of 7
Direct
CP
, Lepton Flavor, and Isospin Asymmetries in the Decays
B
!
K
ðÞ
l
þ
l

B. Aubert,
1
M. Bona,
1
Y. Karyotakis,
1
J. P. Lees,
1
V. Poireau,
1
E. Prencipe,
1
X. Prudent,
1
V. Tisserand,
1
J. Garra Tico,
2
E. Grauges,
2
L. Lopez,
3a,3b
A. Palano,
3a,3b
M. Pappagallo,
3a,3b
G. Eigen,
4
B. Stugu,
4
L. Sun,
4
G. S. Abrams,
5
M. Battaglia,
5
D. N. Brown,
5
R. N. Cahn,
5
R. G. Jacobsen,
5
L. T. Kerth,
5
Yu. G. Kolomensky,
5
G. Lynch,
5
I. L. Osipenkov,
5
M. T. Ronan,
5
K. Tackmann,
5,
*
T. Tanabe,
5
C. M. Hawkes,
6
N. Soni,
6
A. T. Watson,
6
H. Koch,
7
T. Schroeder,
7
D. Walker,
8
D. J. Asgeirsson,
9
B. G. Fulsom,
9
C. Hearty,
9
T. S. Mattison,
9
J. A. McKenna,
9
M. Barrett,
10
A. Khan,
10
V. E. Blinov,
11
A. D. Bukin,
11
A. R. Buzykaev,
11
V. P. Druzhinin,
11
V. B. Golubev,
11
A. P. Onuchin,
11
S. I. Serednyakov,
11
Yu. I. Skovpen,
11
E. P. Solodov,
11
K. Yu. Todyshev,
11
M. Bondioli,
12
S. Curry,
12
I. Eschrich,
12
D. Kirkby,
12
A. J. Lankford,
12
P. Lund,
12
M. Mandelkern,
12
E. C. Martin,
12
D. P. Stoker,
12
S. Abachi,
13
C. Buchanan,
13
J. W. Gary,
14
F. Liu,
14
O. Long,
14
B. C. Shen,
14,
*
G. M. Vitug,
14
Z. Yasin,
14
L. Zhang,
14
V. Sharma,
15
C. Campagnari,
16
T. M. Hong,
16
D. Kovalskyi,
16
M. A. Mazur,
16
J. D. Richman,
16
T. W. Beck,
17
A. M. Eisner,
17
C. J. Flacco,
17
C. A. Heusch,
17
J. Kroseberg,
17
W. S. Lockman,
17
T. Schalk,
17
B. A. Schumm,
17
A. Seiden,
17
L. Wang,
17
M. G. Wilson,
17
L. O. Winstrom,
17
C. H. Cheng,
18
D. A. Doll,
18
B. Echenard,
18
F. Fang,
18
D. G. Hitlin,
18
I. Narsky,
18
T. Piatenko,
18
F. C. Porter,
18
R. Andreassen,
19
G. Mancinelli,
19
B. T. Meadows,
19
K. Mishra,
19
M. D. Sokoloff,
19
P. C. Bloom,
20
W. T. Ford,
20
A. Gaz,
20
J. F. Hirschauer,
20
M. Nagel,
20
U. Nauenberg,
20
J. G. Smith,
20
K. A. Ulmer,
20
S. R. Wagner,
20
R. Ayad,
21,
A. Soffer,
21,
W. H. Toki,
21
R. J. Wilson,
21
D. D. Altenburg,
22
E. Feltresi,
22
A. Hauke,
22
H. Jasper,
22
M. Karbach,
22
J. Merkel,
22
A. Petzold,
22
B. Spaan,
22
K. Wacker,
22
M. J. Kobel,
23
W. F. Mader,
23
R. Nogowski,
23
K. R. Schubert,
23
R. Schwierz,
23
J. E. Sundermann,
23
A. Volk,
23
D. Bernard,
24
G. R. Bonneaud,
24
E. Latour,
24
Ch. Thiebaux,
24
M. Verderi,
24
P. J. Clark,
25
W. Gradl,
25
S. Playfer,
25
J. E. Watson,
25
M. Andreotti,
26a,26b
D. Bettoni,
26a
C. Bozzi,
26a
R. Calabrese,
26a,26b
A. Cecchi,
26a,26b
G. Cibinetto,
26a,26b
P. Franchini,
26a,26b
E. Luppi,
26a,26b
M. Negrini,
26a,26b
A. Petrella,
26a,26b
L. Piemontese,
26a
V. Santoro,
26a,26b
R. Baldini-Ferroli,
27
A. Calcaterra,
27
R. de Sangro,
27
G. Finocchiaro,
27
S. Pacetti,
27
P. Patteri,
27
I. M. Peruzzi,
27,
x
M. Piccolo,
27
M. Rama,
27
A. Zallo,
27
A. Buzzo,
28a
R. Contri,
28a,28b
M. Lo Vetere,
28a,28b
M. M. Macri,
28a
M. R. Monge,
28a,28b
S. Passaggio,
28a
C. Patrignani,
28a,28b
E. Robutti,
28a
A. Santroni,
28a,28b
S. Tosi,
28a,28b
K. S. Chaisanguanthum,
29
M. Morii,
29
J. Marks,
30
S. Schenk,
30
U. Uwer,
30
V. Klose,
31
H. M. Lacker,
31
D. J. Bard,
32
P. D. Dauncey,
32
J. A. Nash,
32
W. Panduro Vazquez,
32
M. Tibbetts,
32
P. K. Behera,
33
X. Chai,
33
M. J. Charles,
33
U. Mallik,
33
J. Cochran,
34
H. B. Crawley,
34
L. Dong,
34
W. T. Meyer,
34
S. Prell,
34
E. I. Rosenberg,
34
A. E. Rubin,
34
Y. Y. Gao,
35
A. V. Gritsan,
35
Z. J. Guo,
35
C. K. Lae,
35
A. G. Denig,
36
M. Fritsch,
36
G. Schott,
36
N. Arnaud,
37
J. Be
́
quilleux,
37
A. D’Orazio,
37
M. Davier,
37
J. Firmino da Costa,
37
G. Grosdidier,
37
A. Ho
̈
cker,
37
V. Lepeltier,
37
F. Le Diberder,
37
A. M. Lutz,
37
S. Pruvot,
37
P. Roudeau,
37
M. H. Schune,
37
J. Serrano,
37
V. Sordini,
37,
k
A. Stocchi,
37
G. Wormser,
37
D. J. Lange,
38
D. M. Wright,
38
I. Bingham,
39
J. P. Burke,
39
C. A. Chavez,
39
J. R. Fry,
39
E. Gabathuler,
39
R. Gamet,
39
D. E. Hutchcroft,
39
D. J. Payne,
39
C. Touramanis,
39
A. J. Bevan,
40
C. K. Clarke,
40
K. A. George,
40
F. Di Lodovico,
40
R. Sacco,
40
M. Sigamani,
40
G. Cowan,
41
H. U. Flaecher,
41
D. A. Hopkins,
41
S. Paramesvaran,
41
F. Salvatore,
41
A. C. Wren,
41
D. N. Brown,
42
C. L. Davis,
42
K. E. Alwyn,
43
D. Bailey,
43
R. J. Barlow,
43
Y. M. Chia,
43
C. L. Edgar,
43
G. Jackson,
43
G. D. Lafferty,
43
T. J. West,
43
J. I. Yi,
43
J. Anderson,
44
C. Chen,
44
A. Jawahery,
44
D. A. Roberts,
44
G. Simi,
44
J. M. Tuggle,
44
C. Dallapiccola,
45
X. Li,
45
E. Salvati,
45
S. Saremi,
45
R. Cowan,
46
D. Dujmic,
46
P. H. Fisher,
46
K. Koeneke,
46
G. Sciolla,
46
M. Spitznagel,
46
F. Taylor,
46
R. K. Yamamoto,
46
M. Zhao,
46
P. M. Patel,
47
S. H. Robertson,
47
A. Lazzaro,
48a,48b
V. Lombardo,
48a
F. Palombo,
48a,48b
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
M. Simard,
50
P. Taras,
50
F. B. Viaud,
50
H. Nicholson,
51
G. De Nardo,
52a,52b
L. Lista,
52a
D. Monorchio,
52a,52b
G. Onorato,
52a,52b
C. Sciacca,
52a,52b
G. Raven,
53
H. L. Snoek,
53
C. P. Jessop,
54
K. J. Knoepfel,
54
J. M. LoSecco,
54
W. F. Wang,
54
G. Benelli,
54
L. A. Corwin,
55
K. Honscheid,
55
H. Kagan,
55
R. Kass,
55
J. P. Morris,
55
A. M. Rahimi,
55
J. J. Regensburger,
55
S. J. Sekula,
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
R. Rahmat,
56
N. B. Sinev,
56
D. Strom,
56
J. Strube,
56
E. Torrence,
56
G. Castelli,
57a,57b
N. Gagliardi,
57a,57b
M. Margoni,
57a,57b
M. Morandin,
57a
M. Posocco,
57a
M. Rotondo,
57a
F. Simonetto,
57a,57b
R. Stroili,
57a,57b
C. Voci,
57a,57b
P. del Amo Sanchez,
58
E. Ben-Haim,
58
H. Briand,
58
G. Calderini,
58
J. Chauveau,
58
P. David,
58
L. Del Buono,
58
O. Hamon,
58
Ph. Leruste,
58
J. Ocariz,
58
A. Perez,
58
J. Prendki,
58
S. Sitt,
58
L. Gladney,
59
M. Biasini,
60a,60b
R. Covarelli,
60a,60b
E. Manoni,
60a,60b
C. Angelini,
61a,61b
G. Batignani,
61a,61b
S. Bettarini,
61a,61b
M. Carpinelli,
61a,61b,
A. Cervelli,
61a,61b
F. Forti,
61a,61b
M. A. Giorgi,
61a,61b
A. Lusiani,
61a,61c
G. Marchiori,
61a,61b
M. Morganti,
61a,61b
N. Neri,
61a,61b
E. Paoloni,
61a,61b
G. Rizzo,
61a,61b
J. J. Walsh,
61a
D. Lopes Pegna,
62
C. Lu,
62
J. Olsen,
62
A. J. S. Smith,
62
A. V. Telnov,
62
F. Anulli,
63a
E. Baracchini,
63a,63b
G. Cavoto,
63a
D. del Re,
63a,63b
PRL
102,
091803 (2009)
PHYSICAL REVIEW LETTERS
week ending
6 MARCH 2009
0031-9007
=
09
=
102(9)
=
091803(7)
091803-1
Ó
2009 The American Physical Society
E. Di Marco,
63a,63b
R. Faccini,
63a,63b
F. Ferrarotto,
63a
F. Ferroni,
63a,63b
M. Gaspero,
63a,63b
P. D. Jackson,
63a
L. Li Gioi,
63a
M. A. Mazzoni,
63a
S. Morganti,
63a
G. Piredda,
63a
F. Polci,
63a,63b
F. Renga,
63a,63b
C. Voena,
63a
M. Ebert,
64
T. Hartmann,
64
H. Schro
̈
der,
64
R. Waldi,
64
T. Adye,
65
B. Franek,
65
E. O. Olaiya,
65
F. F. Wilson,
65
S. Emery,
66
M. Escalier,
66
L. Esteve,
66
S. F. Ganzhur,
66
G. Hamel de Monchenault,
66
W. Kozanecki,
66
G. Vasseur,
66
Ch. Ye
`
che,
66
M. Zito,
66
X. R. Chen,
67
H. Liu,
67
W. Park,
67
M. V. Purohit,
67
R. M. White,
67
J. R. Wilson,
67
M. T. Allen,
68
D. Aston,
68
R. Bartoldus,
68
P. Bechtle,
68
J. F. Benitez,
68
R. Cenci,
68
J. P. Coleman,
68
M. R. Convery,
68
J. C. Dingfelder,
68
J. Dorfan,
68
G. P. Dubois-Felsmann,
68
W. Dunwoodie,
68
R. C. Field,
68
A. M. Gabareen,
68
S. J. Gowdy,
68
M. T. Graham,
68
P. Grenier,
68
C. Hast,
68
W. R. Innes,
68
J. Kaminski,
68
M. H. Kelsey,
68
H. Kim,
68
P. Kim,
68
M. L. Kocian,
68
D. W. G. S. Leith,
68
S. Li,
68
B. Lindquist,
68
S. Luitz,
68
V. Luth,
68
H. L. Lynch,
68
D. B. MacFarlane,
68
H. Marsiske,
68
R. Messner,
68
D. R. Muller,
68
H. Neal,
68
S. Nelson,
68
C. P. O’Grady,
68
I. Ofte,
68
A. Perazzo,
68
M. Perl,
68
B. N. Ratcliff,
68
A. Roodman,
68
A. A. Salnikov,
68
R. H. Schindler,
68
J. Schwiening,
68
A. Snyder,
68
D. Su,
68
M. K. Sullivan,
68
K. Suzuki,
68
S. K. Swain,
68
J. M. Thompson,
68
J. Va’vra,
68
A. P. Wagner,
68
M. Weaver,
68
C. A. West,
68
W. J. Wisniewski,
68
M. Wittgen,
68
D. H. Wright,
68
H. W. Wulsin,
68
A. K. Yarritu,
68
K. Yi,
68
C. C. Young,
68
V. Ziegler,
68
P. R. Burchat,
69
A. J. Edwards,
69
S. A. Majewski,
69
T. S. Miyashita,
69
B. A. Petersen,
69
L. Wilden,
69
S. Ahmed,
70
M. S. Alam,
70
J. A. Ernst,
70
B. Pan,
70
M. A. Saeed,
70
S. B. Zain,
70
S. M. Spanier,
71
B. J. Wogsland,
71
R. Eckmann,
72
J. L. Ritchie,
72
A. M. Ruland,
72
C. J. Schilling,
72
R. F. Schwitters,
72
B. W. Drummond,
73
J. M. Izen,
73
X. C. Lou,
73
F. Bianchi,
74a,74b
D. Gamba,
74a,74b
M. Pelliccioni,
74a,74b
M. Bomben,
75a,75b
L. Bosisio,
75a,75b
C. Cartaro,
75a,75b
G. Della Ricca,
75a,75b
L. Lanceri,
75a,75b
L. Vitale,
75a,75b
V. Azzolini,
76
N. Lopez-March,
76
F. Martinez-Vidal,
76
D. A. Milanes,
76
A. Oyanguren,
76
J. Albert,
77
Sw. Banerjee,
77
B. Bhuyan,
77
H. H. F. Choi,
77
K. Hamano,
77
R. Kowalewski,
77
M. J. Lewczuk,
77
I. M. Nugent,
77
J. M. Roney,
77
R. J. Sobie,
77
T. J. Gershon,
78
P. F. Harrison,
78
J. Ilic,
78
T. E. Latham,
78
G. B. Mohanty,
78
H. R. Band,
79
X. Chen,
79
S. Dasu,
79
K. T. Flood,
79
Y. Pan,
79
M. Pierini,
79
R. Prepost,
79
C. O. Vuosalo,
79
and S. L. Wu
79
(
B
A
B
AR
Collaboration)
1
Laboratoire de Physique des Particules, IN2P3/CNRS et Universite
́
de Savoie, F-74941 Annecy-Le-Vieux, France
2
Universitat de Barcelona, Facultat de Fisica, Departament ECM, E-08028 Barcelona, Spain
3a
INFN Sezione di Bari, I-70126 Bari, Italy
3b
Dipartmento di Fisica, Universita
`
di Bari, I-70126 Bari, Italy
4
University of Bergen, Institute of Physics, N-5007 Bergen, Norway
5
Lawrence Berkeley National Laboratory and University of California, Berkeley, California 94720, USA
6
University of Birmingham, Birmingham, B15 2TT, United Kingdom
7
Ruhr Universita
̈
t Bochum, Institut fu
̈
r Experimentalphysik 1, D-44780 Bochum, Germany
8
University of Bristol, Bristol BS8 1TL, United Kingdom
9
University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z1
10
Brunel University, Uxbridge, Middlesex UB8 3PH, United Kingdom
11
Budker Institute of Nuclear Physics, Novosibirsk 630090, Russia
12
University of California at Irvine, Irvine, California 92697, USA
13
University of California at Los Angeles, Los Angeles, California 90024, USA
14
University of California at Riverside, Riverside, California 92521, USA
15
University of California at San Diego, La Jolla, California 92093, USA
16
University of California at Santa Barbara, Santa Barbara, California 93106, USA
17
University of California at Santa Cruz, Institute for Particle Physics, Santa Cruz, California 95064, USA
18
California Institute of Technology, Pasadena, California 91125, USA
19
University of Cincinnati, Cincinnati, Ohio 45221, USA
20
University of Colorado, Boulder, Colorado 80309, USA
21
Colorado State University, Fort Collins, Colorado 80523, USA
22
Technische Universita
̈
t Dortmund, Fakulta
̈
t Physik, D-44221 Dortmund, Germany
23
Technische Universita
̈
t Dresden, Institut fu
̈
r Kern- und Teilchenphysik, D-01062 Dresden, Germany
24
Laboratoire Leprince-Ringuet, CNRS/IN2P3, Ecole Polytechnique, F-91128 Palaiseau, France
25
University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom
26a
INFN Sezione di Ferrara, I-44100 Ferrara, Italy
26b
Dipartimento di Fisica, Universita
`
di Ferrara, I-44100 Ferrara, Italy
27
INFN Laboratori Nazionali di Frascati, I-00044 Frascati, Italy
28a
INFN Sezione di Genova, I-16146 Genova, Italy
28b
Dipartimento di Fisica, Universita
`
di Genova, I-16146 Genova, Italy
29
Harvard University, Cambridge, Massachusetts 02138, USA
PRL
102,
091803 (2009)
PHYSICAL REVIEW LETTERS
week ending
6 MARCH 2009
091803-2
30
Universita
̈
t Heidelberg, Physikalisches Institut, Philosophenweg 12, D-69120 Heidelberg, Germany
31
Humboldt-Universita
̈
t zu Berlin, Institut fu
̈
r Physik, Newtonstrasse 15, D-12489 Berlin, 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, 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
48a
INFN Sezione di Milano, I-20133 Milano, Italy
48b
Dipartimento di Fisica, Universita
`
di Milano, 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
52a
INFN Sezione di Napoli, I-80126 Napoli, Italy
52b
Dipartimento di Scienze Fisiche, 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
57a
INFN Sezione di Padova, I-35131 Padova, Italy
57b
Dipartimento di Fisica, Universita
`
di Padova, I-35131 Padova, Italy
58
Laboratoire de Physique Nucle
́
aire et de Hautes Energies, IN2P3/CNRS, Universite
́
Pierre et Marie Curie-Paris6,
Universite
́
Denis Diderot-Paris7, F-75252 Paris, France
59
University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
60a
INFN Sezione di Perugia, I-06100 Perugia, Italy
60b
Dipartimento di Fisica, Universita
`
di Perugia, I-06100 Perugia, Italy
61a
INFN Sezione di Pisa, I-56127 Pisa, Italy
61b
Dipartimento di Fisica, Universita
`
di Pisa, I-56127 Pisa, Italy
61c
Scuola Normale Superiore di Pisa, I-56127 Pisa, Italy
62
Princeton University, Princeton, New Jersey 08544, USA
63a
INFN Sezione di Roma, I-00185 Roma, Italy
63b
Dipartimento di Fisica, Universita
`
di Roma La Sapienza, I-00185 Roma, Italy
64
Universita
̈
t Rostock, D-18051 Rostock, Germany
65
Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX11 0QX, United Kingdom
66
DSM/Irfu, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, France
67
University of South Carolina, Columbia, South Carolina 29208, USA
68
Stanford Linear Accelerator Center, Stanford, California 94309, USA
69
Stanford University, Stanford, California 94305-4060, USA
70
State University of New York, Albany, New York 12222, USA
71
University of Tennessee, Knoxville, Tennessee 37996, USA
72
University of Texas at Austin, Austin, Texas 78712, USA
73
University of Texas at Dallas, Richardson, Texas 75083, USA
74a
INFN Sezione di Torino, I-10125 Torino, Italy
74b
Dipartimento di Fisica Sperimentale, Universita
`
di Torino, I-10125 Torino, Italy
75a
INFN Sezione di Trieste, I-34127 Trieste, Italy
75b
Dipartimento di Fisica, Universita
`
di Trieste, I-34127 Trieste, Italy
76
IFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spain
77
University of Victoria, Victoria, British Columbia, Canada V8W 3P6
78
Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
79
University of Wisconsin, Madison, Wisconsin 53706, USA
PRL
102,
091803 (2009)
PHYSICAL REVIEW LETTERS
week ending
6 MARCH 2009
091803-3
(Received 25 July 2008; published 4 March 2009)
We measure branching fractions and integrated rate asymmetries for the rare decays
B
!
K
ðÞ
l
þ
l

,
where
l
þ
l

is either
e
þ
e

or

þ


, using a sample of
384

10
6
B

B
events collected with the
BABAR
detector at the PEP-II
e
þ
e

collider. We find no evidence for direct
CP
or lepton-flavor asymmetries.
However, for dilepton masses below the
J=
c
resonance, we find evidence for unexpectedly large isospin
asymmetries in both
B
!
Kl
þ
l

and
B
!
K

l
þ
l

which differ, respectively, by
3
:
2

and
2
:
7

, including
systematic uncertainties, from the standard model expectations.
DOI:
10.1103/PhysRevLett.102.091803
PACS numbers: 13.20.He, 11.30.Er, 11.30.Hv
The decays
B
!
K
ðÞ
l
þ
l

, where
l
þ
l

is either
e
þ
e

or

þ


, arise from flavor-changing neutral current pro-
cesses that are forbidden at the tree level in the standard
model (SM). The lowest-order SM processes contributing
to these decays are a
W
þ
W

box diagram, and the radia-
tive photon and electroweak
Z
penguin diagrams [
1
]. Their
amplitudes are expressed in terms of hadronic form factors
and effective Wilson coefficients
C
eff
7
,
C
eff
9
, and
C
eff
10
, rep-
resenting the electromagnetic penguin diagram, and the
vector part and the axial-vector part of the
Z
penguin and
W
þ
W

box diagrams, respectively [
2
]. New physics con-
tributions may enter the penguin and box diagrams at the
same order as the SM diagrams, modifying the Wilson
coefficients from their SM expectations [
3
].
We report results herein on exclusive branching frac-
tions, direct
CP
asymmetries, the ratio of rates to dimuon
and dielectron final states, and isospin asymmetries, mea-
sured in two regions of dilepton mass squared chosen to
exclude the region of the
J=
c
resonance: a low
q
2
region
0
:
1
<q
2

m
2
ll
<
7
:
02 GeV
2
=c
4
and a high
q
2
region
q
2
>
10
:
24 GeV
2
=c
4
. We also present results for the two
regions combined. The
c
ð
2
S
Þ
resonance is removed from
the high
q
2
region by vetoing events with
12
:
96
<q
2
<
14
:
06 GeV
2
=c
4
.For
K

e
þ
e

final states, we also report
results in extended low and extended combined
q
2
regions
including events
q
2
<
0
:
1 GeV
2
=c
4
, where there is an
enhanced coupling to the photonic penguin amplitude
unique to this mode. Recent
BABAR
results on angular
observables using the same data set and similar event
selection as is used here are reported in [
1
].
The
B
!
Kl
þ
l

branching fraction is predicted to be
ð
0
:
35

0
:
12
Þ
10

6
, while
B
!
K

l
þ
l

for
q
2
>
0
:
1 GeV
2
=c
4
is expected to be roughly 3 times larger at
ð
1
:
19

0
:
39
Þ
10

6
[
3
]. The

30%
uncertainties are due
to lack of knowledge about the form factors that model the
hadronic effects in the
B
!
K
and
B
!
K

transitions.
Thus, measurements of decay rates to exclusive final states
are less suited to searches for new physics than rate asym-
metries, where many theory uncertainties cancel [
4
].
The direct
CP
asymmetry
A
K
ðÞ
CP

B
ð

B
!

K
ðÞ
l
þ
l

Þ
B
ð
B
!
K
ðÞ
l
þ
l

Þ
B
ð

B
!

K
ðÞ
l
þ
l

Þþ
B
ð
B
!
K
ðÞ
l
þ
l

Þ
(1)
is expected to be
O
ð
10

3
Þ
in the SM, but new physics at the
electroweak scale could produce a significant enhancement
[
5
].
The ratio of rates to dimuon and dielectron final states
R
K
ðÞ

B
ð
B
!
K
ðÞ

þ


Þ
B
ð
B
!
K
ðÞ
e
þ
e

Þ
(2)
is unity in the SM to within a few percent [
6
]. In two-
Higgs-doublet models, including supersymmetry, these
ratios are sensitive to the presence of a neutral Higgs
boson, which might, at large
tan

, increase
R
K
ðÞ
by

10%
[
7
]. In the region
q
2
<
ð
2
m

Þ
2
, where only the
e
þ
e

modes are allowed, there is a large enhancement of
B
!
K

e
þ
e

due to a
1
=q
2
scaling of the photon penguin
contribution. The expected SM value of
R
K

including this
region is 0.75 [
6
], and we fit the
K

data set over the
extended combined and extended low
q
2
regions in order
to test this prediction.
The
CP
-averaged isospin asymmetry
A
K
ðÞ
I

B
ð
B
0
!
K
ðÞ
0
l
þ
l

Þ
r
B
ð
B

!
K
ðÞ
l
þ
l

Þ
B
ð
B
0
!
K
ðÞ
0
l
þ
l

Þþ
r
B
ð
B

!
K
ðÞ
l
þ
l

Þ
;
(3)
where
r
¼

0
=
þ
¼
1
=
ð
1
:
07

0
:
01
Þ
is the ratio of the
B
0
and
B
þ
lifetimes [
8
], has a SM expectation of
þ
6%
13%
as
q
2
!
0 GeV
2
=c
4
[
9
]. This is consistent with the mea-
sured asymmetry of
3%

3%
in
B
!
K


[
8
]. A calcu-
lation of the predicted
K
l
þ
l

and
K

0
l
þ
l

rates
integrated over the low
q
2
region gives
A
K

I
¼
0
:
005

0
:
020
[
10
,
11
]. In the high
q
2
region, contributions from
charmonium states may provide an additional source of
isospin asymmetry, although the measured asymmetry in
J=
c
K
ðÞ
is at most a few percent [
8
].
We use a data sample of
384

10
6
B

B
pairs collected at
the

ð
4
S
Þ
resonance with the
BABAR
detector [
12
] at the
PEP-II asymmetric-energy
e
þ
e

collider at SLAC. Our
selection of charged and neutral particle candidates, as well
as reconstruction of

0
,
K
0
S
, and
K

candidates, are de-
scribed at [
1
]. We reconstruct signal events in ten sepa-
rate final states containing an
e
þ
e

or

þ


pair, and a
K
0
S
ð!

þ


Þ
,
K
þ
,or
K

ð
892
Þ
candidate with an invariant
mass
0
:
82
<M
ð
K
Þ
<
0
:
97 GeV
=c
2
. We reconstruct
K

0
candidates in the final state
K
þ


, and
K
candidates in
the final states
K
þ

0
and
K
0
S

þ
(charge conjugation is
implied throughout except as explicitly noted). We also
PRL
102,
091803 (2009)
PHYSICAL REVIEW LETTERS
week ending
6 MARCH 2009
091803-4
study final states
K
ðÞ
h



, where
h
is a track with no
particle identification requirement applied, to characterize
backgrounds from hadrons misidentified as muons.
B
!
K
ðÞ
l
þ
l

decays are reconstructed using the kine-
matic variables
m
ES
¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
s=
4

p

2
B
q
and

E
¼
E

B

ffiffiffi
s
p
=
2
, where
p

B
and
E

B
are the
B
momentum and energy
in the

ð
4
S
Þ
center-of-mass (c.m.) frame, and
ffiffiffi
s
p
is the
total c.m. energy. We define a fit region
m
ES
>
5
:
2 GeV
=c
2
, with

0
:
07
<

E<
0
:
04
(

0
:
04
<

E<
0
:
04
) GeV for
e
þ
e

(

þ


) final states in the low and
extended low
q
2
region, and

0
:
08
<

E<
0
:
05
(

0
:
05
<

E<
0
:
05
) GeV for high
q
2
.
The main backgrounds arise from random combinations
of leptons from semileptonic
B
and
D
decays, which are
suppressed through the use of neural networks (NN) whose
construction is described in detail in [
1
]. For each of the ten
final states we use separate NN optimized to suppress
either continuum or
B

B
backgrounds in the low, extended
low or high
q
2
regions. We use simulated samples of signal
and background events in the construction of the NN, and
assume rates consistent with accepted values [
8
].
There is a further background contribution from
B
!
D
ð!
K
ðÞ

Þ

decays, where both pions are misidentified
as leptons. The pion misidentification rates are 2%–3% for
muons and
<
0
:
1%
for electrons, so this background is only
significant in the

þ


final states. We veto these events
by assigning the pion mass to a muon candidate, and
requiring the invariant mass of the hypothetical
K
ðÞ

system to be outside the range
1
:
84
1
:
90 GeV
=c
2
. After
all the above selections have been applied, the final recon-
struction efficiency for signal events varies from 3.5% for
K
þ

0

þ


for the combined
q
2
region, to 22% for
K
þ


e
þ
e

in the high
q
2
region.
We perform unbinned maximum likelihood fits to
m
ES
distributions to obtain signal and background yields. We
use an ARGUS shape [
13
] to describe the combinatorial
background, allowing the shape parameter to float in the
fits. For the signal, we use a fixed Gaussian shape unique to
each final state, with mean and width determined from fits
to the analogous final states in the vetoed
J=
c
K
ðÞ
events.
We account for a small residual contribution from mis-
identified hadrons by constructing a probability density
function (PDF) using
K
ðÞ
h



events weighted by the
probability for the
h

to be misidentified as a muon. We
also account for background events that peak in the
m
ES
signal region, arising from charmonium events that escape
the veto, and for contributions from misreconstructed sig-
nal events. We test our fits in each final state using the large
samples of vetoed
J=
c
K
ðÞ
and
c
ð
2
S
Þ
K
ðÞ
events, and find
that all the branching fractions are in good agreement with
accepted values [
14
]. We perform simultaneous fits for
A
K
ðÞ
CP
,
R
K
ðÞ
and
A
K
ðÞ
I
summed over all the signal modes
that contribute to the particular measurement.
We estimate the statistical significance of our fits by
generating ensembles of 1000 data sets for each of the
ten final states in each
q
2
region of interest, and fitting each
data set with the full fit model described above. These tests
also confirm the unbiased nature and proper error scaling
of our fit methodology.
For the total
B
!
Kl
þ
l

and
B
!
K

l
þ
l

branching
fractions averaged assuming isospin and lepton-flavor
symmetry, we measure
ð
0
:
394
þ
0
:
073

0
:
069

0
:
020
Þ
10

6
and
ð
1
:
11
þ
0
:
19

0
:
18

0
:
07
Þ
10

6
, respectively, where the first
uncertainty is statistical and the second is systematic.
Complete branching fraction results in all final states and
q
2
regions, along with the statistical significance of each
measurement and frequentist upper limits for measure-
ments with
<
4

statistical significance, are available on-
line [
15
]. All results are in good agreement with previous
measurements [
8
].
Table
I
summarizes the results for
A
K
ðÞ
CP
. In the fits to the
separate
B
and

B
data sets in charge-conjugate final states,
we assume a common background ARGUS shape parame-
ter. Our final results are consistent with the SM expectation
of negligible direct
CP
asymmetry. Table
II
shows the
TABLE I.
A
K
ðÞ
CP
results in each relevant
q
2
region. The uncertainties are statistical and system-
atic, respectively.
Mode
Combined
q
2
Low
q
2
High
q
2
K
þ
l
þ
l


0
:
18
þ
0
:
18

0
:
18

0
:
01

0
:
18
þ
0
:
19

0
:
19

0
:
01

0
:
09
þ
0
:
36

0
:
39

0
:
02
K

0
l
þ
l

0
:
02
þ
0
:
20

0
:
20

0
:
02

0
:
23
þ
0
:
38

0
:
38

0
:
02
0
:
17
þ
0
:
24

0
:
24

0
:
02
K
l
þ
l

0
:
01
þ
0
:
26

0
:
24

0
:
02
0
:
10
þ
0
:
25

0
:
24

0
:
02

0
:
18
þ
0
:
45

0
:
55

0
:
04
K

l
þ
l

0
:
01
þ
0
:
16

0
:
15

0
:
01
0
:
01
þ
0
:
21

0
:
20

0
:
01
0
:
09
þ
0
:
21

0
:
21

0
:
02
TABLE II.
R
K
ðÞ
results in each
q
2
region. The extended
(‘‘ext.’’) regions are relevant only for
R
K

. The uncertainties
are statistical and systematic, respectively.
q
2
Region
R
K

R
K
Combined
1
:
37
þ
0
:
53

0
:
40

0
:
09
0
:
96
þ
0
:
44

0
:
34

0
:
05
Ext. combined
1
:
10
þ
0
:
42

0
:
32

0
:
07

Low
1
:
01
þ
0
:
58

0
:
44

0
:
08
0
:
40
þ
0
:
30

0
:
23

0
:
02
Ext. low
0
:
56
þ
0
:
29

0
:
23

0
:
04

High
2
:
15
þ
1
:
42

0
:
78

0
:
15
1
:
06
þ
0
:
81

0
:
51

0
:
06
PRL
102,
091803 (2009)
PHYSICAL REVIEW LETTERS
week ending
6 MARCH 2009
091803-5
results for
R
K
and
R
K

, which are also consistent with the
SM expectations.
Table
III
shows the results for the isospin asymmetry
A
K
ðÞ
I
. We directly fit the data for
A
K
ðÞ
I
taking into account
the differing lifetimes of
B
0
and
B
þ
. Figure
1
shows the
charged and neutral low
q
2
data sets with overlaid fit
projections. We find no significant isospin asymmetries
in the high and combined
q
2
regions, or for
K

e
þ
e

fits
in the extended regions. However, we find evidence for
large negative asymmetries in the low
q
2
region.
We calculate the statistical significance with which a
null isospin asymmetry hypothesis is rejected using the
change in log likelihood
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2 ln
L
p
between the nominal fit
to the data and a fit with
A
K
ðÞ
I
¼
0
fixed. Figure
2
shows the
likelihood curves obtained from the
Kl
þ
l

and
K

l
þ
l

fits. The parabolic nature of the curves in the
A
K
ðÞ
I
>

1
region demonstrates the essentially Gaussian nature of our
fit results in the physical region, and the right-side axis of
Fig.
2
shows purely statistical significances based on
Gaussian coverage. Incorporating the relatively small sys-
tematic uncertainties as a scaling factor on the change in
log likelihood, the significance in the low
q
2
region that
A
K
ðÞ
I
is different from zero is
3
:
2

for
Kl
þ
l

and
2
:
7

for
K

l
þ
l

. We have verified these confidence intervals by
performing fits to ensembles of simulated data sets gener-
ated with
A
K
ðÞ
I
¼
0
fixed, and we find frequentist coverage
consistent with the
ln
L
calculations. The highly negative
A
K
ðÞ
I
values for both
Kl
þ
l

and
K

l
þ
l

at low
q
2
suggest
that this asymmetry may be insensitive to the hadronic final
state, and so we sum the likelihood curves as shown in
Fig.
2
and obtain
A
K
ðÞ
I
¼
0
:
64
þ
0
:
15

0
:
14

0
:
03
. Including
systematics, this is a
3
:
9

difference from a null
A
K
ðÞ
I
hypothesis.
We consider systematic uncertainties associated with
reconstruction efficiencies; hadronic background parame-
trization in dimuon final states; peaking background con-
tributions obtained from simulated events; and possible
CP
, lepton flavor, and isospin asymmetries in the back-
ground PDFs. We quantify the efficiency systematics using
the vetoed
J=
c
K
ðÞ
samples. These include charged track,

0
, and
K
0
S
reconstruction, particle identification, NN se-
lection, and the

E
and
K

mass selections. The largest
contributions to the systematic uncertainties on the rates
are particle identification, the characterization of the had-
)
2
Events / (0.0045 GeV/c
10
20
30
-
l
+
l
+
K
(a)
0
5
10
-
l
+
l
0
K
(b)
)
2
(GeV/c
ES
m
5.2 5.22 5.24 5.26 5.28
)
2
Events / (0.0045 GeV/c
20
40
-
l
+
l
*+
K
(c)
)
2
(GeV/c
ES
m
5.2
5.22 5.24 5.26 5.28
10
20
-
l
+
l
*0
K
(d)
FIG. 1 (color online). Charged and neutral fit projections in the
low
q
2
region. Total fit (solid), combinatoric background (long
dash), signal (medium dash), hadronic background (short dash),
peaking background (dots).
(*)
K
I
A
-2
-1.5
-1
-0.5
0
log(L)
0
2
4
6
8
10
12
14
16
σ
1
σ
2
σ
3
σ
4
σ
5
FIG. 2. Low
q
2
region
A
K
ðÞ
I
fit likelihood curves.
Kl
þ
l

(long
dash),
K

l
þ
l

(short dash),
ð
K; K

Þ
l
þ
l

(solid).
TABLE III.
A
K
ðÞ
I
results in each
q
2
region. The uncertainties are statistical and systematic,
respectively. The last table row shows
K

e
þ
e

results for the extended regions.
Mode
Combined
q
2
Low
q
2
High
q
2
K
þ


0
:
13
þ
0
:
29

0
:
37

0
:
04

0
:
91
þ
1
:
2
1

0
:
18
0
:
39
þ
0
:
35

0
:
46

0
:
04
Ke
þ
e


0
:
73
þ
0
:
39

0
:
50

0
:
04

1
:
41
þ
0
:
49

0
:
69

0
:
04
0
:
21
þ
0
:
32

0
:
41

0
:
03
Kl
þ
l


0
:
37
þ
0
:
27

0
:
34

0
:
04

1
:
43
þ
0
:
56

0
:
85

0
:
05
0
:
28
þ
0
:
24

0
:
30

0
:
03
K


þ



0
:
00
þ
0
:
36

0
:
26

0
:
05

0
:
26
þ
0
:
50

0
:
34

0
:
05

0
:
08
þ
0
:
37

0
:
27

0
:
05
K

e
þ
e


0
:
20
þ
0
:
22

0
:
20

0
:
03

0
:
66
þ
0
:
19

0
:
17

0
:
02
0
:
32
þ
0
:
75

0
:
45

0
:
03
K

l
þ
l


0
:
12
þ
0
:
18

0
:
16

0
:
04

0
:
56
þ
0
:
17

0
:
15

0
:
03
0
:
18
þ
0
:
36

0
:
28

0
:
04
K

e
þ
e

(ext.)

0
:
27
þ
0
:
21

0
:
18

0
:
03

0
:
25
þ
0
:
20

0
:
18

0
:
03

PRL
102,
091803 (2009)
PHYSICAL REVIEW LETTERS
week ending
6 MARCH 2009
091803-6
ronic background and the signal
m
ES
PDF shape. All of
these cancel at least partially in the rate asymmetries, and
the final systematic uncertainties are small compared to the
statistical ones.
We perform several additional checks of effects that
might cause a bias in our final results. We vary the parame-
trization of the hadronic background PDFs, and of the
random combinatorial background ARGUS shapes in the
low
q
2
region, to test the robustness of the large
A
K
ðÞ
I
asymmetries. We remove all the NN selections, and per-
form separate fits to the two
K
final states, and observe
no significant variation in the
A
K
ðÞ
I
results. To understand if
an isospin asymmetry might be induced by the combina-
torial background, we compare data and simulated back-
ground events within a larger region
j

E
j
<
0
:
25 GeV
outside our

E
selection window and in the
5
:
2
<m
ES
<
5
:
27 GeV
=c
2
region. We find that the numbers of simu-
lated and data events in this larger region agree well. No
signal isospin asymmetry is found using simulated events
within the fit region.
In summary, we have measured branching fractions, and
studied direct
CP
violation, ratios of rates to dimuon and
dielectron final states, and isospin asymmetries in the rare
decays
B
!
K
ðÞ
l
þ
l

. Our branching fraction results agree
with both SM predictions and previous measurements. Our
results for the direct
CP
asymmetries and lepton-flavor rate
ratios are in good agreement with their respective SM
predictions of zero and one. The isospin asymmetries in
the high and combined
q
2
regions are consistent with zero,
but in the low
q
2
region in both
B
!
Kl
þ
l

and
B
!
K

l
þ
l

we measure large negative asymmetries that are
each about
3

different from zero, including systematic
uncertainties. Combining these results, we obtain
A
K
ðÞ
I
¼

0
:
64
þ
0
:
15

0
:
14

0
:
03
, with a
3
:
9

difference (including sys-
tematics) from
A
K
ðÞ
I
¼
0
. Such large negative asymmetries
are unexpected in the SM, which predicts essentially no
isospin asymmetry integrated over our low
q
2
region and,
as
q
2
!
0
, an asymmetry of
10%
, opposite in sign to
our observation in the low
q
2
region.
We are grateful for the excellent luminosity and machine
conditions provided by our PEP-II colleagues, and for the
substantial dedicated effort from the computing organiza-
tions that support
BABAR
. The collaborating institutions
wish to thank SLAC for its support and kind hospitality.
This work is supported by DOE and NSF (U.S.), NSERC
(Canada), CEA and CNRS-IN2P3 (France), BMBF and
DFG (Germany), INFN (Italy), FOM (The Netherlands),
NFR (Norway), MES (Russia), MEC (Spain), and
STFC (U.K.). Individuals have received support from the
Marie Curie EIF (European Union) and the A. P. Sloan
Foundation.
*
Deceased.
Now at Temple University, Philadelphia, PA 19122, USA.
Now at Tel Aviv University, Tel Aviv, 69978, Israel.
x
Also with Universita
`
di Perugia, Dipartimento di Fisica,
Perugia, Italy.
k
Also with Universita
`
di Roma La Sapienza, I-00185
Roma, Italy.
{
Now at University of South Alabama, Mobile, AL 36688,
USA.
**
Also with Universita
`
di Sassari, Sassari, Italy.
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PRL
102,
091803 (2009)
PHYSICAL REVIEW LETTERS
week ending
6 MARCH 2009
091803-7