of 8
Angular distributions in the decay
B
!
K

l
þ
l

B. Aubert,
1
M. Bona,
1
Y. Karyotakis,
1
J. P. Lees,
1
V. Poireau,
1
X. Prudent,
1
V. Tisserand,
1
A. Zghiche,
1
J. Garra Tico,
2
E. Grauges,
2
L. Lopez,
3
A. Palano,
3
M. Pappagallo,
3
G. Eigen,
4
B. Stugu,
4
L. Sun,
4
G. S. Abrams,
5
M. Battaglia,
5
D. N. Brown,
5
J. Button-Shafer,
5
R. N. Cahn,
5
R. G. Jacobsen,
5
J. A. Kadyk,
5
L. T. Kerth,
5
Yu. G. Kolomensky,
5
G. Kukartsev,
5
G. Lynch,
5
I. L. Osipenkov,
5
M. T. Ronan,
5,
*
K. Tackmann,
5
T. Tanabe,
5
W. A. Wenzel,
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
T. Cuhadar-Donszelmann,
9
B. G. Fulsom,
9
C. Hearty,
9
T. S. Mattison,
9
J. A. McKenna,
9
M. Barrett,
10
A. Khan,
10
M. Saleem,
10
L. Teodorescu,
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
F. Blanc,
20
P. C. Bloom,
20
W. T. Ford,
20
J. F. Hirschauer,
20
A. Kreisel,
20
M. Nagel,
20
U. Nauenberg,
20
A. Olivas,
20
J. G. Smith,
20
K. A. Ulmer,
20
S. R. Wagner,
20
R. Ayad,
21,
A. M. Gabareen,
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
V. Klose,
23
M. J. Kobel,
23
H. M. Lacker,
23
W. F. Mader,
23
R. Nogowski,
23
J. Schubert,
23
K. R. Schubert,
23
R. Schwierz,
23
J. E. Sundermann,
23
A. Volk,
23
D. Bernard,
24
G. R. Bonneaud,
24
E. Latour,
24
Ch. Thiebaux,
24
M. Verderi,
24
P. J. Clark,
25
W. Gradl,
25
S. Playfer,
25
A. I. Robertson,
25
J. E. Watson,
25
M. Andreotti,
26
D. Bettoni,
26
C. Bozzi,
26
R. Calabrese,
26
A. Cecchi,
26
G. Cibinetto,
26
P. Franchini,
26
E. Luppi,
26
M. Negrini,
26
A. Petrella,
26
L. Piemontese,
26
E. Prencipe,
26
V. Santoro,
26
F. Anulli,
27
R. Baldini-Ferroli,
27
A. Calcaterra,
27
R. de Sangro,
27
G. Finocchiaro,
27
S. Pacetti,
27
P. Patteri,
27
I. M. Peruzzi,
27,
x
M. Piccolo,
27
M. Rama,
27
A. Zallo,
27
A. Buzzo,
28
R. Contri,
28
M. Lo Vetere,
28
M. M. Macri,
28
M. R. Monge,
28
S. Passaggio,
28
C. Patrignani,
28
E. Robutti,
28
A. Santroni,
28
S. Tosi,
28
K. S. Chaisanguanthum,
29
M. Morii,
29
R. S. Dubitzky,
30
J. Marks,
30
S. Schenk,
30
U. Uwer,
30
D. J. Bard,
31
P. D. Dauncey,
31
J. A. Nash,
31
W. Panduro Vazquez,
31
M. Tibbetts,
31
P. K. Behera,
32
X. Chai,
32
M. J. Charles,
32
U. Mallik,
32
J. Cochran,
33
H. B. Crawley,
33
L. Dong,
33
W. T. Meyer,
33
S. Prell,
33
E. I. Rosenberg,
33
A. E. Rubin,
33
Y. Y. Gao,
34
A. V. Gritsan,
34
Z. J. Guo,
34
C. K. Lae,
34
A. G. Denig,
35
M. Fritsch,
35
G. Schott,
35
N. Arnaud,
36
J. Be
́
quilleux,
36
A. D’Orazio,
36
M. Davier,
36
J. Firmino da Costa,
36
G. Grosdidier,
36
A. Ho
̈
cker,
36
V. Lepeltier,
36
F. Le Diberder,
36
A. M. Lutz,
36
S. Pruvot,
36
P. Roudeau,
36
M. H. Schune,
36
J. Serrano,
36
V. Sordini,
36
A. Stocchi,
36
W. F. Wang,
36
G. Wormser,
36
D. J. Lange,
37
D. M. Wright,
37
I. Bingham,
38
J. P. Burke,
38
C. A. Chavez,
38
J. R. Fry,
38
E. Gabathuler,
38
R. Gamet,
38
D. E. Hutchcroft,
38
D. J. Payne,
38
C. Touramanis,
38
A. J. Bevan,
39
K. A. George,
39
F. Di Lodovico,
39
R. Sacco,
39
M. Sigamani,
39
G. Cowan,
40
H. U. Flaecher,
40
D. A. Hopkins,
40
S. Paramesvaran,
40
F. Salvatore,
40
A. C. Wren,
40
D. N. Brown,
41
C. L. Davis,
41
K. E. Alwyn,
42
N. R. Barlow,
42
R. J. Barlow,
42
Y. M. Chia,
42
C. L. Edgar,
42
G. D. Lafferty,
42
T. J. West,
42
J. I. Yi,
42
J. Anderson,
43
C. Chen,
43
A. Jawahery,
43
D. A. Roberts,
43
G. Simi,
43
J. M. Tuggle,
43
C. Dallapiccola,
44
S. S. Hertzbach,
44
X. Li,
44
E. Salvati,
44
S. Saremi,
44
R. Cowan,
45
D. Dujmic,
45
P. H. Fisher,
45
K. Koeneke,
45
G. Sciolla,
45
M. Spitznagel,
45
F. Taylor,
45
R. K. Yamamoto,
45
M. Zhao,
45
S. E. Mclachlin,
46,
*
P. M. Patel,
46
S. H. Robertson,
46
A. Lazzaro,
47
V. Lombardo,
47
F. Palombo,
47
J. M. Bauer,
48
L. Cremaldi,
48
V. Eschenburg,
48
R. Godang,
48
R. Kroeger,
48
D. A. Sanders,
48
D. J. Summers,
48
H. W. Zhao,
48
S. Brunet,
49
D. Co
ˆ
te
́
,
49
M. Simard,
49
P. Taras,
49
F. B. Viaud,
49
H. Nicholson,
50
G. De Nardo,
51
L. Lista,
51
D. Monorchio,
51
C. Sciacca,
51
M. A. Baak,
52
G. Raven,
52
H. L. Snoek,
52
C. P. Jessop,
53
K. J. Knoepfel,
53
J. M. LoSecco,
53
G. Benelli,
54
L. A. Corwin,
54
K. Honscheid,
54
H. Kagan,
54
R. Kass,
54
J. P. Morris,
54
A. M. Rahimi,
54
J. J. Regensburger,
54
S. J. Sekula,
54
Q. K. Wong,
54
N. L. Blount,
55
J. Brau,
55
R. Frey,
55
O. Igonkina,
55
J. A. Kolb,
55
M. Lu,
55
R. Rahmat,
55
N. B. Sinev,
55
D. Strom,
55
J. Strube,
55
E. Torrence,
55
G. Castelli,
56
N. Gagliardi,
56
A. Gaz,
56
M. Margoni,
56
M. Morandin,
56
M. Posocco,
56
M. Rotondo,
56
F. Simonetto,
56
R. Stroili,
56
C. Voci,
56
P. del Amo Sanchez,
57
E. Ben-Haim,
57
H. Briand,
57
G. Calderini,
57
J. Chauveau,
57
P. David,
57
L. Del Buono,
57
O. Hamon,
57
Ph. Leruste,
57
J. Ocariz,
57
A. Perez,
57
J. Prendki,
57
L. Gladney,
58
M. Biasini,
59
R. Covarelli,
59
E. Manoni,
59
C. Angelini,
60
G. Batignani,
60
S. Bettarini,
60
M. Carpinelli,
60,
k
A. Cervelli,
60
F. Forti,
60
M. A. Giorgi,
60
A. Lusiani,
60
G. Marchiori,
60
M. Morganti,
60
N. Neri,
60
E. Paoloni,
60
G. Rizzo,
60
J. J. Walsh,
60
J. Biesiada,
61
Y. P. Lau,
61
D. Lopes Pegna,
61
C. Lu,
61
J. Olsen,
61
A. J. S. Smith,
61
A. V. Telnov,
61
E. Baracchini,
62
PHYSICAL REVIEW D
79,
031102(R) (2009)
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1550-7998
=
2009
=
79(3)
=
031102(8)
031102-1
Ó
2009 The American Physical Society
G. Cavoto,
62
D. del Re,
62
E. Di Marco,
62
R. Faccini,
62
F. Ferrarotto,
62
F. Ferroni,
62
M. Gaspero,
62
P. D. Jackson,
62
L. Li Gioi,
62
M. A. Mazzoni,
62
S. Morganti,
62
G. Piredda,
62
F. Polci,
62
F. Renga,
62
C. Voena,
62
M. Ebert,
63
T. Hartmann,
63
H. Schro
̈
der,
63
R. Waldi,
63
T. Adye,
64
B. Franek,
64
E. O. Olaiya,
64
W. Roethel,
64
F. F. Wilson,
64
S. Emery,
65
M. Escalier,
65
L. Esteve,
65
A. Gaidot,
65
S. F. Ganzhur,
65
G. Hamel de Monchenault,
65
W. Kozanecki,
65
G. Vasseur,
65
Ch. Ye
`
che,
65
M. Zito,
65
X. R. Chen,
66
H. Liu,
66
W. Park,
66
M. V. Purohit,
66
R. M. White,
66
J. R. Wilson,
66
M. T. Allen,
67
D. Aston,
67
R. Bartoldus,
67
P. Bechtle,
67
J. F. Benitez,
67
R. Cenci,
67
J. P. Coleman,
67
M. R. Convery,
67
J. C. Dingfelder,
67
J. Dorfan,
67
G. P. Dubois-Felsmann,
67
W. Dunwoodie,
67
R. C. Field,
67
S. J. Gowdy,
67
M. T. Graham,
67
P. Grenier,
67
C. Hast,
67
W. R. Innes,
67
J. Kaminski,
67
M. H. Kelsey,
67
H. Kim,
67
P. Kim,
67
M. L. Kocian,
67
D. W. G. S. Leith,
67
S. Li,
67
B. Lindquist,
67
S. Luitz,
67
V. Luth,
67
H. L. Lynch,
67
D. B. MacFarlane,
67
H. Marsiske,
67
R. Messner,
67
D. R. Muller,
67
H. Neal,
67
S. Nelson,
67
C. P. O’Grady,
67
I. Ofte,
67
A. Perazzo,
67
M. Perl,
67
B. N. Ratcliff,
67
A. Roodman,
67
A. A. Salnikov,
67
R. H. Schindler,
67
J. Schwiening,
67
A. Snyder,
67
D. Su,
67
M. K. Sullivan,
67
K. Suzuki,
67
S. K. Swain,
67
J. M. Thompson,
67
J. Va’vra,
67
A. P. Wagner,
67
M. Weaver,
67
C. A. West,
67
W. J. Wisniewski,
67
M. Wittgen,
67
D. H. Wright,
67
H. W. Wulsin,
67
A. K. Yarritu,
67
K. Yi,
67
C. C. Young,
67
V. Ziegler,
67
P. R. Burchat,
68
A. J. Edwards,
68
S. A. Majewski,
68
T. S. Miyashita,
68
B. A. Petersen,
68
L. Wilden,
68
S. Ahmed,
69
M. S. Alam,
69
R. Bula,
69
J. A. Ernst,
69
B. Pan,
69
M. A. Saeed,
69
S. B. Zain,
69
S. M. Spanier,
70
B. J. Wogsland,
70
R. Eckmann,
71
J. L. Ritchie,
71
A. M. Ruland,
71
C. J. Schilling,
71
R. F. Schwitters,
71
B. W. Drummond,
72
J. M. Izen,
72
X. C. Lou,
72
S. Ye,
72
F. Bianchi,
73
D. Gamba,
73
M. Pelliccioni,
73
M. Bomben,
74
L. Bosisio,
74
C. Cartaro,
74
G. Della Ricca,
74
L. Lanceri,
74
L. Vitale,
74
V. Azzolini,
75
N. Lopez-March,
75
F. Martinez-Vidal,
75
D. A. Milanes,
75
A. Oyanguren,
75
J. Albert,
76
Sw. Banerjee,
76
B. Bhuyan,
76
H. H. F. Choi,
76
K. Hamano,
76
R. Kowalewski,
76
M. J. Lewczuk,
76
I. M. Nugent,
76
J. M. Roney,
76
R. J. Sobie,
76
T. J. Gershon,
77
P. F. Harrison,
77
J. Ilic,
77
T. E. Latham,
77
G. B. Mohanty,
77
H. R. Band,
78
X. Chen,
78
S. Dasu,
78
K. T. Flood,
78
Y. Pan,
78
M. Pierini,
78
R. Prepost,
78
C. O. Vuosalo,
78
and S. L. Wu
78
(
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
3
Universita
`
di Bari, Dipartimento di Fisica and INFN, 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
Universita
̈
t Dortmund, Institut fu
̈
r 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
26
Universita
`
di Ferrara, Dipartimento di Fisica and INFN, I-44100 Ferrara, Italy
27
Laboratori Nazionali di Frascati dell’INFN, I-00044 Frascati, Italy
28
Universita
`
di Genova, Dipartimento di Fisica and INFN, I-16146 Genova, Italy
29
Harvard University, Cambridge, Massachusetts 02138, USA
30
Universita
̈
t Heidelberg, Physikalisches Institut, Philosophenweg 12, D-69120 Heidelberg, Germany
31
Imperial College London, London, SW7 2AZ, United Kingdom
32
University of Iowa, Iowa City, Iowa 52242, USA
33
Iowa State University, Ames, Iowa 50011-3160, USA
34
Johns Hopkins University, Baltimore, Maryland 21218, USA
B. AUBERT
et al.
PHYSICAL REVIEW D
79,
031102(R) (2009)
RAPID COMMUNICATIONS
031102-2
35
Universita
̈
t Karlsruhe, Institut fu
̈
r Experimentelle Kernphysik, D-76021 Karlsruhe, Germany
36
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
37
Lawrence Livermore National Laboratory, Livermore, California 94550, USA
38
University of Liverpool, Liverpool L69 7ZE, United Kingdom
39
Queen Mary, University of London, E1 4NS, United Kingdom
40
University of London, Royal Holloway and Bedford New College, Egham, Surrey TW20 0EX, United Kingdom
41
University of Louisville, Louisville, Kentucky 40292, USA
42
University of Manchester, Manchester M13 9PL, United Kingdom
43
University of Maryland, College Park, Maryland 20742, USA
44
University of Massachusetts, Amherst, Massachusetts 01003, USA
45
Massachusetts Institute of Technology, Laboratory for Nuclear Science, Cambridge, Massachusetts 02139, USA
46
McGill University, Montre
́
al, Que
́
bec, Canada H3A 2T8
47
Universita
`
di Milano, Dipartimento di Fisica and INFN, I-20133 Milano, Italy
48
University of Mississippi, University, Mississippi 38677, USA
49
Universite
́
de Montre
́
al, Physique des Particules, Montre
́
al, Que
́
bec, Canada H3C 3J7
50
Mount Holyoke College, South Hadley, Massachusetts 01075, USA
51
Universita
`
di Napoli Federico II, Dipartimento di Scienze Fisiche and INFN, I-80126, Napoli, Italy
52
NIKHEF, National Institute for Nuclear Physics and High Energy Physics, NL-1009 DB Amsterdam, The Netherlands
53
University of Notre Dame, Notre Dame, Indiana 46556, USA
54
Ohio State University, Columbus, Ohio 43210, USA
55
University of Oregon, Eugene, Oregon 97403, USA
56
Universita
`
di Padova, Dipartimento di Fisica and INFN, I-35131 Padova, Italy
57
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
58
University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
59
Universita
`
di Perugia, Dipartimento di Fisica and INFN, I-06100 Perugia, Italy
60
Universita
`
di Pisa, Dipartimento di Fisica, Scuola Normale Superiore and INFN, I-56127 Pisa, Italy
61
Princeton University, Princeton, New Jersey 08544, USA
62
Universita
`
di Roma La Sapienza, Dipartimento di Fisica and INFN, I-00185 Roma, Italy
63
Universita
̈
t Rostock, D-18051 Rostock, Germany
64
Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX11 0QX, United Kingdom
65
DSM/Dapnia, CEA/Saclay, F-91191 Gif-sur-Yvette, France
66
University of South Carolina, Columbia, South Carolina 29208, USA
67
Stanford Linear Accelerator Center, Stanford, California 94309, USA
68
Stanford University, Stanford, California 94305-4060, USA
69
State University of New York, Albany, New York 12222, USA
70
University of Tennessee, Knoxville, Tennessee 37996, USA
71
University of Texas at Austin, Austin, Texas 78712, USA
72
University of Texas at Dallas, Richardson, Texas 75083, USA
73
Universita
`
di Torino, Dipartimento di Fisica Sperimentale and INFN, I-10125 Torino, Italy
74
Universita
`
di Trieste, Dipartimento di Fisica and INFN, I-34127 Trieste, Italy
75
IFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spain
76
University of Victoria, Victoria, British Columbia, Canada V8W 3P6
77
Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
78
University of Wisconsin, Madison, Wisconsin 53706, USA
(Received 28 April 2008; published 26 February 2009)
We use a sample of
384

10
6
B

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

collider to study angular distributions in the rare decays
B
!
K

þ

, where
þ

is either
e
þ
e

or

þ


. For low dilepton invariant masses,
m
‘‘
<
2
:
5 GeV
=c
2
, we measure a lepton forward-backward
asymmetry
A
FB
¼
0
:
24
þ
0
:
18

0
:
23

0
:
05
and
K

longitudinal polarization
F
L
¼
0
:
35

0
:
16

0
:
04
. For
m
‘‘
>
3
:
2 GeV
=c
2
, we measure
A
FB
¼
0
:
76
þ
0
:
52

0
:
32

0
:
07
and
F
L
¼
0
:
71
þ
0
:
20

0
:
22

0
:
04
.
DOI:
10.1103/PhysRevD.79.031102
PACS numbers: 13.20.He
Now at Tel Aviv University, Tel Aviv, 69978, Israel.
k
Also with Universita’ di Sassari, Sassari, Italy.
Now at Temple University, Philadelphia, Pennsylvania 19122, USA.
x
Also with Universita
`
di Perugia, Dipartimento di Fisica, Perugia, Italy.
*
Deceased.
ANGULAR DISTRIBUTIONS IN THE DECAY
...
PHYSICAL REVIEW D
79,
031102(R) (2009)
RAPID COMMUNICATIONS
031102-3
The decays
B
!
K

þ

, where
K

!
K
and
þ

is
either an
e
þ
e

or

þ


pair, arise from flavor-changing
neutral currents (FCNC), which are forbidden at tree level
in the standard model (SM). The lowest-order SM pro-
cesses contributing to these decays are the photon or
Z
penguin and the
W
þ
W

box diagrams shown in Fig.
1
. The
amplitudes can be expressed in terms of effective Wilson
coefficients for the electromagnetic penguin,
C
eff
7
, and the
vector and axial-vector electroweak contributions,
C
eff
9
and
C
eff
10
, respectively, arising from the interference of the
Z
penguin and
W
þ
W

box diagrams [
1
]. The angular dis-
tributions in these decays as a function of dilepton mass
squared
q
2
¼
m
2
þ

are sensitive to many possible new
physics contributions [
2
].
We describe measurements of the distribution of the
angle

K
between the
K
and the
B
directions in the
K

rest frame. A fit to
cos

K
of the form [
3
]
3
2
F
L
cos
2

K
þ
3
4
ð
1

F
L
Þð
1

cos
2

K
Þ
(1)
determines
F
L
, the
K

longitudinal polarization fraction.
We also describe measurements of the distribution of the
angle

between the
þ
ð

Þ
and the
B
ð

B
Þ
direction in the
þ

rest frame. A fit to
cos

of the form [
3
]
3
4
F
L
ð
1

cos
2

Þþ
3
8
ð
1

F
L
Þð
1
þ
cos
2

Þþ
A
FB
cos

(2)
determines
A
FB
, the lepton forward-backward asymme-
try. These measurements are done in a low
q
2
region
0
:
1
<
q
2
<
6
:
25 GeV
2
=c
4
, and in a high
q
2
region above
10
:
24 GeV
2
=c
4
. We remove the
J=
c
and
c
ð
2
S
Þ
reso-
nances by vetoing events in the regions
q
2
¼
6
:
25
10
:
24 GeV
2
=c
4
and
q
2
¼
12
:
96
14
:
06 GeV
2
=c
4
respectively.
The SM predicts a distinctive variation of
A
FB
arising
from the interference between the different amplitudes.
The expected SM dependence of
A
FB
and
F
L
on
q
2
along
with variations due to opposite-sign Wilson coefficients are
shown in Fig.
3
.Atlow
q
2
, where
C
eff
7
dominates,
A
FB
is
expected to be small with a zero-crossing point at
q
2

4 GeV
2
=c
4
[
4
6
]. There is an experimental constraint on
the magnitude of
C
eff
7
coming from the branching fraction
for
b
!
s
[
6
,
7
], which corresponds to the limit
q
2
!
0
.
However, a reversal of the sign of
C
eff
7
is allowed. At high
q
2
, the product of
C
eff
9
and
C
eff
10
is expected to give a large
positive asymmetry. Right-handed weak currents have an
opposite-sign
C
eff
9
C
eff
10
which would give a negative
A
FB
at
high
q
2
. Contributions from non-SM processes can change
the magnitudes and relative signs of
C
eff
7
,
C
eff
9
and
C
eff
10
, and
may introduce complex phases between them [
3
,
8
]. An
experimental determination of
F
L
is required to obtain a
model-independent
A
FB
result, and thus avoid drawing
possibly incorrect inferences about new physics from our
observations.
We reconstruct signal events in six separate flavor-
specific final states containing an
e
þ
e

or

þ


pair,
and a
K

ð
892
Þ
candidate reconstructed as
K
þ


,
K
þ

0
or
K
0
S

þ
(or their charge conjugates). To understand combi-
natorial backgrounds we also reconstruct samples contain-
ing the same hadronic final states and
e



pairs, where
no signal is expected because of lepton-flavor conserva-
tion. To understand backgrounds from hadrons (
h
) mis-
identified as muons, we similarly reconstruct samples
containing
h



pairs with no particle identification re-
quirement for the
h

.
We use a data set of
384

10
6
B

B
pairs collected at the

ð
4
S
Þ
resonance with the
BABAR
detector [
9
] at the PEP-II
asymmetric-energy
e
þ
e

collider. Tracking is provided by
a five-layer silicon vertex tracker and a 40-layer drift
chamber in a 1.5 T magnetic field. We identify electrons
with a CsI(Tl) electromagnetic calorimeter, muons with an
instrumented magnetic flux return, and
K
þ
using a detector
of internally reflected Cherenkov light as well as ionization
energy loss information. Charged tracks other than identi-
fied
e
,

and
K
candidates are treated as pions. Electrons
(muons) are required to have momenta
p>
0
:
3
ð
0
:
7
Þ
GeV
=c
in the laboratory frame. We add photons
to electrons when they are consistent with bremsstrahlung,
and do not use electrons that arise from photon conversions
to low-mass
e
þ
e

pairs. Neutral
K
0
S
!

þ


candidates
are required to have an invariant mass consistent with the
nominal
K
0
mass [
10
], and a flight distance from the
e
þ
e

interaction point which is more than 3 times its uncertainty.
Neutral pion candidates are formed from two photons with
E

>
50 MeV
, and an invariant mass between 115 and
155 MeV
=c
2
. We require
K

ð
892
Þ
candidates to have an
invariant mass
0
:
82
<M
ð
K
Þ
<
0
:
97 GeV
=c
2
.
B
!
K

þ

decays are characterized by the kinematic
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 reconstructed
B
momentum and
energy in the center-of-mass (CM) frame, and
ffiffiffi
s
p
is the
total CM energy. We define a fit region
m
ES
>
5
:
2 GeV
=c
2
,
with

0
:
07
<

E<
0
:
04
ð
0
:
04
<

E<
0
:
04
Þ
GeV
for
e
þ
e

(

þ


) final states in the low
q
2
region, and

0
:
08
<

E<
0
:
05
ð
0
:
05
<

E<
0
:
05
Þ
GeV
for high
q
2
. We use the wider (narrower)

E
windows to select
the
e



(
h



) background samples.
The most significant background arises from random
combinations of leptons from semileptonic
B
and
D
de-
q
q
bs
t,c,u
W
γ
, Z
l
+
l
q
q
bs
t,c,u
W
+
W
ν
l
l
+
FIG. 1. Lowest-order Feynman diagrams for
b
!
s‘
þ

.
B. AUBERT
et al.
PHYSICAL REVIEW D
79,
031102(R) (2009)
RAPID COMMUNICATIONS
031102-4
cays. In
B

B
events the leptons are kinematically correlated
if they come from
B
!
D
ðÞ
‘
,
D
!
K
ðÞ
‘
. Uncorrelated
backgrounds combine leptons from separate
B
decays or
from continuum
e
þ
e

!
c

c
events. We suppress these
types of combinatorial background through the use of
neural networks (NN). For each final state we use four
separate NN designed to suppress either continuum or
B

B
backgrounds in either the low or high
q
2
regions, and
different selections of NN inputs are used depending on
q
2
bin (low, high), the identity of the leptons in the final
state (
e
,

), and the type of background (
B

B
, continuum).
Inputs include:
(i) event thrust;
(ii) ratio of second-to-zeroth Fox-Wolfram moments
[
11
];
(iii)
m
ES
and
E
of the rest of the event (ROE), compris-
ing all charged tracks and neutral energy deposits not
used to reconstruct the signal candidate;
(iv) the magnitude of the total event transverse momen-
tum, which is correlated with missing energy due to
unreconstructed neutrinos in background semilep-
tonic decays;
(v) dilepton system’s distance of closest approach along
the beam axis, and separately in the plane perpen-
dicular to the beam axis, to the primary interaction
point;
(vi) vertex probability of the signal candidate and, sepa-
rately, of the dilepton system;
(vii) the cosines in the CM frame of the angle between the
B
candidate’s momentum and the beam axis, the
angle between the event thrust axis and the beam
axis (

thrust
), the angle between the ROE thrust axis
and the beam axis (

ROE
thrust
), and the angle between

ROE
thrust
and

thrust
.
There is also a background contribution in the signal
region from
B
!
D
ð
K


Þ

decays, where both pions are
misidentified. The misidentification rates for muons and
electrons are

2%
and

0
:
1%
, respectively, so this back-
ground is only significant in the

þ


final states. These
events are vetoed if the invariant mass of the
K


system is
in the range
1
:
84
1
:
90 GeV
=c
2
.
We optimize the NN and

E
selections for each final
state in each
q
2
bin to give the best combined statistical
signal significance in the
m
ES
signal region
m
ES
>
5
:
27 GeV
=c
2
for the sum of all six final states. After all
these selections have been applied, the final reconstruction
efficiencies and expected yields for signal events (calcu-
lated using world average branching fractions [
7
]), as well
as expected yields for background events in the signal
region, are shown in Table
I
.
For each
q
2
region, we combine events from all six final
states and perform three successive unbinned maximum
likelihood fits. Because of the relatively small number of
signal candidates in each
q
2
region, a simultaneous fit over
m
ES
,
cos

K
, and
cos

is unlikely to converge and a
sequential fitting procedure is required. We initially fit
the
m
ES
distribution using events with
m
ES
>
5
:
2 GeV
=c
2
to obtain the signal and background yields,
N
S
and
N
B
, respectively. We use an ARGUS shape [
12
]
with a free shape parameter to describe the combinatorial
background in this fit. For the signal, we use a Gaussian
shape with a mean
m
ES
¼
5
:
2791

0
:
0001 GeV
=c
2
and

¼
2
:
60

0
:
03 MeV
=c
2
, which are determined from a
fit to the vetoed charmonium samples. In this and subse-
quent fits we account for a small contribution from mis-
identified hadrons by subtracting the
K

h



events,
weighted by the probability for the
h

to be misidentified
as a muon. We also account in all fits for charmonium
events that escape the veto, and for misreconstructed signal
events. We estimate contributions from nonresonant
K
decays by fitting events outside the
K

mass window in the
range
0
:
7
1
:
1 GeV
=c
2
. We find no signal-like events that
are not accounted for by the tails of the resonant mass
distribution, and thus do not expect any significant contri-
bution from nonresonant events within the mass window.
The second fit is to the cosine of the helicity angle of the
K

decay,
cos

K
, for events with
m
ES
>
5
:
27 GeV
=c
2
.In
this fit, the only free parameter is
F
L
, with the normal-
izations for signal and combinatorial background events
taken from the initial
m
ES
fit. The background normaliza-
tion is obtained by integrating, for
m
ES
>
5
:
27 GeV
=c
2
,
the ARGUS shape resulting from the
m
ES
fit. We model the
cos

K
shape of the combinatorial background using
e
þ
e

and

þ


events, as well as lepton-flavor violating
e
þ


and

þ
e

events, in the
5
:
20
<m
ES
<
5
:
27 GeV
=c
2
side-
band. The signal distribution given in Eq. (
1
) is folded with
the detector acceptance as a function of
cos

K
, which is
obtained from simulated signal events.
The final fit is to the cosine of the lepton helicity angle,
cos

, for events with
m
ES
>
5
:
27 GeV
=c
2
. The only free
parameter in this fit is
A
FB
, with the signal distribution
given in Eq. (
2
) folded with the detector acceptance as a
function of
cos

. In this fit, the value of
F
L
is fixed from
the result of the second fit, and normalizations for signal
and combinatorial background events are identical to those
used in the second fit. We constrain the
cos

shape of the
TABLE I. Signal efficiencies (%), and expected signal and
background yields for
m
ES
>
5
:
27 GeV
=c
2
, for low and high
q
2
regions.
Signal Eff. Signal Yield Bkgd. Yield
Mode
low high low high low high
K
þ

0

þ


1.6 3.1
1.0
1.8
0.7
3.8
K
0
S

þ

þ


3.6 5.5
3.0
4.5
0.3
1.4
K
þ



þ


4.5 8.1
5.5
9.6
0.0
3.1
K
þ

0
e
þ
e

4.6 5.3
2.8
3.1
1.7
2.4
K
0
S

þ
e
þ
e

7.0 5.4
5.9
4.4
0.3
1.4
K
þ


e
þ
e

8.6 10.3 10.5 12.2
1.7
2.4
Total Yield
28.6 35.8
4.8 14.5
ANGULAR DISTRIBUTIONS IN THE DECAY
...
PHYSICAL REVIEW D
79,
031102(R) (2009)
RAPID COMMUNICATIONS
031102-5
combinatorial background using the same sideband
samples as for the
cos

K
fit. The correlated leptons from
B
!
D
ðÞ
‘
,
D
!
K
ðÞ
‘
give rise to an
m
ES
-dependent
peak in the combinatorial background at
cos

>
0
:
7
, and
we consider this correlation in our study of systematic
errors. No such correlation is observed for
cos

K
.
We test our fits using the large sample of vetoed char-
monium events. The branching fractions (BF) and
K

polarization for
B
!
J=
c
K

are well known [
10
,
13
], and
A
FB
is expected to be zero. The results of the fits to the six
final states are all consistent with expected values (see
Table
II
). We further test our methodology by performing
the
m
ES
and
cos

fits on a sample of
B
þ
!
K
þ
þ

decays. The results are given in Table
III
and are consistent
with negligible forward-backward asymmetry, as expected
in the SM and most new physics models [
14
].
We validate the fit model by performing ensembles of
fits to datasets with events drawn from simulated signal and
background event samples. The input SM values of
F
L
and
A
FB
are reproduced with the expected statistical errors. A
few percent of the fits do not converge due to small signal
yields. We have also performed fits using signal events
generated with widely varying values of
C
eff
7
,
C
eff
9
, and
C
eff
10
covering the physically allowed regions of
F
L
and
A
FB
,
and find minimal bias in our fits.
The systematic errors on the fitted values of
F
L
and
A
FB
are summarized in Table
IV
. The uncertainties in the fitted
signal yields
N
S
, due to variations in the ARGUS shape in
the
m
ES
fits, are propagated into the angular fits. The errors
on the fitted
F
L
values are propagated into the
A
FB
fits.
We vary the combinatorial background shapes by dividing
the sideband sample into two disjoint regions in
m
ES
.We
vary the signal model using simulated events generated
with different form factors [
5
,
15
], and with a range of
values of
C
eff
7
,
C
eff
9
, and
C
eff
10
, to determine an average fit
bias. Finally, the modeling of misreconstructed signal
events is constrained by the fits to the charmonium samples
(Table
II
), where it is the largest systematic uncertainty.
The final fits to the
K

þ

samples are shown in Fig.
2
.
The results for
F
L
and
A
FB
are given in Table
III
and are
shown in Fig.
3
. In the low
q
2
region, where we expect
TABLE II. Results for the
B
!
J=
c
K

control samples.
BF
are the differences between the measured branching fractions
and the world average value [
10
]. The previously measured
F
L
¼
0
:
56

0
:
01
[
13
], and the expected
A
FB
¼
0
.
Mode
BF
(
10

3
)
F
L
A
FB
K
þ

0

þ


þ
0
:
09

0
:
12 0
:
54

0
:
03

0
:
04

0
:
05
K
0
S

þ

þ


þ
0
:
02

0
:
11 0
:
55

0
:
02
þ
0
:
00

0
:
05
K
þ



þ



0
:
03

0
:
07 0
:
56

0
:
02

0
:
02

0
:
02
K
þ

0
e
þ
e

þ
0
:
16

0
:
10 0
:
54

0
:
03
þ
0
:
02

0
:
03
K
0
S

þ
e
þ
e

þ
0
:
07

0
:
10 0
:
55

0
:
02

0
:
02

0
:
04
K
þ


e
þ
e

þ
0
:
02

0
:
07 0
:
56

0
:
02
þ
0
:
01

0
:
02
TABLE III. Results for the fits to the
K‘
þ

and
K

þ

samples.
N
S
is the number of signal events in the
m
ES
fit. The
quoted errors are statistical only.
Decay
q
2
N
S
F
L
A
FB
K‘
þ

low
26
:
0

5
:
7
þ
0
:
04
þ
0
:
16

0
:
24
high
26
:
5

6
:
7
þ
0
:
20
þ
0
:
14

0
:
22
K

þ

low
27
:
2

6
:
30
:
35

0
:
16
þ
0
:
24
þ
0
:
18

0
:
23
high
36
:
6

9
:
60
:
71
þ
0
:
20

0
:
22
þ
0
:
76
þ
0
:
52

0
:
32
TABLE IV. Systematic errors on the measurements of
F
L
and
A
FB
in the
K

þ

samples.
Source of error
F
L
A
FB
low
q
2
high
q
2
low
q
2
high
q
2
m
ES
fit yields
0.001 0.016 0.003 0.002
F
L
fit error
0.025 0.022
Background shape
0.011 0.008 0.017 0.021
Signal model
0.036 0.034 0.030 0.038
Fit bias
0.012 0.020 0.023 0.052
Misreconstructed signal 0.010 0.010 0.020 0.020
Total
0.041 0.044 0.052 0.074
]
2
mES [GeV/c
5.2
5.22
5.24
5.26
5.28
10
20
(b)
(b)
)
K
θ
cos(
-1
-0.5
0
0.5
1
Events / ( 0.2 )
0
5
10
(c)
(c)
)
K
θ
cos(
-1
-0.5
0
0.5
1
0
10
20
(d)
)
l
θ
cos(
-1
-0.5
0
0.5
1
5
10
15
20
(f)
)
l
θ
cos(
-1
-0.5
0
0.5
1
Events / ( 0.2 )
5
10
(e)
]
2
mES [GeV/c
5.2
5.22
5.24
5.26
5.28
)
2
Events / ( 0.003 GeV/c
5
10
15
(a)
FIG. 2 (color online).
K

þ

fits: (a) low
q
2
m
ES
, (b) high
q
2
m
ES
, (c) low
q
2
cos

K
, (d) high
q
2
cos

K
, (e) low
q
2
cos

,
(f) high
q
2
cos

; with combinatorial (dotted line) and peaking
(long dashed line) background, signal (short dashed line) and
total (solid line) fit distributions superimposed on the data points.
B. AUBERT
et al.
PHYSICAL REVIEW D
79,
031102(R) (2009)
RAPID COMMUNICATIONS
031102-6
A
FB

0
:
03
and
F
L

0
:
63
from the SM, we measure
A
FB
¼
0
:
24
þ
0
:
18

0
:
23

0
:
05
and
F
L
¼
0
:
35

0
:
16

0
:
04
,
where the first error is statistical and the second is system-
atic. In the high
q
2
region, the SM expectation is
A
FB

0
:
38
and
F
L

0
:
40
, and we measure
A
FB
¼
0
:
76
þ
0
:
52

0
:
32

0
:
07
and
F
L
¼
0
:
71
þ
0
:
20

0
:
22

0
:
04
, with a signal yield of
36
:
6

9
:
6
events. Theoretical uncertainties on the ex-
pected SM
F
L
and
A
FB
values are generally difficult to
characterize in the high
q
2
region, and although under
better control for
1
<q
2
<
6 GeV
2
=c
4
, the extension of
our low
q
2
region below
1 GeV
2
=c
4
makes estimates of
uncertainties there difficult also. The quoted values are
obtained using our implementation of the physics models
described in [
4
,
15
], corresponding to the SM curves in
Fig.
3
.
The expected SM value of
C
eff
10
at next-to-next-to-
leading logarithmic (NNLL) order is
C
eff
10
¼
4
:
43
[
16
].
A more recent NNLL calculation which evaluates contri-
butions from the full set of seven form factors gives
C
eff
10
¼

4
:
13
[
17
]. The magnitude of possible contributions from
new physics to
C
10
can be constrained if
A
FB
>
0
at high
q
2
. By combining such a constraint on
A
FB
with inclusive
b
!
s‘
þ

branching fraction results, an upper bound of
j
C
NP
10
j
&
7
can be obtained, improving on an upper bound
derived solely from branching fraction results of
j
C
NP
10
j
&
10
[
18
]. Our results are consistent with measurements by
Belle [
19
], and replace the earlier
BABAR
results in which
only a lower limit on
A
FB
was set in the low
q
2
region
[
20
].
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 (USA), NSERC
(Canada), CEA and CNRS-IN2P3 (France), BMBF and
DFG (Germany), INFN (Italy), FOM (The Netherlands),
NFR (Norway), MES (Russia), MEC (Spain), and STFC
(United Kingdom). Individuals have received support from
the Marie Curie EIF (European Union) and the A. P. Sloan
Foundation.
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FB
A
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
1
1.2
(a)
(2S)
ψ
ψ
J/
]
4
/c
2
[GeV
2
q
02468101214161820
L
F
0
0.2
0.4
0.6
0.8
1
(b)
(2S)
ψ
ψ
J/
FIG. 3 (color online). Plots of our results for (a)
A
FB
and
(b)
F
L
for the decay
B
!
K

þ

showing comparisons with
SM (solid line);
C
eff
7
¼
C
eff
7
(long dashed line);
C
eff
9
C
eff
10
¼

C
eff
9
C
eff
10
(short dashed line);
C
eff
7
¼
C
eff
7
,
C
eff
9
C
eff
10
¼

C
eff
9
C
eff
10
(dash-dotted line). Statistical and systematic errors
are added in quadrature. Expected
F
L
values integrated over
each
q
2
region are also shown. The
F
L
curves with
C
eff
9
C
eff
¼

C
eff
9
C
eff
10
are nearly identical to the two curves shown.
ANGULAR DISTRIBUTIONS IN THE DECAY
...
PHYSICAL REVIEW D
79,
031102(R) (2009)
RAPID COMMUNICATIONS
031102-7
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B. AUBERT
et al.
PHYSICAL REVIEW D
79,
031102(R) (2009)
RAPID COMMUNICATIONS
031102-8