], the former finding evidence to confirm the bð1SÞ. The improvement in resolution from the
converted photon sample could allow a precise measure-ment of the bð1SÞ mass. However, because E for the
ð2SÞ ! bð1SÞ transition is 613 MeV (compared to
920 MeV in the ð3SÞ data), its measurement is more difficult due to a lower detection efficiency and larger inclusive photon background. Studying this energy range is nonetheless useful, since the branching fractions for bJð1PÞ ! ð1SÞ have had large uncertainties [4,6,7]
until very recently [15], and the values are necessary inputs to the analysis described in Sec. V. The J ¼ 0 decay has also only recently been observed . These external measure-ments were unavailable when this analysis was initiated.
We parametrize the bJð1PÞ transition line shape with a
Doppler-broadened Crystal Ball function, as described in Sec. V. The ISR and ð2SÞ ! bð1SÞ line shapes are
modeled with a Crystal Ball function and a relativistic Breit-Wigner function convolved with a Crystal Ball func-tion, respectively. The line-shape parameters are deter-mined from MC samples. Several different natural widths are tested for the bð1SÞ, and, because the Crystal Ball
parameter values (related to Eresolution) are found to be
independent of the width, the values averaged over all samples are used. In the fit to the data, all of the parameters
TABLE III. Summary of the analysis of the 300 E 600 MeV region of the ð3SÞ data.
The E column lists the transition energy assumed in this analysis. Errors on the yield are
statistical only. For the derived branching fractions, the BABAR values are from this work, and the CLEO results are from [14,15]. The upper limit is given at the 90% confidence level.
Transition E Yield Derived branching fractionð103Þ
(MeV) (%) BABAR CLEO
ð3SÞ ! b2ð1PÞ 433.1 9699 318 0.794 10:5 0:3þ0:70:6 7:7 1:3
ð3SÞ ! b1ð1PÞ 452.2 483 315 0.818 0:5 0:3þ0:20:1ð<1:0Þ 1:6 0:5
ð3SÞ ! b0ð1PÞ 483.5 2273 307 0.730 2:7 0:4 0:2 3:0 1:1
are fixed to these MC-determined values, except for the yields for the bJð1PÞ, ISR, and bð1SÞ signals, the mass
of the bð1SÞ, the inclusive background shape parameters,
and an overall Escale offset. The width of bð1SÞ is fixed
to 10 MeV.
Figure7 shows the converted photon energy spectrum before and after the subtraction of the inclusive back-ground, with an inset focusing on the region of the ex-pected ð2SÞ ! bð1SÞ transition. The E resolution
provides clear separation of the b1;2ð1PÞ-related peaks,
allowing for the first direct measurement of these transi-tions in an inclusive sample. The results of the fit are summarized in Table IV. We find no evidence for b0ð1PÞ ! ð1SÞ decay. The ð1SÞ yield from ISR
pro-duction is consistent, within large uncertainties, with the result scaled from the previous BABAR measurement [18]. As expected from signal extraction studies on simulated
datasets, the search for a signal in the ð2SÞ ! bð1SÞ
energy region does not find a reliable result. Estimating the statistical significance from the change in 2of the fit with and without this component results in the equivalent of a less than 2:5 effect. The E scale offset in this energy
range is0:9þ0:50:4MeV.
The systematic uncertainties on these measurements are related to the choice of background shape, the fit mechan-ics, the effect of fixing parameters to the MC-determined values, uncertainty in the photon conversion efficiency, uncertainty in the ðmSÞ counting, uncertainties in the bottomonium masses, and assumptions on the bð1SÞ
width. The methodology for the evaluation of these un-certainties has been described for the most part in Sec.IV. The systematic uncertainty related to the bð1SÞ width is
estimated by finding the maximal change in yield when the fit is repeated using a range of widths between 2.5–15 MeV, values consistent with a wide range of theoretical predic-tions. While varying the assumed bð1SÞ width affects the
event yield, it is found to have a negligible impact on the significance of the signal. For the b1;2ð1PÞ ! ð1SÞ
transitions, the largest sources of uncertainty are related to the fixed line-shape parameters (3–4%), uncertainty in the bottomonium masses (4% for b2ð2PÞ, and domi-nant for the E scale uncertainty), and the conversion
efficiency (5.2%). Each of the remaining sources contrib-utes less than 2%. For the bð1SÞ signal, systematic
un-certainties dominate the result. The largest effects are due to varying the background shape (31%), the bottomo-nium masses (25%), the MC-determined parameters (22%), and the bð1SÞ width ( 16%).
We measure Bðð2SÞ ! bJð1PÞÞ BðbJð1PÞ ! ð1SÞÞ ¼ ð8:3 5:6þ3:72:6Þ 104, ð24:1 0:6 1:5Þ 103, and ð13:9 0:5þ0:91:1Þ 103, for J ¼ 0, 1 and 2, respectively. Using Bðð2SÞ ! bJð1PÞÞ from the PDG [27], we derive BðbJð1PÞ ! ð1SÞÞ ¼ ð2:2 1:5þ1:0
0:7 0:2Þ%, ð34:9 0:8 2:2 2:0Þ%, and
ð19:5 0:7þ1:3
1:5 1:0Þ%, where the uncertainties are
sta-tistical, systematic, and from the uncertainty on Bðð2SÞ ! bJð1PÞÞ, respectively. We calculate a 90%
confidence-level upper limit of Bðb0ð1PÞ ! ð1SÞÞ < 4:6%. As previously, we rescale the existing results [4,6] using the most up-to-date secondary branching fraction values [27] to obtain the results quoted in Table IV. Our bJð1PÞ transition results agree with the previous
measure-ments, but they represent a two- to three-fold reduction in the total uncertainty. We find reasonable agreement with, and a comparable precision to, the recent measurements from CLEO [15]. When the yield-related systematic un-certainties on the measurement of the bð1SÞ candidate are
taken into account (excluding those due to the bð1SÞ
width), the result is further reduced in significance to an equivalent of 1:7 . We find no evidence for an bð1SÞ signal in this analysis of the ð2SÞ dataset, and set a corresponding limit ofBðð2SÞ ! bð1SÞÞ < 0:21%. (GeV) * γ E 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 Events / (1 MeV) 0 500 1000 1500 2000 2500 3000 3500 (a) (GeV) * γ E 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 Events / (2 MeV) 0 500 1000 1500 2000 (b) (1P) b0 χ (1P) b1 χ (1P) b2 χ ISR (1S) b η (GeV) * γ E 0.5 0.55 0.6 0.65 0.7 Events/(4 MeV) -300 -200 -100 0 100 200 300 ISR ηb(1S)
FIG. 7. Fit to the 300 E 800 MeV region of the ð2SÞ
data (a) for all of the data, and (b) after subtraction of the fitted background contribution, where the inset focuses on the ð2SÞ ! bð1SÞ region of the fit. The thin lines indicate the
VII.ð3SÞ: 600 E 1100 MeV
The analysis of the 600 E 1100 MeV region for
the ð3SÞ, shown in Fig.8, is very similar to that in Sec.VI of the 300 E 800 MeV region for the ð2SÞ. Again,
we study potential signals from three bJð2PÞ ! ð1SÞ
transitions, ð1SÞ production from ISR, and ð3SÞ ! bð1SÞ. In this case, the calorimeter-based analysis of
the same region produced the discovery of the bð1SÞ [17].
The higher E value for ð3SÞ ! bð1SÞ offers the
advantages of both an increased efficiency and a lower background level compared to the analogous analysis in ð2SÞ data, and therefore a better sensitivity for the ob-servation of bð1SÞ. There is also the possibility of
updat-ing the measurements of bJð2PÞ ! ð1SÞ transitions,
including confirmation of the decay of the J ¼ 0 state [10,12].
We parametrize the signal line shape in the same manner as described in Sec. VI, with Doppler-broadened Crystal Ball functions for the bJð2PÞ transitions, a Crystal Ball
function for ISR production of the ð1SÞ, and the relativ-istic Breit-Wigner Crystal Ball convolution for the bð1SÞ
signal. As before, all of the line-shape parameters are fixed to their MC-determined values, with the yields for the bJð2PÞ, ISR, and bð1SÞ signals, the mass of the
bð1SÞ, the inclusive background shape parameters, and
an overall Escale offset free to vary in the fit. An bð1SÞ
width of 10 MeV is assumed.
Figure8 shows the converted photon energy spectrum and fitted yields before and after the subtraction of the inclusive background, with an inset focusing on the E
region of the expected ð3SÞ ! bð1SÞ transition. The
results are summarized in Table V. Although the b1;2ð1PÞ-related peaks overlap, the E resolution is still
sufficient to measure the separate contributions. We find no evidence for b0ð2PÞ ! ð1SÞ decay. The ð1SÞ
yield from ISR production is in agreement with the expec-tation from the previous BABAR measurement [17]. The best fit for a signal in the E range corresponding to
TABLE IV. Summary of the analysis of the 300 E 800 MeV region of the ð2SÞ data. The E column lists the transition
energy assumed in this analysis, or in the case of ð2SÞ ! bð1SÞ, the most significant ð1:7 Þ feature in the relevant Eregion.
Errors on the yield are statistical only. Regarding the derived branching fractions, the BABAR values are from this paper; the Crystal Ball (CB) and CUSB columns are derivations based on [4,6] using up-to-date secondary branching fractions from the PDG [27]; and the CLEO results are from [15]. For the BABAR results, the listed uncertainties are statistical, systematic, and from the uncertainties on secondary branching fractions, respectively. Upper limits are given at the 90% confidence level. Hyphens indicate that no value has been reported in the relevant reference.
Transition E Yield Derived branching fraction (%)
(MeV) (%) BABAR CB CUSB CLEO
b0ð1PÞ ! ð1SÞ 391.5 391 267 0.496 2:2 1:5þ1:00:7 0:2ð<4:6Þ <5 <12 1:7 0:4 b1ð1PÞ ! ð1SÞ 423.0 12 604 285 0.548 34:9 0:8 2:2 2:0 34 7 40 10 33:0 2:6 b2ð1PÞ ! ð1SÞ 442.0 7665þ270272 0.576 19:5 0:7þ1:31:5 1:0 25 6 19 8 18:5 1:4 ð2SÞ ! bð1SÞ 613:7þ3:0þ0:72:61:1 1109 348 1.050 0:11 0:04þ0:070:05ð<0:21Þ (GeV) * γ E 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1 Events / (1 MeV) 0 500 1000 1500 2000 2500 (a) (GeV) * γ E 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1 Events / (2 MeV) 0 500 1000 1500 2000 (2P) b0 χ (2P) b1 χ (2P) b2 χ ISR (1S) b η (GeV) * γ E 0.8 0.82 0.84 0.86 0.88 0.9 0.92 0.94 0.96 0.98 1 Events/(4 MeV) -200 -150 -100 -50 0 50 100 150 200 250 300 ISR (1S) b η (b)
FIG. 8. Fit to the 600 E 1100 MeV region of the ð3SÞ
data (a) for all of the data, and (b) after subtraction of the fitted background contribution, where the inset focuses on the ð3SÞ ! bð1SÞ region of the fit. The thin lines indicate the
individual fit components. For this fit, 2=ndof ¼ 442:9=487.
ð3SÞ ! bð1SÞ has E 908 MeV, which is a
depar-ture from, but not significantly inconsistent with, the nomi-nal PDG value of 920:6þ2:83:2 MeV [27]. Estimating the statistical significance from the change in 2 of the fit with and without this component results in the equivalent of a less than 2:9 effect. Based predominantly on the positions of the b1;2ð2PÞ transition peaks, the E scale
offset in this energy range is0:9þ0:40:9 MeV. We further verify that the Escale is correct by repeating the fit with
the peak positions of the bJð2PÞ and ISR components
allowed to vary, and they are found at the expected loca-tions. We also repeat the analysis with the Escale offset
forced to reproduce an bð1SÞ result corresponding to the
Evalue for the nominal mbð1SÞ. The assumption that the observed mass difference is due to an offset in the energy scale by 12 MeV is completely inconsistent with the photon energies observed for the well-established b1;2ð2PÞ states. Even with only a 5 MeV shift, the fit
returns bJð2PÞ ! ð1SÞ yields that disagree with the
world average [27] by more than a factor of 2, and a 2=ndof 840=492.
The sources of systematic uncertainty and their evalu-ation are identical to those listed in Sec. VI. The main difference between the two energy regions is that, as previously remarked, the improved efficiency and back-ground conditions in the 600 E 1100 MeV region of
the ð3SÞ data set lead to fit results that are more stable. For the b1;2ð2PÞ-related measurements, the dominant
sys-tematic uncertainty is due to the conversion efficiency (3.6%), and all other sources are less than 2%. For the bð1SÞ signal, the largest uncertainty in the yield is related
to the assumed bð1SÞ width (þ1727%). Of the remaining
systematic uncertainties, the largest two are due to the MC parametrization (15%) and bottomonium masses ( 4%), both enhancing the yield in a positive direction. Uncertainty due to the background shape, the largest factor in the equivalent ð2SÞ analysis, is well controlled in the ð3SÞ data set and contributes less than 3% to the total uncertainty. The uncertainty in Eis dominated by
statis-tical uncertainty, and the largest systematic contribution is
related to uncertainty in the Escale via the uncertainty in
the other bottomonium masses [27].
We measure Bðð3SÞ ! bJð2PÞÞ BðbJð2PÞ ! ð1SÞÞ ¼ ð3:9 2:2þ1:20:6Þ 104, ð12:4 0:3 0:6Þ 103, and ð9:2 0:3 0:4Þ 103, for J ¼ 0,
1 and 2, respectively. Using Bðð3SÞ ! bJð2PÞÞ from the PDG [27], we derive BðbJð2PÞ ! ð1SÞÞ ¼ ð0:7 0:4þ0:2
0:1 0:1Þ%, ð9:9 0:3þ0:50:4 0:9Þ%, and
ð7:0 0:2 0:3 0:9Þ%, where the uncertainties are statistical, systematic, and from the uncertainty on Bðð3SÞ ! bJð2PÞÞ, respectively. From these values,
we calculate a 90% confidence-level upper limit of Bðb0ð2PÞ ! ð1SÞÞ < 1:2%. As before, we rescale
the previous results [10,12] using the relevant branching fractions [27] to produce the values for comparison in Table V. For the Bðb0ð2PÞ ! ð1SÞÞ value from CUSB II [10], we convert the result to an upper limit of <1:9% at the 90% confidence level. Our bJð2PÞ transition
results agree with the previous measurements and are the most precise measurements to date. Assuming the peak near E¼ 900 MeV to be due to decays to
bð1SÞ, our best fit result is Bðð3SÞ ! bð1SÞÞ ¼
ð5:8 1:6þ1:4
1:6Þ 104. The total significance of this result
once systematic uncertainties are included is2:7 , and we set a limit ofBðð3SÞ ! bð1SÞ < 8:5 104. We repeat the fit with the bð1SÞ mass constrained to the PDG
value and its uncertainty [27]. The significance of this constrained result is <1:9 . We measure Bðð3SÞ ! bð1SÞ ¼ 3:8 1:6þ0:91:0Þ, which translates into an upper
limit ofBðð3SÞ ! bð1SÞ < 6:1 104. VIII. DISCUSSION
To conclude, we review the results of this study and their broader implications. The results for BðbJðnPÞ ! ðmSÞÞ presented here are the first derived directly from a measurement of the photon spectrum. For J ¼ 1 and 2, we have made some of the most precise measure-ments of these branching fractions to date, thus helping to resolve some discrepancies between previous experimental
TABLE V. Summary of the analysis of the 600 E 1100 MeV region of the ð3SÞ data. The E column lists the transition
energy assumed in this analysis, or, in the case of ð3SÞ ! bð1SÞ, the most significant ð2:7 Þ feature in the relevant Eregion.
Errors on the yield are statistical only. Regarding the derived branching fractions, the BABAR values are from this paper, while the CUSB and CLEO columns are derivations based on [10,12] using up-to-date secondary branching fractions from [27]. For the BABAR results, the listed uncertainties are statistical, systematic, and from the uncertainties on secondary branching fractions, respectively. Upper limits are given at the 90% confidence level. Hyphens indicate that no value has been measured in the quoted reference.
Transition E Yield Derived branching fraction (%)
(MeV) (%) BABAR CUSB CLEO
b0ð2PÞ ! ð1SÞ 742.7 469þ260259 1.025 0:7 0:4þ0:20:1 0:1ð<1:2Þ <1:9 <2:2
b1ð2PÞ ! ð1SÞ 764.1 14 965þ381383 1.039 9:9 0:3þ0:50:4 0:9 7:5 1:3 10:4 2:4
b2ð2PÞ ! ð1SÞ 776.4 11 283þ384385 1.056 7:0 0:2 0:3 0:9 6:1 1:2 7:7 2:0
results (i.e. in bJð2PÞ ! ð2SÞ decays). TableVIshows
a comparison of our results with some theoretical predic-tions [34]. These predicpredic-tions are in reasonable agreement with our experimental results.
Our observations of ð3SÞ ! b0;2ð1PÞ decays
con-firm the general features seen in previous measurements [14,15,36]: decays to J ¼ 1 are suppressed compared to J ¼ 2 and 0. This is unusual compared to all other S ! P radiative transitions in the heavy quarkonium system mea-sured thus far. As noted previously [44], the wave-function overlap in theh33S
1j r j 13PJi matrix elements is
unusu-ally small. Therefore, predictions for these decay rates are largely dependent on higher-order relativistic corrections and are thus sensitive to specific details of the chosen theoretical model. That said, the comparison of our results with a selection of theoretical predictions [44,45] shown in TableVII(where we have converted our branching fraction measurements into partial widths) finds no good agreement with any particular model. Indeed, even the hierarchy of the decay rates (J ¼ 2 > 0 > 1) is generally not well pre-dicted. Further work, both theoretical and experimental, will be required to understand these decays.
The searches for bð1SÞ and bð2SÞ states using
the converted photon energy spectrum are largely
inconclusive. Over a range of approximately 9974 < mbð2SÞ< 10015 MeV=c
2, we findBðð3SÞ !
bð2SÞÞ<
1:9 103. This value is consistent with, but does not improve upon, previous measurements [14]. Because of low efficiency and high background, no evidence for ð2SÞ ! bð1SÞ is found. In the ð3SÞ system, the
most significant peaking structure in the Eenergy region
expected for the ð3SÞ ! bð1SÞ transition has E
908 MeV. If interpreted as an bð1SÞ signal, this value
trends toward the most recent potential model [46] and lattice [47] predictions, but we caution that the significance of this result is insufficient to draw such a conclusion regarding the bð1SÞ mass. Taking advantage of the
im-proved resolution from a converted photon technique to make a definitive measurement of the bð1SÞ mass and
width will require more data from future experiments.
ACKNOWLEDGMENTS
We are grateful for the extraordinary contributions of our PEP-II colleagues in achieving the excellent luminos-ity and machine conditions that have made this work possible. The success of this project also relies critically on the expertise and dedication of the computing organizations that support BABAR. The collaborating in-stitutions wish to thank SLAC for its support and the kind hospitality extended to them. This work is supported by the U.S. Department of Energy and National Science Foundation, the Natural Sciences and Engineering Research Council (Canada), the Commissariat a` l’Energie Atomique and Institut National de Physique Nucle´aire et de Physique des Particules (France), the Bundesministerium fu¨r Bildung und Forschung and Deutsche Forschungsgemeinschaft (Germany), the Istituto Nazionale di Fisica Nucleare (Italy), the Foundation for Fundamental Research on Matter (The Netherlands), the Research Council of Norway, the Ministry of Education and Science of the Russian Federation, Ministerio de Ciencia e Innovacio´n (Spain), and the Science and Technology Facilities Council (United Kingdom). Individuals have received support from the Marie-Curie IEF program (European Union), the A. P. Sloan Foundation (USA) and the Binational Science Foundation (USA-Israel).
APPENDIX A: SYSTEMATIC UNCERTAINTIES ON MC-DETERMINED EFFICIENCIES Branching fraction measurements in this analysis rely on MC-generated signal decays to determine the photon con-version and reconstruction efficiency. This efficiency is dependent on the detector material model. To evaluate a systematic effect due to the understanding of the detector in the simulation, a comparison of eþe and þ samples between data and MC is made. Inclusive decays to an eþe or þ pair plus a photon are selected by
TABLE VI. Comparison of the experimental branching frac-tion results from this work (BABAR) and some theoretical predictions [34].
Decay BABAR (%) Theory (%)
Bðb0ð2PÞ ! ð2SÞÞ (<2:8) 1.27 Bðb1ð2PÞ ! ð2SÞÞ 18:9 2:4 20.2 Bðb2ð2PÞ ! ð2SÞÞ 8:3 1:4 10.1 Bðb0ð2PÞ ! ð1SÞÞ (<1:2) 0.96 Bðb1ð2PÞ ! ð1SÞÞ 9:9 1:1 11.8 Bðb2ð2PÞ ! ð1SÞÞ 7:0 1:0 5.3 Bðb0ð1PÞ ! ð1SÞÞ (<4:6) 3.2 Bðb1ð1PÞ ! ð1SÞÞ 34:9 3:1 46.1 Bðb2ð1PÞ ! ð1SÞÞ 19:5þ1:81:9 22.2
TABLE VII. Comparison of our results with predictions [44,45] for ð3SÞ ! bJð1PÞ decays. We convert our results
into partial widths (in units of eV) using a total width of ð3SÞ¼
20:32 1:85 keV [27], absorbing this additional uncertainty into the total.
Source J ¼ 0 J ¼ 1 J ¼ 2 BABAR 55þ109 <21 214þ2524 Moxhay-Rosner 25 25 150 Grotch et al. 114 3.4 194 Daghighian-Silverman 16 100 650 Fulcher 10 20 30 La¨hde 150 110 40 Ebert et al. 27 67 97
![TABLE VI. Comparison of the experimental branching frac- frac-tion results from this work (BABAR) and some theoretical predictions [ 34 ].](https://thumb-eu.123doks.com/thumbv2/123dokorg/4406961.28237/15.918.76.446.125.323/table-comparison-experimental-branching-results-babar-theoretical-predictions.webp)
