of 16
Measurement of angular asymmetries in the decays
B
K

þ
J. P. Lees,
1
V. Poireau,
1
V. Tisserand,
1
E. Grauges,
2
A. Palano,
3a,3b
G. Eigen,
4
B. Stugu,
4
D. N. Brown,
5
L. T. Kerth,
5
Yu. G. Kolomensky,
5
M. J. Lee,
5
G. Lynch,
5
H. Koch,
6
T. Schroeder,
6
C. Hearty,
7
T. S. Mattison,
7
J. A. McKenna,
7
R. Y. So,
7
A. Khan,
8
V. E. Blinov,
9a,9b,9c
A. R. Buzykaev,
9a
V. P. Druzhinin,
9a,9b
V. B. Golubev,
9a,9b
E. A. Kravchenko,
9a,9b
A. P. Onuchin,
9a,9b,9c
S. I. Serednyakov,
9a,9b
Yu. I. Skovpen,
9a,9b
E. P. Solodov,
9a,9b
K. Yu. Todyshev,
9a,9b
A. J. Lankford,
10
B. Dey,
11
J. W. Gary,
11
O. Long,
11
M. Franco Sevilla,
12
T. M. Hong,
12
D. Kovalskyi,
12
J. D. Richman,
12
C. A. West,
12
A. M. Eisner,
13
W. S. Lockman,
13
W. Panduro Vazquez,
13
B. A. Schumm,
13
A. Seiden,
13
D. S. Chao,
14
C. H. Cheng,
14
B. Echenard,
14
K. T. Flood,
14
D. G. Hitlin,
14
T. S. Miyashita,
14
P. Ongmongkolkul,
14
F. C. Porter,
14
M. Röhrken,
14
R. Andreassen,
15
Z. Huard,
15
B. T. Meadows,
15
B. G. Pushpawela,
15
M. D. Sokoloff,
15
L. Sun,
15
P. C. Bloom,
16
W. T. Ford,
16
A. Gaz,
16
J. G. Smith,
16
S. R. Wagner,
16
R. Ayad,
17
,
W. H. Toki,
17
B. Spaan,
18
D. Bernard,
19
M. Verderi,
19
S. Playfer,
20
D. Bettoni,
21a
C. Bozzi,
21a
R. Calabrese,
21a,21b
G. Cibinetto,
21a,21b
E. Fioravanti,
21a,21b
I. Garzia,
21a,21b
E. Luppi,
21a,21b
L. Piemontese,
21a
V. Santoro,
21a
A. Calcaterra,
22
R. de Sangro,
22
G. Finocchiaro,
22
S. Martellotti,
22
P. Patteri,
22
I. M. Peruzzi,
22
M. Piccolo,
22
A. Zallo,
22
R. Contri,
23a,23b
M. R. Monge,
23a,23b
S. Passaggio,
23a
C. Patrignani,
23a,23b
B. Bhuyan,
24
V. Prasad,
24
A. Adametz,
25
U. Uwer,
25
H. M. Lacker,
26
U. Mallik,
27
C. Chen,
28
J. Cochran,
28
S. Prell,
28
H. Ahmed,
29
A. V. Gritsan,
30
N. Arnaud,
31
M. Davier,
31
D. Derkach,
31
G. Grosdidier,
31
F. Le Diberder,
31
A. M. Lutz,
31
B. Malaescu,
31
,
P. Roudeau,
31
A. Stocchi,
31
G. Wormser,
31
D. J. Lange,
32
D. M. Wright,
32
J. P. Coleman,
33
J. R. Fry,
33
E. Gabathuler,
33
D. E. Hutchcroft,
33
D. J. Payne,
33
C. Touramanis,
33
A. J. Bevan,
34
F. Di Lodovico,
34
R. Sacco,
34
G. Cowan,
35
D. N. Brown,
36
C. L. Davis,
36
A. G. Denig,
37
M. Fritsch,
37
W. Gradl,
37
K. Griessinger,
37
A. Hafner,
37
K. R. Schubert,
37
R. J. Barlow,
38
G. D. Lafferty,
38
R. Cenci,
39
B. Hamilton,
39
A. Jawahery,
39
D. A. Roberts,
39
R. Cowan,
40
R. Cheaib,
41
P. M. Patel,
41
,*
S. H. Robertson,
41
N. Neri,
42a
F. Palombo,
42a,42b
L. Cremaldi,
43
R. Godang,
43
,
D. J. Summers,
43
M. Simard,
44
P. Taras,
44
G. De Nardo,
45a,45b
G. Onorato,
45a,45b
C. Sciacca,
45a,45b
G. Raven,
46
C. P. Jessop,
47
J. M. LoSecco,
47
K. Honscheid,
48
R. Kass,
48
M. Margoni,
49a,49b
M. Morandin,
49a
M. Posocco,
49a
M. Rotondo,
49a
G. Simi,
49a,49b
F. Simonetto,
49a,49b
R. Stroili,
49a,49b
S. Akar,
50
E. Ben-Haim,
50
M. Bomben,
50
G. R. Bonneaud,
50
H. Briand,
50
G. Calderini,
50
J. Chauveau,
50
Ph. Leruste,
50
G. Marchiori,
50
J. Ocariz,
50
M. Biasini,
51a,51b
E. Manoni,
51a
A. Rossi,
51a
C. Angelini,
52a,52b
G. Batignani,
52a,52b
S. Bettarini,
52a,52b
M. Carpinelli,
52a,52b
G. Casarosa,
52a,52b
M. Chrzaszcz,
52a
F. Forti,
52a,52b
M. A. Giorgi,
52a,52b
A. Lusiani,
52a,52c
B. Oberhof,
52a,52b
E. Paoloni,
52a,52b
M. Rama,
52a
G. Rizzo,
52a,52b
J. J. Walsh,
52a
D. Lopes Pegna,
53
J. Olsen,
53
A. J. S. Smith,
53
F. Anulli,
54a
R. Faccini,
54a,54b
F. Ferrarotto,
54a
F. Ferroni,
54a,54b
M. Gaspero,
54a,54b
A. Pilloni,
54a,54b
G. Piredda,
54a
C. Bünger,
55
S. Dittrich,
55
O. Grünberg,
55
M. Hess,
55
T. Leddig,
55
C. Voß,
55
R. Waldi,
55
T. Adye,
56
E. O. Olaiya,
56
F. F. Wilson,
56
S. Emery,
57
G. Vasseur,
57
D. Aston,
58
D. J. Bard,
58
C. Cartaro,
58
M. R. Convery,
58
J. Dorfan,
58
G. P. Dubois-Felsmann,
58
W. Dunwoodie,
58
M. Ebert,
58
R. C. Field,
58
B. G. Fulsom,
58
M. T. Graham,
58
C. Hast,
58
W. R. Innes,
58
P. Kim,
58
D. W. G. S. Leith,
58
S. Luitz,
58
V. Luth,
58
D. B. MacFarlane,
58
D. R. Muller,
58
H. Neal,
58
T. Pulliam,
58
B. N. Ratcliff,
58
A. Roodman,
58
R. H. Schindler,
58
A. Snyder,
58
D. Su,
58
M. K. Sullivan,
58
J. Va
vra,
58
W. J. Wisniewski,
58
H. W. Wulsin,
58
M. V. Purohit,
59
J. R. Wilson,
59
A. Randle-Conde,
60
S. J. Sekula,
60
M. Bellis,
61
P. R. Burchat,
61
E. M. T. Puccio,
61
M. S. Alam,
62
J. A. Ernst,
62
R. Gorodeisky,
63
N. Guttman,
63
D. R. Peimer,
63
A. Soffer,
63
S. M. Spanier,
64
J. L. Ritchie,
65
R. F. Schwitters,
65
J. M. Izen,
66
X. C. Lou,
66
F. Bianchi,
67a,67b
F. De Mori,
67a,67b
A. Filippi,
67a
D. Gamba,
67a,67b
L. Lanceri,
68a,68b
L. Vitale,
68a,68b
F. Martinez-Vidal,
69
A. Oyanguren,
69
J. Albert,
70
Sw. Banerjee,
70
A. Beaulieu,
70
F. U. Bernlochner,
70
H. H. F. Choi,
70
G. J. King,
70
R. Kowalewski,
70
M. J. Lewczuk,
70
T. Lueck,
70
I. M. Nugent,
70
J. M. Roney,
70
R. J. Sobie,
70
N. Tasneem,
70
T. J. Gershon,
71
P. F. Harrison,
71
T. E. Latham,
71
H. R. Band,
72
S. Dasu,
72
Y. Pan,
72
R. Prepost,
72
and S. L. Wu
72
(The
BABAR
Collaboration)
1
Laboratoire d
Annecy-le-Vieux de Physique des Particules (LAPP), Université de Savoie,
CNRS/IN2P3, 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
Dipartimento di Fisica, Università 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
Ruhr Universität Bochum, Institut für Experimentalphysik 1, D-44780 Bochum, Germany
7
University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z1
8
Brunel University, Uxbridge, Middlesex UB8 3PH, United Kingdom
9a
Budker Institute of Nuclear Physics SB RAS, Novosibirsk 630090, Russia
9b
Novosibirsk State University, Novosibirsk 630090, Russia
9c
Novosibirsk State Technical University, Novosibirsk 630092, Russia
10
University of California at Irvine, Irvine, California 92697, USA
PHYSICAL REVIEW D
93,
052015 (2016)
2470-0010
=
2016
=
93(5)
=
052015(16)
052015-1
© 2016 American Physical Society
11
University of California at Riverside, Riverside, California 92521, USA
12
University of California at Santa Barbara, Santa Barbara, California 93106, USA
13
University of California at Santa Cruz, Institute for Particle Physics, Santa Cruz, California 95064, USA
14
California Institute of Technology, Pasadena, California 91125, USA
15
University of Cincinnati, Cincinnati, Ohio 45221, USA
16
University of Colorado, Boulder, Colorado 80309, USA
17
Colorado State University, Fort Collins, Colorado 80523, USA
18
Technische Universität Dortmund, Fakultät Physik, D-44221 Dortmund, Germany
19
Laboratoire Leprince-Ringuet, Ecole Polytechnique, CNRS/IN2P3, F-91128 Palaiseau, France
20
University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom
21a
INFN Sezione di Ferrara, I-44122 Ferrara, Italy
21b
Dipartimento di Fisica e Scienze della Terra, Università di Ferrara, I-44122 Ferrara, Italy
22
INFN Laboratori Nazionali di Frascati, I-00044 Frascati, Italy
23a
INFN Sezione di Genova, I-16146 Genova, Italy
23b
Dipartimento di Fisica, Università di Genova, I-16146 Genova, Italy
24
Indian Institute of Technology Guwahati, Guwahati, Assam 781 039, India
25
Universität Heidelberg, Physikalisches Institut, D-69120 Heidelberg, Germany
26
Humboldt-Universität zu Berlin, Institut für Physik, D-12489 Berlin, Germany
27
University of Iowa, Iowa City, Iowa 52242, USA
28
Iowa State University, Ames, Iowa 50011-3160, USA
29
Physics Department, Jazan University, Jazan 22822, Kingdom of Saudi Arabia
30
Johns Hopkins University, Baltimore, Maryland 21218, USA
31
Laboratoire de l
Accélérateur Linéaire, IN2P3/CNRS et Université Paris-Sud 11,
Centre Scientifique d
Orsay, F-91898 Orsay Cedex, France
32
Lawrence Livermore National Laboratory, Livermore, California 94550, USA
33
University of Liverpool, Liverpool L69 7ZE, United Kingdom
34
Queen Mary, University of London, London E1 4NS, United Kingdom
35
University of London, Royal Holloway and Bedford New College, Egham,
Surrey TW20 0EX, United Kingdom
36
University of Louisville, Louisville, Kentucky 40292, USA
37
Johannes Gutenberg-Universität Mainz, Institut für Kernphysik, D-55099 Mainz, Germany
38
University of Manchester, Manchester M13 9PL, United Kingdom
39
University of Maryland, College Park, Maryland 20742, USA
40
Massachusetts Institute of Technology, Laboratory for Nuclear Science, Cambridge,
Massachusetts 02139, USA
41
McGill University, Montréal, Québec, Canada H3A 2T8
42a
INFN Sezione di Milano, I-20133 Milano, Italy
42b
Dipartimento di Fisica, Università di Milano, I-20133 Milano, Italy
43
University of Mississippi, University, Mississippi 38677, USA
44
Université de Montréal, Physique des Particules, Montréal, Québec, Canada H3C 3J7
45a
INFN Sezione di Napoli, I-80126 Napoli, Italy
45b
Dipartimento di Scienze Fisiche, Università di Napoli Federico II, I-80126 Napoli, Italy
46
NIKHEF, National Institute for Nuclear Physics and High Energy Physics,
NL-1009 DB Amsterdam, The Netherlands
47
University of Notre Dame, Notre Dame, Indiana 46556, USA
48
Ohio State University, Columbus, Ohio 43210, USA
49a
INFN Sezione di Padova, I-35131 Padova, Italy
49b
Dipartimento di Fisica, Università di Padova, I-35131 Padova, Italy
50
Laboratoire de Physique Nucléaire et de Hautes Energies, IN2P3/CNRS, Université Pierre et Marie
Curie-Paris6, Université Denis Diderot-Paris7, F-75252 Paris, France
51a
INFN Sezione di Perugia, I-06123 Perugia, Italy
51b
Dipartimento di Fisica, Università di Perugia, I-06123 Perugia, Italy
52a
INFN Sezione di Pisa, I-56127 Pisa, Italy
52b
Dipartimento di Fisica, Università di Pisa, I-56127 Pisa, Italy
52c
Scuola Normale Superiore di Pisa, I-56127 Pisa, Italy
53
Princeton University, Princeton, New Jersey 08544, USA
54a
INFN Sezione di Roma, I-00185 Roma, Italy
54b
Dipartimento di Fisica, Università di Roma La Sapienza, I-00185 Roma, Italy
55
Universität Rostock, D-18051 Rostock, Germany
56
Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX11 0QX, United Kingdom
J. P. LEES
et al.
PHYSICAL REVIEW D
93,
052015 (2016)
052015-2
57
CEA, Irfu, SPP, Centre de Saclay, F-91191 Gif-sur-Yvette, France
58
SLAC National Accelerator Laboratory, Stanford, California 94309 USA
59
University of South Carolina, Columbia, South Carolina 29208, USA
60
Southern Methodist University, Dallas, Texas 75275, USA
61
Stanford University, Stanford, California 94305-4060, USA
62
State University of New York, Albany, New York 12222, USA
63
Tel Aviv University, School of Physics and Astronomy, Tel Aviv 69978, Israel
64
University of Tennessee, Knoxville, Tennessee 37996, USA
65
University of Texas at Austin, Austin, Texas 78712, USA
66
University of Texas at Dallas, Richardson, Texas 75083, USA
67a
INFN Sezione di Torino, I-10125 Torino, Italy
67b
Dipartimento di Fisica, Università di Torino, I-10125 Torino, Italy
68a
INFN Sezione di Trieste, I-34127 Trieste, Italy
68b
Dipartimento di Fisica, Università di Trieste, I-34127 Trieste, Italy
69
IFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spain
70
University of Victoria, Victoria, British Columbia, Canada V8W 3P6
71
Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
72
University of Wisconsin, Madison, Wisconsin 53706, USA
(Received 1 September 2015; published 28 March 2016)
We study the lepton forward-backward asymmetry
A
FB
and the longitudinal
K

polarization
F
L
, as well
as an observable
P
2
derived from them, in the rare decays
B
K

þ
, where
þ
is either
e
þ
e
or
μ
þ
μ
, using the full sample of 471 million
B
̄
B
events collected at the
Υ
ð
4
S
Þ
resonance with the
BABAR
,
detector at the PEP-II
e
þ
e
collider. We separately fit and report results for the
K

0
ð
892
Þ
þ
and
K
ð
892
Þ
þ
final states, as well as their combination
K

þ
, in five disjoint dilepton mass-squared
bins. An angular analysis of
B
þ
K
þ
decays is presented here for the first time.
DOI:
10.1103/PhysRevD.93.052015
I. INTRODUCTION
The decays
B
K

ð
892
Þ
þ
, where
K

K
π
(here-
inafter, unless explicitly stated otherwise,
K

refers generi-
cally to the
K

ð
892
Þ
) and
þ
is either an
e
þ
e
or
μ
þ
μ
pair, arise from flavor-changing neutral-current (FCNC)
processes, which are forbidden at tree level in the Standard
Model (SM). The lowest-order SM processes contributing
to these decays are the photon penguin, the
Z
penguin and
the
W
þ
W
box diagrams shown in Fig.
1
. Their amplitudes
are expressed in terms of hadronic form factors and
perturbatively calculable effective Wilson coefficients,
C
eff
7
,
C
eff
9
and
C
eff
10
, which represent the electromagnetic
penguin diagram, and the vector part and the axial-vector
part of the linear combination of the
Z
penguin and
W
þ
W
box diagrams, respectively
[1
7]
. Non-SM physics may
add new penguin and/or box diagrams, as well as possible
contributions from new scalar, pseudoscalar, and/or tensor
currents, which can contribute at the same order as the SM
diagrams, modifying the effective Wilson coefficients from
their SM expectations
[8
17]
. An example of a non-SM
physics loop process is shown in Fig.
2
; other possible
processes could involve e.g., non-SM Higgs, charginos,
gauginos, neutralinos and/or squarks. As a function of
dilepton mass-squared
q
2
¼
m
2
þ
, the angular distribu-
tions in
B
K

þ
decays are notably sensitive to many
possible sources of new physics, with several collabora-
tions presenting results over the past few years
[18
25]
.
At any particular
q
2
value, the kinematic distribution of
the decay products of
B
K

þ
and the
CP
-conjugate
̄
B
̄
K

þ
process depends on six transversity ampli-
tudes which, neglecting
CP
-violating effects and terms of
order
m
2
and higher, can be expressed as a triply differ-
ential cross section in three angles:
θ
K
, the angle between
the
K
and the
B
directions in the
K

rest frame;
θ
, the
angle between the
þ
ð
Þ
and the
B
ð
̄
B
Þ
direction in the
þ
rest frame; and
φ
, the angle between the
þ
and
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 SM Feynman diagrams for
b
s
þ
.
*
Deceased.
Now at University of Tabuk, Tabuk 71491, Saudi Arabia.
Now at Laboratoire de Physique Nucléaire et de Hautes
Energies, IN2P3/CNRS, F-75252 Paris, France.
§
Now at University of Huddersfield, Huddersfield HD1 3DH,
United Kingdom.
Now at University of South Alabama, Mobile, Alabama
36688, USA.
Also at Università di Sassari, I-07100 Sassari, Italy.
MEASUREMENT OF ANGULAR ASYMMETRIES IN THE
...
PHYSICAL REVIEW D
93,
052015 (2016)
052015-3
K
π
decay planes in the
B
rest frame. From the distribution
of the angle
θ
K
obtained after integrating over
φ
and
θ
,we
determine the
K

longitudinal polarization fraction
F
L
using a fit to cos
θ
K
of the form
[6]
1
Γ
ð
q
2
Þ
d
Γ
d
ð
cos
θ
K
Þ
¼
3
2
F
L
ð
q
2
Þ
cos
2
θ
K
þ
3
4
ð
1
F
L
ð
q
2
ÞÞð
1
cos
2
θ
K
Þ
:
ð
1
Þ
We similarly determine the lepton forward-backward
asymmetry
A
FB
from the distribution of the angle
θ
obtained after integrating over
φ
and
θ
K
,
[6]
1
Γ
ð
q
2
Þ
d
Γ
d
ð
cos
θ
Þ
¼
3
4
F
L
ð
q
2
Þð
1
cos
2
θ
l
Þ
þ
3
8
ð
1
F
L
ð
q
2
ÞÞð
1
þ
cos
2
θ
l
Þ
þ
A
FB
ð
q
2
Þ
cos
θ
l
:
ð
2
Þ
We ignore here possible contributions from nonresonant
S-wave
B
K
π
þ
events. The rate for such events has
been shown to be consistent with zero
[26]
, with an upper
limit (68% C.L.) across the entire dilepton mass-squared
range of
<
4%
of the
B
K

ð
K
π
Þ
þ
branching frac-
tion
[21]
. The presence of an S-wave component at this
level was shown to lead to a relatively small absolute bias
on the order of 0.01 for
F
L
and
A
FB
; this small bias is
ignored here given the relatively larger magnitude of our
statistical and systematic uncertainties. Essentially no
contributions from low-mass tails of the higher
K

reso-
nances are expected in the
K

ð
892
Þ
mass region consid-
ered here.
We ignore small
q
2
-dependent theory corrections in the
large-recoil
q
2
2
GeV
2
=c
4
region given the current
experimental uncertainties on the angular observables,
which are relatively large compared to these small correc-
tions in the underlying SM theory expectations
[2]
.We
determine
F
L
and
A
FB
in the five disjoint bins of
q
2
defined
in Table
I
. We also present results in a
q
2
range
1
.
0
<q
2
0
<
6
.
0
GeV
2
=c
4
, the perturbative window away
from the
q
2
0
photon pole and the
c
̄
c
resonances at
higher
q
2
, where theory uncertainties are considered to be
under good control. An angular analysis of the decays
B
þ
K
þ
is presented here for the first time. We
additionally present results for an observable derived from
F
L
and
A
FB
,
P
2
¼ð
2
=
3
Þ
A
FB
=
ð
1
F
L
Þ
, with less
theory uncertainty, and hence greater sensitivity to non-
SM contributions, than either
F
L
or
A
FB
alone
[27,28]
.
II. EVENT SELECTION
We use a data sample of
471
million
B
̄
B
pairs,
corresponding to
424
.
2

1
.
8
fb
1
[30]
, collected at the
Υ
ð
4
S
Þ
resonance with the
BABAR
, detector
[31]
at the
PEP-II asymmetric-energy
e
þ
e
collider at the SLAC
National Accelerator Laboratory. Charged particle tracking
is provided by a five-layer silicon vertex tracker and a
40-layer drift chamber in a 1.5 T solenoidal magnetic field.
We identify electrons and photons with a CsI(Tl) electro-
magnetic calorimeter, and muons using an instrumented
magnetic flux return. We identify charged kaons using a
detector of internally reflected Cherenkov light, as well as
d
E=
d
x
information from the drift chamber. Charged tracks
other than identified
e
,
μ
and
K
candidates are treated
as pions.
We reconstruct
B
K

þ
signal events in the fol-
lowing final states (charge conjugation is implied through-
out unless explicitly noted):
(i)
B
þ
K
ð
K
0
S
π
þ
Þ
μ
þ
μ
;
(ii)
B
0
K

0
ð
K
þ
π
Þ
μ
þ
μ
;
(iii)
B
þ
K
ð
K
þ
π
0
Þ
e
þ
e
;
(iv)
B
þ
K
ð
K
0
S
π
þ
Þ
e
þ
e
;
(v)
B
0
K

0
ð
K
þ
π
Þ
e
þ
e
.
We do not include the decays
B
þ
K
ð
K
þ
π
0
Þ
μ
þ
μ
and
B
0
K

0
ð
K
0
S
π
0
Þ
þ
in our analysis. The
expected signal-to-background ratio for these final states
relative to the five chosen signal modes listed above is very
poor, with ensembles of pseudo-experiments showing that
inclusion of these extra modes would yield no additional
sensitivity.
We require
K

candidates to have an invariant mass
0
.
72
<m
ð
K
π
Þ
<
1
.
10
GeV
=c
2
. Electron and muon can-
didates are required to have momenta
p>
0
.
3
GeV
=c
in
the laboratory frame. The muon and electron misidentifi-
cation rates determined from high-purity data control
bs
q
χ
h
0
μ
+
μ
FIG. 2. Feynman diagram of a non-SM Higgs penguin process.
TABLE I. Definition of the
q
2
bins used in the analysis. The
nominal
B
and
K

invariant masses
[29]
are given by
m
B
and
m
K

, respectively.
q
2
bin
q
2
min
ð
GeV
2
=c
4
Þ
q
2
max
ð
GeV
2
=c
4
Þ
q
2
1
0.10
2.00
q
2
2
2.00
4.30
q
2
3
4.30
8.12
q
2
4
10.11
12.89
q
2
5
14.21
ð
m
B
m
K

Þ
2
q
2
0
1.00
6.00
J. P. LEES
et al.
PHYSICAL REVIEW D
93,
052015 (2016)
052015-4
samples are, respectively,
2%
and
0
.
1%
[31]
, and
backgrounds from particle misidentification are thus sig-
nificant for
B
K

μ
þ
μ
candidates only. We combine up
to three photons with an electron candidate when the
photons are consistent with bremsstrahlung from the
electron. We do not use electrons that are associated with
photon conversions to low-mass
e
þ
e
pairs. We reconstruct
K
0
S
candidates in the
π
þ
π
final state, requiring an invariant
mass consistent with the nominal
K
0
mass, and a flight
distance from the
e
þ
e
interaction point that is more
than three times the flight distance uncertainty. Neutral
pion candidates are formed from two photons with
E
γ
>
50
MeV, and an invariant mass between 115 and
155
MeV
=c
2
. In each final state, we utilize the kinematic
variables
m
ES
¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
E
2
CM
=
4
p

2
B
p
and
Δ
E
¼
E

B
E
CM
=
2
,
where
p

B
and
E

B
are the
B
momentum and energy in the
Υ
ð
4
S
Þ
center-of-mass (CM) frame, and
E
CM
is the total CM
energy. We reject events with
m
ES
<
5
.
2
GeV
=c
2
.
To characterize backgrounds from hadrons misidentified
as muons, we study
K

h

μ
candidates, where
h
is a
charged track with no particle identification requirement
applied. We additionally use a
K

e

μ
sample, where no
signal is expected because of lepton-flavor conservation, to
model the combinatorial background from two random
leptons. For both
e
þ
e
and
μ
þ
μ
modes, we veto the
J=
ψ
ð
2
.
85
<m
þ
<
3
.
18
GeV
=c
2
Þ
and
ψ
ð
2
S
Þð
3
.
59
<
m
þ
<
3
.
77
GeV
=c
2
Þ
mass regions. These vetoed events
provide high-statistics control samples of decays to final
states identical to the signal modes here that we use to
validate our fitting procedures.
Random combinations of leptons from semileptonic
B
and
D
decays are the predominant source of backgrounds.
These combinatorial backgrounds occur in both
B
̄
B
events
(
B
̄
B
backgrounds
) and
e
þ
e
q
̄
q
continuum events
(
q
̄
q
backgrounds
, where
q
¼
u
,
d
,
s
,
c
), and are sup-
pressed using eight bagged decision trees (BDTs)
[32]
trained for suppression of
(i)
B
̄
B
backgrounds in
e
þ
e
modes at low
q
2
(ii)
B
̄
B
backgrounds in
e
þ
e
modes at high
q
2
(iii)
B
̄
B
backgrounds in
μ
þ
μ
modes at low
q
2
(iv)
B
̄
B
backgrounds in
μ
þ
μ
modes at high
q
2
(v)
q
̄
q
backgrounds in
e
þ
e
modes at low
q
2
(vi)
q
̄
q
backgrounds in
e
þ
e
modes at high
q
2
(vii)
q
̄
q
backgrounds in
μ
þ
μ
modes at low
q
2
(viii)
q
̄
q
backgrounds in
μ
þ
μ
modes at high
q
2
,
where low (high)
q
2
is defined as the mass-squared region
below (above) the vetoed
J=
ψ
region. In order to treat the
K

e

μ
control sample equivalently to the
e
þ
e
and
μ
þ
μ
data sets, we similarly train four BDTs for
B
̄
B
and
q
̄
q
background suppression in the low and high
q
2
regions,
using a high-statistics sample of simulated
B
K

e

μ
events. The
μ
þ
μ
BDTs are used to characterize the
K

h

μ
data set. We draw our BDT training data sets
for both signal and combinatoric backgrounds from simu-
lated events. We find good agreement in the distribution of
BDT outputs between simulated events and the charmo-
nium control samples; we find similarly good agreement
between data and simulation in the purely combinatoric
background off-resonance data.
Each of the above BDTs uses a subset of the following
observables as its input parameters:
(i) the
B
candidate
Δ
E
(ii) the ratio of Fox-Wolfram moments
R
2
[33]
and the
ratio of the second-to-zeroth angular moments of the
energy flow
L
2
=L
0
[34]
, both of which are event
shape parameters calculated using charged and
neutral particles in the CM frame
(iii) the mass and
Δ
E
of the other
B
meson in the event
computed in the laboratory frame by summing the
momenta and energies of all charged particles and
photons that are not used to reconstruct the signal
candidate
(iv) the magnitude of the total transverse momentum
of the event
(v) the
χ
2
probability of the vertex fitted from all the B
candidate tracks
(vi) the cosines of four angles, all defined in the CM
frame: the angle between the
B
candidate momen-
tum and the beam axis, the angle between the event
thrust axis and the beam axis, the angle between the
thrust axis of the rest of the event and the beam axis,
and the angle between the event thrust axis and the
thrust axis of the rest of the event. The thrust
T
of an
event comprised of
N
particles, or analogously for a
subset of particles in an event, is defined as
[35]
T
¼
P
N
i
¼
1
j
~
p
i
·
ˆ
t
j
P
N
i
¼
1
j
~
p
i
j
;
where the thrust axis
ˆ
t
maximizes the magnitude of
the thrust
T
, up to a two-fold ambiguity in direction
(forward and backward are equivalent).
As an example, Fig.
3
shows histograms of BDT output
normalized to unit area for simulated
K
0
S
π
þ
e
þ
e
and
K
0
S
π
þ
μ
þ
μ
signal and combinatorial background events
in the
q
2
1
bin. The BDT outputs for the other final states and
q
2
bins demonstrate similar discriminating power.
Backgrounds from
B
D
ð
K
ðÞ
π
Þ
π
hadronic decays
occur if two hadrons are misidentified as leptons, which
happens at a non-negligible rate only in dimuon final
states. These events are vetoed by requiring the invariant
mass of the
K

π
system to be outside the range
1
.
84
1
.
90
GeV
=c
2
after assigning the pion mass hypothesis to
MEASUREMENT OF ANGULAR ASYMMETRIES IN THE
...
PHYSICAL REVIEW D
93,
052015 (2016)
052015-5
the muon candidates. Residual muon misidentification
backgrounds remaining after this selection are character-
ized using the
K

h

μ
data set.
For the last steps in the event selection, we adopt (a) the
Δ
E
regions used in our recent related analyses of rates and
rate asymmetries in exclusive
B
K
ðÞ
þ
and inclusive
B
X
s
þ
decays
[26,36]
,
0
.
1
ð
0
.
05
Þ
<
Δ
E<
0
.
05
GeV for
e
þ
e
(
μ
þ
μ
) modes and (b) the
q
̄
q
BDT
>
0
.
4
selection used in the inclusive
B
X
s
þ
analysis
[26]
. After all other selection criteria have been imposed,
this
q
̄
q
BDT selection removes
70%
90%
of
q
̄
q
back-
ground events, with a concommitant decrease of
6%
10%
in signal efficiencies.
At the conclusion of the event selection process, some
events have multiple reconstructed
B
candidates which
typically differ by one charged or neutral pion in the
hadronic system. The signal candidate multiplicity aver-
aged across final states and
q
2
bins is
1
.
4
(
1
.
1
)
candidates per event in dielectron (dimuon) modes. In
events with multiple signal candidates, the candidate with
the
Δ
E
value closest to zero is selected.
III. ANGULAR OBSERVABLES
EXTRACTION METHOD
A. General strategy
We extract the angular observables
F
L
and
A
FB
from the
data using a series of likelihood (LH) fits which proceed in
several steps:
(1) In each
q
2
bin, for each of the five signal modes
separately and using the full
m
ES
>
5
.
2
GeV
=c
2
data set, an initial unbinned maximum LH fit of
m
ES
,
m
ð
K
π
Þ
and a likelihood ratio [
L
R
, defined
below in Eq.
(3)
] that discriminates against random
combinatorial
B
̄
B
backgrounds is performed. After
this first fit, all normalizations and the
m
ES
-
dependent,
m
ð
K
π
Þ
-dependent and
L
R
-dependent
probability density function (pdf) shapes are fixed.
(2) Second, in each
q
2
bin and for each of the five signal
modes separately,
m
ES
,
m
ð
K
π
Þ
and
L
R
pdfs and
normalizations are defined for
m
ES
>
5
.
27
GeV
=c
2
events (the
m
ES
angular fit region
) using the
results of the prior three-dimensional fits. Only
BDT Output
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
d(BDT) / 0.01
-4
10
-3
10
-2
10
-1
10
BDT Output
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
d(BDT) / 0.01
-4
10
-3
10
-2
10
-1
10
BDT Output
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
d(BDT) / 0.01
-3
10
-2
10
-1
10
BDT Output
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
d(BDT) / 0.01
-3
10
-2
10
-1
10
FIG. 3. BDT outputs normalized to unit area for simulated signal (solid blue line) and background (red dashed line)
q
2
1
events.
J. P. LEES
et al.
PHYSICAL REVIEW D
93,
052015 (2016)
052015-6
m
ES
angular fit region events and pdfs are sub-
sequently used in the fits for
F
L
and
A
FB
.
(3) Next, cos
θ
K
is added as a fourth dimension to the
likelihood function, in addition to
m
ES
,
m
ð
K
π
Þ
and
L
R
, and four-dimensional likelihoods with
F
L
as the
only free parameter are defined for
m
ES
angular fit
region events. As above, each
q
2
bin and each
of the five signal modes has its own separate
four-dimensional LH function. However, a common
value of
F
L
is shared among all of the four-
dimensional LH functions in any given
q
2
bin.
Thus, by combining LH functions from multiple
final states, it becomes possible to extract
F
L
and
A
FB
for arbitrary combinations of the five final
states here. In particular, we quote results using three
different sets of our five signal modes:
(a)
B
þ
K
þ
, comprised of
(i)
B
þ
K
ð
K
0
S
π
þ
Þ
μ
þ
μ
,
(ii)
B
þ
K
ð
K
þ
π
0
Þ
e
þ
e
,
(iii)
B
þ
K
ð
K
0
S
π
þ
Þ
e
þ
e
,
(b)
B
0
K

0
þ
, comprised of
(i)
B
0
K

0
ð
K
þ
π
Þ
μ
þ
μ
,
(ii)
B
0
K

0
ð
K
þ
π
Þ
e
þ
e
.
(c)
B
K

þ
, comprised of
(i)
B
þ
K
ð
K
0
S
π
þ
Þ
μ
þ
μ
,
(ii)
B
0
K

0
ð
K
þ
π
Þ
μ
þ
μ
,
(iii)
B
þ
K
ð
K
þ
π
0
Þ
e
þ
e
,
(iv)
B
þ
K
ð
K
0
S
π
þ
Þ
e
þ
e
,
(v)
B
0
K

0
ð
K
þ
π
Þ
e
þ
e
.
(4) In the final step, we use the fitted value of
F
L
from
the previous fit step as input to a similar four-
dimensional fit for
A
FB
, in which cos
θ
replaces
cos
θ
K
as the fourth dimension in the LH function, in
addition to
m
ES
,
m
ð
K
π
Þ
and
L
R
.
As mentioned above, we define a likelihood ratio
L
R
as
the third dimension in the initial fit,
L
R
P
sig
P
sig
þ
P
bkg
;
ð
3
Þ
where
P
sig
and
P
bkg
are probabilities calculated from the
B
̄
B
BDT output for signal and
B
̄
B
backgrounds, respec-
tively.
P
sig
and
P
bkg
are modeled using several different
functional forms depending on
q
2
bin and final state. After
the multiple candidate selection described at the conclusion
of the preceding section and before fitting a data set, a final
requirement of
L
R
>
0
.
6
is made. This drastically reduces
the number of background events at the cost of a relatively
small loss, dependent on final state and
q
2
bin, in signal
efficiency. Table
II
shows final signal efficiencies in the
m
ES
angular fit region for each final state and
q
2
bin.
The initial three-dimensional fit is an unbinned maxi-
mum likelihood fit with minimization performed by
MINUIT
[37]
. Each angular result is subsequently deter-
mined by direct construction and examination of the
negative log-likelihood curves resulting from a scan across
the entire
F
L
or
A
FB
parameter space, including unphysical
regions which provide a statistically consistent description
of the data.
B. Event classes
We characterize
m
ES
,
m
ð
K
π
Þ
,
L
R
, cos
θ
K
and cos
θ
probability density functions in our likelihood fit model for
several classes of events:
(i) correctly reconstructed (
true
) signal events;
(ii) misreconstructed (
cross-feed
) signal events, from
both the five signal modes as well as from other
b
s
þ
decays;
(iii) random combinatorial backgrounds;
(iv) backgrounds from
J=
ψ
and
ψ
ð
2
S
Þ
decays which
escape the dilepton mass veto windows;
(v) for the
μ
þ
μ
modes only, backgrounds from had-
ronic decays in which there is muon misidentifica-
tion of hadrons (this background is negligible in
e
þ
e
final states due to the much smaller, relative to
muons, electron misidentification probability).
1. True and cross-feed signal events
True signal events have all final state daughter particles
correctly reconstructed. The true signal normalization for
each final state in each
q
2
bin is a free parameter in the initial
three-dimensional fits. For each final state, the
m
ES
signal
pdf is parameterized as a Gaussian with a mean and width
fixed to values obtained from a fit to the vetoed
J=
ψ
data
events in the same final state. Similarly, for the resonant
K

line shape in each final state, the signal
m
ð
K
π
Þ
pdf uses a
relativistic Breit-Wigner (BW) with width and pole mass
fixed from the vetoed
J=
ψ
data events in the same final state.
True signal
L
R
pdfs for each final state in each
q
2
bin are
derived from simulated signal events, and are parameterized
using histograms. There is good agreement between the
L
R
shapes derived from simulated events and the
L
R
shapes
observed in the charmonium control sample data.
TABLE II. Final signal efficiencies in the
m
ES
angular fit region
by mode and
q
2
bin.
Mode
q
2
0
q
2
1
q
2
2
q
2
3
q
2
4
q
2
5
K
0
S
π
þ
μ
þ
μ
0.14 0.13 0.15 0.15 0.14 0.11
K
þ
π
μ
þ
μ
0.18 0.15 0.19 0.20 0.19 0.16
K
þ
π
0
e
þ
e
0.12 0.11 0.12 0.12 0.11 0.08
K
0
S
π
þ
e
þ
e
0.18 0.16 0.19 0.17 0.15 0.11
K
þ
π
e
þ
e
0.23 0.20 0.23 0.23 0.21 0.15
MEASUREMENT OF ANGULAR ASYMMETRIES IN THE
...
PHYSICAL REVIEW D
93,
052015 (2016)
052015-7
Equations
(1)
and
(2)
, showing the dependence of
F
L
and
A
FB
on cos
θ
K
and cos
θ
respectively, are purely
theoretical expressions which must be modified to take into
account the experimental acceptance. We characterize the
angular acceptance using simulated signal events to obtain
parameterizations of the cos
θ
K
and cos
θ
efficiency for
each final state in each
q
2
bin.
Signal cross feed typically occurs when a low-energy
π

or
π
0
is swapped, added or removed from the set of daughter
particles used to reconstruct an otherwise correctly recon-
structed signal candidate. There can be self-cross-feed within
one signal mode, feed-across between two different signal
modes with the same final state particle multiplicity, or (up)
down cross feed from (lower) higher multiplicity
s
þ
modes. Simulated signal events are used to model these
types of decays, with normalization relative to the fitted true
signal yield. Averaged over the five signal modes and
disjoint
q
2
bins
q
2
1
q
2
5
, the fraction of cross-feed events
relative to correctly reconstructed signal decays is
0
.
4
for events in the
m
ES
>
5
.
27
GeV
=c
2
angular fit region.
Generator-level variations in the production of cross-feed
events are considered as part of the study of systematic
uncertainties related to the modeling of signal decays.
2. Combinatorial backgrounds
The largest source of background is from semileptonic
B
and
D
decays, where leptons from two such decays and a
K

candidate combine to form a
B
candidate. The
m
ES
pdf
for the combinatorial background is modeled with a
kinematic threshold function
[38]
whose single shape
parameter is a free parameter in the fits. Events in the
lepton-flavor violating (LFV) modes
K

e

μ
, which are
forbidden in the SM and for which stringent experimental
limits exist
[29]
, are reconstructed and selected analogously
to the final event selection in order to characterize the
combinatorial background
m
ð
K
π
Þ
and
L
R
pdfs. We obtain
the angular pdfs for the combinatorial backgrounds in the
m
ES
angular fit region using events in the
m
ES
sideband
region
5
.
2
<m
ES
<
5
.
27
GeV
=c
2
. The LFV events addi-
tionally provide an alternative model for the combinatorial
angular pdfs, which is used in the characterization of
systematic uncertainties in the angular fits.
3. Charmonium and other physics backgrounds
Some misreconstructed charmonium events escape
the charmonium vetoes and appear in our
q
2
bins.
This typically occurs through bremsstrahlung by elec-
trons, followed by incorrect recovery of the missing
energy. The pdfs for this residual charmonium back-
ground are modeled using simulated charmonium signal
events.
In order to use the vetoed charmonium events as a data
control sample, we construct a set of pdfs equivalent to
those used in the
B
K

þ
angular fits but which are
appropriate for
J=
ψ
and
ψ
ð
2
S
Þ
events inside, rather than
outside, their respective vetoed mass windows. The BDTs
in the low (high)
q
2
bin are used to calculate
L
R
for events
within the
J=
ψ
(
ψ
ð
2
S
Þ
) mass window.
Gamma conversions from
B
K

γ
events and Dalitz
decays
ð
π
0
;
η
Þ
e
þ
e
γ
of hadronic
B
decay daughters give
rise to small backgrounds in
q
2
1
. However, since less than a
single event from these sources is expected in the final
angular fits, we do not include them in our fit model.
4. Muon misidentification backgrounds
In dimuon modes only, some events pass the final
selection but have misidentified hadron(s) taking the place
of one or both muon candidates. To model these events, we
follow a procedure similar to that described in Ref.
[39]
by selecting a sample of
K

μ

h
events requiring that the
μ

candidate be identified as a muon and the
h
candidate
fail identification as an electron. Using weights obtained
from data control samples where a charged particle
s
species can be identified with high precision and accuracy
without using particle identification information, the
K

μ

h
data set is weighted event-by-event to characterize
expected contributions in our fits due to the presence of
misidentified muon candidates. The pdfs for these events
are implemented as a sum of weighted histograms, with
normalizations obtained by construction directly from the
weighted control sample data.
C. Initial
m
ES
,
m
ð
K
π
Þ
and
L
R
fit
As discussed above, the initial three-dimensional fits to
m
ES
,
m
ð
K
π
Þ
and
L
R
are done using events in the full
m
ES
>
5
.
2
GeV
=c
2
range; each final state in each
q
2
bin is
separately fit in order to establish the normalizations and
pdf shapes subsequently used in extracting the angular
observables from the
m
ES
>
5
.
27
GeV
=c
2
angular fit
region. Table
III
gives the resulting fitted signal yields
along with statistical uncertainties for the three different
combinations of particular final states for which the angular
TABLE III. Fitted signal yields with statistical uncertainties.
Mode
q
2
0
q
2
1
q
2
2
q
2
3
q
2
4
q
2
5
B
K

þ
40
.
8

8
.
431
.
7

7
.
111
.
9

5
.
521
.
3

8
.
531
.
9

9
.
233
.
2

7
.
8
B
þ
K
þ
17
.
7

5
.
28
.
7

4
.
13
.
8

4
.
07
.
7

5
.
69
.
0

4
.
89
.
4

4
.
2
B
0
K

0
þ
23
.
1

6
.
622
.
9

5
.
88
.
1

3
.
813
.
7

6
.
422
.
8

7
.
823
.
8

6
.
6
J. P. LEES
et al.
PHYSICAL REVIEW D
93,
052015 (2016)
052015-8