arXiv:1508.07960v1 [hep-ex] 31 Aug 2015
B
A
B
AR
-PUB-15/002
SLAC-PUB-16384
Measurement of Angular Asymmetries in the Decays
B
→
K
∗
ℓ
+
ℓ
−
J. P. Lees, V. Poireau, and V. Tisserand
Laboratoire d’Annecy-le-Vieux de Physique des Particules
(LAPP),
Universit ́e de Savoie, CNRS/IN2P3, F-74941 Annecy-Le-Vie
ux, France
E. Grauges
Universitat de Barcelona, Facultat de Fisica, Departament
ECM, E-08028 Barcelona, Spain
A. Palano
ab
INFN Sezione di Bari
a
; Dipartimento di Fisica, Universit`a di Bari
b
, I-70126 Bari, Italy
G. Eigen and B. Stugu
University of Bergen, Institute of Physics, N-5007 Bergen,
Norway
D. N. Brown, L. T. Kerth, Yu. G. Kolomensky, M. J. Lee, and G. Lyn
ch
Lawrence Berkeley National Laboratory and University of Ca
lifornia, Berkeley, California 94720, USA
H. Koch and T. Schroeder
Ruhr Universit ̈at Bochum, Institut f ̈ur Experimentalphys
ik 1, D-44780 Bochum, Germany
C. Hearty, T. S. Mattison, J. A. McKenna, and R. Y. So
University of British Columbia, Vancouver, British Columb
ia, Canada V6T 1Z1
A. Khan
Brunel University, Uxbridge, Middlesex UB8 3PH, United Kin
gdom
V. E. Blinov
abc
, A. R. Buzykaev
a
, V. P. Druzhinin
ab
, V. B. Golubev
ab
, E. A. Kravchenko
ab
,
A. P. Onuchin
abc
, S. I. Serednyakov
ab
, Yu. I. Skovpen
ab
, E. P. Solodov
ab
, and K. Yu. Todyshev
ab
Budker Institute of Nuclear Physics SB RAS, Novosibirsk 630
090
a
,
Novosibirsk State University, Novosibirsk 630090
b
,
Novosibirsk State Technical University, Novosibirsk 6300
92
c
, Russia
A. J. Lankford
University of California at Irvine, Irvine, California 926
97, USA
B. Dey, J. W. Gary, and O. Long
University of California at Riverside, Riverside, Califor
nia 92521, USA
M. Franco Sevilla, T. M. Hong, D. Kovalskyi, J. D. Richman, and C. A. W
est
University of California at Santa Barbara, Santa Barbara, C
alifornia 93106, USA
A. M. Eisner, W. S. Lockman, W. Panduro Vazquez, B. A. Schumm, a
nd A. Seiden
University of California at Santa Cruz, Institute for Parti
cle Physics, Santa Cruz, California 95064, USA
D. S. Chao, C. H. Cheng, B. Echenard, K. T. Flood, D. G. Hitlin,
T. S. Miyashita, P. Ongmongkolkul, F. C. Porter, and M. R ̈ohrken
California Institute of Technology, Pasadena, California
91125, USA
R. Andreassen, Z. Huard, B. T. Meadows, B. G. Pushpawela, M. D.
Sokoloff, and L. Sun
University of Cincinnati, Cincinnati, Ohio 45221, USA
2
P. C. Bloom, W. T. Ford, A. Gaz, J. G. Smith, and S. R. Wagner
University of Colorado, Boulder, Colorado 80309, USA
R. Ayad
∗
and W. H. Toki
Colorado State University, Fort Collins, Colorado 80523, U
SA
B. Spaan
Technische Universit ̈at Dortmund, Fakult ̈at Physik, D-44
221 Dortmund, Germany
D. Bernard and M. Verderi
Laboratoire Leprince-Ringuet, Ecole Polytechnique, CNRS
/IN2P3, F-91128 Palaiseau, France
S. Playfer
University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom
D. Bettoni
a
, C. Bozzi
a
, R. Calabrese
ab
, G. Cibinetto
ab
, E. Fioravanti
ab
,
I. Garzia
ab
, E. Luppi
ab
, L. Piemontese
a
, and V. Santoro
a
INFN Sezione di Ferrara
a
; Dipartimento di Fisica e Scienze della Terra, Universit`a
di Ferrara
b
, I-44122 Ferrara, Italy
A. Calcaterra, R. de Sangro, G. Finocchiaro, S. Martellotti, P. Pat
teri, I. M. Peruzzi, M. Piccolo, and A. Zallo
INFN Laboratori Nazionali di Frascati, I-00044 Frascati, I
taly
R. Contri
ab
, M. R. Monge
ab
, S. Passaggio
a
, and C. Patrignani
ab
INFN Sezione di Genova
a
; Dipartimento di Fisica, Universit`a di Genova
b
, I-16146 Genova, Italy
B. Bhuyan and V. Prasad
Indian Institute of Technology Guwahati, Guwahati, Assam,
781 039, India
A. Adametz and U. Uwer
Universit ̈at Heidelberg, Physikalisches Institut, D-691
20 Heidelberg, Germany
H. M. Lacker
Humboldt-Universit ̈at zu Berlin, Institut f ̈ur Physik, D-
12489 Berlin, Germany
U. Mallik
University of Iowa, Iowa City, Iowa 52242, USA
C. Chen, J. Cochran, and S. Prell
Iowa State University, Ames, Iowa 50011-3160, USA
H. Ahmed
Physics Department, Jazan University, Jazan 22822, Kingdo
m of Saudi Arabia
A. V. Gritsan
Johns Hopkins University, Baltimore, Maryland 21218, USA
N. Arnaud, M. Davier, D. Derkach, G. Grosdidier, F. Le Diberder,
A. M. Lutz, B. Malaescu,
†
P. Roudeau, A. Stocchi, and G. Wormser
Laboratoire de l’Acc ́el ́erateur Lin ́eaire, IN2P3/CNRS et
Universit ́e Paris-Sud 11,
Centre Scientifique d’Orsay, F-91898 Orsay Cedex, France
D. J. Lange and D. M. Wright
Lawrence Livermore National Laboratory, Livermore, Calif
ornia 94550, USA
J. P. Coleman, J. R. Fry, E. Gabathuler, D. E. Hutchcroft, D. J. P
ayne, and C. Touramanis
University of Liverpool, Liverpool L69 7ZE, United Kingdom
A. J. Bevan, F. Di Lodovico, and R. Sacco
3
Queen Mary, University of London, London, E1 4NS, United Kin
gdom
G. Cowan
University of London, Royal Holloway and Bedford New Colleg
e, Egham, Surrey TW20 0EX, United Kingdom
D. N. Brown and C. L. Davis
University of Louisville, Louisville, Kentucky 40292, USA
A. G. Denig, M. Fritsch, W. Gradl, K. Griessinger, A. Hafner, and K.
R. Schubert
Johannes Gutenberg-Universit ̈at Mainz, Institut f ̈ur Ker
nphysik, D-55099 Mainz, Germany
R. J. Barlow
‡
and G. D. Lafferty
University of Manchester, Manchester M13 9PL, United Kingd
om
R. Cenci, B. Hamilton, A. Jawahery, and D. A. Roberts
University of Maryland, College Park, Maryland 20742, USA
R. Cowan
Massachusetts Institute of Technology, Laboratory for Nuc
lear Science, Cambridge, Massachusetts 02139, USA
R. Cheaib, P. M. Patel,
§
and S. H. Robertson
McGill University, Montr ́eal, Qu ́ebec, Canada H3A 2T8
N. Neri
a
and F. Palombo
ab
INFN Sezione di Milano
a
; Dipartimento di Fisica, Universit`a di Milano
b
, I-20133 Milano, Italy
L. Cremaldi, R. Godang,
¶
and D. J. Summers
University of Mississippi, University, Mississippi 38677
, USA
M. Simard and P. Taras
Universit ́e de Montr ́eal, Physique des Particules, Montr ́
eal, Qu ́ebec, Canada H3C 3J7
G. De Nardo
ab
, G. Onorato
ab
, and C. Sciacca
ab
INFN Sezione di Napoli
a
; Dipartimento di Scienze Fisiche,
Universit`a di Napoli Federico II
b
, I-80126 Napoli, Italy
G. Raven
NIKHEF, National Institute for Nuclear Physics and High Ene
rgy Physics, NL-1009 DB Amsterdam, The Netherlands
C. P. Jessop and J. M. LoSecco
University of Notre Dame, Notre Dame, Indiana 46556, USA
K. Honscheid and R. Kass
Ohio State University, Columbus, Ohio 43210, USA
M. Margoni
ab
, M. Morandin
a
, M. Posocco
a
, M. Rotondo
a
, G. Simi
ab
, F. Simonetto
ab
, and R. Stroili
ab
INFN Sezione di Padova
a
; Dipartimento di Fisica, Universit`a di Padova
b
, I-35131 Padova, Italy
S. Akar, E. Ben-Haim, M. Bomben, G. R. Bonneaud, H. Briand,
G. Calderini, J. Chauveau, Ph. Leruste, G. Marchiori, and J. Ocariz
Laboratoire de Physique Nucl ́eaire et de Hautes Energies,
IN2P3/CNRS, Universit ́e Pierre et Marie Curie-Paris6,
Universit ́e Denis Diderot-Paris7, F-75252 Paris, France
M. Biasini
ab
, E. Manoni
a
, and A. Rossi
a
INFN Sezione di Perugia
a
; Dipartimento di Fisica, Universit`a di Perugia
b
, I-06123 Perugia, Italy
C. Angelini
ab
, G. Batignani
ab
, S. Bettarini
ab
, M. Carpinelli
ab
,
∗∗
G. Casarosa
ab
, M. Chrzaszcz
a
, F. Forti
ab
,
4
M. A. Giorgi
ab
, A. Lusiani
ac
, B. Oberhof
ab
, E. Paoloni
ab
, M. Rama
a
, G. Rizzo
ab
, and J. J. Walsh
a
INFN Sezione di Pisa
a
; Dipartimento di Fisica, Universit`a di Pisa
b
; Scuola Normale Superiore di Pisa
c
, I-56127 Pisa, Italy
D. Lopes Pegna, J. Olsen, and A. J. S. Smith
Princeton University, Princeton, New Jersey 08544, USA
F. Anulli
a
, R. Faccini
ab
, F. Ferrarotto
a
, F. Ferroni
ab
, M. Gaspero
ab
, A. Pilloni
ab
, and G. Piredda
a
INFN Sezione di Roma
a
; Dipartimento di Fisica,
Universit`a di Roma La Sapienza
b
, I-00185 Roma, Italy
C. B ̈unger, S. Dittrich, O. Gr ̈unberg, M. Hess, T. Leddig, C. Voß
, and R. Waldi
Universit ̈at Rostock, D-18051 Rostock, Germany
T. Adye, E. O. Olaiya, and F. F. Wilson
Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX
11 0QX, United Kingdom
S. Emery and G. Vasseur
CEA, Irfu, SPP, Centre de Saclay, F-91191 Gif-sur-Yvette, F
rance
D. Aston, D. J. Bard, C. Cartaro, M. R. Convery, J. Dorfan, G. P
. Dubois-Felsmann, W. Dunwoodie,
M. Ebert, R. C. Field, B. G. Fulsom, M. T. Graham, C. Hast, W. R. Inn
es, P. Kim, D. W. G. S. Leith,
S. Luitz, V. Luth, D. B. MacFarlane, D. R. Muller, H. Neal, T. Pulliam, B
. N. Ratcliff, A. Roodman,
R. H. Schindler, A. Snyder, D. Su, M. K. Sullivan, J. Va’vra, W. J. Wisn
iewski, and H. W. Wulsin
SLAC National Accelerator Laboratory, Stanford, Californ
ia 94309 USA
M. V. Purohit and J. R. Wilson
University of South Carolina, Columbia, South Carolina 292
08, USA
A. Randle-Conde and S. J. Sekula
Southern Methodist University, Dallas, Texas 75275, USA
M. Bellis, P. R. Burchat, and E. M. T. Puccio
Stanford University, Stanford, California 94305-4060, US
A
M. S. Alam and J. A. Ernst
State University of New York, Albany, New York 12222, USA
R. Gorodeisky, N. Guttman, D. R. Peimer, and A. Soffer
Tel Aviv University, School of Physics and Astronomy, Tel Av
iv, 69978, Israel
S. M. Spanier
University of Tennessee, Knoxville, Tennessee 37996, USA
J. L. Ritchie and R. F. Schwitters
University of Texas at Austin, Austin, Texas 78712, USA
J. M. Izen and X. C. Lou
University of Texas at Dallas, Richardson, Texas 75083, USA
F. Bianchi
ab
, F. De Mori
ab
, A. Filippi
a
, and D. Gamba
ab
INFN Sezione di Torino
a
; Dipartimento di Fisica, Universit`a di Torino
b
, I-10125 Torino, Italy
L. Lanceri
ab
and L. Vitale
ab
INFN Sezione di Trieste
a
; Dipartimento di Fisica, Universit`a di Trieste
b
, I-34127 Trieste, Italy
F. Martinez-Vidal and A. Oyanguren
IFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spa
in
5
J. Albert, Sw. Banerjee, A. Beaulieu, F. U. Bernlochner, H. H. F. C
hoi, G. J. King, R. Kowalewski,
M. J. Lewczuk, T. Lueck, I. M. Nugent, J. M. Roney, R. J. Sobie, a
nd N. Tasneem
University of Victoria, Victoria, British Columbia, Canad
a V8W 3P6
T. J. Gershon, P. F. Harrison, and T. E. Latham
Department of Physics, University of Warwick, Coventry CV4
7AL, United Kingdom
H. R. Band, S. Dasu, Y. Pan, R. Prepost, and S. L. Wu
University of Wisconsin, Madison, Wisconsin 53706, USA
We study the lepton forward-backward asymmetry
A
F B
and the longitudinal
K
∗
polarization
F
L
,
as well as an observable
P
2
derived from them, in the rare decays
B
→
K
∗
ℓ
+
ℓ
−
, where
ℓ
+
ℓ
−
is either
e
+
e
−
or
μ
+
μ
−
, using the full sample of 471 million
B
B
events collected at the
Υ
(4
S
) resonance
with the
B
A
B
AR
detector at the PEP-II
e
+
e
−
collider. We separately fit and report results for the
K
∗
0
(892)
ℓ
+
ℓ
−
and
K
∗
+
(892)
ℓ
+
ℓ
−
final states, as well as their combination
K
∗
ℓ
+
ℓ
−
, in five disjoint
dilepton mass-squared bins. An angular analysis of
B
+
→
K
∗
+
ℓ
+
ℓ
−
decays is presented here for
the first time.
PACS numbers: 13.20.He, 12.15.-y, 11.30.Er
I. INTRODUCTION
The decays
B
→
K
∗
(892)
ℓ
+
ℓ
−
, where
K
∗
→
Kπ
(hereinafter, unless explicitly stated otherwise,
K
∗
refers
generically to the
K
∗
(892)) and
ℓ
+
ℓ
−
is either an
e
+
e
−
or
μ
+
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 pro-
cesses contributing to these decays are the photon pen-
guin, the
Z
penguin and the
W
+
W
−
box diagrams shown
in Fig. 1. Their amplitudes are expressed in terms of
hadronic form factors and perturbatively-calculable ef-
fective 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 combi-
nation of the
Z
penguin and
W
+
W
−
box diagrams, re-
spectively [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 dia-
grams, 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
=
m
2
ℓ
+
ℓ
−
, the angular distri-
butions in
B
→
K
∗
ℓ
+
ℓ
−
decays are notably sensitive to
many possible sources of new physics, with several collab-
orations presenting results over the past few years [18–
∗
Now at: University of Tabuk, Tabuk 71491, Saudi Arabia
†
Now at: Laboratoire de Physique Nucl ́eaire et de Hautes Ener
gies,
IN2P3/CNRS, F-75252 Paris, France
‡
Now at: University of Huddersfield, Huddersfield HD1 3DH, UK
§
Deceased
¶
Now at: University of South Alabama, Mobile, Alabama 36688,
USA
∗∗
Also at: Universit`a di Sassari, I-07100 Sassari, Italy
25].
q
q
b
s
t,c,u
W
−
γ
, Z
l
+
l
−
q
q
b
s
t,c,u
W
+
W
−
ν
l
−
l
+
FIG. 1: Lowest-order SM Feynman diagrams for
b
→
sℓ
+
ℓ
−
.
At any particular
q
2
value, the kinematic distribution
of the decay products of
B
→
K
∗
ℓ
+
ℓ
−
and the
CP
-
conjugate
B
→
K
∗
ℓ
+
ℓ
−
process depends on six transver-
sity amplitudes which, neglecting
CP
-violating effects
and terms of order
m
2
ℓ
and higher, can be expressed as
a triply differential cross-section in three angles:
θ
K
, the
angle between the
K
and the
B
directions in the
K
∗
rest frame;
θ
ℓ
, the angle between the
ℓ
+
(
ℓ
−
) and the
B
(
B
) direction in the
ℓ
+
ℓ
−
rest frame; and
φ
, the angle
between the
ℓ
+
ℓ
−
and
Kπ
decay planes in the
B
rest
frame. From the distribution of the angle
θ
K
obtained
after integrating over
φ
and
θ
ℓ
, we determine the
K
∗
lon-
gitudinal polarization fraction
F
L
using a fit to cos
θ
K
of
the form [6]
1
Γ(
q
2
)
dΓ
d(cos
θ
K
)
=
3
2
F
L
(
q
2
) cos
2
θ
K
+
3
4
(1
−
F
L
(
q
2
))(1
−
cos
2
θ
K
)
.
(1)
We similarly determine the lepton forward-backward
asymmetry
A
F B
from the distribution of the angle
θ
ℓ
6
b
s
q
∼
χ
∼
−
h
0
μ
+
μ
−
FIG. 2: Feynman diagram of a non-SM Higgs penguin pro-
cess.
obtained after integrating over
φ
and
θ
K
, [6]
1
Γ(
q
2
)
dΓ
d(cos
θ
ℓ
)
=
3
4
F
L
(
q
2
)(1
−
cos
2
θ
l
) +
3
8
(1
−
F
L
(
q
2
))(1 + cos
2
θ
l
) +
A
F B
(
q
2
) cos
θ
l
.
(2)
We ignore here possible contributions from non-resonant
S-wave
B
→
Kπℓ
+
ℓ
−
events. The rate for such events
has been shown to be consistent with zero [26], with an
upper limit (68% CL) across the entire dilepton mass-
squared range of
<
4% of the
B
→
K
∗
(
Kπ
)
ℓ
+
ℓ
−
branch-
ing fraction [21]. The presence of an S-wave component
at this level was shown to lead to a relatively small abso-
lute bias on the order of 0.01 for
F
L
and
A
F B
; this small
bias is ignored here given the relatively larger magnitude
of our statistical and systematic uncertainties. Essen-
tially no contributions from low-mass tails of the higher
K
∗
resonances are expected in the
K
∗
(892) mass region
considered 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 cor-
rections in the underlying SM theory expectations [2].
We determine
F
L
and
A
F B
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 de-
cays
B
+
→
K
∗
+
ℓ
+
ℓ
−
is presented here for the first time.
We additionally present results for an observable derived
from
F
L
and
A
F B
,
P
2
= (
−
2
/
3)
∗A
F B
/
(1
−
F
L
), with less
theory uncertainty, and hence greater sensitivity to non-
SM contributions, than either
F
L
or
A
F B
alone [28, 29].
II. EVENT SELECTION
We use a data sample of
∼
471 million
B
B
pairs, corre-
sponding to 424
.
2
±
1
.
8 fb
−
1
[30], collected at the
Υ
(4
S
)
resonance with the
B
A
B
AR
detector [31] at the PEP-II
asymmetric-energy
e
+
e
−
collider at the SLAC National
Accelerator Laboratory. Charged particle tracking is pro-
vided 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
∗
ℓ
+
ℓ
−
signal events in the
following final states (charge conjugation is implied
throughout unless explicitly noted):
•
B
+
→
K
∗
+
(
→
K
0
S
π
+
)
μ
+
μ
−
;
•
B
0
→
K
∗
0
(
→
K
+
π
−
)
μ
+
μ
−
;
•
B
+
→
K
∗
+
(
→
K
+
π
0
)
e
+
e
−
;
•
B
+
→
K
∗
+
(
→
K
0
S
π
+
)
e
+
e
−
;
•
B
0
→
K
∗
0
(
→
K
+
π
−
)
e
+
e
−
.
We do not include the decays
B
+
→
K
∗
+
(
→
K
+
π
0
)
μ
+
μ
−
and
B
0
→
K
∗
0
(
→
K
0
S
π
0
)
ℓ
+
ℓ
−
in our anal-
ysis. 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
(
Kπ
)
<
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 misiden-
tification rates determined from high-purity data control
samples are, respectively,
∼
2% and
<
∼
0
.
1% [31], and
backgrounds from particle misidentification are thus sig-
nificant for
B
→
K
∗
μ
+
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
TABLE I: Definition of the
q
2
bins used in the analysis. The
nominal
B
and
K
∗
invariant masses [27] are given by
m
B
and
m
K
∗
, respectively.
q
2
bin
q
2
min ( GeV
2
/c
4
)
q
2
max ( GeV
2
/c
4
)
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
(
m
B
−
m
K
∗
)
2
q
2
0
1.00
6.00
7
with photon conversions to low-mass
e
+
e
−
pairs. We
reconstruct
K
0
S
candidates in the
π
+
π
−
final state, re-
quiring an invariant mass consistent with the nominal
K
0
mass, and a flight distance from the
e
+
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 uti-
lize the kinematic variables
m
ES
=
√
E
2
CM
/
4
−
p
∗
2
B
and
∆
E
=
E
∗
B
−
E
CM
/
2, where
p
∗
B
and
E
∗
B
are the
B
momen-
tum and energy in the
Υ
(4
S
) 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 misidenti-
fied 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 conserva-
tion, to model the combinatorial background from two
random leptons. For both
e
+
e
−
and
μ
+
μ
−
modes, we
veto the
J/ψ
(2
.
85
< m
ℓ
+
ℓ
−
<
3
.
18 GeV
/c
2
) and
ψ
(2
S
)
(3
.
59
< m
ℓ
+
ℓ
−
<
3
.
77 GeV
/c
2
) mass regions. These ve-
toed events provide high-statistics control samples of de-
cays 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 back-
grounds. These combinatorial backgrounds occur in both
B
B
events (“
B
B
backgrounds”) and
e
+
e
−
→
q
q
con-
tinuum events (“
q
q
backgrounds”, where
q
=
u,d,s,c
),
and are suppressed using eight bagged decision trees
(BDTs) [32] trained for suppression of:
•
B
B
backgrounds in
e
+
e
−
modes at low
q
2
;
•
B
B
backgrounds in
e
+
e
−
modes at high
q
2
;
•
B
B
backgrounds in
μ
+
μ
−
modes at low
q
2
;
•
B
B
backgrounds in
μ
+
μ
−
modes at high
q
2
;
•
q
q
backgrounds in
e
+
e
−
modes at low
q
2
;
•
q
q
backgrounds in
e
+
e
−
modes at high
q
2
;
•
q
q
backgrounds in
μ
+
μ
−
modes at low
q
2
;
•
q
q
backgrounds in
μ
+
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
+
e
−
and
μ
+
μ
−
datasets, 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
+
μ
−
BDTs are used to characterize the
K
∗
h
±
μ
∓
dataset.
Each of the above BDTs uses a subset of the following
observables as its input parameters:
•
the
B
candidate ∆
E
;
•
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;
•
the mass and ∆
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;
•
the magnitude of the total transverse momentum
of the event;
•
the
χ
2
probability of the vertex fitted from all the
B candidate tracks;
•
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
=
N
∑
i
=1
|
~p
i
·
ˆ
t
|
N
∑
i
=1
|
~p
i
|
,
where the thrust axis
ˆ
t
maximizes the magnitude
of the thrust
T
, up to a two-fold ambiguity in di-
rection (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
+
e
+
e
−
and
K
0
S
π
+
μ
+
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
(
→
K
(
∗
)
π
)
π
hadronic de-
cays 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 in-
variant mass of the
K
∗
π
system to be outside the range
1
.
84
−
1
.
90 GeV
/c
2
after assigning the pion mass hypoth-
esis to the muon candidates. Residual muon misiden-
tification backgrounds remaining after this selection are
characterized using the
K
∗
h
±
μ
∓
dataset.
For the last steps in the event selection, we adopt
(a) the ∆
E
regions used in our recent related analy-
ses of rates and rate asymmetries in exclusive
B
→
K
(
∗
)
ℓ
+
ℓ
−
and inclusive
B
→
X
s
ℓ
+
ℓ
−
decays [26, 36],
−
0
.
1(
−
0
.
05)
<
∆
E <
0
.
05 GeV for
e
+
e
−
(
μ
+
μ
−
) modes;
and (b) the
q
q
BDT
>
0
.
4 selection used in the inclusive
B
→
X
s
ℓ
+
ℓ
−
analysis [26]. After all other selection cri-
teria have been imposed, this
q
q
BDT selection removes
8
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
(a)
e
+
e
−
BDT output for
B
B
background suppression in
B
+
→
K
0
S
π
+
e
+
e
−
.
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
(b)
e
+
e
−
BDT output for
q
q
background suppression in
B
+
→
K
0
S
π
+
e
+
e
−
.
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
(c)
μ
+
μ
−
BDT output for
B
B
background suppression in
B
+
→
K
0
S
π
+
μ
+
μ
−
.
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
(d)
μ
+
μ
−
BDT output for
q
q
background suppression in
B
+
→
K
0
S
π
+
μ
+
μ
−
.
FIG. 3: BDT outputs normalized to unit area for simulated sig
nal (solid blue line) and background (red dashed line)
q
2
1
events.
most
q
q
background events with only trivial decreases 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) candi-
dates per event in dielectron (dimuon) modes. In events
with multiple signal candidates, the candidate with the
∆
E
value closest to zero is selected.
III. ANGULAR OBSERVABLES EXTRACTION
METHOD
A. General Strategy
We extract the angular observables
F
L
and
A
F B
from
the data using a series of likelihood (LH) fits which pro-
ceed in several steps:
•
In each
q
2
bin, for each of the five signal modes
separately and using the full
m
ES
>
5
.
2 GeV
/c
2
dataset, an initial unbinned maximum LH fit of
m
ES
,
m
(
Kπ
) and a likelihood ratio (
L
R
, defined
below in Eq. 3) that discriminates against random
combinatorial
B
B
backgrounds is performed. Af-
ter this first fit, all normalizations and the
m
ES
-
dependent,
m
(
Kπ
)-dependent and
L
R
-dependent
probability density function (pdf) shapes are fixed.
•
Second, in each
q
2
bin and for each of the five signal
modes separately,
m
ES
,
m
(
Kπ
) 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 re-
sults of the prior three-dimensional fits. Only
m
ES
angular fit region events and pdfs are subsequently
used in the fits for
F
L
and
A
F B
.
•
Next, cos
θ
K
is added as a fourth dimension to the
likelihood function, in addition to
m
ES
,
m
(
Kπ
) 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 4-d
LH function. However, a common value of
F
L
is
9
shared among all of the 4-d 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
F B
for arbitrary combinations of
the five final states here. In particular, we quote
results using three different sets of our five signal
modes:
–
B
+
→
K
∗
+
ℓ
+
ℓ
−
, comprised of
B
+
→
K
∗
+
(
→
K
0
S
π
+
)
μ
+
μ
−
,
B
+
→
K
∗
+
(
→
K
+
π
0
)
e
+
e
−
,
B
+
→
K
∗
+
(
→
K
0
S
π
+
)
e
+
e
−
,
–
B
0
→
K
∗
0
ℓ
+
ℓ
−
, comprised of
B
0
→
K
∗
0
(
→
K
+
π
−
)
μ
+
μ
−
,
B
0
→
K
∗
0
(
→
K
+
π
−
)
e
+
e
−
.
–
B
→
K
∗
ℓ
+
ℓ
−
, comprised of
B
+
→
K
∗
+
(
→
K
0
S
π
+
)
μ
+
μ
−
,
B
0
→
K
∗
0
(
→
K
+
π
−
)
μ
+
μ
−
,
B
+
→
K
∗
+
(
→
K
+
π
0
)
e
+
e
−
,
B
+
→
K
∗
+
(
→
K
0
S
π
+
)
e
+
e
−
,
B
0
→
K
∗
0
(
→
K
+
π
−
)
e
+
e
−
.
•
In the final step, we use the fitted value of
F
L
from
the previous fit step as input to a similar 4-d fit for
A
F B
, in which cos
θ
ℓ
replaces cos
θ
K
as the fourth
dimension in the LH function, in addition to
m
ES
,
m
(
Kπ
) 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
+
P
bkg
,
(3)
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 differ-
ent 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
dataset, 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 sig-
nal efficiencies in the
m
ES
angular fit region for each final
state and
q
2
bin.
The initial 3-d fit is an unbinned maximum likelihood
fit with minimization performed by MINUIT [37]. Each
angular result is subsequently determined by direct con-
struction and examination of the negative log-likelihood
(NLL) curves resulting from a scan across the entire
F
L
or
A
F B
parameter space, including unphysical regions
which provide a statistically consistent description of the
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
+
μ
+
μ
−
0.143 0.130 0.146 0.145 0.143 0.108
K
+
π
−
μ
+
μ
−
0.184 0.152 0.185 0.195 0.194 0.157
K
+
π
0
e
+
e
−
0.121 0.105 0.124 0.121 0.110 0.075
K
0
S
π
+
e
+
e
−
0.182 0.160 0.185 0.174 0.151 0.109
K
+
π
−
e
+
e
−
0.230 0.195 0.233 0.229 0.209 0.151
B. Event Classes
We characterize
m
ES
,
m
(
Kπ
),
L
R
, cos
θ
K
and cos
θ
ℓ
probability density functions in our likelihood fit model
for several classes of events:
•
correctly reconstructed (“true”) signal events;
•
misreconstructed (“crossfeed”) signal events, from
both the five signal modes as well as from other
b
→
sℓ
+
ℓ
−
decays;
•
random combinatorial backgrounds;
•
backgrounds from
J/ψ
and
ψ
(2
S
) decays which es-
cape the dilepton mass veto windows;
•
for the
μ
+
μ
−
modes only, backgrounds from
hadronic decays in which there is muon misidenti-
fication of hadrons (this background is negligible in
e
+
e
−
final states due to the much smaller, relative
to muons, electron misidentification probability).
1. True and Crossfeed 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 3-d 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
∗
lineshape in each final state, the signal
m
(
Kπ
) 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.
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.
Equations 1 and 2, showing the dependence of
F
L
and
A
F B
on cos
θ
K
and cos
θ
ℓ
respectively, are purely theoret-
ical expressions which must be modified to take into ac-
count the experimental acceptance. We characterize the
10
angular acceptance using simulated signal events to ob-
tain parameterizations of the cos
θ
K
and cos
θ
ℓ
efficiency
for each final state in each
q
2
bin.
Signal crossfeed 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 cor-
rectly reconstructed signal candidate. There can be self-
crossfeed within one signal mode, feed-across between
two different signal modes with the same final state par-
ticle multiplicity, or (up) down crossfeed from (lower)
higher multiplicity
sℓ
+
ℓ
−
modes. Simulated signal events
are used to model these types of decays, with normaliza-
tion 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 frac-
tion of crossfeed 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 pro-
duction 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 mod-
eled 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 exper-
imental limits exist [27], are reconstructed and selected
analogously to the final event selection in order to char-
acterize the combinatorial background
m
(
Kπ
) 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 additionally provide an alternative model for
the combinatorial angular pdfs, which is used in the char-
acterization 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 typ-
ically occurs through bremsstrahlung by electrons, fol-
lowed by incorrect recovery of the missing energy. The
pdfs for this residual charmonium background are mod-
eled 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
∗
ℓ
+
ℓ
−
angular fits but which
are appropriate for
J/ψ
and
ψ
(2
S
) 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
(2
S
)) mass window.
Gamma conversions from
B
→
K
∗
γ
events and Dalitz
decays (
π
0
,η
)
→
e
+
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 selec-
tion 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 par-
ticle’s species can be identified with high precision and
accuracy without using particle identification informa-
tion, the
K
∗
μ
±
h
∓
dataset 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 his-
tograms, with normalizations obtained by construction
directly from the weighted control sample data.
C. Initial
m
ES
,
m
(
Kπ
)
and
L
R
Fit
As discussed above, the initial three-dimensional fits
to
m
ES
,
m
(
Kπ
) 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 normaliza-
tions and pdf shapes subsequently used in extracting the
angular observables from the
m
ES
>
5
.
27 GeV
/c
2
angu-
lar 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 observables are extracted. As examples of
typical fits, Fig. 4 shows fit projections in each of the
three initial fit dimensions for
B
0
→
K
+
π
−
e
+
e
−
and
B
0
→
K
+
π
−
μ
+
μ
−
in the
q
2
5
bin. Validation of the ini-
tial 3-d fit model is done using events in the
J/ψ
and
ψ
(2
S
) dilepton mass veto windows, where we find good
agreement between our fit results and the nominal PDG
values for the
B
→
J/ψK
∗
and
B
→
ψ
(2
S
)
K
∗
branching
fractions [27] into our final states.
D. Angular Fit Results
Prior to fitting the
B
→
K
∗
ℓ
+
ℓ
−
angular data, we
validate our angular fit model by using it to extract the
K
∗
longitudinal polarization
F
L
for
B
→
J/ψK
∗
and
B
→
ψ
(2
S
)
K
∗
decays into our signal final states, and
11
TABLE III: Fitted signal yields with statistical uncertain
ties.
Mode
q
2
0
q
2
1
q
2
2
q
2
3
q
2
4
q
2
5
B
→
K
∗
ℓ
+
ℓ
−
40
.
8
±
8
.
4
31
.
7
±
7
.
1
11
.
9
±
5
.
5
21
.
3
±
8
.
5
31
.
9
±
9
.
2
33
.
2
±
7
.
8
B
+
→
K
∗
+
ℓ
+
ℓ
−
17
.
7
±
5
.
2
8
.
7
±
4
.
1
3
.
8
±
4
.
0
7
.
7
±
5
.
6
9
.
0
±
4
.
8
9
.
4
±
4
.
2
B
0
→
K
∗
0
ℓ
+
ℓ
−
23
.
1
±
6
.
6
22
.
9
±
5
.
8
8
.
1
±
3
.
8
13
.
7
±
6
.
4
22
.
8
±
7
.
8
23
.
8
±
6
.
6
ES
m
5.2
5.22
5.24
5.26
5.28
Events / ( 0.0045 )
5
10
15
(a)
m
ES
:
B
0
→
K
+
π
−
e
+
e
−
.
π
K
m
0.7
0.8
0.9
1
1.1
Events / ( 0.02 )
5
10
15
(b)
m
Kπ
:
B
0
→
K
+
π
−
e
+
e
−
.
R
L
0.6
0.7
0.8
0.9
Events / ( 0.04 )
5
10
15
20
(c)
L
R
:
B
0
→
K
+
π
−
e
+
e
−
.
ES
m
5.2
5.22
5.24
5.26
5.28
Events / ( 0.0045 )
5
10
15
20
25
(d)
m
ES
:
B
0
→
K
+
π
−
μ
+
μ
−
.
π
K
m
0.7
0.8
0.9
1
1.1
Events / ( 0.02 )
2
4
6
8
10
12
(e)
m
Kπ
:
B
0
→
K
+
π
−
μ
+
μ
−
.
R
L
0.6
0.7
0.8
0.9
Events / ( 0.04 )
5
10
15
20
25
(f)
L
R
:
B
0
→
K
+
π
−
μ
+
μ
−
.
FIG. 4: Initial 3-d fit projections for
B
0
→
K
+
π
−
e
+
e
−
(top row) and
B
0
→
K
+
π
−
μ
+
μ
−
(bottom row) in
q
2
5
. The plots show
the stacked contributions from each event class: combinato
rial (magenta long dash), charmonium (black dots), crossfe
ed (red
short dash), total pdf (solid blue) and, in the bottom row of p
lots only, muon mis-identification (blue dash dots). The sig
nal
pdf is represented by the area between the dash red and solid b
lue lines.
comparing our results to previously reported PDG val-
ues [27]. We also perform similar validation fits for
A
F B
,
which is expected in the SM to approach zero for lepton
pairs from
B
decays to final states including charmonia.
Recalculating the PDG averages after removing all con-
tributing
B
A
B
AR
results, we find no significant deviations
from the expected values in any individual final state or
for the particular combinations of final states used in our
main analysis.
Having validated our fit model with the vetoed charmo-
nium events, we proceed to the extraction of the angular
observables in each
q
2
bin. Our results are tabulated in
Tables IV and V; Figs. 5 and 6 show the
B
+
→
K
∗
+
ℓ
+
ℓ
−
and
B
0
→
K
∗
0
ℓ
+
ℓ
−
cos
θ
K
and cos
θ
ℓ
fit projections in
q
2
0
and
q
2
5
. Fig. 7 graphically shows our
F
L
and
A
F B
results
in disjoint
q
2
bins alongside other published results and
the SM theory expectations, the latter of which typically
have 5-10% theory uncertainties (absolute) in the regions
below and above the charmonium resonances. Fig. 8 sim-
ilarly compares the
q
2
0
results obtained here with those
of other experiments and the SM theory expectation.
E. Systematic Uncertainties
We describe below the systematic uncertainties in the
angular results arising from:
•
the purely statistical uncertainties in the parame-
ters obtained from the initial 3-d
m
ES
,m
(
Kπ
) fit
which are used in the angular fits;
•
the
F
L
statistical uncertainty, which is propagated
into the
A
F B
fit; and
•
the modeling of the random combinatorial back-
ground pdfs and the signal angular efficiencies.
12
TABLE IV:
F
L
angular fit results with, respectively, statistical and sys
tematic uncertainties.
B
+
→
K
∗
+
ℓ
+
ℓ
−
B
0
→
K
∗
0
ℓ
+
ℓ
−
B
→
K
∗
ℓ
+
ℓ
−
q
2
0
+0
.
05
+0
.
09
−
0
.
10
+0
.
02
−
0
.
10
+0
.
43
+0
.
12
−
0
.
13
+0
.
02
−
0
.
02
+0
.
24
+0
.
09
−
0
.
08
+0
.
02
−
0
.
02
q
2
1
−
0
.
02
+0
.
18
−
0
.
13
+0
.
09
−
0
.
14
+0
.
34
+0
.
15
−
0
.
10
+0
.
15
−
0
.
02
+0
.
29
+0
.
09
−
0
.
12
+0
.
13
−
0
.
05
q
2
2
−
0
.
24
+0
.
27
−
0
.
39
+0
.
18
−
0
.
10
+0
.
18
+0
.
16
−
0
.
12
+0
.
02
−
0
.
10
+0
.
17
+0
.
14
−
0
.
15
+0
.
02
−
0
.
02
q
2
3
+0
.
15
+0
.
14
−
0
.
13
+0
.
05
−
0
.
08
+0
.
48
+0
.
14
−
0
.
16
+0
.
05
−
0
.
05
+0
.
30
+0
.
12
−
0
.
11
+0
.
05
−
0
.
07
q
2
4
+0
.
05
+0
.
27
−
0
.
16
+0
.
16
−
0
.
15
+0
.
45
+0
.
09
−
0
.
14
+0
.
06
−
0
.
06
+0
.
34
+0
.
15
−
0
.
10
+0
.
07
−
0
.
10
q
2
5
+0
.
72
+0
.
20
−
0
.
31
+0
.
10
−
0
.
21
+0
.
48
+0
.
12
−
0
.
12
+0
.
02
−
0
.
11
+0
.
53
+0
.
10
−
0
.
12
+0
.
07
−
0
.
14
TABLE V:
A
F B
angular fit results with, respectively, statistical and sys
tematic uncertainties.
B
+
→
K
∗
+
ℓ
+
ℓ
−
B
0
→
K
∗
0
ℓ
+
ℓ
−
B
→
K
∗
ℓ
+
ℓ
−
q
2
0
+0
.
32
+0
.
18
−
0
.
18
+0
.
08
−
0
.
05
+0
.
06
+0
.
15
−
0
.
18
+0
.
06
−
0
.
05
+0
.
21
+0
.
10
−
0
.
15
+0
.
07
−
0
.
09
q
2
1
+0
.
44
+0
.
20
−
0
.
22
+0
.
13
−
0
.
16
−
0
.
12
+0
.
23
−
0
.
21
+0
.
10
−
0
.
21
+0
.
10
+0
.
16
−
0
.
15
+0
.
08
−
0
.
19
q
2
2
+0
.
70
+0
.
21
−
0
.
38
+0
.
36
−
0
.
49
+0
.
33
+0
.
21
−
0
.
30
+0
.
12
−
0
.
11
+0
.
44
+0
.
15
−
0
.
18
+0
.
14
−
0
.
11
q
2
3
+0
.
11
+0
.
22
−
0
.
28
+0
.
08
−
0
.
20
+0
.
17
+0
.
14
−
0
.
16
+0
.
08
−
0
.
08
+0
.
15
+0
.
14
−
0
.
12
+0
.
08
−
0
.
05
q
2
4
+0
.
21
+0
.
32
−
0
.
33
+0
.
11
−
0
.
24
+0
.
40
+0
.
12
−
0
.
18
+0
.
17
−
0
.
16
+0
.
42
+0
.
11
−
0
.
17
+0
.
14
−
0
.
13
q
2
5
+0
.
40
+0
.
26
−
0
.
21
+0
.
18
−
0
.
17
+0
.
29
+0
.
14
−
0
.
17
+0
.
10
−
0
.
10
+0
.
29
+0
.
07
−
0
.
10
+0
.
10
−
0
.
12
We additionally examined several other possible
sources of systematic uncertainty, but found no signifi-
cant contributions due to:
•
modeling of the signal crossfeed contributions to
the angular fits;
•
the parameterization of the signal Gaussian
m
ES
and resonant
m
(
Kπ
) shapes that are extracted
from the relatively high-statistics
J/ψ
control sam-
ples;
•
possible fit biases which, to relatively very good
precision, were not observed in any of the data con-
trol sample angular fits;
•
characterization of
m
ES
peaking backgrounds from
muon mis-identification and charmonium leakage;
•
variations in event selection.
We combine in quadrature the individual systematic
uncertainties to obtain the total systematic uncertainty
on each of the angular observables; these are are given
in Table X, which is placed after the detailed discussion
below for each family of systematic uncertainties.
In the initial fits that determine the signal yields, we
allow the random combinatorial
m
ES
shape and normal-
isation, as well as the signal yield, to float. We then
fix these parameters at their central values for the an-
gular fits. To study the systematic uncertainty associ-
ated with these fixed parameters, we vary each param-
eter from its central value by its
±
1
σ
statistical uncer-
tainty, accounting for correlations among the fit param-
eters, and then redo the angular fit. To control for sys-
tematic fit results that deviate from the nominal central
value mainly from statistical effects rather than system-
atic ones, we additionally examine fit results obtained
from
±
(0
.
8
,
0
.
9
,
1
.
1
,
1
.
2)
σ
variations. These small varia-
tions on the
±
1
σ
values should also result in similarly
small variations, in the absence of any statistical effects,
on a
±
1
σ
systematic fit result. For the bulk of the sys-
tematics, where the series of fit results for each of the ad-
ditional variations is linearly distributed around the mid-
dle 1
σ
fit result, the 1
σ
variation is considered robust. In
the relatively few cases where the disagreement between
the nominal 1
σ
variation and the value of the 1
σ
variation
interpolated from the additional (0
.
8
,
0
.
9
,
1
.
1
,
1
.
2)
σ
varia-
tions is statistically significant, the interpolated 1
σ
value
is used to assign the systematic. All deviations from the
nominal fit central value are then added in quadrature to
obtain the overall systematic uncertainty attributable to
this source, which is given in Table VI.
The cos
θ
K
fit yields the central value and statistical
uncertainty for
F
L
in each
q
2
bin, which is subsequently
used in the fit to the cos
θ
ℓ
distributions to extract
A
F B
.
To study the systematic uncertainty on
A
F B
due to the