BABAR-PUB-06/067
SLAC-PUB-12442
Search for the Radiative Leptonic Decay B+ → γℓ+νℓ
B. Aubert,1 M. Bona,1 D. Boutigny,1 Y. Karyotakis,1 J. P. Lees,1 V. Poireau,1 X. Prudent,1 V. Tisserand,1
A. Zghiche,1 E. Grauges,2 A. Palano,3 J. C. Chen,4 N. D. Qi,4 G. Rong,4 P. Wang,4 Y. S. Zhu,4 G. Eigen,5 I. Ofte,5
B. Stugu,5 G. S. Abrams,6 M. Battaglia,6 D. N. Brown,6 J. Button-Shafer,6 R. N. Cahn,6 Y. Groysman,6
R. G. Jacobsen,6 J. A. Kadyk,6 L. T. Kerth,6 Yu. G. Kolomensky,6 G. Kukartsev,6 D. Lopes Pegna,6 G. Lynch,6
L. M. Mir,6 T. J. Orimoto,6 M. Pripstein,6 N. A. Roe,6 M. T. Ronan,6, ∗ K. Tackmann,6 W. A. Wenzel,6
P. del Amo Sanchez,7 M. Barrett,7 T. J. Harrison,7 A. J. Hart,7 C. M. Hawkes,7 A. T. Watson,7 T. Held,8
H. Koch,8 B. Lewandowski,8 M. Pelizaeus,8 K. Peters,8 T. Schroeder,8 M. Steinke,8 J. T. Boyd,9 J. P. Burke,9
W. N. Cottingham,9 D. Walker,9 D. J. Asgeirsson,10 T. Cuhadar-Donszelmann,10 B. G. Fulsom,10
C. Hearty,10 N. S. Knecht,10 T. S. Mattison,10 J. A. McKenna,10 A. Khan,11 P. Kyberd,11 M. Saleem,11
D. J. Sherwood,11 L. Teodorescu,11 V. E. Blinov,12 A. D. Bukin,12 V. P. Druzhinin,12 V. B. Golubev,12
A. P. Onuchin,12 S. I. Serednyakov,12 Yu. I. Skovpen,12 E. P. Solodov,12 K. Yu Todyshev,12 M. Bondioli,13
M. Bruinsma,13 M. Chao,13 S. Curry,13 I. Eschrich,13 D. Kirkby,13 A. J. Lankford,13 P. Lund,13 M. Mandelkern,13
E. C. Martin,13 W. Roethel,13 D. P. Stoker,13 S. Abachi,14 C. Buchanan,14 S. D. Foulkes,15 J. W. Gary,15
O. Long,15 B. C. Shen,15 L. Zhang,15 E. J. Hill,16 H. P. Paar,16 S. Rahatlou,16 V. Sharma,16 J. W. Berryhill,17
C. Campagnari,17 A. Cunha,17 B. Dahmes,17 T. M. Hong,17 D. Kovalskyi,17 J. D. Richman,17 T. W. Beck,18
A. M. Eisner,18 C. J. Flacco,18 C. A. Heusch,18 J. Kroseberg,18 W. S. Lockman,18 G. Nesom,18 T. Schalk,18
B. A. Schumm,18 A. Seiden,18 D. C. Williams,18 M. G. Wilson,18 L. O. Winstrom,18 J. Albert,19 E. Chen,19
C. H. Cheng,19 A. Dvoretskii,19 F. Fang,19 D. G. Hitlin,19 I. Narsky,19 T. Piatenko,19 F. C. Porter,19
G. Mancinelli,20 B. T. Meadows,20 K. Mishra,20 M. D. Sokoloff,20 F. Blanc,21 P. C. Bloom,21 S. Chen,21
W. T. Ford,21 J. F. Hirschauer,21 A. Kreisel,21 M. Nagel,21 U. Nauenberg,21 A. Olivas,21 J. G. Smith,21
K. A. Ulmer,21 S. R. Wagner,21 J. Zhang,21 A. Chen,22 E. A. Eckhart,22 A. Soffer,22 W. H. Toki,22 R. J. Wilson,22
F. Winklmeier,22 Q. Zeng,22 D. D. Altenburg,23 E. Feltresi,23 A. Hauke,23 H. Jasper,23 J. Merkel,23 A. Petzold,23
B. Spaan,23 T. Brandt,24 V. Klose,24 H. M. Lacker,24 W. F. Mader,24 R. Nogowski,24 J. Schubert,24
K. R. Schubert,24 R. Schwierz,24 J. E. Sundermann,24 A. Volk,24 D. Bernard,25 G. R. Bonneaud,25 E. Latour,25
Ch. Thiebaux,25 M. Verderi,25 P. J. Clark,26 W. Gradl,26 F. Muheim,26 S. Playfer,26 A. I. Robertson,26
Y. Xie,26 M. Andreotti,27 D. Bettoni,27 C. Bozzi,27 R. Calabrese,27 G. Cibinetto,27 E. Luppi,27 M. Negrini,27
A. Petrella,27 L. Piemontese,27 E. Prencipe,27 F. Anulli,28 R. Baldini-Ferroli,28 A. Calcaterra,28 R. de Sangro,28
G. Finocchiaro,28 S. Pacetti,28 P. Patteri,28 I. M. Peruzzi,28, † M. Piccolo,28 M. Rama,28 A. Zallo,28 A. Buzzo,29
R. Contri,29 M. Lo Vetere,29 M. M. Macri,29 M. R. Monge,29 S. Passaggio,29 C. Patrignani,29 E. Robutti,29
A. Santroni,29 S. Tosi,29 K. S. Chaisanguanthum,30 M. Morii,30 J. Wu,30 R. S. Dubitzky,31 J. Marks,31 S. Schenk,31
U. Uwer,31 D. J. Bard,32 P. D. Dauncey,32 R. L. Flack,32 J. A. Nash,32 M. B. Nikolich,32 W. Panduro Vazquez,32
P. K. Behera,33 X. Chai,33 M. J. Charles,33 U. Mallik,33 N. T. Meyer,33 V. Ziegler,33 J. Cochran,34 H. B. Crawley,34
L. Dong,34 V. Eyges,34 W. T. Meyer,34 S. Prell,34 E. I. Rosenberg,34 A. E. Rubin,34 A. V. Gritsan,35 A. G. Denig,36
M. Fritsch,36 G. Schott,36 N. Arnaud,37 M. Davier,37 G. Grosdidier,37 A. Höcker,37 V. Lepeltier,37 F. Le Diberder,37
A. M. Lutz,37 S. Pruvot,37 S. Rodier,37 P. Roudeau,37 M. H. Schune,37 J. Serrano,37 A. Stocchi,37 W. F. Wang,37
G. Wormser,37 D. J. Lange,38 D. M. Wright,38 C. A. Chavez,39 I. J. Forster,39 J. R. Fry,39 E. Gabathuler,39
R. Gamet,39 K. A. George,39 D. E. Hutchcroft,39 D. J. Payne,39 K. C. Schofield,39 C. Touramanis,39 A. J. Bevan,40
F. Di Lodovico,40 W. Menges,40 R. Sacco,40 G. Cowan,41 H. U. Flaecher,41 D. A. Hopkins,41 P. S. Jackson,41
T. R. McMahon,41 F. Salvatore,41 A. C. Wren,41 D. N. Brown,42 C. L. Davis,42 J. Allison,43 N. R. Barlow,43
R. J. Barlow,43 Y. M. Chia,43 C. L. Edgar,43 G. D. Lafferty,43 T. J. West,43 J. C. Williams,43 J. I. Yi,43
C. Chen,44 W. D. Hulsbergen,44 A. Jawahery,44 C. K. Lae,44 D. A. Roberts,44 G. Simi,44 G. Blaylock,45
C. Dallapiccola,45 S. S. Hertzbach,45 X. Li,45 T. B. Moore,45 E. Salvati,45 S. Saremi,45 R. Cowan,46 G. Sciolla,46
S. J. Sekula,46 M. Spitznagel,46 F. Taylor,46 R. K. Yamamoto,46 H. Kim,47 S. E. Mclachlin,47 P. M. Patel,47
S. H. Robertson,47 A. Lazzaro,48 V. Lombardo,48 F. Palombo,48 J. M. Bauer,49 L. Cremaldi,49 V. Eschenburg,49
R. Godang,49 R. Kroeger,49 D. A. Sanders,49 D. J. Summers,49 H. W. Zhao,49 S. Brunet,50 D. Côté,50 M. Simard,50
P. Taras,50 F. B. Viaud,50 H. Nicholson,51 N. Cavallo,52, ‡ G. De Nardo,52 F. Fabozzi,52, ‡ C. Gatto,52 L. Lista,52
D. Monorchio,52 P. Paolucci,52 D. Piccolo,52 C. Sciacca,52 M. A. Baak,53 G. Raven,53 H. L. Snoek,53 C. P. Jessop,54
http://arxiv.org/abs/0704.1478v1
J. M. LoSecco,54 G. Benelli,55 L. A. Corwin,55 K. K. Gan,55 K. Honscheid,55 D. Hufnagel,55 P. D. Jackson,55
H. Kagan,55 R. Kass,55 J. P. Morris,55 A. M. Rahimi,55 J. J. Regensburger,55 R. Ter-Antonyan,55 Q. K. Wong,55
N. L. Blount,56 J. Brau,56 R. Frey,56 O. Igonkina,56 J. A. Kolb,56 M. Lu,56 C. T. Potter,56 R. Rahmat,56
N. B. Sinev,56 D. Strom,56 J. Strube,56 E. Torrence,56 A. Gaz,57 M. Margoni,57 M. Morandin,57 A. Pompili,57
M. Posocco,57 M. Rotondo,57 F. Simonetto,57 R. Stroili,57 C. Voci,57 E. Ben-Haim,58 H. Briand,58 J. Chauveau,58
P. David,58 L. Del Buono,58 Ch. de la Vaissière,58 O. Hamon,58 B. L. Hartfiel,58 Ph. Leruste,58 J. Malclès,58
J. Ocariz,58 L. Gladney,59 M. Biasini,60 R. Covarelli,60 C. Angelini,61 G. Batignani,61 S. Bettarini,61 G. Calderini,61
M. Carpinelli,61 R. Cenci,61 F. Forti,61 M. A. Giorgi,61 A. Lusiani,61 G. Marchiori,61 M. A. Mazur,61
M. Morganti,61 N. Neri,61 E. Paoloni,61 G. Rizzo,61 J. J. Walsh,61 M. Haire,62 D. Judd,62 D. E. Wagoner,62
J. Biesiada,63 P. Elmer,63 Y. P. Lau,63 C. Lu,63 J. Olsen,63 A. J. S. Smith,63 A. V. Telnov,63 F. Bellini,64
G. Cavoto,64 A. D’Orazio,64 D. del Re,64 E. Di Marco,64 R. Faccini,64 F. Ferrarotto,64 F. Ferroni,64 M. Gaspero,64
L. Li Gioi,64 M. A. Mazzoni,64 S. Morganti,64 G. Piredda,64 F. Polci,64 F. Safai Tehrani,64 C. Voena,64 M. Ebert,65
H. Schröder,65 R. Waldi,65 T. Adye,66 B. Franek,66 E. O. Olaiya,66 S. Ricciardi,66 F. F. Wilson,66 R. Aleksan,67
S. Emery,67 A. Gaidot,67 S. F. Ganzhur,67 G. Hamel de Monchenault,67 W. Kozanecki,67 M. Legendre,67
G. Vasseur,67 Ch. Yèche,67 M. Zito,67 X. R. Chen,68 H. Liu,68 W. Park,68 M. V. Purohit,68 J. R. Wilson,68
M. T. Allen,69 D. Aston,69 R. Bartoldus,69 P. Bechtle,69 N. Berger,69 R. Claus,69 J. P. Coleman,69 M. R. Convery,69
J. C. Dingfelder,69 J. Dorfan,69 G. P. Dubois-Felsmann,69 D. Dujmic,69 W. Dunwoodie,69 R. C. Field,69
T. Glanzman,69 S. J. Gowdy,69 M. T. Graham,69 P. Grenier,69 V. Halyo,69 C. Hast,69 T. Hryn’ova,69 W. R. Innes,69
M. H. Kelsey,69 P. Kim,69 D. W. G. S. Leith,69 S. Li,69 S. Luitz,69 V. Luth,69 H. L. Lynch,69 D. B. MacFarlane,69
H. Marsiske,69 R. Messner,69 D. R. Muller,69 C. P. O’Grady,69 V. E. Ozcan,69 A. Perazzo,69 M. Perl,69
T. Pulliam,69 B. N. Ratcliff,69 A. Roodman,69 A. A. Salnikov,69 R. H. Schindler,69 J. Schwiening,69 A. Snyder,69
J. Stelzer,69 D. Su,69 M. K. Sullivan,69 K. Suzuki,69 S. K. Swain,69 J. M. Thompson,69 J. Va’vra,69 N. van Bakel,69
A. P. Wagner,69 M. Weaver,69 W. J. Wisniewski,69 M. Wittgen,69 D. H. Wright,69 H. W. Wulsin,69 A. K. Yarritu,69
K. Yi,69 C. C. Young,69 P. R. Burchat,70 A. J. Edwards,70 S. A. Majewski,70 B. A. Petersen,70 L. Wilden,70
S. Ahmed,71 M. S. Alam,71 R. Bula,71 J. A. Ernst,71 V. Jain,71 B. Pan,71 M. A. Saeed,71 F. R. Wappler,71
S. B. Zain,71 W. Bugg,72 M. Krishnamurthy,72 S. M. Spanier,72 R. Eckmann,73 J. L. Ritchie,73 C. J. Schilling,73
R. F. Schwitters,73 J. M. Izen,74 X. C. Lou,74 S. Ye,74 F. Bianchi,75 F. Gallo,75 D. Gamba,75 M. Pelliccioni,75
M. Bomben,76 L. Bosisio,76 C. Cartaro,76 F. Cossutti,76 G. Della Ricca,76 L. Lanceri,76 L. Vitale,76 V. Azzolini,77
N. Lopez-March,77 F. Martinez-Vidal,77 A. Oyanguren,77 Sw. Banerjee,78 B. Bhuyan,78 K. Hamano,78
R. Kowalewski,78 I. M. Nugent,78 J. M. Roney,78 R. J. Sobie,78 J. J. Back,79 P. F. Harrison,79 T. E. Latham,79
G. B. Mohanty,79 M. Pappagallo,79, § H. R. Band,80 X. Chen,80 S. Dasu,80 K. T. Flood,80 J. J. Hollar,80
P. E. Kutter,80 B. Mellado,80 Y. Pan,80 M. Pierini,80 R. Prepost,80 S. L. Wu,80 Z. Yu,80 and H. Neal81
(The BABAR Collaboration)
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
4Institute of High Energy Physics, Beijing 100039, China
5University of Bergen, Institute of Physics, N-5007 Bergen, Norway
6Lawrence Berkeley National Laboratory and University of California, Berkeley, California 94720, USA
7University of Birmingham, Birmingham, B15 2TT, United Kingdom
8Ruhr Universität Bochum, Institut für Experimentalphysik 1, D-44780 Bochum, Germany
9University of Bristol, Bristol BS8 1TL, United Kingdom
10University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z1
11Brunel University, Uxbridge, Middlesex UB8 3PH, United Kingdom
12Budker Institute of Nuclear Physics, Novosibirsk 630090, Russia
13University of California at Irvine, Irvine, California 92697, USA
14University of California at Los Angeles, Los Angeles, California 90024, USA
15University of California at Riverside, Riverside, California 92521, USA
16University of California at San Diego, La Jolla, California 92093, USA
17University of California at Santa Barbara, Santa Barbara, California 93106, USA
18University of California at Santa Cruz, Institute for Particle Physics, Santa Cruz, California 95064, USA
19California Institute of Technology, Pasadena, California 91125, USA
20University of Cincinnati, Cincinnati, Ohio 45221, USA
21University of Colorado, Boulder, Colorado 80309, USA
22Colorado State University, Fort Collins, Colorado 80523, USA
23Universität Dortmund, Institut für Physik, D-44221 Dortmund, Germany
24Technische Universität Dresden, Institut für Kern- und Teilchenphysik, D-01062 Dresden, Germany
25Laboratoire Leprince-Ringuet, CNRS/IN2P3, Ecole Polytechnique, F-91128 Palaiseau, France
26University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom
27Università di Ferrara, Dipartimento di Fisica and INFN, I-44100 Ferrara, Italy
28Laboratori Nazionali di Frascati dell’INFN, I-00044 Frascati, Italy
29Università di Genova, Dipartimento di Fisica and INFN, I-16146 Genova, Italy
30Harvard University, Cambridge, Massachusetts 02138, USA
31Universität Heidelberg, Physikalisches Institut, Philosophenweg 12, D-69120 Heidelberg, Germany
32Imperial College London, London, SW7 2AZ, United Kingdom
33University of Iowa, Iowa City, Iowa 52242, USA
34Iowa State University, Ames, Iowa 50011-3160, USA
35Johns Hopkins University, Baltimore, Maryland 21218, USA
36Universität Karlsruhe, Institut für Experimentelle Kernphysik, D-76021 Karlsruhe, Germany
37Laboratoire de l’Accélérateur Linéaire, IN2P3/CNRS et Université Paris-Sud 11,
Centre Scientifique d’Orsay, B. P. 34, F-91898 ORSAY Cedex, France
38Lawrence Livermore National Laboratory, Livermore, California 94550, USA
39University of Liverpool, Liverpool L69 7ZE, United Kingdom
40Queen Mary, University of London, E1 4NS, United Kingdom
41University of London, Royal Holloway and Bedford New College, Egham, Surrey TW20 0EX, United Kingdom
42University of Louisville, Louisville, Kentucky 40292, USA
43University of Manchester, Manchester M13 9PL, United Kingdom
44University of Maryland, College Park, Maryland 20742, USA
45University of Massachusetts, Amherst, Massachusetts 01003, USA
46Massachusetts Institute of Technology, Laboratory for Nuclear Science, Cambridge, Massachusetts 02139, USA
47McGill University, Montréal, Québec, Canada H3A 2T8
48Università di Milano, Dipartimento di Fisica and INFN, I-20133 Milano, Italy
49University of Mississippi, University, Mississippi 38677, USA
50Université de Montréal, Physique des Particules, Montréal, Québec, Canada H3C 3J7
51Mount Holyoke College, South Hadley, Massachusetts 01075, USA
52Università di Napoli Federico II, Dipartimento di Scienze Fisiche and INFN, I-80126, Napoli, Italy
53NIKHEF, National Institute for Nuclear Physics and High Energy Physics, NL-1009 DB Amsterdam, The Netherlands
54University of Notre Dame, Notre Dame, Indiana 46556, USA
55Ohio State University, Columbus, Ohio 43210, USA
56University of Oregon, Eugene, Oregon 97403, USA
57Università di Padova, Dipartimento di Fisica and INFN, I-35131 Padova, Italy
58Laboratoire de Physique Nucléaire et de Hautes Energies,
IN2P3/CNRS, Université Pierre et Marie Curie-Paris6,
Université Denis Diderot-Paris7, F-75252 Paris, France
59University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
60Università di Perugia, Dipartimento di Fisica and INFN, I-06100 Perugia, Italy
61Università di Pisa, Dipartimento di Fisica, Scuola Normale Superiore and INFN, I-56127 Pisa, Italy
62Prairie View A&M University, Prairie View, Texas 77446, USA
63Princeton University, Princeton, New Jersey 08544, USA
64Università di Roma La Sapienza, Dipartimento di Fisica and INFN, I-00185 Roma, Italy
65Universität Rostock, D-18051 Rostock, Germany
66Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX11 0QX, United Kingdom
67DSM/Dapnia, CEA/Saclay, F-91191 Gif-sur-Yvette, France
68University of South Carolina, Columbia, South Carolina 29208, USA
69Stanford Linear Accelerator Center, Stanford, California 94309, USA
70Stanford University, Stanford, California 94305-4060, USA
71State University of New York, Albany, New York 12222, USA
72University of Tennessee, Knoxville, Tennessee 37996, USA
73University of Texas at Austin, Austin, Texas 78712, USA
74University of Texas at Dallas, Richardson, Texas 75083, USA
75Università di Torino, Dipartimento di Fisica Sperimentale and INFN, I-10125 Torino, Italy
76Università di Trieste, Dipartimento di Fisica and INFN, I-34127 Trieste, Italy
77IFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spain
78University of Victoria, Victoria, British Columbia, Canada V8W 3P6
79Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
80University of Wisconsin, Madison, Wisconsin 53706, USA
81Yale University, New Haven, Connecticut 06511, USA
(Dated: November 5, 2018)
We present the results of a search for B+ → γℓ+νℓ, where ℓ = e, µ. We use a sample of 232
million BB̄ pairs recorded at the Υ (4S) with the BABAR detector at the PEP-II B Factory. We
measure a partial branching fraction ∆B in a restricted region of phase space that reduces the effect
of theoretical uncertainties, requiring the lepton energy to be between 1.875 and 2.850GeV, the
photon energy to be between 0.45 and 2.35GeV, and the cosine of the angle between the lepton and
photon momenta to be less than −0.36, with all quantities computed in the Υ (4S) center-of-mass
frame. We find ∆B(B+ → γℓ+νℓ) = (−0.3
−1.5(stat)± 0.6(syst)± 0.1(th))× 10
−6, assuming lepton
universality. Interpreted as a 90% C.L. Bayesian upper limit, the result corresponds to 1.7 × 10−6
for a prior flat in amplitude, and 2.3× 10−6 for a prior flat in branching fraction.
PACS numbers: 13.20.He, 13.30.Ce, 12.38.Qk, 14.40.Nd
At tree level, the branching fraction (BF) for radiative
leptonic B decays is given by:
B(B+ → γℓ+νℓ) = α
G2F |Vub|
288π2
f2BτBm
where mB is the B
+ meson mass, mb is the MS b quark
mass, τB is the B
+ meson lifetime, fB is the B meson
decay constant, Qi is the charge of quark flavor i and λB
is the first inverse moment of the B light-cone distribu-
tion amplitude [1, 2], a quantity that enters into theo-
retical calculations [3] of the BF of hadronic B decays
such as B → ππ, and is typically taken to be of the order
of ΛQCD. Thus, a measurement of B(B
+ → γℓ+νℓ) can
provide a determination of λB free of hadronic final-state
uncertainties. The best current 90% C.L. upper limit on
the full BF is 5.2× 10−5[4], for B+ → γµ+νµ.
However, Eq.(1) is based on the assumption that the
factorization relation for the vector and axial-vector form
factors is valid over the entire phase space. Instead, one
can relate, at tree-level, λB to a partial BF, ∆B, over a
restricted region of phase space [5]:
∆B = α
G2F |Vub|
f2BτBm
a+ bL+ cL2
, (2)
where L = (mB/3)(1/λB + 1/(2mb)), the first term de-
scribes the effects of photon radiation from the lepton,
the third term the internal photon emission, and second
their interference. The constants a, b, and c can be pre-
dicted model-independently using factorization at large
photon energy, the kinematic region for our analysis.
We present herein the results of a search for charged
B meson decays B+ → γℓ+νℓ, where ℓ = e, µ (“elec-
tron channel”,“muon channel”)[6]. Our measurements
are based on a sample of 232 million BB pairs recorded
with the BABAR detector [7] at the PEP-II asymmetric-
energy e+e− storage rings, comprising an integrated lu-
minosity of 210.5 fb−1 collected at the Υ (4S) resonance
(“on-peak”). We also use 21.6 fb−1 recorded approxi-
mately 40 MeV below the Υ (4S) (“off-peak”).
The analysis procedure consists of selecting a lepton
and photon recoiling against a reconstructedB, and iden-
tifying signal candidates by reconstructing the neutrino
using missing energy and momentum. We use a variety
of selection criteria, optimized using Monte Carlo (MC)
samples, to discriminate signal from background. We
then extract the number of signal events in data using a
binned maximum-likelihood (ML) fit.
The backgrounds are divided into three categories:
continuum (non-BB), specific exclusive b → uℓνℓ decays,
and “generic B” decays, defined as a combination of all
B hadronic decays, b → cℓνℓ decays, and the remain-
ing inclusive b → uℓνℓ decays. In particular, we study
the seven exclusive b → uℓνℓ modes: B
+ → h0ℓ+νℓ
(h0 = π0, ρ0, η, η′, ω) and B0 → h−ℓ+νℓ (h
− = π−, ρ−),
referred to below, for each h, as the “h mode”.
Our signal MC samples were generated using the tree-
level model of Ref. [1]. The π0 and π± mode samples
were generated using the form factor parameterization of
Ref. [8], with the value of the shape parameter based on
lattice QCD results [9]. Light cone sum rule-based form
factor models were used to generate samples for the ρ0,
ρ±, and ω modes [10], and η and η′ modes [11].
We find an excess of events in the off-peak data com-
pared to continuum MC (e+e− → qq, τ+τ−, and in the
muon channel, µ+µ−γ), with the excess more pronounced
in the electron channel. This is likely to result from
unmodeled higher-order QED and hadronic two-photon
events. We thus use off-peak data instead of continuum
MC to represent continuum background in our analysis.
We take as the signal lepton and photon the high-
est center-of-mass (CM) energy electron (muon) and the
highest CM energy photon candidate in each event. The
remaining charged tracks, each assigned a pion mass, and
neutral clusters, treated as photons, are assigned to the
“recoil B” candidate. We reconstruct the recoil B in two
ways: we construct an “unscaled” recoil momentum as
the sum of the CM 3-momenta of its constituents, and
we define a “scaled” recoil momentum in the direction of
the unscaled recoil, with its magnitude determined from
the CM energy of the Υ (4S) and the B± mass. Using
either the scaled or unscaled momentum, we reconstruct
the 3-momentum of a corresponding scaled or unscaled
signal neutrino candidate. The reconstructed neutrino
CM energy is calculated as the difference between the
CM beam energy and the sum of the lepton and photon
candidates’ CM energies.
We optimize a set of selection criteria for the best sig-
nal sensitivity at a significance of 3σ using MC samples,
splitting each in half, with one sample used for the opti-
mization and the other used to evaluate its performance.
On the signal side, we require that the electron (muon)
have a CM energy between 2.00 and 2.85 (1.875 and
2.775)GeV. We require that the photon have a CM en-
ergy between 0.65 and 2.35 (0.45 and 2.35) GeV. We
define cos θℓγ to be the cosine of the angle between
the lepton and photon in the CM frame, and require
its value to be less than −0.42 (−0.36). We require
−1.10(−1.05) < cos θBY < 1.10(1.00), where cos θBY
is the cosine of the angle between the signal B and the
lepton-photon combination Y in the CM frame [12], com-
puted from the known B mass, the beam energy, and the
3-momenta of the signal lepton and photon.
In order to reduce background from neutral hadrons,
we require the lateral moment [13] of the electromagnetic
calorimeter energy distribution of the signal photon can-
didate to be less than 0.55 for both channels. The polar
angle of the photon candidate in the laboratory frame
is required to be between 0.326 and 2.443 rad for both
channels. We pair the candidate with every other neutral
cluster in the event and reject events with a pair invariant
mass in the π0 mass range 123–147 (116–148) MeV.
We require the difference between the total CM energy
of the recoil B constituents and the CM beam energy to
be between −5.0 and 0.9 (−2.5 and 0.7) GeV. For the
neutrino reconstruction, we require that both the scaled
and unscaled neutrino polar angle in the laboratory frame
be between 0.300 and 2.443 rad for both channels.
To reduce continuum background, we require the ratio
of the second to zeroth Fox-Wolfram moment [14] of all
charged tracks and neutral clusters to be less than 0.5,
and the absolute value of the cosine of the angle between
the CM thrust axes of the recoil B and the lepton-photon
system be less than 0.98 (0.86). We use a Fisher discrim-
inant, F ≡ a0L0+a2L2, calculated from the momentum-
weighted zeroth and second Legendre moments, L0 and
L2, of the recoil B about the lepton-photon CM thrust
axis, with coefficients a0 and a2 equal to 0.43 and −1.86
(0.008 and −1.590), respectively. F is required to be
greater than 1.50 (0.310).
In the electron channel, we veto two-photon events
via the charge-angle correlation of the signal lepton aris-
ing from the initial state. For a positively (negatively)-
charged signal electron, we require the cosine of its CM
polar angle to be between −0.74 and 0.78 (−0.94 and
0.70). In the muon channel, we require this variable to
be between −1.00 and 0.78 for both charges. These crite-
ria were optimized on a loosely-selected sample of events,
where the off-peak data are used for the continuum, and
the MC for the signal and other backgrounds.
We also reject two-photon events using a parameter-
ized combination of the missing CM momentum in the
beam direction and the invariant mass of the hypotheti-
cal two-photon system. For the muon channel, the entire
observed event is taken as the two-photon system, while
 (GeV)ESm
4.9 4.95 5 5.05 5.1 5.15 5.2 5.25 5.3
FIG. 1: Electron-channel ∆EP vs. mES signal MC, using a
color scale to represent relative contents of each bin.
for the electron channel, the signal electron is assumed
to be from the initial state, and so is excluded from the
two-photon system. The selection criterion was adjusted
to preserve a 94% efficiency for signal for both channels.
After applying our selection criteria, we use the two-
dimensional distribution of ∆EP , the difference between
the scaled neutrino candidate’s CM energy and the mag-
nitude of its 3-momentum, and mES, the invariant mass
of the recoil B, calculated from its unscaled CM 3-
momentum and the CM beam energy, as inputs to the
ML fit. These distributions provide distinct signatures
for signal, B background, and continuum, with the sig-
nal distribution shown in Fig. 1. The signal (S) and three
sideband (B1, B2, B3) regions were selected to maximize
separation of signal fromBB and continuum background.
We extract signal events by fitting on-peak data for the
contributions of signal and background, while allowing
the predicted shapes of signal and background to vary
within statistical uncertainties. The scale of signal and
generic B contributions are allowed to vary, while the
scale of off-peak data is fixed using the on-peak/off-peak
luminosity ratio. For the seven semileptonic (SL) modes,
we fit for three of the BFs and relate the other four to
them as follows: The π± and ρ± mode BFs are obtained
from BABAR measurements [12], and the η mode BF is
obtained from CLEO [15]. The charged and neutral π
and ρ modes are related by the lifetime ratio, τB±/τB0 =
1.071 ± 0.009 [16], and an isospin factor of 2. The ω
mode BF is taken as equal to the ρ0 mode BF. We take
the ratio of the η to η′ mode BFs to be 2.057± 0.020[17].
We maximize a likelihood function consisting of the
product of four Poisson probability distribution functions
(PDFs), modeling the total counts in each of the four
regions, three Gaussian PDFs for the BFs of the three
SL modes, and 40 Poisson PDFs for the 4-region shapes
of the various samples. All of the shapes are obtained
from MC, except for continuum, where off-peak data are
used, introducing a larger statistical uncertainty.
Each Poisson PDF that models the total count in one
of the four fit regions has a measured value obtained from
the on-peak data count, and an expected value based
on the fitted contributions of signal and background, in-
cluding fitted variations of the shapes. For the seven
SL modes (where three of the fitted BFs are indepen-
dent), the variances of the three Gaussian likelihoods are
obtained from the published statistical and experimental
systematic uncertainties, combined in quadrature. In all,
there are 47 PDFs, and 45 free parameters.
We fit for the partial BF ∆B for the kinematic region
with lepton CM energy between 1.875 and 2.850GeV,
photon CM energy between 0.45 and 2.35GeV, and
cos θℓγ less than −0.36 — the union of the electron and
muon channel regions. We perform three fits: separate
electron and muon channel fits, and a joint fit in which
the signal and three SL BFs are constrained to be equal
for the two channels. For each fit, errors on the fitted sig-
nal BF are obtained by finding the two values at which
the signal BF likelihood decreased by a factor of e−1/2.
Table I shows the results from the joint fit.
TABLE I: Comparison of fit results and experimental obser-
vations for the joint fit to the muon and electron channels.
For each of the four fit regions, the individual fitted contri-
butions from continuum (cont.), BB background, and signal
are shown, along with their total. The on-peak and off-peak
(scaled to the integrated on-peak luminosity) observations are
shown for comparison, in indented rows, and are not included
in the “Total fit” value shown.
Muon channel
S B1 B2 B3
Fit cont. 20.0±11.8 116.3±14.7 42.6±12.8 213.2±42.1
Off-peak 23.0±16.2 158.1±40.8 17.4±12.3 219.7±45.8
Fit BB 59.1± 8.5 61.0± 9.9 61.7± 9.8 286.6±46.6
Fit signal −5.2±13.8 −1.3± 3.4 −0.4± 1.0 −0.2± 0.5
Total fit 74.0± 8.1 176.0±12.4 103.9± 9.8 500.0±22.1
On-peak 73.0± 8.5 170.0±13.0 111.0±10.5 498.0±22.3
Electron channel
S B1 B2 B3
Fit cont. 55.4±20.5 181.1±16.2 48.9±14.1 356.7±54.4
Off-peak 41.4±20.7 239.7±48.9 79.0±27.9 294.5±52.9
Fit BB 69.2± 8.5 59.2± 8.5 140.1±15.5 393.8±57.2
Fit signal −8.4±22.3 −1.5± 3.9 −1.2± 3.3 −0.4± 1.0
Total fit 116.2±10.3 238.7±14.5 187.7±12.5 750.2±26.5
On-peak 119.0±10.9 231.0±15.2 176.0±13.3 764.0±27.6
Table II shows all systematic uncertainties on ∆B ex-
cept for theoretical uncertainties on the signal model,
which are shown in Table III.
The experimental systematic errors result from un-
certainties on the data/MC consistency with respect to
tracking efficiency of the signal lepton, particle identifica-
tion efficiency of the signal lepton, reconstruction of the
signal photon energy, selection criteria efficiency uncer-
tainties, and uncertainties on the data/MC consistency
in the shape of ∆EP andmES. All of these were evaluated
using a number of control samples, including µ+µ−γ,
e+e−γ, and B+ → π+D0(→ K+π−).
The uncertainty on the number of produced BB pairs
is 1.1%. In our fits, we further assumed a charged-to-
neutral B production ratio of 1.0, and determine the
systematic uncertainty by varying within the measured
interval 1.020± 0.034 [16].
For systematic errors due to the theoretical uncertain-
ties on the π and ρ mode BFs and form factor models,
we refit, applying correlated variations in the BFs and
form factor models, and take the magnitude of the largest
change in signal BF as the associated systematic.
For systematic errors arising from the theoretical un-
certainties on the η and η′ mode BFs, we vary the as-
sumed BFs by ±10%[15] and refit to obtain a systematic
error. We find a negligible systematic from the uncer-
tainty on the ratio of the η to η′ mode BFs.
In the generic B sample, a significant fraction of events
contributing to our fit are non-resonant B → Xuℓ
events. We obtain the systematic error due to uncer-
tainty on the B → Xuℓ
+νℓ BF by fixing the total contri-
bution of generic B decays, as predicted by MC.
TABLE II: Systematic uncertainties on ∆B. All additive sys-
tematic values have been multiplied by 106.
Multiplicative Muon Electron Joint
Tracking efficiency 1.3% 1.3% 1.3%
Particle ID 3.5% 2.2% 2.1%
Neutral reconstruction 1.6% 1.6% 1.6%
Selection efficiency 6.0% 5.0% 6.0%
B counting 1.1% 1.1% 1.1%
Charged to neutral B ratio 9.4% 9.4% 9.4%
Additive
Shape of ∆EP vs. mES 0.3 0.2 0.3
η mode BF 0.3 0.1 0.2
π,ρ mode BF, ff 0.3 0.4 0.4
B → Xuℓ
νℓ BF 0.4 0.2 0.3
The theoretical uncertainty within the kinematic re-
gion of ∆B is conservatively estimated by evaluating the
change in efficiency when the model of Ref. [1] is modified
by setting the axial vector form factor equal to zero.
The results for ∆B are given in Tables III and IV. We
determine 90% C.L. Bayesian upper limits by integrating
the signal BF likelihood with two different priors, both
of which take values of 0 for negative values of the signal
BF: a prior flat in the BF (“flat BF prior”), and a prior
flat in the square root of the BF (“flat amplitude prior”),
equivalent to assuming a flat prior for |Vub| or fB.
For our kinematic region, the constants a, b, and c
of Eq.(2) are 0.88, −3.24, and 3.25, respectively[5]. Us-
ing input values of fB = 216MeV [18], |Vub| = 4.31 ×
10−3 [16], τB = 1.638 ps [16], and mb = 4.20GeV [16],
TABLE III: Comparison of ∆B two-sided results for all three
fits. All values have been multiplied by 106.
All Central Statistical Systematic Theoretical
values ×106 value uncertainty uncertainty uncertainty
Muon −1.33
+1.74 +0.80
−2.20 −0.87
Electron 0.11
+1.73 +0.61
−2.13 −0.59
Joint −0.25
+1.33 +0.60
−1.53 −0.64
TABLE IV: The 90% Bayesian upper-limits for all three fits,
for the two different choices of prior, in terms of ∆B.
Prior flat in amplitude Prior flat in BF
Muon < 1.5× 10−6 < 2.1× 10−6
Electron < 2.2× 10−6 < 2.8× 10−6
Joint < 1.7× 10−6 < 2.3× 10−6
our 90% C.L. Bayesian limits on ∆B correspond to val-
ues of λB of > 669MeV and > 591MeV, for the choice
of the flat amplitude and flat BF priors, respectively.
Given a theoretical model, a measurement of ∆B may
be converted into an estimate of the total BF. In the
model of Ref. [1], the result of the joint fit corresponds
to a BF of (−0.6+3.0−3.4(stat)
−1.4(syst)) × 10
−6, and 90%
C.L. Bayesian upper limits of 3.8× 10−6 and 5.0× 10−6
for the flat amplitude and flat BF priors, respectively.
We thank D. Pirjol for help on the signal model, and
C. S. Kim and Y. Yang for advice on the η mode. We
are grateful for the excellent luminosity and machine con-
ditions provided by our PEP-II colleagues, and for the
substantial dedicated effort from the computing organi-
zations that support BABAR. The collaborating institu-
tions wish to thank SLAC for its support and kind hospi-
tality. This work is supported by DOE and NSF (USA),
NSERC (Canada), IHEP (China), CEA and CNRS-
IN2P3 (France), BMBF and DFG (Germany), INFN
(Italy), FOM (The Netherlands), NFR (Norway), MIST
(Russia), MEC (Spain), and PPARC (United Kingdom).
Individuals have received support from the Marie Curie
EIF (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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	References

  We present the results of a search for $B^{+}\to\gamma \ell^{+}\nu_{\ell}$,
where $\ell = e, \mu$. We use a sample of 232 million $B\bar{B}$ pairs recorded
at the $\Upsilon(4S)$ with the BaBar detector at the PEP-II $B$ Factory. We
measure a partial branching fraction $\Delta\mathcal{B}$ in a restricted region
of phase space that reduces the effect of theoretical uncertainties, requiring
the lepton energy to be between 1.875 and 2.850GeV, the photon energy to be
between 0.45 and 2.35GeV, and the cosine of the angle between the lepton and
photon momenta to be less than -0.36, with all quantities computed in the
$\Upsilon(4S)$ center-of-mass frame. We find $\Delta\mathcal{B}(B^{+}\to\gamma
\ell^{+}\nu_{\ell}) = (-0.3^{+1.3}_{-1.5} ({stat}) \pm 0.6 ({syst}) \pm 0.1
({th})) \times 10^{-6}$, assuming lepton universality. Interpreted as a 90%
C.L. Bayesian upper limit, the result corresponds to $1.7\times10^{-6}$ for a
prior flat in amplitude, and $2.3\times10^{-6}$ for a prior flat in branching
fraction.

BABAR-PUB-06/067
SLAC-PUB-12442
Search for the Radiative Leptonic Decay B+ → γℓ+νℓ
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
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F. Winklmeier,22 Q. Zeng,22 D. D. Altenburg,23 E. Feltresi,23 A. Hauke,23 H. Jasper,23 J. Merkel,23 A. Petzold,23
B. Spaan,23 T. Brandt,24 V. Klose,24 H. M. Lacker,24 W. F. Mader,24 R. Nogowski,24 J. Schubert,24
K. R. Schubert,24 R. Schwierz,24 J. E. Sundermann,24 A. Volk,24 D. Bernard,25 G. R. Bonneaud,25 E. Latour,25
Ch. Thiebaux,25 M. Verderi,25 P. J. Clark,26 W. Gradl,26 F. Muheim,26 S. Playfer,26 A. I. Robertson,26
Y. Xie,26 M. Andreotti,27 D. Bettoni,27 C. Bozzi,27 R. Calabrese,27 G. Cibinetto,27 E. Luppi,27 M. Negrini,27
A. Petrella,27 L. Piemontese,27 E. Prencipe,27 F. Anulli,28 R. Baldini-Ferroli,28 A. Calcaterra,28 R. de Sangro,28
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http://arxiv.org/abs/0704.1478v1
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H. Schröder,65 R. Waldi,65 T. Adye,66 B. Franek,66 E. O. Olaiya,66 S. Ricciardi,66 F. F. Wilson,66 R. Aleksan,67
S. Emery,67 A. Gaidot,67 S. F. Ganzhur,67 G. Hamel de Monchenault,67 W. Kozanecki,67 M. Legendre,67
G. Vasseur,67 Ch. Yèche,67 M. Zito,67 X. R. Chen,68 H. Liu,68 W. Park,68 M. V. Purohit,68 J. R. Wilson,68
M. T. Allen,69 D. Aston,69 R. Bartoldus,69 P. Bechtle,69 N. Berger,69 R. Claus,69 J. P. Coleman,69 M. R. Convery,69
J. C. Dingfelder,69 J. Dorfan,69 G. P. Dubois-Felsmann,69 D. Dujmic,69 W. Dunwoodie,69 R. C. Field,69
T. Glanzman,69 S. J. Gowdy,69 M. T. Graham,69 P. Grenier,69 V. Halyo,69 C. Hast,69 T. Hryn’ova,69 W. R. Innes,69
M. H. Kelsey,69 P. Kim,69 D. W. G. S. Leith,69 S. Li,69 S. Luitz,69 V. Luth,69 H. L. Lynch,69 D. B. MacFarlane,69
H. Marsiske,69 R. Messner,69 D. R. Muller,69 C. P. O’Grady,69 V. E. Ozcan,69 A. Perazzo,69 M. Perl,69
T. Pulliam,69 B. N. Ratcliff,69 A. Roodman,69 A. A. Salnikov,69 R. H. Schindler,69 J. Schwiening,69 A. Snyder,69
J. Stelzer,69 D. Su,69 M. K. Sullivan,69 K. Suzuki,69 S. K. Swain,69 J. M. Thompson,69 J. Va’vra,69 N. van Bakel,69
A. P. Wagner,69 M. Weaver,69 W. J. Wisniewski,69 M. Wittgen,69 D. H. Wright,69 H. W. Wulsin,69 A. K. Yarritu,69
K. Yi,69 C. C. Young,69 P. R. Burchat,70 A. J. Edwards,70 S. A. Majewski,70 B. A. Petersen,70 L. Wilden,70
S. Ahmed,71 M. S. Alam,71 R. Bula,71 J. A. Ernst,71 V. Jain,71 B. Pan,71 M. A. Saeed,71 F. R. Wappler,71
S. B. Zain,71 W. Bugg,72 M. Krishnamurthy,72 S. M. Spanier,72 R. Eckmann,73 J. L. Ritchie,73 C. J. Schilling,73
R. F. Schwitters,73 J. M. Izen,74 X. C. Lou,74 S. Ye,74 F. Bianchi,75 F. Gallo,75 D. Gamba,75 M. Pelliccioni,75
M. Bomben,76 L. Bosisio,76 C. Cartaro,76 F. Cossutti,76 G. Della Ricca,76 L. Lanceri,76 L. Vitale,76 V. Azzolini,77
N. Lopez-March,77 F. Martinez-Vidal,77 A. Oyanguren,77 Sw. Banerjee,78 B. Bhuyan,78 K. Hamano,78
R. Kowalewski,78 I. M. Nugent,78 J. M. Roney,78 R. J. Sobie,78 J. J. Back,79 P. F. Harrison,79 T. E. Latham,79
G. B. Mohanty,79 M. Pappagallo,79, § H. R. Band,80 X. Chen,80 S. Dasu,80 K. T. Flood,80 J. J. Hollar,80
P. E. Kutter,80 B. Mellado,80 Y. Pan,80 M. Pierini,80 R. Prepost,80 S. L. Wu,80 Z. Yu,80 and H. Neal81
(The BABAR Collaboration)
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
4Institute of High Energy Physics, Beijing 100039, China
5University of Bergen, Institute of Physics, N-5007 Bergen, Norway
6Lawrence Berkeley National Laboratory and University of California, Berkeley, California 94720, USA
7University of Birmingham, Birmingham, B15 2TT, United Kingdom
8Ruhr Universität Bochum, Institut für Experimentalphysik 1, D-44780 Bochum, Germany
9University of Bristol, Bristol BS8 1TL, United Kingdom
10University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z1
11Brunel University, Uxbridge, Middlesex UB8 3PH, United Kingdom
12Budker Institute of Nuclear Physics, Novosibirsk 630090, Russia
13University of California at Irvine, Irvine, California 92697, USA
14University of California at Los Angeles, Los Angeles, California 90024, USA
15University of California at Riverside, Riverside, California 92521, USA
16University of California at San Diego, La Jolla, California 92093, USA
17University of California at Santa Barbara, Santa Barbara, California 93106, USA
18University of California at Santa Cruz, Institute for Particle Physics, Santa Cruz, California 95064, USA
19California Institute of Technology, Pasadena, California 91125, USA
20University of Cincinnati, Cincinnati, Ohio 45221, USA
21University of Colorado, Boulder, Colorado 80309, USA
22Colorado State University, Fort Collins, Colorado 80523, USA
23Universität Dortmund, Institut für Physik, D-44221 Dortmund, Germany
24Technische Universität Dresden, Institut für Kern- und Teilchenphysik, D-01062 Dresden, Germany
25Laboratoire Leprince-Ringuet, CNRS/IN2P3, Ecole Polytechnique, F-91128 Palaiseau, France
26University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom
27Università di Ferrara, Dipartimento di Fisica and INFN, I-44100 Ferrara, Italy
28Laboratori Nazionali di Frascati dell’INFN, I-00044 Frascati, Italy
29Università di Genova, Dipartimento di Fisica and INFN, I-16146 Genova, Italy
30Harvard University, Cambridge, Massachusetts 02138, USA
31Universität Heidelberg, Physikalisches Institut, Philosophenweg 12, D-69120 Heidelberg, Germany
32Imperial College London, London, SW7 2AZ, United Kingdom
33University of Iowa, Iowa City, Iowa 52242, USA
34Iowa State University, Ames, Iowa 50011-3160, USA
35Johns Hopkins University, Baltimore, Maryland 21218, USA
36Universität Karlsruhe, Institut für Experimentelle Kernphysik, D-76021 Karlsruhe, Germany
37Laboratoire de l’Accélérateur Linéaire, IN2P3/CNRS et Université Paris-Sud 11,
Centre Scientifique d’Orsay, B. P. 34, F-91898 ORSAY Cedex, France
38Lawrence Livermore National Laboratory, Livermore, California 94550, USA
39University of Liverpool, Liverpool L69 7ZE, United Kingdom
40Queen Mary, University of London, E1 4NS, United Kingdom
41University of London, Royal Holloway and Bedford New College, Egham, Surrey TW20 0EX, United Kingdom
42University of Louisville, Louisville, Kentucky 40292, USA
43University of Manchester, Manchester M13 9PL, United Kingdom
44University of Maryland, College Park, Maryland 20742, USA
45University of Massachusetts, Amherst, Massachusetts 01003, USA
46Massachusetts Institute of Technology, Laboratory for Nuclear Science, Cambridge, Massachusetts 02139, USA
47McGill University, Montréal, Québec, Canada H3A 2T8
48Università di Milano, Dipartimento di Fisica and INFN, I-20133 Milano, Italy
49University of Mississippi, University, Mississippi 38677, USA
50Université de Montréal, Physique des Particules, Montréal, Québec, Canada H3C 3J7
51Mount Holyoke College, South Hadley, Massachusetts 01075, USA
52Università di Napoli Federico II, Dipartimento di Scienze Fisiche and INFN, I-80126, Napoli, Italy
53NIKHEF, National Institute for Nuclear Physics and High Energy Physics, NL-1009 DB Amsterdam, The Netherlands
54University of Notre Dame, Notre Dame, Indiana 46556, USA
55Ohio State University, Columbus, Ohio 43210, USA
56University of Oregon, Eugene, Oregon 97403, USA
57Università di Padova, Dipartimento di Fisica and INFN, I-35131 Padova, Italy
58Laboratoire de Physique Nucléaire et de Hautes Energies,
IN2P3/CNRS, Université Pierre et Marie Curie-Paris6,
Université Denis Diderot-Paris7, F-75252 Paris, France
59University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
60Università di Perugia, Dipartimento di Fisica and INFN, I-06100 Perugia, Italy
61Università di Pisa, Dipartimento di Fisica, Scuola Normale Superiore and INFN, I-56127 Pisa, Italy
62Prairie View A&M University, Prairie View, Texas 77446, USA
63Princeton University, Princeton, New Jersey 08544, USA
64Università di Roma La Sapienza, Dipartimento di Fisica and INFN, I-00185 Roma, Italy
65Universität Rostock, D-18051 Rostock, Germany
66Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX11 0QX, United Kingdom
67DSM/Dapnia, CEA/Saclay, F-91191 Gif-sur-Yvette, France
68University of South Carolina, Columbia, South Carolina 29208, USA
69Stanford Linear Accelerator Center, Stanford, California 94309, USA
70Stanford University, Stanford, California 94305-4060, USA
71State University of New York, Albany, New York 12222, USA
72University of Tennessee, Knoxville, Tennessee 37996, USA
73University of Texas at Austin, Austin, Texas 78712, USA
74University of Texas at Dallas, Richardson, Texas 75083, USA
75Università di Torino, Dipartimento di Fisica Sperimentale and INFN, I-10125 Torino, Italy
76Università di Trieste, Dipartimento di Fisica and INFN, I-34127 Trieste, Italy
77IFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spain
78University of Victoria, Victoria, British Columbia, Canada V8W 3P6
79Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
80University of Wisconsin, Madison, Wisconsin 53706, USA
81Yale University, New Haven, Connecticut 06511, USA
(Dated: November 5, 2018)
We present the results of a search for B+ → γℓ+νℓ, where ℓ = e, µ. We use a sample of 232
million BB̄ pairs recorded at the Υ (4S) with the BABAR detector at the PEP-II B Factory. We
measure a partial branching fraction ∆B in a restricted region of phase space that reduces the effect
of theoretical uncertainties, requiring the lepton energy to be between 1.875 and 2.850GeV, the
photon energy to be between 0.45 and 2.35GeV, and the cosine of the angle between the lepton and
photon momenta to be less than −0.36, with all quantities computed in the Υ (4S) center-of-mass
frame. We find ∆B(B+ → γℓ+νℓ) = (−0.3
−1.5(stat)± 0.6(syst)± 0.1(th))× 10
−6, assuming lepton
universality. Interpreted as a 90% C.L. Bayesian upper limit, the result corresponds to 1.7 × 10−6
for a prior flat in amplitude, and 2.3× 10−6 for a prior flat in branching fraction.
PACS numbers: 13.20.He, 13.30.Ce, 12.38.Qk, 14.40.Nd
At tree level, the branching fraction (BF) for radiative
leptonic B decays is given by:
B(B+ → γℓ+νℓ) = α
G2F |Vub|
288π2
f2BτBm
where mB is the B
+ meson mass, mb is the MS b quark
mass, τB is the B
+ meson lifetime, fB is the B meson
decay constant, Qi is the charge of quark flavor i and λB
is the first inverse moment of the B light-cone distribu-
tion amplitude [1, 2], a quantity that enters into theo-
retical calculations [3] of the BF of hadronic B decays
such as B → ππ, and is typically taken to be of the order
of ΛQCD. Thus, a measurement of B(B
+ → γℓ+νℓ) can
provide a determination of λB free of hadronic final-state
uncertainties. The best current 90% C.L. upper limit on
the full BF is 5.2× 10−5[4], for B+ → γµ+νµ.
However, Eq.(1) is based on the assumption that the
factorization relation for the vector and axial-vector form
factors is valid over the entire phase space. Instead, one
can relate, at tree-level, λB to a partial BF, ∆B, over a
restricted region of phase space [5]:
∆B = α
G2F |Vub|
f2BτBm
a+ bL+ cL2
, (2)
where L = (mB/3)(1/λB + 1/(2mb)), the first term de-
scribes the effects of photon radiation from the lepton,
the third term the internal photon emission, and second
their interference. The constants a, b, and c can be pre-
dicted model-independently using factorization at large
photon energy, the kinematic region for our analysis.
We present herein the results of a search for charged
B meson decays B+ → γℓ+νℓ, where ℓ = e, µ (“elec-
tron channel”,“muon channel”)[6]. Our measurements
are based on a sample of 232 million BB pairs recorded
with the BABAR detector [7] at the PEP-II asymmetric-
energy e+e− storage rings, comprising an integrated lu-
minosity of 210.5 fb−1 collected at the Υ (4S) resonance
(“on-peak”). We also use 21.6 fb−1 recorded approxi-
mately 40 MeV below the Υ (4S) (“off-peak”).
The analysis procedure consists of selecting a lepton
and photon recoiling against a reconstructedB, and iden-
tifying signal candidates by reconstructing the neutrino
using missing energy and momentum. We use a variety
of selection criteria, optimized using Monte Carlo (MC)
samples, to discriminate signal from background. We
then extract the number of signal events in data using a
binned maximum-likelihood (ML) fit.
The backgrounds are divided into three categories:
continuum (non-BB), specific exclusive b → uℓνℓ decays,
and “generic B” decays, defined as a combination of all
B hadronic decays, b → cℓνℓ decays, and the remain-
ing inclusive b → uℓνℓ decays. In particular, we study
the seven exclusive b → uℓνℓ modes: B
+ → h0ℓ+νℓ
(h0 = π0, ρ0, η, η′, ω) and B0 → h−ℓ+νℓ (h
− = π−, ρ−),
referred to below, for each h, as the “h mode”.
Our signal MC samples were generated using the tree-
level model of Ref. [1]. The π0 and π± mode samples
were generated using the form factor parameterization of
Ref. [8], with the value of the shape parameter based on
lattice QCD results [9]. Light cone sum rule-based form
factor models were used to generate samples for the ρ0,
ρ±, and ω modes [10], and η and η′ modes [11].
We find an excess of events in the off-peak data com-
pared to continuum MC (e+e− → qq, τ+τ−, and in the
muon channel, µ+µ−γ), with the excess more pronounced
in the electron channel. This is likely to result from
unmodeled higher-order QED and hadronic two-photon
events. We thus use off-peak data instead of continuum
MC to represent continuum background in our analysis.
We take as the signal lepton and photon the high-
est center-of-mass (CM) energy electron (muon) and the
highest CM energy photon candidate in each event. The
remaining charged tracks, each assigned a pion mass, and
neutral clusters, treated as photons, are assigned to the
“recoil B” candidate. We reconstruct the recoil B in two
ways: we construct an “unscaled” recoil momentum as
the sum of the CM 3-momenta of its constituents, and
we define a “scaled” recoil momentum in the direction of
the unscaled recoil, with its magnitude determined from
the CM energy of the Υ (4S) and the B± mass. Using
either the scaled or unscaled momentum, we reconstruct
the 3-momentum of a corresponding scaled or unscaled
signal neutrino candidate. The reconstructed neutrino
CM energy is calculated as the difference between the
CM beam energy and the sum of the lepton and photon
candidates’ CM energies.
We optimize a set of selection criteria for the best sig-
nal sensitivity at a significance of 3σ using MC samples,
splitting each in half, with one sample used for the opti-
mization and the other used to evaluate its performance.
On the signal side, we require that the electron (muon)
have a CM energy between 2.00 and 2.85 (1.875 and
2.775)GeV. We require that the photon have a CM en-
ergy between 0.65 and 2.35 (0.45 and 2.35) GeV. We
define cos θℓγ to be the cosine of the angle between
the lepton and photon in the CM frame, and require
its value to be less than −0.42 (−0.36). We require
−1.10(−1.05) < cos θBY < 1.10(1.00), where cos θBY
is the cosine of the angle between the signal B and the
lepton-photon combination Y in the CM frame [12], com-
puted from the known B mass, the beam energy, and the
3-momenta of the signal lepton and photon.
In order to reduce background from neutral hadrons,
we require the lateral moment [13] of the electromagnetic
calorimeter energy distribution of the signal photon can-
didate to be less than 0.55 for both channels. The polar
angle of the photon candidate in the laboratory frame
is required to be between 0.326 and 2.443 rad for both
channels. We pair the candidate with every other neutral
cluster in the event and reject events with a pair invariant
mass in the π0 mass range 123–147 (116–148) MeV.
We require the difference between the total CM energy
of the recoil B constituents and the CM beam energy to
be between −5.0 and 0.9 (−2.5 and 0.7) GeV. For the
neutrino reconstruction, we require that both the scaled
and unscaled neutrino polar angle in the laboratory frame
be between 0.300 and 2.443 rad for both channels.
To reduce continuum background, we require the ratio
of the second to zeroth Fox-Wolfram moment [14] of all
charged tracks and neutral clusters to be less than 0.5,
and the absolute value of the cosine of the angle between
the CM thrust axes of the recoil B and the lepton-photon
system be less than 0.98 (0.86). We use a Fisher discrim-
inant, F ≡ a0L0+a2L2, calculated from the momentum-
weighted zeroth and second Legendre moments, L0 and
L2, of the recoil B about the lepton-photon CM thrust
axis, with coefficients a0 and a2 equal to 0.43 and −1.86
(0.008 and −1.590), respectively. F is required to be
greater than 1.50 (0.310).
In the electron channel, we veto two-photon events
via the charge-angle correlation of the signal lepton aris-
ing from the initial state. For a positively (negatively)-
charged signal electron, we require the cosine of its CM
polar angle to be between −0.74 and 0.78 (−0.94 and
0.70). In the muon channel, we require this variable to
be between −1.00 and 0.78 for both charges. These crite-
ria were optimized on a loosely-selected sample of events,
where the off-peak data are used for the continuum, and
the MC for the signal and other backgrounds.
We also reject two-photon events using a parameter-
ized combination of the missing CM momentum in the
beam direction and the invariant mass of the hypotheti-
cal two-photon system. For the muon channel, the entire
observed event is taken as the two-photon system, while
 (GeV)ESm
4.9 4.95 5 5.05 5.1 5.15 5.2 5.25 5.3
FIG. 1: Electron-channel ∆EP vs. mES signal MC, using a
color scale to represent relative contents of each bin.
for the electron channel, the signal electron is assumed
to be from the initial state, and so is excluded from the
two-photon system. The selection criterion was adjusted
to preserve a 94% efficiency for signal for both channels.
After applying our selection criteria, we use the two-
dimensional distribution of ∆EP , the difference between
the scaled neutrino candidate’s CM energy and the mag-
nitude of its 3-momentum, and mES, the invariant mass
of the recoil B, calculated from its unscaled CM 3-
momentum and the CM beam energy, as inputs to the
ML fit. These distributions provide distinct signatures
for signal, B background, and continuum, with the sig-
nal distribution shown in Fig. 1. The signal (S) and three
sideband (B1, B2, B3) regions were selected to maximize
separation of signal fromBB and continuum background.
We extract signal events by fitting on-peak data for the
contributions of signal and background, while allowing
the predicted shapes of signal and background to vary
within statistical uncertainties. The scale of signal and
generic B contributions are allowed to vary, while the
scale of off-peak data is fixed using the on-peak/off-peak
luminosity ratio. For the seven semileptonic (SL) modes,
we fit for three of the BFs and relate the other four to
them as follows: The π± and ρ± mode BFs are obtained
from BABAR measurements [12], and the η mode BF is
obtained from CLEO [15]. The charged and neutral π
and ρ modes are related by the lifetime ratio, τB±/τB0 =
1.071 ± 0.009 [16], and an isospin factor of 2. The ω
mode BF is taken as equal to the ρ0 mode BF. We take
the ratio of the η to η′ mode BFs to be 2.057± 0.020[17].
We maximize a likelihood function consisting of the
product of four Poisson probability distribution functions
(PDFs), modeling the total counts in each of the four
regions, three Gaussian PDFs for the BFs of the three
SL modes, and 40 Poisson PDFs for the 4-region shapes
of the various samples. All of the shapes are obtained
from MC, except for continuum, where off-peak data are
used, introducing a larger statistical uncertainty.
Each Poisson PDF that models the total count in one
of the four fit regions has a measured value obtained from
the on-peak data count, and an expected value based
on the fitted contributions of signal and background, in-
cluding fitted variations of the shapes. For the seven
SL modes (where three of the fitted BFs are indepen-
dent), the variances of the three Gaussian likelihoods are
obtained from the published statistical and experimental
systematic uncertainties, combined in quadrature. In all,
there are 47 PDFs, and 45 free parameters.
We fit for the partial BF ∆B for the kinematic region
with lepton CM energy between 1.875 and 2.850GeV,
photon CM energy between 0.45 and 2.35GeV, and
cos θℓγ less than −0.36 — the union of the electron and
muon channel regions. We perform three fits: separate
electron and muon channel fits, and a joint fit in which
the signal and three SL BFs are constrained to be equal
for the two channels. For each fit, errors on the fitted sig-
nal BF are obtained by finding the two values at which
the signal BF likelihood decreased by a factor of e−1/2.
Table I shows the results from the joint fit.
TABLE I: Comparison of fit results and experimental obser-
vations for the joint fit to the muon and electron channels.
For each of the four fit regions, the individual fitted contri-
butions from continuum (cont.), BB background, and signal
are shown, along with their total. The on-peak and off-peak
(scaled to the integrated on-peak luminosity) observations are
shown for comparison, in indented rows, and are not included
in the “Total fit” value shown.
Muon channel
S B1 B2 B3
Fit cont. 20.0±11.8 116.3±14.7 42.6±12.8 213.2±42.1
Off-peak 23.0±16.2 158.1±40.8 17.4±12.3 219.7±45.8
Fit BB 59.1± 8.5 61.0± 9.9 61.7± 9.8 286.6±46.6
Fit signal −5.2±13.8 −1.3± 3.4 −0.4± 1.0 −0.2± 0.5
Total fit 74.0± 8.1 176.0±12.4 103.9± 9.8 500.0±22.1
On-peak 73.0± 8.5 170.0±13.0 111.0±10.5 498.0±22.3
Electron channel
S B1 B2 B3
Fit cont. 55.4±20.5 181.1±16.2 48.9±14.1 356.7±54.4
Off-peak 41.4±20.7 239.7±48.9 79.0±27.9 294.5±52.9
Fit BB 69.2± 8.5 59.2± 8.5 140.1±15.5 393.8±57.2
Fit signal −8.4±22.3 −1.5± 3.9 −1.2± 3.3 −0.4± 1.0
Total fit 116.2±10.3 238.7±14.5 187.7±12.5 750.2±26.5
On-peak 119.0±10.9 231.0±15.2 176.0±13.3 764.0±27.6
Table II shows all systematic uncertainties on ∆B ex-
cept for theoretical uncertainties on the signal model,
which are shown in Table III.
The experimental systematic errors result from un-
certainties on the data/MC consistency with respect to
tracking efficiency of the signal lepton, particle identifica-
tion efficiency of the signal lepton, reconstruction of the
signal photon energy, selection criteria efficiency uncer-
tainties, and uncertainties on the data/MC consistency
in the shape of ∆EP andmES. All of these were evaluated
using a number of control samples, including µ+µ−γ,
e+e−γ, and B+ → π+D0(→ K+π−).
The uncertainty on the number of produced BB pairs
is 1.1%. In our fits, we further assumed a charged-to-
neutral B production ratio of 1.0, and determine the
systematic uncertainty by varying within the measured
interval 1.020± 0.034 [16].
For systematic errors due to the theoretical uncertain-
ties on the π and ρ mode BFs and form factor models,
we refit, applying correlated variations in the BFs and
form factor models, and take the magnitude of the largest
change in signal BF as the associated systematic.
For systematic errors arising from the theoretical un-
certainties on the η and η′ mode BFs, we vary the as-
sumed BFs by ±10%[15] and refit to obtain a systematic
error. We find a negligible systematic from the uncer-
tainty on the ratio of the η to η′ mode BFs.
In the generic B sample, a significant fraction of events
contributing to our fit are non-resonant B → Xuℓ
events. We obtain the systematic error due to uncer-
tainty on the B → Xuℓ
+νℓ BF by fixing the total contri-
bution of generic B decays, as predicted by MC.
TABLE II: Systematic uncertainties on ∆B. All additive sys-
tematic values have been multiplied by 106.
Multiplicative Muon Electron Joint
Tracking efficiency 1.3% 1.3% 1.3%
Particle ID 3.5% 2.2% 2.1%
Neutral reconstruction 1.6% 1.6% 1.6%
Selection efficiency 6.0% 5.0% 6.0%
B counting 1.1% 1.1% 1.1%
Charged to neutral B ratio 9.4% 9.4% 9.4%
Additive
Shape of ∆EP vs. mES 0.3 0.2 0.3
η mode BF 0.3 0.1 0.2
π,ρ mode BF, ff 0.3 0.4 0.4
B → Xuℓ
νℓ BF 0.4 0.2 0.3
The theoretical uncertainty within the kinematic re-
gion of ∆B is conservatively estimated by evaluating the
change in efficiency when the model of Ref. [1] is modified
by setting the axial vector form factor equal to zero.
The results for ∆B are given in Tables III and IV. We
determine 90% C.L. Bayesian upper limits by integrating
the signal BF likelihood with two different priors, both
of which take values of 0 for negative values of the signal
BF: a prior flat in the BF (“flat BF prior”), and a prior
flat in the square root of the BF (“flat amplitude prior”),
equivalent to assuming a flat prior for |Vub| or fB.
For our kinematic region, the constants a, b, and c
of Eq.(2) are 0.88, −3.24, and 3.25, respectively[5]. Us-
ing input values of fB = 216MeV [18], |Vub| = 4.31 ×
10−3 [16], τB = 1.638 ps [16], and mb = 4.20GeV [16],
TABLE III: Comparison of ∆B two-sided results for all three
fits. All values have been multiplied by 106.
All Central Statistical Systematic Theoretical
values ×106 value uncertainty uncertainty uncertainty
Muon −1.33
+1.74 +0.80
−2.20 −0.87
Electron 0.11
+1.73 +0.61
−2.13 −0.59
Joint −0.25
+1.33 +0.60
−1.53 −0.64
TABLE IV: The 90% Bayesian upper-limits for all three fits,
for the two different choices of prior, in terms of ∆B.
Prior flat in amplitude Prior flat in BF
Muon < 1.5× 10−6 < 2.1× 10−6
Electron < 2.2× 10−6 < 2.8× 10−6
Joint < 1.7× 10−6 < 2.3× 10−6
our 90% C.L. Bayesian limits on ∆B correspond to val-
ues of λB of > 669MeV and > 591MeV, for the choice
of the flat amplitude and flat BF priors, respectively.
Given a theoretical model, a measurement of ∆B may
be converted into an estimate of the total BF. In the
model of Ref. [1], the result of the joint fit corresponds
to a BF of (−0.6+3.0−3.4(stat)
−1.4(syst)) × 10
−6, and 90%
C.L. Bayesian upper limits of 3.8× 10−6 and 5.0× 10−6
for the flat amplitude and flat BF priors, respectively.
We thank D. Pirjol for help on the signal model, and
C. S. Kim and Y. Yang for advice on the η mode. We
are grateful for the excellent luminosity and machine con-
ditions provided by our PEP-II colleagues, and for the
substantial dedicated effort from the computing organi-
zations that support BABAR. The collaborating institu-
tions wish to thank SLAC for its support and kind hospi-
tality. This work is supported by DOE and NSF (USA),
NSERC (Canada), IHEP (China), CEA and CNRS-
IN2P3 (France), BMBF and DFG (Germany), INFN
(Italy), FOM (The Netherlands), NFR (Norway), MIST
(Russia), MEC (Spain), and PPARC (United Kingdom).
Individuals have received support from the Marie Curie
EIF (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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	References
