Measurement of Decay Amplitudes of B -->(c cbar) Kstar with an Angular
  Analysis, for (c cbar)=J/psi, psi(2S) and chi_c1
BABAR-PUB-07/009
SLAC-PUB-12430
hep-ex/0704.0522
Measurement of Decay Amplitudes of B → (cc)K∗ with an Angular Analysis, for
(cc) = J/ψ , ψ(2S) and χ
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 J. Garra Tico,2 E. Grauges,2 L. Lopez,3 A. Palano,3 G. Eigen,4 I. Ofte,4 B. Stugu,4 L. Sun,4
G. S. Abrams,5 M. Battaglia,5 D. N. Brown,5 J. Button-Shafer,5 R. N. Cahn,5 Y. Groysman,5 R. G. Jacobsen,5
J. A. Kadyk,5 L. T. Kerth,5 Yu. G. Kolomensky,5 G. Kukartsev,5 D. Lopes Pegna,5 G. Lynch,5 L. M. Mir,5
T. J. Orimoto,5 M. Pripstein,5 N. A. Roe,5 M. T. Ronan,5, ∗ K. Tackmann,5 W. A. Wenzel,5 P. del Amo Sanchez,6
C. M. Hawkes,6 A. T. Watson,6 T. Held,7 H. Koch,7 B. Lewandowski,7 M. Pelizaeus,7 T. Schroeder,7
M. Steinke,7 W. N. Cottingham,8 D. Walker,8 D. J. Asgeirsson,9 T. Cuhadar-Donszelmann,9 B. G. Fulsom,9
C. Hearty,9 N. S. Knecht,9 T. S. Mattison,9 J. A. McKenna,9 A. Khan,10 M. Saleem,10 L. Teodorescu,10
V. E. Blinov,11 A. D. Bukin,11 V. P. Druzhinin,11 V. B. Golubev,11 A. P. Onuchin,11 S. I. Serednyakov,11
Yu. I. Skovpen,11 E. P. Solodov,11 K. Yu Todyshev,11 M. Bondioli,12 S. Curry,12 I. Eschrich,12 D. Kirkby,12
A. J. Lankford,12 P. Lund,12 M. Mandelkern,12 E. C. Martin,12 D. P. Stoker,12 S. Abachi,13 C. Buchanan,13
S. D. Foulkes,14 J. W. Gary,14 F. Liu,14 O. Long,14 B. C. Shen,14 L. Zhang,14 H. P. Paar,15 S. Rahatlou,15
V. Sharma,15 J. W. Berryhill,16 C. Campagnari,16 A. Cunha,16 B. Dahmes,16 T. M. Hong,16 D. Kovalskyi,16
J. D. Richman,16 T. W. Beck,17 A. M. Eisner,17 C. J. Flacco,17 C. A. Heusch,17 J. Kroseberg,17 W. S. Lockman,17
T. Schalk,17 B. A. Schumm,17 A. Seiden,17 D. C. Williams,17 M. G. Wilson,17 L. O. Winstrom,17 E. Chen,18
C. H. Cheng,18 A. Dvoretskii,18 F. Fang,18 D. G. Hitlin,18 I. Narsky,18 T. Piatenko,18 F. C. Porter,18
G. Mancinelli,19 B. T. Meadows,19 K. Mishra,19 M. D. Sokoloff,19 F. Blanc,20 P. C. Bloom,20 S. Chen,20
W. T. Ford,20 J. F. Hirschauer,20 A. Kreisel,20 M. Nagel,20 U. Nauenberg,20 A. Olivas,20 J. G. Smith,20
K. A. Ulmer,20 S. R. Wagner,20 J. Zhang,20 A. M. Gabareen,21 A. Soffer,21 W. H. Toki,21 R. J. Wilson,21
F. Winklmeier,21 Q. Zeng,21 D. D. Altenburg,22 E. Feltresi,22 A. Hauke,22 H. Jasper,22 J. Merkel,22 A. Petzold,22
B. Spaan,22 K. Wacker,22 T. Brandt,23 V. Klose,23 H. M. Lacker,23 W. F. Mader,23 R. Nogowski,23 J. Schubert,23
K. R. Schubert,23 R. Schwierz,23 J. E. Sundermann,23 A. Volk,23 D. Bernard,24 G. R. Bonneaud,24 E. Latour,24
V. Lombardo,24 Ch. Thiebaux,24 M. Verderi,24 P. J. Clark,25 W. Gradl,25 F. Muheim,25 S. Playfer,25
A. I. Robertson,25 Y. Xie,25 M. Andreotti,26 D. Bettoni,26 C. Bozzi,26 R. Calabrese,26 A. Cecchi,26 G. Cibinetto,26
P. Franchini,26 E. Luppi,26 M. Negrini,26 A. Petrella,26 L. Piemontese,26 E. Prencipe,26 V. Santoro,26 F. Anulli,27
R. Baldini-Ferroli,27 A. Calcaterra,27 R. de Sangro,27 G. Finocchiaro,27 S. Pacetti,27 P. Patteri,27 I. M. Peruzzi,27, †
M. Piccolo,27 M. Rama,27 A. Zallo,27 A. Buzzo,28 R. Contri,28 M. Lo Vetere,28 M. M. Macri,28 M. R. Monge,28
S. Passaggio,28 C. Patrignani,28 E. Robutti,28 A. Santroni,28 S. Tosi,28 K. S. Chaisanguanthum,29 M. Morii,29
J. Wu,29 R. S. Dubitzky,30 J. Marks,30 S. Schenk,30 U. Uwer,30 D. J. Bard,31 P. D. Dauncey,31 R. L. Flack,31
J. A. Nash,31 M. B. Nikolich,31 W. Panduro Vazquez,31 P. K. Behera,32 X. Chai,32 M. J. Charles,32 U. Mallik,32
N. T. Meyer,32 V. Ziegler,32 J. Cochran,33 H. B. Crawley,33 L. Dong,33 V. Eyges,33 W. T. Meyer,33 S. Prell,33
E. I. Rosenberg,33 A. E. Rubin,33 A. V. Gritsan,34 Z. J. Guo,34 C. K. Lae,34 A. G. Denig,35 M. Fritsch,35
G. Schott,35 N. Arnaud,36 J. Béquilleux,36 M. Davier,36 G. Grosdidier,36 A. Höcker,36 V. Lepeltier,36
F. Le Diberder,36 A. M. Lutz,36 S. Pruvot,36 S. Rodier,36 P. Roudeau,36 M. H. Schune,36 J. Serrano,36 V. Sordini,36
A. Stocchi,36 W. F. Wang,36 G. Wormser,36 D. J. Lange,37 D. M. Wright,37 C. A. Chavez,38 I. J. Forster,38
J. R. Fry,38 E. Gabathuler,38 R. Gamet,38 D. E. Hutchcroft,38 D. J. Payne,38 K. C. Schofield,38 C. Touramanis,38
A. J. Bevan,39 K. A. George,39 F. Di Lodovico,39 W. Menges,39 R. Sacco,39 G. Cowan,40 H. U. Flaecher,40
D. A. Hopkins,40 P. S. Jackson,40 T. R. McMahon,40 F. Salvatore,40 A. C. Wren,40 D. N. Brown,41 C. L. Davis,41
J. Allison,42 N. R. Barlow,42 R. J. Barlow,42 Y. M. Chia,42 C. L. Edgar,42 G. D. Lafferty,42 T. J. West,42
J. I. Yi,42 J. Anderson,43 C. Chen,43 A. Jawahery,43 D. A. Roberts,43 G. Simi,43 J. M. Tuggle,43 G. Blaylock,44
C. Dallapiccola,44 S. S. Hertzbach,44 X. Li,44 T. B. Moore,44 E. Salvati,44 S. Saremi,44 R. Cowan,45 P. H. Fisher,45
G. Sciolla,45 S. J. Sekula,45 M. Spitznagel,45 F. Taylor,45 R. K. Yamamoto,45 S. E. Mclachlin,46 P. M. Patel,46
S. H. Robertson,46 A. Lazzaro,47 F. Palombo,47 J. M. Bauer,48 L. Cremaldi,48 V. Eschenburg,48 R. Godang,48
R. Kroeger,48 D. A. Sanders,48 D. J. Summers,48 H. W. Zhao,48 S. Brunet,49 D. Côté,49 M. Simard,49 P. Taras,49
http://arxiv.org/abs/0704.0522v2
F. B. Viaud,49 H. Nicholson,50 G. De Nardo,51 F. Fabozzi,51, ‡ L. Lista,51 D. Monorchio,51 C. Sciacca,51
M. A. Baak,52 G. Raven,52 H. L. Snoek,52 C. P. Jessop,53 J. M. LoSecco,53 G. Benelli,54 L. A. Corwin,54
K. K. Gan,54 K. Honscheid,54 D. Hufnagel,54 H. Kagan,54 R. Kass,54 J. P. Morris,54 A. M. Rahimi,54
J. J. Regensburger,54 R. Ter-Antonyan,54 Q. K. Wong,54 N. L. Blount,55 J. Brau,55 R. Frey,55 O. Igonkina,55
J. A. Kolb,55 M. Lu,55 R. Rahmat,55 N. B. Sinev,55 D. Strom,55 J. Strube,55 E. Torrence,55 N. Gagliardi,56 A. Gaz,56
M. Margoni,56 M. Morandin,56 A. Pompili,56 M. Posocco,56 M. Rotondo,56 F. Simonetto,56 R. Stroili,56 C. Voci,56
E. Ben-Haim,57 H. Briand,57 J. Chauveau,57 P. David,57 L. Del Buono,57 Ch. de la Vaissière,57 O. Hamon,57
B. L. Hartfiel,57 Ph. Leruste,57 J. Malclès,57 J. Ocariz,57 A. Perez,57 L. Gladney,58 M. Biasini,59 R. Covarelli,59
E. Manoni,59 C. Angelini,60 G. Batignani,60 S. Bettarini,60 G. Calderini,60 M. Carpinelli,60 R. Cenci,60
A. Cervelli,60 F. Forti,60 M. A. Giorgi,60 A. Lusiani,60 G. Marchiori,60 M. A. Mazur,60 M. Morganti,60 N. Neri,60
E. Paoloni,60 G. Rizzo,60 J. J. Walsh,60 M. Haire,61 J. Biesiada,62 P. Elmer,62 Y. P. Lau,62 C. Lu,62 J. Olsen,62
A. J. S. Smith,62 A. V. Telnov,62 E. Baracchini,63 F. Bellini,63 G. Cavoto,63 A. D’Orazio,63 D. del Re,63 E. Di
Marco,63 R. Faccini,63 F. Ferrarotto,63 F. Ferroni,63 M. Gaspero,63 P. D. Jackson,63 L. Li Gioi,63 M. A. Mazzoni,63
S. Morganti,63 G. Piredda,63 F. Polci,63 F. Renga,63 C. Voena,63 M. Ebert,64 H. Schröder,64 R. Waldi,64 T. Adye,65
G. Castelli,65 B. Franek,65 E. O. Olaiya,65 S. Ricciardi,65 W. Roethel,65 F. F. Wilson,65 R. Aleksan,66 S. Emery,66
M. Escalier,66 A. Gaidot,66 S. F. Ganzhur,66 G. Hamel de Monchenault,66 W. Kozanecki,66 M. Legendre,66
G. Vasseur,66 Ch. Yèche,66 M. Zito,66 X. R. Chen,67 H. Liu,67 W. Park,67 M. V. Purohit,67 J. R. Wilson,67
M. T. Allen,68 D. Aston,68 R. Bartoldus,68 P. Bechtle,68 N. Berger,68 R. Claus,68 J. P. Coleman,68 M. R. Convery,68
J. C. Dingfelder,68 J. Dorfan,68 G. P. Dubois-Felsmann,68 D. Dujmic,68 W. Dunwoodie,68 R. C. Field,68
T. Glanzman,68 S. J. Gowdy,68 M. T. Graham,68 P. Grenier,68 C. Hast,68 T. Hryn’ova,68 W. R. Innes,68
M. H. Kelsey,68 H. Kim,68 P. Kim,68 D. W. G. S. Leith,68 S. Li,68 S. Luitz,68 V. Luth,68 H. L. Lynch,68
D. B. MacFarlane,68 H. Marsiske,68 R. Messner,68 D. R. Muller,68 C. P. O’Grady,68 A. Perazzo,68 M. Perl,68
T. Pulliam,68 B. N. Ratcliff,68 A. Roodman,68 A. A. Salnikov,68 R. H. Schindler,68 J. Schwiening,68 A. Snyder,68
J. Stelzer,68 D. Su,68 M. K. Sullivan,68 K. Suzuki,68 S. K. Swain,68 J. M. Thompson,68 J. Va’vra,68 N. van Bakel,68
A. P. Wagner,68 M. Weaver,68 W. J. Wisniewski,68 M. Wittgen,68 D. H. Wright,68 A. K. Yarritu,68 K. Yi,68
C. C. Young,68 P. R. Burchat,69 A. J. Edwards,69 S. A. Majewski,69 B. A. Petersen,69 L. Wilden,69 S. Ahmed,70
M. S. Alam,70 R. Bula,70 J. A. Ernst,70 V. Jain,70 B. Pan,70 M. A. Saeed,70 F. R. Wappler,70 S. B. Zain,70
W. Bugg,71 M. Krishnamurthy,71 S. M. Spanier,71 R. Eckmann,72 J. L. Ritchie,72 A. M. Ruland,72 C. J. Schilling,72
R. F. Schwitters,72 J. M. Izen,73 X. C. Lou,73 S. Ye,73 F. Bianchi,74 F. Gallo,74 D. Gamba,74 M. Pelliccioni,74
M. Bomben,75 L. Bosisio,75 C. Cartaro,75 F. Cossutti,75 G. Della Ricca,75 L. Lanceri,75 L. Vitale,75 V. Azzolini,76
N. Lopez-March,76 F. Martinez-Vidal,76 D. A. Milanes,76 A. Oyanguren,76 J. Albert,77 Sw. Banerjee,77 B. Bhuyan,77
K. Hamano,77 R. Kowalewski,77 I. M. Nugent,77 J. M. Roney,77 R. J. Sobie,77 J. J. Back,78 P. F. Harrison,78
T. E. Latham,78 G. B. Mohanty,78 M. Pappagallo,78, § H. R. Band,79 X. Chen,79 S. Dasu,79 K. T. Flood,79
J. J. Hollar,79 P. E. Kutter,79 Y. Pan,79 M. Pierini,79 R. Prepost,79 S. L. Wu,79 Z. Yu,79 and H. Neal80
(The BABAR Collaboration)
1Laboratoire de Physique des Particules, IN2P3/CNRS et Université de Savoie, F-74941 Annecy-Le-Vieux, France
2Universitat de Barcelona, Facultat de Fisica, Departament ECM, E-08028 Barcelona, Spain
3Università di Bari, Dipartimento di Fisica and INFN, 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
6University of Birmingham, Birmingham, B15 2TT, United Kingdom
7Ruhr Universität Bochum, Institut für Experimentalphysik 1, D-44780 Bochum, Germany
8University of Bristol, Bristol BS8 1TL, United Kingdom
9University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z1
10Brunel University, Uxbridge, Middlesex UB8 3PH, United Kingdom
11Budker Institute of Nuclear Physics, Novosibirsk 630090, Russia
12University of California at Irvine, Irvine, California 92697, USA
13University of California at Los Angeles, Los Angeles, California 90024, USA
14University of California at Riverside, Riverside, California 92521, USA
15University of California at San Diego, La Jolla, California 92093, USA
16University of California at Santa Barbara, Santa Barbara, California 93106, USA
17University of California at Santa Cruz, Institute for Particle Physics, Santa Cruz, California 95064, USA
18California Institute of Technology, Pasadena, California 91125, USA
19University of Cincinnati, Cincinnati, Ohio 45221, USA
20University of Colorado, Boulder, Colorado 80309, USA
21Colorado State University, Fort Collins, Colorado 80523, USA
22Universität Dortmund, Institut für Physik, D-44221 Dortmund, Germany
23Technische Universität Dresden, Institut für Kern- und Teilchenphysik, D-01062 Dresden, Germany
24Laboratoire Leprince-Ringuet, CNRS/IN2P3, Ecole Polytechnique, F-91128 Palaiseau, France
25University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom
26Università di Ferrara, Dipartimento di Fisica and INFN, I-44100 Ferrara, Italy
27Laboratori Nazionali di Frascati dell’INFN, I-00044 Frascati, Italy
28Università di Genova, Dipartimento di Fisica and INFN, I-16146 Genova, Italy
29Harvard University, Cambridge, Massachusetts 02138, USA
30Universität Heidelberg, Physikalisches Institut, Philosophenweg 12, D-69120 Heidelberg, Germany
31Imperial College London, London, SW7 2AZ, United Kingdom
32University of Iowa, Iowa City, Iowa 52242, USA
33Iowa State University, Ames, Iowa 50011-3160, USA
34Johns Hopkins University, Baltimore, Maryland 21218, USA
35Universität Karlsruhe, Institut für Experimentelle Kernphysik, D-76021 Karlsruhe, Germany
36Laboratoire de l’Accélérateur Linéaire, IN2P3/CNRS et Université Paris-Sud 11,
Centre Scientifique d’Orsay, B. P. 34, F-91898 ORSAY Cedex, France
37Lawrence Livermore National Laboratory, Livermore, California 94550, USA
38University of Liverpool, Liverpool L69 7ZE, United Kingdom
39Queen Mary, University of London, E1 4NS, United Kingdom
40University of London, Royal Holloway and Bedford New College, Egham, Surrey TW20 0EX, United Kingdom
41University of Louisville, Louisville, Kentucky 40292, USA
42University of Manchester, Manchester M13 9PL, United Kingdom
43University of Maryland, College Park, Maryland 20742, USA
44University of Massachusetts, Amherst, Massachusetts 01003, USA
45Massachusetts Institute of Technology, Laboratory for Nuclear Science, Cambridge, Massachusetts 02139, USA
46McGill University, Montréal, Québec, Canada H3A 2T8
47Università di Milano, Dipartimento di Fisica and INFN, I-20133 Milano, Italy
48University of Mississippi, University, Mississippi 38677, USA
49Université de Montréal, Physique des Particules, Montréal, Québec, Canada H3C 3J7
50Mount Holyoke College, South Hadley, Massachusetts 01075, USA
51Università di Napoli Federico II, Dipartimento di Scienze Fisiche and INFN, I-80126, Napoli, Italy
52NIKHEF, National Institute for Nuclear Physics and High Energy Physics, NL-1009 DB Amsterdam, The Netherlands
53University of Notre Dame, Notre Dame, Indiana 46556, USA
54Ohio State University, Columbus, Ohio 43210, USA
55University of Oregon, Eugene, Oregon 97403, USA
56Università di Padova, Dipartimento di Fisica and INFN, I-35131 Padova, Italy
57Laboratoire de Physique Nucléaire et de Hautes Energies,
IN2P3/CNRS, Université Pierre et Marie Curie-Paris6,
Université Denis Diderot-Paris7, F-75252 Paris, France
58University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
59Università di Perugia, Dipartimento di Fisica and INFN, I-06100 Perugia, Italy
60Università di Pisa, Dipartimento di Fisica, Scuola Normale Superiore and INFN, I-56127 Pisa, Italy
61Prairie View A&M University, Prairie View, Texas 77446, USA
62Princeton University, Princeton, New Jersey 08544, USA
63Università di Roma La Sapienza, Dipartimento di Fisica and INFN, I-00185 Roma, Italy
64Universität Rostock, D-18051 Rostock, Germany
65Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX11 0QX, United Kingdom
66DSM/Dapnia, CEA/Saclay, F-91191 Gif-sur-Yvette, France
67University of South Carolina, Columbia, South Carolina 29208, USA
68Stanford Linear Accelerator Center, Stanford, California 94309, USA
69Stanford University, Stanford, California 94305-4060, USA
70State University of New York, Albany, New York 12222, USA
71University of Tennessee, Knoxville, Tennessee 37996, USA
72University of Texas at Austin, Austin, Texas 78712, USA
73University of Texas at Dallas, Richardson, Texas 75083, USA
74Università di Torino, Dipartimento di Fisica Sperimentale and INFN, I-10125 Torino, Italy
75Università di Trieste, Dipartimento di Fisica and INFN, I-34127 Trieste, Italy
76IFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spain
77University of Victoria, Victoria, British Columbia, Canada V8W 3P6
78Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
79University of Wisconsin, Madison, Wisconsin 53706, USA
80Yale University, New Haven, Connecticut 06511, USA
(Dated: November 4, 2018)
We perform the first three-dimensional measurement of the amplitudes of B → ψ(2S)K∗ and
B → χc1K
∗ decays and update our previous measurement for B → J/ψK∗. We use a data sample
collected with the BABAR detector at the PEP-II storage ring, corresponding to 232 million BB
pairs. The longitudinal polarization of decays involving a JPC = 1++ χc1 meson is found to be
larger than that with a 1−− J/ψ or ψ(2S) meson. No direct CP -violating charge asymmetry is
observed.
PACS numbers: 13.25.Hw, 12.15.Hh, 11.30.Er
In the context of measuring the parameters of the
Unitarity Triangle of the CKM matrix, B0 decays to
charmonium-containing final states (J/ψ , ψ(2S), χc1)K
defined collectively here as B0 → (cc̄)K∗, are of in-
terest for the precise measurement of sin 2β, where
β ≡ arg[−VcdV ∗cb/VtdV ∗tb], in a similar way as for B0 →
J/ψK0. Furthermore, the J/ψK∗ channel allows the
measurement of cos 2β [1].
For the modes considered in this paper, the final state
consists of two spin-1 mesons, leading to three possible
values of the total angular momentum with different CP
eigenvalues (L = 1 is odd, while L = 0, 2 are even). The
different contributions must be taken into account in the
measurement of sin 2β. The amplitude for longitudinal
polarization of the two spin-1 mesons is A0. There are
two amplitudes for polarizations of the mesons transverse
to the decay axis, here expressed in the transversity basis
[2]: A‖ for parallel polarization and A⊥ for their perpen-
dicular polarization. Only the relative amplitudes are
measured, so that |A0|2 + |A‖|2 + |A⊥|2 = 1. Previous
measurements by the CLEO [3], CDF [4], BABAR [1] and
Belle [5] collaborations for the B → J/ψK∗ channels are
all compatible with each other, and with a CP -odd in-
tensity fraction |A⊥|2 close to 0.2.
Factorization predicts that the phases of the transver-
sity decay amplitudes are the same. BABAR has observed
[1, 6] a significant departure from this prediction.
Precise measurements of the branching fractions of
B → (cc̄)K∗ decays are now available [7] to test the
theoretical description of the non-factorizable contribu-
tions [8], but polarization measurements are also needed.
In particular, measurements for ψ(2S) and χc1, com-
pared to that of J/ψ , would discriminate the mass de-
pendence from the quantum number dependence. CLEO
has measured the longitudinal polarization of B → ψ(2S)
K∗ decays to be |A0|2 = 0.45 ± 0.11 ± 0.04 [9]. Belle
has studied B → χc1 K∗ decays and obtained |A0|2 =
0.87± 0.09± 0.07 [10].
B → (cc̄)K(∗) decays provide a clean environment
for the measurement of the CKM angle β because one
tree amplitude dominates the decay. Very small direct
CP -violating charge asymmetries are expected in these
decays, and no such signal has been found [7]. While
more than one amplitude with different strong and weak
phases are needed to create a charge asymmetry in a sim-
ple branching fraction measurement, London et al. have
suggested [11] that an angular analysis of vector-vector
decays can detect charge asymmetries even in the case of
vanishing strong phase difference. Belle has looked for,
and not found, such a signal [5].
In this paper we present the amplitude measurement of
charged and neutral B → (cc)K∗ using a selection simi-
lar to that of Ref. [7], and a fitting method similar to that
of Ref. [1]. We use the notation ψ for the 1−− states J/ψ
and ψ(2S). ψ (χc1) candidates are reconstructed in their
decays to ℓ+ℓ− (J/ψγ), where ℓ represents an electron or
a muon. Decays to the flavor eigenstates K∗0 → K±π∓,
K∗± → K0
π± and K∗± → K±π0 are used. The relative
strong phases are known to have a two-fold ambiguity
when measured in an angular analysis alone. In con-
trast to earlier publications [3, 4, 6] we use here the set
of phases predicted in Ref. [12], with arguments based
on the conservation of the s-quark helicity in the decay
of the b quark. We have confirmed experimentally this
prediction through the study of the variation with Kπ in-
variant mass of the phase difference between theK∗(892)
amplitude and a non-resonant Kπ S-wave amplitude [1].
The data were collected with the BABAR detector at the
PEP-II asymmetric e+e− storage ring, and correspond to
an integrated luminosity of about 209 fb−1 at the center-
of-mass energy near the Υ (4S) mass. The BABAR detec-
tor is described in detail elsewhere [13]. Charged-particle
tracking is provided by a five-layer silicon vertex tracker
(SVT) and a 40-layer drift chamber (DCH). For charged-
particle identification (PID), ionization energy loss in the
DCH and SVT, and Cherenkov radiation detected in a
ring-imaging device (DIRC) are used. Photons are iden-
tified by the electromagnetic calorimeter (EMC), which
comprises 6580 thallium-doped CsI crystals. These sys-
tems are mounted inside a 1.5-T solenoidal superconduct-
ing magnet. Muons are identified in the instrumented
flux return (IFR), composed of resistive plate chambers
and layers of iron that return the magnetic flux of the
solenoid. We use the GEANT4 [14] software to simulate
interactions of particles traversing the detector, taking
into account the varying accelerator and detector condi-
tions.
J/ψ → e+e− (µ+µ−) candidates must have a mass
between 2.95 − 3.14 (3.06 − 3.14) GeV/c2. ψ(2S) can-
didates are required to have invariant masses 3.44 <
me+e− < 3.74 GeV/c
2 or 3.64 < mµ+µ− < 3.74 GeV/c
Electron candidates are combined with photon candi-
dates in order to recover some of the energy lost through
Bremsstrahlung. J/ψ candidates and γ candidates with
an energy larger than 150MeV, are combined to form χc1
candidates, which must satisfy 350 < mℓ+ℓ−γ −mℓ+ℓ− <
450 MeV/c2. π0 → γγ candidates must satisfy 113 <
mγγ < 153 MeV/c
2. The energy of each photon has to
be greater than 50MeV. K0
→ π+π− candidates are
required to satisfy 489 < mπ+π− < 507 MeV/c
2. In ad-
dition, the K0
flight distance from the ψ vertex must be
larger than three times its uncertainty. K∗0 and K∗+
candidates are required to satisfy 796 < mKπ < 996
MeV/c2 and 792 < mKπ < 992 MeV/c
2, respectively. In
addition, due to the presence of a large background of
low-energy non-genuine π0’s, the cosine of the angle θK∗
between the K momentum and the B momentum in the
K∗ rest frame has to be less than 0.8 for K∗ → K±π0.
In events where two B’s reconstruct to modes with the
same cc̄ and K candidate, one with a π± and the other
with a π0, the B candidate with a π0 is discarded due to
the high background induced by fake π0’s.
B candidates, reconstructed by combining cc̄ and K∗
candidates, are characterized by two kinematic variables:
the difference between the reconstructed energy of the
B candidate and the beam energy in the center-of-mass
frame ∆E = E∗B −
s/2, and the beam-energy substi-
tuted mass mES ≡
(s/2 + p0 · pB)2/E20 − p2B, where
subscript 0 and B correspond to Υ (4S) and the B can-
didate in the laboratory frame. For a correctly recon-
structed B meson, ∆E is expected to peak near zero and
mES near the B-meson mass 5.279GeV/c
2. The analysis
is performed in a region of the mES vs ∆E plane defined
by 5.2 < mES < 5.3 GeV/c
2 and −120 < ∆E < 120
MeV. The signal region is defined asmES > 5.27 GeV/c
and |∆E| smaller than 40 (30) MeV for channels with
(without) a π0. For events that have multiple candi-
dates, the candidate having the smallest |∆E| is chosen.
mES distributions are available in Ref. [18].
The B decay amplitudes are measured from the dif-
ferential decay distribution, expressed in the transversity
basis [1, 6], Fig. 1, with conventions detailed in Ref. [15].
θK∗ is the helicity angle of the K
∗ decay. It is defined in
FIG. 1: Definition of the transversity angles. Details are given
in the text.
the rest frame of the K∗ meson, and is the angle between
the kaon and the opposite direction of the B meson in
this frame. θtr and φtr are defined in the ψ (χc1) rest
frame and are the polar and azimutal angle of the posi-
tive lepton (J/ψ daughter of χc1) , with respect the axis
defined by:
• xtr: opposite direction of the B meson;
• ytr: perpendicular to xtr, in the (xtr,pK∗) plane,
with a direction such that pK∗ · ytr > 0;
• ztr: to complete the frame, ie: ztr = xtr × ytr.
In terms of the transversity angular variables ω ≡
(cos θK∗ , cos θtr, φtr), the time-integrated differential de-
cay rate for the decay of the B meson is
g(ω;A) ≡ 1
d cos θK∗d cos θtrdφtr
Akfk(ω), (1)
where the amplitude coefficientsAi and the angular func-
tions fk(ω), k = 1 · · · 6 are listed in Table I. The ψ
decays to two spin-1/2 particles, while the χc1 decays
to two vector particles. The angular dependencies are
therefore different [15]. The symbol A ≡ (A0, A‖, A⊥)
denotes the transversity amplitudes for the decay of the
B meson, and A for the B meson decay. In the absence
of direct CP violation, we can choose a phase conven-
tion in which these amplitudes are related by A0 = +A0,
A‖ = +A‖, A⊥ = −A⊥, so that A⊥ is CP -odd and A0
and A‖ are CP -even. The phases δj of the amplitudes,
where j = 0, ‖,⊥, are defined by Aj = |Aj |eiδj . Phases
are defined relative to δ0 = 0.
We perform an unbinned likelihood fit of the three-
dimensional angle probability density function (PDF).
The acceptance of the detector and the efficiency of
the event reconstruction may vary as a function of the
transversity angles, in particular as the angle θK∗ is
strongly correlated with the momentum of the final kaon
and pion. We use the acceptance correction method de-
velopped in Ref. [1]. The PDF of the observed events,
gobs, is :
gobs(ω;A) = g(ω;A)
〈ε〉(A)
, (2)
where
ε(ω) is the angle-dependent acceptance and
〈ε〉(A) ≡
g(ω;A)ε(ω)dω (3)
is the average acceptance. We take into account the pres-
ence of cross-feed from channels with the same cc̄ candi-
date and a differentK∗ candidate that has (due to isospin
symmetry) the same A dependence as the signal. The
observed PDF for channel b (b = K±π∓,K0
π±,K±π0)
is then
gbobs(ω;A) = g(ω;A)
εb(ω)
k=1 Ak(A)Φbk
, (4)
TABLE I: Amplitude coefficients Ak and angular functions fk(ω) that contribute to the differential decay rate. An overall
normalization factor 9/32π (for ψ) and 9/64π (for χc1) has been omitted. In the case of a B decay, the ℑm terms change sign.
i Ak fk(ω) for ψ [1, 6] fk(ω) for χc1 [15]
1 |A0|
2 2 cos2 θK∗
1− sin2 θtr cos
2 φtr
2 cos2 θK∗
1 + sin2 θtr cos
2 φtr
2 |A‖|
2 sin2 θK∗
1− sin2 θtr sin
2 φtr
sin2 θK∗
1 + sin2 θtr sin
2 φtr
3 |A⊥|
2 sin2 θK∗ sin
2 θtr sin
2 θK∗
2 cos2 θtr + sin
2 θtr
4 ℑm(A∗‖A⊥) sin
2 θK∗ sin 2θtr sinφtr − sin
2 θK∗ sin 2θtr sinφtr
5 ℜe(A‖A
sin 2θK∗ sin
2 θtr sin 2φtr
sin 2θK∗ sin
2 θtr sin 2φtr
6 ℑm(A⊥A
sin 2θK∗ sin 2θtr cos φtr −
sin 2θK∗ sin 2θtr cos φtr
where εb(ω) is the efficiency, defined as the ratio between
the reconstructed and generated yield for the process
(B → (cc̄)K∗, K∗ → b), and we do not distinguish be-
tween correctly reconstructed signal and cross-feed in the
numerator
εb(ω) ≡
a→b(ω). (5)
εa→b(ω) is the probability for an event generated in chan-
nel a and with angle ω to be detected as an event in
channel b. Fa, a = K
π0,K±π∓,K±π0,K0
π± denotes
the fraction of each channel in the total branching frac-
tion B → ccK∗,
a Fa = 1. The Φ
k are the fk(ω)
moments of the total efficiency εb, including cross-feed :
Φbk ≡
fk(ω)ε
a→b(ω)dω. (6)
Under the approximations of neglecting the angular
resolution for signal and cross-feed events, and the pos-
sible mis-measurement of the B flavor such as in events
where both daughters inK∗0 → K±π∓ are mis-identified
(K-π swap), the PDF gobs can be expressed as in Eq. (2),
and only the coefficients ΦbK are needed. The biases in-
duced by these approximations have been estimated with
Monte Carlo (MC) based studies and found to be negli-
gible.
The coefficients Φbk are computed with exclusive signal
MC samples obtained using a full simulation of the ex-
periment [14, 16]. PID efficiencies measured with data
control samples are used to adjust the MC simulation to
the observed performance of the detector. Separate co-
efficients are used for different charges of the final state
mesons, in particular to take into account the charge de-
pendence of the interaction of charged kaons with matter,
and a possible charge asymmetry of the detector. Writ-
ing the expression for the log-likelihood Lb(A) for the
PDF gbobs(ωi;A) for a pure signal sample of NS events,
the relevant contribution is
Lb(A) =
ln (g(ωi;A))−NS ln
Ak(A)Φbk
, (7)
since the remaining term
i=1 ln
εb(ωi)
does not de-
pend on the amplitudes.
We use a background correction method [1] in which
background events from a pure background sample of
NB events are added with a negative weight to the log-
likelihood that is maximized
L′b(A) ≡
nB+NS
L(ωi;A)−
L(ωj ;A), (8)
where L(ω;A) = ln(gbobs(ω;A)). The fit is performed
within the mES signal region. Background events used
here for subtraction are from generic (BB, qq) MC sam-
ples. ñB is an estimate of the unknown number nB of
background events that are present in the signal region
in the data sample.
As L′b is not a log-likelihood, the uncertainties yielded
by the minimization program Minuit [17] are biased es-
timates of the actual uncertainties. An unbiased esti-
mation of the uncertainties is described and validated in
Appendix A of Ref. [1]. With this pseudo-log-likelihood
technique, we avoid parametrizing the acceptance as well
as the background angular distributions.
The measurement is affected by several systematic un-
certainties. The branching fractions used in the cross-
feed part of the acceptance cross section are varied by
±1σ, and the largest variation is retained. The uncer-
tainty induced by the finite size of the MC sample used
to compute the coefficients Φbk is estimated by the statis-
tical uncertainty of the angular fit on that MC sample [6].
The uncertainty due to our limited understanding of the
PID efficiency is estimated by using two different meth-
ods to correct for the MC-vs-data differences. The back-
ground uncertainty is obtained by comparing MC and
data shapes of the mES distributions for the combinato-
rial component and by using the corresponding branching
errors for the peaking component. The uncertainty due
to the presence of a Kπ S wave under the K∗(892) peak
is estimated by a fit including it. The differential decay
rate is described by Eqs. (6-9) of Ref. [1].
The results are summarized in Table II. The values of
|A0|2, |A‖|2, |A⊥|2 are negatively correlated due to the
constraint |A0|2+ |A‖|2+ |A⊥|2 = 1. In particular, |A‖|2,
TABLE II: Summary of the measured amplitudes. For decays to χc1, as A⊥ is compatible with zero, its phase is not defined.
Channel |A0|
2 |A‖|
2 |A⊥|
2 δ‖ δ⊥
J/ψK∗ 0.556 ± 0.009 ± 0.010 0.211 ± 0.010 ± 0.006 0.233 ± 0.010 ± 0.005 −2.93 ± 0.08± 0.04 2.91 ± 0.05± 0.03
ψ(2S)K∗ 0.48± 0.05 ± 0.02 0.22 ± 0.06 ± 0.02 0.30± 0.06 ± 0.02 −2.8± 0.4± 0.1 2.8± 0.3± 0.1
∗ 0.77± 0.07 ± 0.04 0.20 ± 0.07 ± 0.04 0.03± 0.04 ± 0.02 0.0± 0.3± 0.1 –
Ψ(2S)
-1 0 1
-1 0 1
-1 0 1
-1 0 1
-1 0 1
-1 0 1
-1 0 1
-1 0 1
-1 0 1
cosθK*
K+π- Ksπ
+ K+π0
-1 0 1
-1 0 1
-1 0 1
-1 0 1
-1 0 1
-1 0 1
-1 0 1
-1 0 1
-1 0 1
cosθtr
K+π- Ksπ
+ K+π0
0 2.5 5
0 2.5 5
0 2.5 5
0 2.5 5
0 2.5 5
0 2.5 5
0 2.5 5
0 2.5 5
0 2.5 5
K+π- Ksπ
+ K+π0
FIG. 2: Angular distributions with PDF from fit overlaid. The asymmetry of the cos θK∗ distributions induced by the S-wave
interference is clearly visible.
TABLE III: Difference between the interference terms mea-
sured in B and B decays to J/ψ .
δA4 δA6
(K+π−) 0.002 ± 0.025 ± 0.005 −0.011 ± 0.043 ± 0.016
(K+π0) −0.017 ± 0.047 ± 0.023 −0.051 ± 0.098 ± 0.064
(K0Sπ
+) −0.008 ± 0.049 ± 0.011 0.075 ± 0.089 ± 0.009
which would be the least precisely measured parameter in
separate one-dimensional fits, is strongly anti-correlated
with |A0|2, which would be the best measured. The
one-dimensional (1D) distributions, acceptance-corrected
with an 1D Ansatz and background-subtracted, are over-
laid with the fit results and shown on Figure 2. In con-
trast with the dedicated method used in the fit, for the
plots, we simply computed the 1D efficiency maps from
the distributions of the accepted events divided by the
1D PDF. As in lower statistics studies, the cos θK∗ for-
ward backward asymmetry due to the interference with
the S wave is clearly visible.
Our measurement of the amplitudes of B decays to
J/ψ are compatible with, and of better precision than,
previous measurements. A comparison of neutral and
charged B decays (not shown) yields results consistent
with isospin symmetry. The strong phase difference δ‖ −
δ⊥ is obtained from a fit in which the phase origin is
δ⊥ ≡ 0. We confirm our previous observation that the
strong phase differences are significantly different from
zero, in contrast with what is predicted by factorization.
For B → J/ψK∗, it amounts to δ‖ − δ⊥ = 0.45± 0.05±
0.02. The presence of direct CP -violating triple-products
in the amplitude would produce a B to B difference in
the interference terms A4 and A6: δA4 and δA6. Our
results (see Table III), with improved precision relative
to Ref. [19], are consistent with no CP violation.
In summary, we have performed the first three-
dimensional analysis of the decays to ψ(2S) and χc1. The
longitudinal polarization of the decay to ψ(2S) is lower
than that to J/ψ , while the CP -odd intensity fraction is
higher (by 1.4 and 1.0 standard deviations, respectively).
This is compatible with the prediction of models of me-
son decays in the framework of factorization. The lon-
gitudinal polarization of the decay to χc1 is found to be
larger than that to J/ψ , in contrast with the predictions
of Ref. [8], which include non-factorizable contributions.
The CP -odd intensity fraction of this decay is compatible
with zero. The parallel and longitudinal amplitudes for
χc1 seem to be aligned (|δ‖ − δ0| ∼ 0) while for ψ they
are anti-aligned (|δ‖ − δ0| ∼ π).
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 pos-
sible. The success of this project also relies critically on
the expertise and dedication of the computing organiza-
tions that support BABAR. The collaborating institutions
wish to thank SLAC for its support and the kind hospi-
tality extended to them. This work is supported by the
US Department of Energy and National Science Foun-
dation, the Natural Sciences and Engineering Research
Council (Canada), the Commissariat à l’Energie Atom-
ique and Institut National de Physique Nucléaire et de
Physique des Particules (France), the Bundesministerium
für Bildung und Forschung and Deutsche Forschungsge-
meinschaft (Germany), the Istituto Nazionale di Fisica
Nucleare (Italy), the Foundation for Fundamental Re-
search on Matter (The Netherlands), the Research Coun-
cil of Norway, the Ministry of Science and Technology of
the Russian Federation, Ministerio de Educación y Cien-
cia (Spain), and the Science and Technology Facilities
Council (United Kingdom). Individuals have received
support from the Marie-Curie IEF program (European
Union) and the A. P. Sloan Foundation.
∗ Deceased
† Also with Università di Perugia, Dipartimento di Fisica,
Perugia, Italy
‡ Also with Università della Basilicata, Potenza, Italy
§ Also with IPPP, Physics Department, Durham Univer-
sity, Durham DH1 3LE, United Kingdom
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