of 18
Measurements of branching fractions, rate asymmetries, and angular distributions in the rare
decays
B
!
K‘


and
B
!
K



B. Aubert,
1
R. Barate,
1
M. Bona,
1
D. Boutigny,
1
F. Couderc,
1
Y. Karyotakis,
1
J. P. Lees,
1
V. Poireau,
1
V. Tisserand,
1
A. Zghiche,
1
E. Grauges,
2
A. Palano,
3
M. Pappagallo,
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
E. Charles,
6
C. T. Day,
6
M. S. Gill,
6
Y. Groysman,
6
R. G. Jacobsen,
6
J. A. Kadyk,
6
L. T. Kerth,
6
Yu. G. Kolomensky,
6
G. Kukartsev,
6
G. Lynch,
6
L. M. Mir,
6
P. J. Oddone,
6
T. J. Orimoto,
6
M. Pripstein,
6
N. A. Roe,
6
M. T. Ronan,
6
W. A. Wenzel,
6
M. Barrett,
7
K. E. Ford,
7
T. J. Harrison,
7
A. J. Hart,
7
C. M. Hawkes,
7
S. E. Morgan,
7
A. T. Watson,
7
K. Goetzen,
8
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
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
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
D. S. Best,
13
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
R. K. Mommsen,
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
K. Wang,
15
L. Zhang,
15
H. K. Hadavand,
16
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
P. Spradlin,
18
D. C. Williams,
18
M. G. Wilson,
18
J. Albert,
19
E. Chen,
19
A. Dvoretskii,
19
D. G. Hitlin,
19
I. Narsky,
19
T. Piatenko,
19
F. C. Porter,
19
A. Ryd,
19
A. Samuel,
19
R. Andreassen,
20
G. Mancinelli,
20
B. T. Meadows,
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
U. Nauenberg,
21
A. Olivas,
21
W. O. Ruddick,
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
B. Spaan,
23
T. Brandt,
24
V. Klose,
24
H. M. Lacker,
24
W. F. Mader,
24
R. Nogowski,
24
A. Petzold,
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
P. Grenier,
25,
*
E. Latour,
25
Ch. Thiebaux,
25
M. Verderi,
25
D. J. Bard,
26
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. Capra,
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
G. Brandenburg,
30
K. S. Chaisanguanthum,
30
M. Morii,
30
J. Wu,
30
R. S. Dubitzky,
31
J. Marks,
31
S. Schenk,
31
U. Uwer,
31
W. Bhimji,
32
D. A. Bowerman,
32
P. D. Dauncey,
32
U. Egede,
32
R. L. Flack,
32
J. R. Gaillard,
32
J. A. Nash,
32
M. B. Nikolich,
32
W. Panduro Vazquez,
32
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
M. Fritsch,
36
G. Schott,
36
N. Arnaud,
37
M. Davier,
37
G. Grosdidier,
37
A. Ho
̈
cker,
37
F. Le Diberder,
37
V. Lepeltier,
37
A. M. Lutz,
37
A. Oyanguren,
37
S. Pruvot,
37
S. Rodier,
37
P. Roudeau,
37
M. H. Schune,
37
A. Stocchi,
37
W. F. Wang,
37
G. Wormser,
37
C. H. Cheng,
38
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
C. L. Brown,
41
G. Cowan,
41
H. U. Flaecher,
41
D. A. Hopkins,
41
P. S. Jackson,
41
T. R. McMahon,
41
S. Ricciardi,
41
F. Salvatore,
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
M. P. Kelly,
43
G. D. Lafferty,
43
M. T. Naisbit,
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
S. Saremi,
45
H. Staengle,
45
S. Y. Willocq,
45
R. Cowan,
46
K. Koeneke,
46
G. Sciolla,
46
S. J. Sekula,
46
M. Spitznagel,
46
F. Taylor,
46
R. K. Yamamoto,
46
H. Kim,
47
P. M. Patel,
47
C. T. Potter,
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
J. Reidy,
49
D. A. Sanders,
49
D. J. Summers,
49
H. W. Zhao,
49
S. Brunet,
50
D. Co
ˆ
te
́
,
50
M. Simard,
50
P. Taras,
50
F. B. Viaud,
50
H. Nicholson,
51
N. Cavallo,
52,‡
G. De Nardo,
52
D. del Re,
52
F. Fabozzi,
52,‡
C. Gatto,
52
L. Lista,
52
D. Monorchio,
52
P. Paolucci,
52
D. Piccolo,
52
C. Sciacca,
52
M. Baak,
53
H. Bulten,
53
G. Raven,
53
H. L. Snoek,
53
C. P. Jessop,
54
J. M. LoSecco,
54
T. Allmendinger,
55
G. Benelli,
55
K. K. Gan,
55
K. Honscheid,
55
D. Hufnagel,
55
P. D. Jackson,
55
H. Kagan,
55
R. Kass,
55
T. Pulliam,
55
A. M. Rahimi,
55
R. Ter-Antonyan,
55
Q. K. Wong,
55
N. L. Blount,
56
J. Brau,
56
R. Frey,
56
O. Igonkina,
56
M. Lu,
56
R. Rahmat,
56
N. B. Sinev,
56
D. Strom,
56
J. Strube,
56
PHYSICAL REVIEW D
73,
092001 (2006)
1550-7998
=
2006
=
73(9)
=
092001(18)
092001-1
©
2006 The American Physical Society
E. Torrence,
56
F. Galeazzi,
57
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
M. Benayoun,
58
J. Chauveau,
58
P. David,
58
L. Del Buono,
58
Ch. de la Vaissie
`
re,
58
O. Hamon,
58
B. L. Hartfiel,
58
M. J. J. John,
58
Ph. Leruste,
58
J. Malcle
`
s,
58
J. Ocariz,
58
L. Roos,
58
G. Therin,
58
P. K. Behera,
59
L. Gladney,
59
J. Panetta,
59
M. Biasini,
60
R. Covarelli,
60
M. Pioppi,
60
C. Angelini,
61
G. Batignani,
61
S. Bettarini,
61
F. Bucci,
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. Walsh,
61
M. Haire,
62
D. Judd,
62
D. E. Wagoner,
62
J. Biesiada,
63
N. Danielson,
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
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. Schro
̈
der,
65
R. Waldi,
65
T. Adye,
66
N. De Groot,
66
B. Franek,
66
E. O. Olaiya,
66
F. F. Wilson,
66
S. Emery,
67
A. Gaidot,
67
S. F. Ganzhur,
67
G. Hamel de Monchenault,
67
W. Kozanecki,
67
M. Legendre,
67
B. Mayer,
67
G. Vasseur,
67
Ch. Ye
`
che,
67
M. Zito,
67
W. Park,
68
M. V. Purohit,
68
A. W. Weidemann,
68
J. R. Wilson,
68
M. T. Allen,
69
D. Aston,
69
R. Bartoldus,
69
P. Bechtle,
69
N. Berger,
69
A. M. Boyarski,
69
R. Claus,
69
J. P. Coleman,
69
M. R. Convery,
69
M. Cristinziani,
69
J. C. Dingfelder,
69
D. Dong,
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
V. Halyo,
69
C. Hast,
69
T. Hryn’ova,
69
W. R. Innes,
69
M. H. Kelsey,
69
P. Kim,
69
M. L. Kocian,
69
D. W. G. S. Leith,
69
S. Li,
69
J. Libby,
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
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
M. Weaver,
69
A. J. R. Weinstein,
69
W. J. Wisniewski,
69
M. Wittgen,
69
D. H. Wright,
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
C. Roat,
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
A. Satpathy,
73
C. J. Schilling,
73
R. F. Schwitters,
73
J. M. Izen,
74
I. Kitayama,
74
X. C. Lou,
74
S. Ye,
74
F. Bianchi,
75
F. Gallo,
75
D. Gamba,
75
M. Bomben,
76
L. Bosisio,
76
C. Cartaro,
76
F. Cossutti,
76
G. Della Ricca,
76
S. Dittongo,
76
S. Grancagnolo,
76
L. Lanceri,
76
L. Vitale,
76
V. Azzolini,
77
F. Martinez-Vidal,
77
Sw. Banerjee,
78
B. Bhuyan,
78
C. M. Brown,
78
D. Fortin,
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
H. R. Band,
80
X. Chen,
80
B. Cheng,
80
S. Dasu,
80
M. Datta,
80
A. M. Eichenbaum,
80
K. T. Flood,
80
J. J. Hollar,
80
J. R. Johnson,
80
P. E. Kutter,
80
H. Li,
80
R. Liu,
80
B. Mellado,
80
A. Mihalyi,
80
A. K. Mohapatra,
80
Y. Pan,
80
M. Pierini,
80
R. Prepost,
80
P. Tan,
80
S. L. Wu,
80
Z. Yu,
80
and H. Neal
81
(
B
A
B
AR
Collaboration)
1
Laboratoire de Physique des Particules, F-74941 Annecy-le-Vieux, France
2
Universitat de Barcelona, Facultat de Fisica Dept. ECM, E-08028 Barcelona, Spain
3
Universita
`
di Bari, Dipartimento di Fisica and INFN, I-70126 Bari, Italy
4
Institute of High Energy Physics, Beijing 100039, China
5
University of Bergen, Institute of Physics, N-5007 Bergen, Norway
6
Lawrence Berkeley National Laboratory and University of California, Berkeley, California 94720, USA
7
University of Birmingham, Birmingham, B15 2TT, United Kingdom
8
Ruhr Universita
̈
t Bochum, Institut fu
̈
r Experimentalphysik 1, D-44780 Bochum, Germany
9
University of Bristol, Bristol BS8 1TL, United Kingdom
10
University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z1
11
Brunel University, Uxbridge, Middlesex UB8 3PH, United Kingdom
12
Budker Institute of Nuclear Physics, Novosibirsk 630090, Russia
13
University of California at Irvine, Irvine, California 92697, USA
14
University of California at Los Angeles, Los Angeles, California 90024, USA
15
University of California at Riverside, Riverside, California 92521, USA
16
University of California at San Diego, La Jolla, California 92093, USA
17
University of California at Santa Barbara, Santa Barbara, California 93106, USA
18
University of California at Santa Cruz, Institute for Particle Physics, Santa Cruz, California 95064, USA
19
California Institute of Technology, Pasadena, California 91125, USA
20
University of Cincinnati, Cincinnati, Ohio 45221, USA
21
University of Colorado, Boulder, Colorado 80309, USA
22
Colorado State University, Fort Collins, Colorado 80523, USA
23
Universita
̈
t Dortmund, Institut fu
̈
r Physik, D-44221 Dortmund, Germany
B. AUBERT
et al.
PHYSICAL REVIEW D
73,
092001 (2006)
092001-2
24
Technische Universita
̈
t Dresden, Institut fu
̈
r Kern- und Teilchenphysik, D-01062 Dresden, Germany
25
Ecole Polytechnique, LLR, F-91128 Palaiseau, France
26
University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom
27
Universita
`
di Ferrara, Dipartimento di Fisica and INFN, I-44100 Ferrara, Italy
28
Laboratori Nazionali di Frascati dell’INFN, I-00044 Frascati, Italy
29
Universita
`
di Genova, Dipartimento di Fisica and INFN, I-16146 Genova, Italy
30
Harvard University, Cambridge, Massachusetts 02138, USA
31
Universita
̈
t Heidelberg, Physikalisches Institut, Philosophenweg 12, D-69120 Heidelberg, Germany
32
Imperial College London, London, SW7 2AZ, United Kingdom
33
University of Iowa, Iowa City, Iowa 52242, USA
34
Iowa State University, Ames, Iowa 50011-3160, USA
35
Johns Hopkins University, Baltimore, Maryland 21218, USA
36
Universita
̈
t Karlsruhe, Institut fu
̈
r Experimentelle Kernphysik, D-76021 Karlsruhe, Germany
37
Laboratoire de l’Acce
́
le
́
rateur Line
́
aire, IN2P3-CNRS et Universite
́
Paris-Sud 11, Centre Scientifique d’Orsay,
B.P. 34, F-91898 ORSAY Cedex, France
38
Lawrence Livermore National Laboratory, Livermore, California 94550, USA
39
University of Liverpool, Liverpool L69 7ZE, United Kingdom
40
Queen Mary, University of London, E1 4NS, United Kingdom
41
University of London, Royal Holloway and Bedford New College, Egham, Surrey TW20 0EX, United Kingdom
42
University of Louisville, Louisville, Kentucky 40292, USA
43
University of Manchester, Manchester M13 9PL, United Kingdom
44
University of Maryland, College Park, Maryland 20742, USA
45
University of Massachusetts, Amherst, Massachusetts 01003, USA
46
Massachusetts Institute of Technology, Laboratory for Nuclear Science, Cambridge, Massachusetts 02139, USA
47
McGill University, Montre
́
al, Que
́
bec, Canada H3A 2T8
48
Universita
`
di Milano, Dipartimento di Fisica and INFN, I-20133 Milano, Italy
49
University of Mississippi, University, Mississippi 38677, USA
50
Universite
́
de Montre
́
al, Physique des Particules, Montre
́
al, Que
́
bec, Canada H3C 3J7
51
Mount Holyoke College, South Hadley, Massachusetts 01075, USA
52
Universita
`
di Napoli Federico II, I-80126, Napoli, Italy
53
NIKHEF, National Institute for Nuclear Physics and High Energy Physics, NL-1009 DB Amsterdam, The Netherlands
54
University of Notre Dame, Notre Dame, Indiana 46556, USA
55
Ohio State University, Columbus, Ohio 43210, USA
56
University of Oregon, Eugene, Oregon 97403, USA
57
Universita
`
di Padova, Dipartimento di Fisica and INFN, I-35131 Padova, Italy
58
Universite
́
s Paris VI et VII, Laboratoire de Physique Nucle
́
aire et de Hautes Energies, F-75252 Paris, France
59
University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
60
Universita
`
di Perugia, Dipartimento di Fisica and INFN, I-06100 Perugia, Italy
61
Universita
`
di Pisa, Dipartimento di Fisica, Scuola Normale Superiore and INFN, I-56127 Pisa, Italy
62
Prairie View A&M University, Prairie View, Texas 77446, USA
63
Princeton University, Princeton, New Jersey 08544, USA
64
Universita
`
di Roma La Sapienza, Dipartimento di Fisica and INFN, I-00185 Roma, Italy
65
Universita
̈
t Rostock, D-18051 Rostock, Germany
66
Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX11 0QX, United Kingdom
67
DSM/Dapnia, CEA/Saclay, F-91191 Gif-sur-Yvette, France
68
University of South Carolina, Columbia, South Carolina 29208, USA
69
Stanford Linear Accelerator Center, Stanford, California 94309, USA
70
Stanford University, Stanford, California 94305-4060, USA
71
State University of New York, Albany, New York 12222, USA
72
University of Tennessee, Knoxville, Tennessee 37996, USA
73
University of Texas at Austin, Austin, Texas 78712, USA
74
University of Texas at Dallas, Richardson, Texas 75083, USA
75
Universita
`
di Torino, Dipartimento di Fisica Sperimentale and INFN, I-10125 Torino, Italy
76
Universita
`
di Trieste, Dipartimento di Fisica and INFN, I-34127 Trieste, Italy
77
IFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spain
78
University of Victoria, Victoria, British Columbia, Canada V8W 3P6
79
Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
80
University of Wisconsin, Madison, Wisconsin 53706, USA
81
Yale University, New Haven, Connecticut 06511, USA
(Received 4 April 2006; published 5 May 2006)
MEASUREMENTS OF BRANCHING FRACTIONS, RATE
...
PHYSICAL REVIEW D
73,
092001 (2006)
092001-3
We present measurements of the flavor-changing neutral current decays
B
!
K‘


and
B
!
K



, where


is either an
e

e

or




pair. The data sample comprises
229

10
6


4
S
!
B

B
decays collected with the
BABAR
detector at the PEP-II
e

e

storage ring. Flavor-changing neutral
current decays are highly suppressed in the standard model and their predicted properties could be
significantly modified by new physics at the electroweak scale. We measure the branching fractions
B

B
!
K‘



0
:
34

0
:
07

0
:
02

10

6
,
B

B
!
K




0
:
78

0
:
19

0
:
17

0
:
11

10

6
, the di-
rect
CP
asymmetries of these decays, and the relative abundances of decays to electrons and muons. For
two regions in


mass, above and below
m
J=
, we measure partial branching fractions and the
forward-backward angular asymmetry of the lepton pair. In these same regions we also measure the
K

longitudinal polarization in
B
!
K



decays. Upper limits are obtained for the lepton-flavor-violating
decays
B
!
Ke
and
B
!
K

e
. All measurements are consistent with standard model expectations.
DOI:
10.1103/PhysRevD.73.092001
PACS numbers: 13.25.Hw, 13.20.He
I. INTRODUCTION
The decays
B
!
K



, where


is either an
e

e

or




pair and
K

denotes either a kaon or
the
K


892

meson, are manifestations of
b
!
s‘


flavor-changing neutral currents (FCNC). In the standard
model (SM), these decays are forbidden at tree level and
can only occur at greatly suppressed rates through higher-
order processes. At lowest order, three amplitudes contrib-
ute: (i) a photon penguin, (ii) a
Z
penguin, and (iii) a
W

W

box diagram (Fig. 1). In all three, a virtual
t
quark
contribution dominates, with secondary contributions from
virtual
c
and
u
quarks. Within the Operator Product
Expansion (OPE) framework, these short-distance contri-
butions are typically described in terms of the effective
Wilson coefficients
C
eff
7
,
C
eff
9
, and
C
eff
10
[1]. Since these
decays proceed via weakly-interacting particles with vir-
tual energies near the electroweak scale, they provide a
promising means to search for effects from new interac-
tions entering with amplitudes comparable to those of the
SM. Such effects are predicted in a wide variety of models
[2 – 6].
In the SM the
B
!
K‘


branching fraction is pre-
dicted to be roughly
0
:
4

10

6
, while the
B
!
K



branching fraction is predicted to be about 3 times larger
[4,7–12]. The
B
!
K



mode receives a significant
contribution from a pole in the photon penguin amplitude
at low values of
q
2
m
2


, which is not present in
B
!
K‘


decays. Because of the lower mass threshold for
producing an
e

e

pair, this enhances the
K

e

e

final
state relative to the
K





state. Currently, theoretical
predictions of the branching fractions have associated un-
certainties of about 30% due to form factors that model the
hadronic effects in the
B
!
K
or
B
!
K

transition.
Previous experimental measurements of the branching
fractions are consistent with the range of theoretical pre-
dictions, with experimental uncertainties comparable in
size to the theoretical uncertainties [13,14].
With larger datasets, it becomes possible to measure
ratios and asymmetries in the rates. These can typically
be predicted more reliably than the total branching frac-
tions. For example, the direct
CP
asymmetry
A
CP



B
!

K






B
!
K







B
!

K






B
!
K




is expected to be vanishingly small in the SM, of order
10

4
in the
B
!
K



mode [15]. However it could be
enhanced by new non-SM weak phases [16]. The ratio
R
K
,
defined as
R
K


B
!
K






B
!
Ke

e


;
also has a precise SM prediction of
R
K

1
:
0000

0
:
0001
[17]. In supersymmetric theories with a large ratio (
tan

)
of vacuum expectation values of Higgs doublets,
R
K
can be
significantly enhanced. This occurs via penguin diagrams
in which the

or
Z
0
is replaced with a neutral Higgs boson
that preferentially couples to the heavier muons [18]. In
B
!
K



this ratio is modified by the photon pole
contribution, thus the SM prediction is
R
K

0
:
75
[4]
with an estimated uncertainty of 0.01 [17] if the pole region
is included, or
R
K

1
:
0
if it is excluded [17].
q
q
bs
t,c,u
W
γ
, Z
l
+
l
q
q
bs
t,c,u
W
+
W
ν
l
l
+
FIG. 1. Examples of standard model Feynman diagrams for
the decays
B
!
K



. For the photon or
Z
penguin dia-
grams on the left, boson emission can occur on any of the
b
,
t
,
c
,
u
,
s
,or
W
lines.
Also with Universita
`
della Basilicata, Potenza, Italy.
Also with Universita
`
di Perugia, Dipartimento di Fisica,
Perugia, Italy.
*
Also with Laboratoire de Physique Corpusculaire, Clermont-
Ferrand, France.
B. AUBERT
et al.
PHYSICAL REVIEW D
73,
092001 (2006)
092001-4
Additional sensitivity to non-SM physics arises from the
fact that
B
!
K



transitions are three-body decays
proceeding through three different electroweak penguin
amplitudes, whose relative contributions vary as a function
of
q
2
. Measurements of partial branching fractions and
angular distributions as a function of the invariant momen-
tum transfer
q
2
are therefore of particular interest. The SM
predicts a distinctive pattern in the forward-backward
asymmetry
A
FB

s

R
1

1
d
cos

d
2


B
!
K




d
cos
ds
Sign

cos


d


B
!
K




=ds
;
where
s
q
2
=m
2
B
, and

is the angle of the lepton with
respect to the flight direction of the
B
meson, measured in
the dilepton rest frame [19]. In the presence of non-SM
physics, the sign and magnitude of this asymmetry can be
altered dramatically [4,9,15]. In particular, at high
q
2
, the
sign of
A
FB
is sensitive to the sign of the product of the
C
eff
9
and
C
eff
10
Wilson coefficients. The value of
A
FB
in
B
!
K‘


provides an important check on this measurement,
as it is expected to result in zero asymmetry for all
q
2
in the
SM and many non-SM scenarios. This condition can be
violated in models in which new operators such as a neutral
Higgs penguin contribute significantly [18]. However even
in this case the resulting asymmetry is expected to be of
order 0.01 or less in the
B
!
K‘


mode for electron or
muon final states [20]. In addition to
A
FB
,in
B
!
K



the fraction of longitudinal polarization
F
L
of the
K

can
be measured from the angular distribution of its decay
products. The value of
F
L
measured at low
q
2
is sensitive
to effects from new left-handed currents with complex
phases different from the SM, resulting in
C
eff
7


C
7

SM

, or effects from new right-handed currents in
the photon penguin amplitude [21]. The predicted distri-
butions of
A
FB

q
2

and
F
L

q
2

are shown for the SM and
for several non-SM scenarios in Fig. 2. The non-SM sce-
narios correspond to those studied in Refs. [4,9,21].
Finally,
the
lepton-flavor-violating
decays
B
!
K

e


can only occur at rates far below current experi-
mental sensitivities in the context of the SM with neutrino
mixing. Observation of these decays would therefore be an
indication of contributions beyond the SM. For example,
such decays are allowed in leptoquark models [6].
II. DETECTOR AND DATASET
The results presented here are based on data collected
with the
BABAR
detector at the PEP-II asymmetric
e

e

collider located at the Stanford Linear Accelerator Center.
The dataset comprises
229

10
6
B

B
pairs, corresponding
to an integrated luminosity of
208 fb

1
collected on the


4
S

resonance at a center-of-mass energy of

s
p

10
:
58 GeV
. An additional
12
:
1fb

1
of data collected at
energies 40 MeV below the nominal on-peak energy is
used to study continuum backgrounds arising from pair
production of
u
,
d
,
s
, and
c
quarks.
The
BABAR
detector is described in detail in Ref. [22].
The measurements described in this paper rely primarily
on the charged-particle tracking and identification proper-
ties of the detector. Tracking is provided by a five-layer
silicon vertex tracker (SVT) and a 40-layer drift chamber
(DCH) in a 1.5-T magnetic field produced by a super-
conducting magnet. Low momentum charged hadrons are
identified by the ionization loss (
dE=dx
) measured in the
SVT and DCH, and higher momentum hadrons by a ring-
imaging detector of internally reflected Cherenkov light
(DIRC). A CsI(Tl) electromagnetic calorimeter (EMC)
provides identification of electrons, and detection of pho-
tons. The steel in the instrumented flux return (IFR) of the
superconducting coil is interleaved with resistive plate
chambers, providing identification of muons and neutral
hadrons.
)
4
/c
2
(GeV
2
q
2 4 6 8 10 12 14 16 18 20
FB
A
-1
-0.8
-0.6
-0.4
-0.2
-0
0.2
0.4
0.6
0.8
1
a)
)
4
/c
2
(GeV
2
q
2 4 6 8 10 12 14 16 18 20
L
F
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
b)
FIG. 2 (color online).
Simulated distribution of (a)
A
FB
and
(b)
F
L
for the decay
B
!
K



. The points represent the
distributions assuming the SM (solid lines),
C
eff
7

C
7

SM

(dotted lines),
C
eff
9
C
eff
10

C
9
C
10

SM

(dashed lines), and
C
eff
7
,
C
eff
9
C
eff
10

C
7

SM

,

C
9
C
10

SM

(dot-dashed lines) generated
using the form factor model of [27]. In the case of
F
L
, the two
solutions with
C
eff
9
C
eff
10

C
9
C
10

SM

are not displayed; they
are nearly identical to the two shown.
MEASUREMENTS OF BRANCHING FRACTIONS, RATE
...
PHYSICAL REVIEW D
73,
092001 (2006)
092001-5
III. EVENT SELECTION
We reconstruct signal candidates in eight final states:
B

!
K



,
B
0
!
K
0
S


,
B
0
!
K

0


,
B

!
K



, where
K

0
!
K



,
K

!
K
0
S


,
K
0
S
!




, and
is either an
e
or

. Throughout this paper,
charge-conjugate modes are implied.
Electrons are required to have momentum above
0
:
3 GeV
=c
and are identified using a likelihood ratio com-
bining information from the EMC, DIRC, and DCH.
Photons that lie in a small angular region around the
electron direction and have
E>
30 MeV
are combined
with electron candidates in order to recover bremsstrah-
lung energy. We suppress backgrounds due to photon con-
versions in the
B
!
Ke

e

channels by removing
e

e

pairs with invariant mass less than
0
:
03 GeV
=c
2
. As there
is a significant contribution to the
B
!
K

e

e

channels
from the pole at low dielectron mass, we preserve accep-
tance by vetoing conversions in these channels only if the
conversion radius is outside the inner radius of the beam
pipe. Muons with momentum
p>
0
:
7 GeV
=c
are identi-
fied with a neural network algorithm using information
from the IFR and the EMC.
The performance of the lepton identification algorithms
is evaluated using high-statistics data control samples. The
electron efficiency is determined from samples of
e

e

!
e

e


events to be approximately 91% over the momen-
tum range considered in this analysis; the pion misidenti-
fication probability is
<
0
:
15%
, evaluated using control
samples of pions from

and
K
0
S
decays. The muon effi-
ciency is approximately 70%, determined from a sample of
e

e

!





decays; the pion misidentification
probability is of order 2 – 3%, as determined from

decays.
These samples are used to correct for any discrepancies
between data and simulation as a function of momentum,
polar angle, azimuthal angle, charge, and run period.
Charged kaons are selected by requiring the Cherenkov
angle measured in the DIRC and the track
dE=dx
to be
consistent with the kaon hypothesis; charged pions
are selected by requiring these measurements to be
inconsistent with the kaon hypothesis.
K
0
S
candidates are
constructed from two oppositely charged tracks having
an
invariant
mass
in
the
range
488
:
7
<m

<
507
:
3 MeV
=c
2
, a common vertex displaced from the pri-
mary vertex by at least 1 mm, and a vertex fit

2
probability
greater than 0.001. The
K
0
S
mass range corresponds to a
window of approximately
3

about the nominal
K
0
S
mass.
Modes that contain a
K

are required to have a charged
K
or
K
0
S
which, when combined with a charged pion, yields
an invariant mass in the range
0
:
7
<m
K
<
1
:
1 GeV
=c
2
.
The performance of the charged hadron selection is
evaluated using control samples of kaons and pions from
the decay
D
0
!
K



, where the
D
0
is selected from the
decay of a
D

. The kaon efficiency is determined to be 80 –
97% over the kinematic range relevant to this analysis. The
pion misidentification probability is
<
3%
for momenta
less than
3 GeV
=c
, and increases to
10%
at
5 GeV
=c
.
As with the leptons, these samples are used to correct for
any discrepancies between the hadron ID performance in
data and simulation.
Correctly reconstructed
B
decays will peak in two kine-
matic variables,
m
ES
and

E
. For a candidate system of
B
daughter particles with total momentum
p
B
in the
laboratory frame and energy
E

B
in the


4
S

center-
of-mass
(CM)
frame,
we
define
m
ES



s=
2

p
0
p
B

2
=E
2
0

p
2
B
q
and

E

E

B


s
p
=
2
, where
E
0
and
p
0
are the energy and momentum of the


4
S

in
the laboratory frame, and

s
p
is the total CM energy of the
e

e

beams. For signal events, the
m
ES
distribution peaks
at the
B
meson mass with resolution

2
:
5 MeV
=c
2
.
The

E
distribution peaks near zero, with a typical width

18 MeV
in the muon channels, and

22 MeV
in
the electron channels.
B
candidates are selected if the reconstructed
m
ES
and

E
are in the ranges
5
:
00
<m
ES
<
5
:
29 GeV
=c
2
and
)
4
/c
2
(GeV
2
q
02468101214161820
FB
A
-1
-0.8
-0.6
-0.4
-0.2
-0
0.2
0.4
0.6
0.8
1
a)
)
4
/c
2
(GeV
2
q
02468101214161820
L
F
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
b)
FIG. 3 (color online).
Predicted distributions of (a)
A
FB

q
2

and (b)
F
L

q
2

in
B
!
K



for the two regions of
q
2
considered.
The lines represent the predictions of the SM (solid lines),
C
eff
7

C
7

SM

(dotted lines),
C
eff
9
C
eff
10

C
9
C
10

SM

(dashed lines),
and
C
eff
7
,
C
eff
9
C
eff
10

C
7

SM

,

C
9
C
10

SM

(dot-dashed lines) with the form factor model of Ref. [27]. In the case of
F
L
, the two
solutions with
C
eff
9
C
eff
10

C
9
C
10

SM

are not displayed; they are nearly identical to the two shown.
B. AUBERT
et al.
PHYSICAL REVIEW D
73,
092001 (2006)
092001-6

0
:
50
<

E<
0
:
50 GeV
. The signal is extracted by per-
forming
a
multidimensional,
unbinned
maximum-
likelihood fit in the region
5
:
20
<m
ES
<
5
:
29 GeV
=c
2
and

0
:
25
<

E<
0
:
25 GeV
, which contains 100% of
the signal candidates that pass all other selection require-
ments. This region remains blind to our inspection until all
selection criteria are established. The events in the side-
band with
5
:
00
<m
ES
<
5
:
20 GeV
=c
2
,or

0
:
50
<

E<

0
:
25 GeV
,or
0
:
25
<

E<
0
:
50 GeV
are used to study
the properties of the combinatorial background.
For the measurements of the partial branching fractions,
A
FB
, and
K

polarization, we subdivide the sample into two
regions of dilepton invariant mass. The first is the region
above the pole and below the
J=
resonance,
0
:
1
<q
2
<
8
:
41 GeV
2
=c
4
;
the
second
is
the
region
q
2
>
10
:
24 GeV
2
=c
4
, above the
J=
resonance. The

2
S

resonance is explicitly excluded from this upper region
as described in further detail in Sec. IV B. The lower bound
of
0
:
1 GeV
2
=c
4
in the first region is chosen to remove
effects from the photon pole in the
B
!
K

e

e

channel.
The forward-backward asymmetry is extracted in each of
these
q
2
regions from the distribution of
cos


, which we
define as the cosine of the angle between the

(

) and
the
B
(

B
) meson, measured in the dilepton rest frame. We
do not measure
A
FB
in the mode
B
0
!
K
0
S


, in which
the flavor of the
B
meson cannot be directly inferred from
the
K
0
S
. The
K

polarization is similarly derived from the
distribution of
cos

K
, defined as the cosine of the angle
between the
K
and the
B
meson, measured in the
K

rest
frame. The predicted distributions of
A
FB
and
F
L
integrated
over these two
q
2
ranges are shown in Fig. 3 for both the
SM and non-SM scenarios.
IV. BACKGROUND SOURCES
A. Combinatorial backgrounds
Combinatorial backgrounds arise either from the con-
tinuum, in which a (
u
,
d
,
s
,or
c
) quark pair is produced, or
from
B

B
events in which the decay products of the two
B
’s
are misreconstructed as a signal candidate. We use the
following variables computed in the CM frame to reject
continuum backgrounds: (i) the ratio of second to zeroth
Fox-Wolfram moments [23], (ii) the angle between the
thrust axis of the
B
and the remaining particles in the event,

thrust
, (iii) the production angle

B
of the
B
candidate with
respect to the beam axis, and (iv) the invariant mass of the
kaon-lepton pair with the charge combination expected
from a semileptonic
D
decay. The first three variables
take advantage of the characteristic jetlike event shape of
continuum backgrounds, versus the more spherical event
shape of
B

B
events. The fourth variable is useful for
rejecting
c

c
events. These frequently occur through decays
such as
D
!
K‘
, resulting in a kaon-lepton invariant
mass which peaks below that of the
D
; for signal events
the kaon-lepton mass is broadly distributed up to approxi-
mately the
B
mass. These four variables are combined into
a linear Fisher discriminant [24], which is optimized using
samples of simulated signal events and off-resonance data.
A separate Fisher discriminant is used for each of the decay
modes considered in this analysis.
Combinatorial
B

B
backgrounds are dominated by events
with two semileptonic
B
!
X‘
decays. We discriminate
against these events by constructing a likelihood ratio
composed of (i) the vertex probability of the dilepton
pair, (ii) the vertex probability of the
B
candidate,
(iii) the angle

B
as in the Fisher discriminant, and
(iv) the total missing energy in the event
E
miss
. Events
with two semileptonic decays will contain at least two
neutrinos; therefore the
E
miss
variable is particularly effec-
tive at rejecting these backgrounds. The probability distri-
bution functions (PDFs) used in the likelihood are derived
by fitting simulated signal events and simulated
B

B
events
in which the signal decays are removed. We derive a
separate likelihood parametrization for each decay mode.
We select those events that pass an optimal Fisher and
B

B
likelihood requirement, based on the figure of merit
S=

S

B
p
for the expected number of signal events
S
and
background events
B
. The selection is optimized simulta-
neously for the Fisher and likelihood, and is derived sepa-
rately for each decay mode.
B. Peaking backgrounds
Backgrounds that peak in the
m
ES
and

E
variables in
the same manner as the signal are either vetoed, or their
rate is estimated from simulated data or control samples.
The largest sources of peaking backgrounds are
B
decays
to charmonium:
B
!
J= K

and
B
!

2
S

K

, where
the
J=
or

2
S

decays to a


pair. We therefore
remove events in which the dilepton invariant mass is
consistent with a
J=
or

2
S

, either with or without
bremsstrahlung recovery in the electron channels. In cases
where the lepton momentum is mismeasured, or the brems-
strahlung recovery algorithm fails to find a radiated pho-
ton, the dilepton mass will be shifted from the charmonium
mass. In addition, the measured

E
will be shifted away
from zero in a correlated manner. We account for this by
constructing a two-dimensional veto region in the
m


vs.

E
plane as shown in Fig. 4; the simulated points
plotted demonstrate the expected background rejection.
Within the veto region in data we find approximately
13700
J=
events and 1000

2
S

events summed over
all decay modes. These provide a high-statistics control
sample useful for evaluating systematic uncertainties and
selection efficiencies. The residual charmonium back-
ground after applying the veto is estimated from simulation
to be between 0.0 and 1.6 events per decay mode.
Because of the 2 – 3% probability for misidentifying
pions as muons, the
B
!
K





channels also receive
a significant peaking background contribution from had-
ronic
B
decays. The largest of these are
B

!
D
0


where
D
0
!
K



or
D
0
!
K



, and

B
0
!
D



MEASUREMENTS OF BRANCHING FRACTIONS, RATE
...
PHYSICAL REVIEW D
73,
092001 (2006)
092001-7
where
D

!

K

0


. These are suppressed by removing
events in which the
K


invariant mass lies in the range
1
:
84
<m
K


<
1
:
90 GeV
=c
2
. The remaining hadronic
backgrounds come from charmless decays such as
B
!
K





,
B
!
K

K



, and
B
!
K

K

K

.We
measure the peaking background from these processes
using data control samples of
B
!
K

h
events. These
samples are selected with the same requirements as signal
events, except hadron identification is required for the
hadron candidate
h
in place of muon identification. This
yields samples of predominantly hadronic
B
decays. We
then weight each event by the muon misidentification rate
for the hadron divided by its hadron identification effi-
ciency. The hadronic peaking background is then extracted
by a fit to the
m
ES
distribution of these weighted events.
This results in a total hadronic peaking background mea-
surement of 0.4 – 2.3 events per muon decay channel. These
backgrounds are suppressed by a factor of approximately
400 in the
B
!
K

e

e

channels due to the much lower
probability of misidentifying pions as electrons.
There is an additional contribution to the peaking back-
grounds in the electron channels from rare two-body de-
cays. These include
B
!
K


with the

converting to an
e

e

pair in the detector, and
B
!
K


0
or
B
!
K

,
where the

0
or
undergoes a Dalitz decay to
e

e


.
These backgrounds are estimated from simulation to con-
tribute 0.0 –1.4 events per electron decay channel.
The sum of peaking backgrounds from all sources is
summarized in Table I. As a function of
q
2
, all of the
backgrounds from
K


and
K


0
are localized in the
region
0
:
0
<q
2
<
0
:
1 GeV
2
=c
4
. Backgrounds from
J=
and
K

populate the region
0
:
1
<q
2
<
8
:
41 GeV
2
=c
4
,
while the

2
S

backgrounds contribute only to the region
q
2
>
10
:
24 GeV
2
=c
4
. The hadronic backgrounds occupy
both
the
0
:
1
<q
2
<
8
:
41 GeV
2
=c
4
and
q
2
>
10
:
24 GeV
2
=c
4
regions.
V. YIELD EXTRACTION PROCEDURE
We extract the signal yield and angular distributions
using a multidimensional unbinned maximum-likelihood
fit. For
B
!
K‘


, the total branching fraction is ob-
tained from a two-dimensional fit to
m
ES
and

E
. In the
B
!
K



modes, we add the reconstructed
K

mass as
a third fit variable. The signal shapes are parametrized in
both
m
ES
and

E
by a Gaussian function plus a radiative
tail described by an exponential power function. This takes
the form
TABLE I. Mean expected peaking backgrounds in
208 fb

1
,
for the individual
K



decay modes after applying all
selection requirements.
Mode
All
q
2
0
:
1
<q
2
<
8
:
41
(
GeV
2
=c
4
)
q
2
>
10
:
24
(
GeV
2
=c
4
)
K

e

e

0
:
7

0
:
20
:
6

0
:
20
:
1

0
:
1
K





2
:
3

0
:
51
:
4

0
:
40
:
9

0
:
1
K
0
S
e

e

0
:
01

0
:
01
0
:
01

0
:
01
0.0
K
0
S




0
:
4

0
:
10
:
3

0
:
10
:
1

0
:
04
K

0
e

e

3
:
0

0
:
61
:
0

0
:
50
:
6

0
:
2
K

0




1
:
4

0
:
80
:
5

0
:
30
:
2

0
:
1
K

e

e

0
:
9

0
:
20
:
2

0
:
20
:
2

0
:
1
K





0
:
6

0
:
30
:
2

0
:
10
:
2

0
:
1
2
2.5
3
3.5
4
-0.2
-0.1
0
0.1
0.2
)
2
c
(GeV/
-
l
+
l
m
(GeV)
E
a)
2
2.5
3
3.5
4
0
500
1000
1500
2000
2500
b)
)
2
c
(GeV/
-
l
+
l
m
2
c
Events / 0.04 GeV/
-0.2
-0.1
0
0.1
0.2
0
200
400
600
800
c)
(GeV)
E
Events / 0.0125 GeV
FIG. 4.
Charmonium veto regions (a) in the
B

!
K

e

e

channel. The points are simulated
J=
and

2
S

events, with
abundance equal to the mean number expected in
208 fb

1
. The projections onto (b)
m


and (c)

E
are shown at right, indicating
the high density of points at

m


;

E

m
;
0
:
0

. The vertical band corresponds to events where the
J=
(

2
S

) and
K

come
from different
B
decays. For

E<
0
it also includes events with misreconstructed
B
!
J= K

,
B
!

2
S

K

, and nonresonant
charmonium decays. The slanted band corresponds to events with mismeasured lepton track momentum.
B. AUBERT
et al.
PHYSICAL REVIEW D
73,
092001 (2006)
092001-8