Search for an Axionlike Particle in
B
Meson Decays
J. P. Lees,
1
V. Poireau,
1
V. Tisserand,
1
E. Grauges,
2
A. Palano,
3
G. Eigen,
4
D. N. Brown,
5
Yu. G. Kolomensky,
5
M. Fritsch,
6
H. Koch,
6
T. Schroeder,
6
R. Cheaib,
7b
C. Hearty,
7a,7b
T. S. Mattison,
7b
J. A. McKenna,
7b
R. Y. So,
7b
V. E. Blinov,
8a,8b,8c
A. R. Buzykaev,
8a
V. P. Druzhinin,
8a,8b
V. B. Golubev,
8a,8b
E. A. Kozyrev,
8a,8b
E. A. Kravchenko,
8a,8b
A. P. Onuchin,
8a,8b,8c
,*
S. I. Serednyakov,
8a,8b
Yu. I. Skovpen,
8a,8b
E. P. Solodov,
8a,8b
K. Yu. Todyshev,
8a,8b
A. J. Lankford,
9
B. Dey,
10
J. W. Gary,
10
O. Long,
10
A. M. Eisner,
11
W. S. Lockman,
11
W. Panduro Vazquez,
11
D. S. Chao,
12
C. H. Cheng,
12
B. Echenard,
12
K. T. Flood,
12
D. G. Hitlin,
12
J. Kim,
12
Y. Li,
12
D. X. Lin,
12
S. Middleton,
12
T. S. Miyashita,
12
P. Ongmongkolkul,
12
J. Oyang,
12
F. C. Porter,
12
M. Röhrken,
12
Z. Huard,
13
B. T. Meadows,
13
B. G. Pushpawela,
13
M. D. Sokoloff,
13
L. Sun,
13
,
†
J. G. Smith,
14
S. R. Wagner,
14
D. Bernard,
15
M. Verderi,
15
D. Bettoni,
16a
C. Bozzi,
16a
R. Calabrese,
16a,16b
G. Cibinetto,
16a,16b
E. Fioravanti,
16a,16b
I. Garzia,
16a,16b
E. Luppi,
16a,16b
V. Santoro,
16a
A. Calcaterra,
17
R. de Sangro,
17
G. Finocchiaro,
17
S. Martellotti,
17
P. Patteri,
17
I. M. Peruzzi,
17
M. Piccolo,
17
M. Rotondo,
17
A. Zallo,
17
S. Passaggio,
18
C. Patrignani,
18
,
‡
I. Flood,
19
N. Nguyen,
19
B. J. Shuve ,
19
H. M. Lacker,
20
B. Bhuyan,
21
U. Mallik,
22
C. Chen,
23
J. Cochran,
23
S. Prell,
23
A. V. Gritsan,
24
N. Arnaud,
25
M. Davier,
25
F. Le Diberder,
25
A. M. Lutz,
25
G. Wormser,
25
D. J. Lange,
26
D. M. Wright,
26
J. P. Coleman,
27
E. Gabathuler,
27
,*
D. E. Hutchcroft,
27
D. J. Payne,
27
C. Touramanis,
27
A. J. Bevan,
28
F. Di Lodovico,
28
,§
R. Sacco,
28
G. Cowan,
29
Sw. Banerjee,
30
D. N. Brown,
30
,
∥
C. L. Davis,
30
A. G. Denig,
31
W. Gradl,
31
K. Griessinger,
31
A. Hafner,
31
K. R. Schubert,
31
R. J. Barlow,
32
,¶
G. D. Lafferty,
32
R. Cenci,
33
A. Jawahery,
33
D. A. Roberts,
33
R. Cowan,
34
S. H. Robertson,
35a,35b
R. M. Seddon,
35b
N. Neri,
36a
F. Palombo,
36a,36b
L. Cremaldi,
37
R. Godang,
37
,**
D. J. Summers,
37
,*
P. Taras,
38
G. De Nardo,
39
C. Sciacca,
39
G. Raven,
40
C. P. Jessop,
41
J. M. LoSecco,
41
K. Honscheid,
42
R. Kass,
42
A. Gaz,
43a
M. Margoni,
43a,43b
M. Posocco,
43a
G. Simi,
43a,43b
F. Simonetto,
43a,43b
R. Stroili,
43a,43b
S. Akar,
44
E. Ben-Haim,
44
M. Bomben,
44
G. R. Bonneaud,
44
G. Calderini,
44
J. Chauveau,
44
G. Marchiori,
44
J. Ocariz,
44
M. Biasini,
45a,45b
E. Manoni,
45a
A. Rossi,
45a
G. Batignani,
46a,46b
S. Bettarini,
46a,46b
M. Carpinelli,
46a,46b
,
††
G. Casarosa,
46a,46b
M. Chrzaszcz,
46a
M. De Nuccio,
46a,46b
F. Forti,
46a,46b
M. A. Giorgi,
46a,46b
A. Lusiani,
46a,46c
B. Oberhof,
46a,46b
E. Paoloni,
46a,46b
M. Rama,
46a
G. Rizzo,
46a,46b
J. J. Walsh,
46a
L. Zani,
46a,46b
A. J. S. Smith,
47
F. Anulli,
48a
R. Faccini,
48a,48b
F. Ferrarotto,
48a
F. Ferroni,
48a
,
‡‡
A. Pilloni,
48a,48b
G. Piredda,
48a
,*
C. Bünger,
49
S. Dittrich,
49
O. Grünberg,
49
M. Heß,
49
T. Leddig,
49
C. Voß,
49
R. Waldi,
49
T. Adye,
50
F. F. Wilson,
50
S. Emery,
51
G. Vasseur,
51
D. Aston,
52
C. Cartaro,
52
M. R. Convery,
52
J. Dorfan,
52
W. Dunwoodie,
52
M. Ebert,
52
R. C. Field,
52
B. G. Fulsom,
52
M. T. Graham,
52
C. Hast,
52
W. R. Innes,
52
,*
P. Kim,
52
D. W. G. S. Leith,
52
,*
S. Luitz,
52
D. B. MacFarlane,
52
D. R. Muller,
52
H. Neal,
52
B. N. Ratcliff,
52
A. Roodman,
52
M. K. Sullivan,
52
J. Va
’
vra,
52
W. J. Wisniewski,
52
M. V. Purohit,
53
J. R. Wilson,
53
A. Randle-Conde,
54
S. J. Sekula,
54
H. Ahmed,
55
N. Tasneem,
55
M. Bellis,
56
P. R. Burchat,
56
E. M. T. Puccio,
56
M. S. Alam,
57
J. A. Ernst,
57
R. Gorodeisky,
58
N. Guttman,
58
D. R. Peimer,
58
A. Soffer,
58
S. M. Spanier,
59
J. L. Ritchie,
60
R. F. Schwitters,
60
J. M. Izen,
61
X. C. Lou,
61
F. Bianchi,
62a,62b
F. De Mori,
62a,62b
A. Filippi,
62a
D. Gamba,
62a,62b
L. Lanceri,
63
L. Vitale,
63
F. Martinez-Vidal,
64
A. Oyanguren,
64
J. Albert,
65b
A. Beaulieu,
65b
F. U. Bernlochner,
65b
G. J. King,
65b
R. Kowalewski,
65b
T. Lueck,
65b
C. Miller,
65b
I. M. Nugent,
65b
J. M. Roney,
65b
R. J. Sobie,
65a,65b
T. J. Gershon,
66
P. F. Harrison,
66
T. E. Latham,
66
R. Prepost,
67
and S. L. Wu
67
(
B
A
B
AR
Collaboration)
1
Laboratoire d
’
Annecy-le-Vieux de Physique des Particules (LAPP), Universit ́
e de Savoie, CNRS/IN2P3,
F-74941 Annecy-Le-Vieux, France
2
Universitat de Barcelona, Facultat de Fisica, Departament ECM, E-08028 Barcelona, Spain
3
INFN Sezione 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
7a
Institute of Particle Physics, Vancouver, British Columbia, Canada V6T 1Z1
7b
University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z1
8a
Budker Institute of Nuclear Physics SB RAS, Novosibirsk 630090, Russia
8b
Novosibirsk State University, Novosibirsk 630090, Russia
8c
Novosibirsk State Technical University, Novosibirsk 630092, Russia
9
University of California at Irvine, Irvine, California 92697, USA
10
University of California at Riverside, Riverside, California 92521, USA
PHYSICAL REVIEW LETTERS
128,
131802 (2022)
0031-9007
=
22
=
128(13)
=
131802(8)
131802-1
Published by the American Physical Society
11
University of California at Santa Cruz, Institute for Particle Physics, Santa Cruz, California 95064, USA
12
California Institute of Technology, Pasadena, California 91125, USA
13
University of Cincinnati, Cincinnati, Ohio 45221, USA
14
University of Colorado, Boulder, Colorado 80309, USA
15
Laboratoire Leprince-Ringuet, Ecole Polytechnique, CNRS/IN2P3, F-91128 Palaiseau, France
16a
INFN Sezione di Ferrara, I-44122 Ferrara, Italy
16b
Dipartimento di Fisica e Scienze della Terra, Universit`
a di Ferrarab, I-44122 Ferrara, Italy
17
INFN Laboratori Nazionali di Frascati, I-00044 Frascati, Italy
18
INFN Sezione di Genova, I-16146 Genova, Italy
19
Harvey Mudd College, Claremont, California 91711, USA
20
Humboldt-Universität zu Berlin, Institut für Physik, D-12489 Berlin, Germany
21
Indian Institute of Technology Guwahati, Guwahati, Assam, 781 039, India
22
University of Iowa, Iowa City, Iowa 52242, USA
23
Iowa State University, Ames, Iowa 50011, USA
24
Johns Hopkins University, Baltimore, Maryland 21218, USA
25
Universit ́
e Paris-Saclay, CNRS/IN2P3, IJCLab, F-91405 Orsay, France
26
Lawrence Livermore National Laboratory, Livermore, California 94550, USA
27
University of Liverpool, Liverpool L69 7ZE, United Kingdom
28
Queen Mary, University of London, London E1 4NS, United Kingdom
29
University of London, Royal Holloway and Bedford New College, Egham, Surrey TW20 0EX, United Kingdom
30
University of Louisville, Louisville, Kentucky 40292, USA
31
Johannes Gutenberg-Universität Mainz, Institut für Kernphysik, D-55099 Mainz, Germany
32
University of Manchester, Manchester M13 9PL, United Kingdom
33
University of Maryland, College Park, Maryland 20742, USA
34
Massachusetts Institute of Technology, Laboratory for Nuclear Science, Cambridge, Massachusetts 02139, USA
35a
Institute of Particle Physics, Montr ́
eal, Qu ́
ebec, Canada H3A 2T8
35b
McGill University, Montr ́
eal, Qu ́
ebec, Canada H3A 2T8
36a
INFN Sezione di Milano, I-20133 Milano, Italy
36b
Dipartimento di Fisica, Universit`
a di Milano, I-20133 Milano, Italy
37
University of Mississippi, University, Mississippi 38677, USA
38
Universit ́
e de Montr ́
eal, Physique des Particules, Montr ́
eal, Qu ́
ebec, Canada H3C 3J7
39
INFN Sezione di Napoli and Dipartimento di Scienze Fisiche, Universit`
a di Napoli Federico II, I-80126 Napoli, Italy
40
NIKHEF, National Institute for Nuclear Physics and High Energy Physics, NL-1009 DB Amsterdam, The Netherlands
41
University of Notre Dame, Notre Dame, Indiana 46556, USA
42
Ohio State University, Columbus, Ohio 43210, USA
43a
INFN Sezione di Padova, I-35131 Padova, Italy
43b
Dipartimento di Fisica, Universit`
a di Padova, I-35131 Padova, Italy
44
Laboratoire de Physique Nucl ́
eaire et de Hautes Energies, Sorbonne Universit ́
e,
Paris Diderot Sorbonne Paris Cit ́
e, CNRS/IN2P3, F-75252 Paris, France
45a
INFN Sezione di Perugia, I-06123 Perugia, Italy
45b
Dipartimento di Fisica, Universit`
a di Perugia, I-06123 Perugia, Italy
46a
INFN Sezione di Pisa, I-56127 Pisa, Italy
46b
Dipartimento di Fisica, Universit`
a di Pisa, I-56127 Pisa, Italy
46c
Scuola Normale Superiore di Pisa, I-56127 Pisa, Italy
47
Princeton University, Princeton, New Jersey 08544, USA
48a
INFN Sezione di Roma, I-00185 Roma, Italy
48b
Dipartimento di Fisica, Universit`
a di Roma La Sapienza, I-00185 Roma, Italy
49
Universität Rostock, D-18051 Rostock, Germany
50
Rutherford Appleton Laboratory, Chilton, Didcot, Oxon OX11 0QX, United Kingdom
51
IRFU, CEA, Universit ́
e Paris-Saclay, F-91191 Gif-sur-Yvette, France
52
SLAC National Accelerator Laboratory, Stanford, California 94309 USA
53
University of South Carolina, Columbia, South Carolina 29208, USA
54
Southern Methodist University, Dallas, Texas 75275, USA
55
St. Francis Xavier University, Antigonish, Nova Scotia, Canada B2G 2W5
56
Stanford University, Stanford, California 94305, USA
57
State University of New York, Albany, New York 12222, USA
58
Tel Aviv University, School of Physics and Astronomy, Tel Aviv 69978, Israel
59
University of Tennessee, Knoxville, Tennessee 37996, USA
60
University of Texas at Austin, Austin, Texas 78712, USA
61
University of Texas at Dallas, Richardson, Texas 75083, USA
PHYSICAL REVIEW LETTERS
128,
131802 (2022)
131802-2
62a
INFN Sezione di Torino, I-10125 Torino, Italy
62b
Dipartimento di Fisica, Universit`
a di Torino, I-10125 Torino, Italy
63
INFN Sezione di Trieste and Dipartimento di Fisica, Universit`
a di Trieste, I-34127 Trieste, Italy
64
IFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spain
65a
Institute of Particle Physics, Victoria, British Columbia, Canada V8W 3P6
65b
University of Victoria, Victoria, British Columbia, Canada V8W 3P6
66
Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
67
University of Wisconsin, Madison, Wisconsin 53706, USA
(Received 4 November 2021; revised 31 January 2022; accepted 7 March 2022; published 1 April 2022)
Axionlike particles (ALPs) are predicted in many extensions of the standard model, and their masses can
naturally be well below the electroweak scale. In the presence of couplings to electroweak bosons, these
particles could be emitted in flavor-changing
B
meson decays. We report herein a search for an ALP,
a
,in
the reaction
B
→
K
a
,
a
→
γγ
using data collected by the
BABAR
experiment at SLAC. No significant
signal is observed, and 90% confidence level upper limits on the ALP coupling to electroweak bosons are
derived as a function of ALP mass, improving current constraints by several orders of magnitude in the
range
0
.
175
GeV
<m
a
<
4
.
78
GeV.
DOI:
10.1103/PhysRevLett.128.131802
The physics of spontaneous symmetry breaking drives
much of the phenomenology of the standard model (SM).
For instance, the Higgs mechanism gives mass to the
fermions and weak gauge bosons of the SM, while the
spontaneous breaking of approximate chiral global sym-
metries gives rise to pseudo-Goldstone bosons, such as the
pions. Many extensions of the SM feature anomalous
global symmetries whose spontaneous breaking leads to
new pseudo-Goldstone bosons known as axionlike particles
(ALPs)
[1
–
4]
. Such particles are ubiquitous in beyond-the-
SM theories, such as supersymmetry
[5
–
7]
, as well as in
string theory
[8
–
11]
. Potentially, ALPs could resolve
several outstanding issues related to the naturalness of
SM parameters, such as the strong
CP
problem
[1
–
4]
or the
hierarchy problem
[12]
, and they may also serve as
mediators to dark sectors
[13
–
16]
. Consequently, ALPs
have motivated a large number of searches in experimental
particle physics and cosmology
[17
–
20]
.
In the simplest models, ALPs predominantly couple to
pairs of SM gauge bosons. While the photon and gluon
couplings are already significantly constrained by collider
and beam-dump experiments for ALP masses in the MeV
–
GeV range
[21
–
28]
, the coupling to
W
bosons is less
explored. This coupling leads to ALP production in flavor-
changing neutral-current decays, which can serve as power-
ful discovery modes. For example, flavor-changing
B
meson and kaon decays already provide the most stringent
bounds on invisibly decaying ALPs over a range of masses
[29]
. The search presented here is the first for visibly
decaying ALPs produced in
B
meson decays. Its sensitivity
complements existing studies of
K
→
πγγ
[30
–
32]
, which
have been conservatively reinterpreted to obtain limits on
ALP couplings
[29]
.
In the following, we consider a minimal ALP (
a
) model
with coupling
g
aW
to the SU
ð
2
Þ
W
gauge-boson field
strengths,
W
b
μν
, and Lagrangian
L
¼
−
g
aW
4
aW
b
μν
̃
W
b
μν
;
ð
1
Þ
where
̃
W
b
μν
is the dual field-strength tensor. This coupling
leads to the production of ALPs at one loop in the process
B
→
K
a
, where the ALP is emitted from an internal
W
boson
[29]
. Electroweak symmetry breaking and the
resulting gauge-boson mixing generates an ALP coupling
to a pair of photons, and the branching fraction for
a
→
γγ
in this model is nearly 100% for
m
a
<m
W
. The same ALP
production and decay modes also occur in models with
axion couplings to gluons
[33,34]
.
We report herein the first search for an ALP in the
reaction
B
→
K
a
,
a
→
γγ
in the range
0
.
175
GeV
<
m
a
<m
B
þ
−
m
K
þ
≈
4
.
78
GeV, excluding the mass inter-
vals 0.45
–
0.63 GeV and 0.91
–
1.01 GeV because of large
peaking backgrounds from
η
and
η
0
mesons, respectively.
Note that existing searches already constrain
m
a
<
0
.
1
GeV in the range of couplings to which our search
is sensitive
[22
–
26]
, while the mass range
0
.
1
GeV
<
m
a
<
0
.
175
GeV is excluded from our analysis due to
large peaking
π
0
contributions. The
B
→
K
a
,
a
→
γγ
product branching fraction is measured assuming all
signal observed is produced in
B
→
K
a
with
a
de-
caying promptly. However, the ALP has a decay
width
Γ
a
¼
g
2
aW
m
3
a
sin
4
θ
W
=
64
π
, where
θ
W
is the weak
mixing angle, and the present search has sensitivity to
couplings predicting long-lived ALPs for
m
a
<
2
.
5
GeV.
Published by the American Physical Society under the terms of
the
Creative Commons Attribution 4.0 International
license.
Further distribution of this work must maintain attribution to
the author(s) and the published article
’
s title, journal citation,
and DOI. Funded by SCOAP
3
.
PHYSICAL REVIEW LETTERS
128,
131802 (2022)
131802-3
We additionally determine the branching fraction for
c
τ
a
values of 1, 10, and 100 mm in this mass range.
The search is based on a sample of
4
.
72
×
10
8
B
̄
B
meson
pairs corresponding to
424
fb
−
1
of integrated luminosity
collected at the
Υ
ð
4
S
Þ
resonance by the
BABAR
detector at
the PEP-II
e
þ
e
−
storage ring at the SLAC National
Accelerator Laboratory
[35]
. The
BABAR
detector is
described in detail elsewhere
[36,37]
. A small sample,
corresponding to 8% of the total data set, is used to
optimize the search strategy and is subsequently discarded.
Signal Monte Carlo (MC) events are simulated using
EVTGEN
[38]
, with MC samples generated at 24 masses
(from 0.1
–
4.8 GeV) for promptly decaying ALPs and 16
masses for long-lived ALPs (from 0.1
–
2.5 GeV). We
simulate the following reactions to study the background:
e
þ
e
−
→
e
þ
e
−
ð
γ
Þ
(
BHWIDE
[39]
),
e
þ
e
−
→
μ
þ
μ
−
ð
γ
Þ
,
e
þ
e
−
→
τ
þ
τ
−
ð
γ
Þ
(
KK
with
TAUOLA
library
[40,41]
), con-
tinuum
e
þ
e
−
→
q
̄
q
with
q
¼
u
,
d
,
s
, and
c
(
JETSET
[42]
),
and
e
þ
e
−
→
B
̄
B
(
EVTGEN
). Each background MC sample
is weighted to match the luminosity of the dataset. The
detector acceptance and reconstruction efficiencies are
estimated with a simulation based on
GEANT
4
[43]
.
We reconstruct signal
B
candidates by combining a pair
of photons with a track identified as a kaon by particle
identification algorithms
[36]
. All other reconstructed
tracks and neutral clusters in the event are collectively
referred to as the rest of the event (ROE). To suppress
backgrounds, we require an energy-substituted mass
m
ES
¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ð
s=
2
þ
⃗
p
i
·
⃗
p
B
Þ
2
=E
2
i
−
p
2
B
p
>
5
.
0
GeV and an energy
difference
Δ
E
¼j
ffiffiffi
s
p
=
2
−
E
B
j
<
0
.
3
GeV, where
ffiffiffi
s
p
denotes the center-of-mass (c.m.) energy,
⃗
p
B
and
E
B
are
the
B
momentum and energy in the lab frame,
E
B
is the
B
energy in the c.m. frame, and
E
i
and
⃗
p
i
are the energy
and momentum of the initial state in the lab frame. A
kinematic fit is performed on the selected
B
candidates,
requiring the photon and kaon candidates to originate from
the measured beam interaction region, and constraining
their total energy and invariant mass to the nominal
B
meson mass and measured c.m. beam energy.
Two boosted decision trees (BDTs)
[44]
are used to
further separate signal from each of the main backgrounds:
one BDT is trained using continuum MC background
events and the other using
B
þ
B
−
MC background events.
For the signal sample, we combine events from all
simulated ALP masses with prompt decays to obtain a
uniform distribution in diphoton invariant mass
ð
m
γγ
Þ
. Each
BDT includes the following 13 observables: invariant mass
of the ROE; cosine of the angle between two sphericity
axes, one computed with the
B
constituents and the other
with the ROE; second Legendre moment of the ROE,
calculated relative to the
B
thrust axis;
m
ES
and
Δ
E
;
particle identification information for the
K
; helicity angle
of the
K
, which is the angle between the
K
and the
Υ
ð
4
S
Þ
as measured in the
B
frame; helicity angle and
energy of the most energetic photon forming the
a
; three
invariant masses
m
ð
γ
i
γ
P
j
Þ
, where
γ
i
is an ALP-daughter
photon,
γ
P
j
is a photon in the ROE, and
γ
i
and
γ
P
j
are chosen
so that
m
ð
γ
i
γ
P
j
Þ
is closest to the nominal mass of each of
P
¼
π
0
;
η
;
η
0
; and, multiplicity of neutral candidates in
the event.
The BDT score distributions for data, signal MC, and
background MC are provided in the Supplemental Material
[45]
. For our final signal region selection, we apply the
criteria on the two BDT scores shown in Ref.
[45]
, allowing
multiple candidates per event. The BDT selection criteria
are independent of the ALP mass hypothesis. The signal
efficiency estimated from MC varies between 2% for
m
a
¼
4
.
78
GeV to 33% for
m
a
¼
0
.
3
GeV. The resulting
m
γγ
distribution is shown in Fig.
1
.
The background is dominated by continuum events and
by peaking contributions from
B
→
K
h
0
and
B
→
π
h
0
decays where
h
0
¼
π
0
;
η
;
η
0
. The continuum back-
ground arises from random combinations of photons and
charged hadrons. The observed deviations between MC and
data above 1 GeV are due to the challenges of modeling
continuum events in this mass range. This is particularly
true above 4 GeV where initial-state radiation contributes
substantially to the background but is absent from our
continuum MC. Over narrow regions of order a few
hundred MeV, the data-to-MC ratio is relatively flat for
m
γγ
<
4
GeV and MC can be used to model the continuum
shape in intervals of this width. Nonresonant
B
→
K
γγ
decays and
B
→
K
γ
;K
→
K
γ
decays are negligible, as
they have total branching fractions
≲
10
−
7
[46,47]
and do
not give a peak in
m
γγ
. The
B
→
K
η
c
;
η
c
→
γγ
decay is
not included in our background MC; we observe an excess
at the
η
c
mass, with a local significance of
2
.
6
σ
as
determined by the signal extraction procedure defined
below. The measured product branching fraction is
consistent with the world average value of
B
ð
B
→
K
η
c
Þ
B
ð
η
c
→
γγ
Þ
[47]
. Because of the relatively small
(GeV)
γ
γ
m
0
0.5
1
1.5
2
2.5
3
3.5
Entries / 0.1 (GeV)
1
10
2
10
3
10
4
10
Data
0
B
0
B
-
e
+
e
-
B
+
B
-
e
+
eq
q
-
e
+
e
44.5
FIG. 1. The diphoton mass distribution of ALP candidates,
together with Monte Carlo predictions of leading background
processes normalized to the data luminosity.
PHYSICAL REVIEW LETTERS
128,
131802 (2022)
131802-4
η
c
background compared to the
π
0
,
η
, and
η
0
, we do not
exclude signal mass hypotheses in the vicinity of the
η
c
mass.
We extract the signal yield of promptly decaying ALPs
by performing a series of unbinned maximum likelihood
fits of a hypothetical signal peak over a smooth background
to the data shown in Fig.
1
. We perform fits for 461 signal
mass hypotheses with a scan step size equal to the signal
resolution,
σ
γγ
. The latter is determined for each simulated
ALP mass by fitting the signal sample with a double-sided
Crystal Ball function
[48]
, taking the square root of the
variance of the Crystal Ball function as
σ
γγ
. We use an
interpolating function to determine the value of
σ
γγ
at
intermediate ALP masses. The resolution ranges from
8 MeV near
m
a
¼
0
.
175
GeV to 14 MeV near
m
a
¼
2
GeV, and decreasing back to 2 MeV near
m
a
¼
4
.
78
GeV as a result of the constraint imposed on the mass
of the
B
meson candidate in the kinematic fit. The MC
predictions are validated using a sample of
B
→
K
π
0
and
B
→
K
η
decays. The simulated
π
0
and
η
mass
resolutions agree with the data to within 3%.
Each unbinned likelihood fit is performed over an
m
γγ
interval with a width in the range
ð
24
–
60
Þ
σ
γγ
. The mass-
dependent interval width is chosen to be sufficiently broad
as to fix the continuum background shape. We have verified
that our results are independent of minor variations of the fit
interval widths. The probability density function (pdf)
includes contributions from signal, continuum background
components, and, where needed, peaking components
describing the
π
0
,
η
,
η
0
, and
η
c
.
The signal pdf is described by a nonparametric kernel
density function modeled from signal MC and extrapolated
between adjacent simulated mass points
[49]
. The con-
tinuum background is modeled for
m
a
<
4
GeV by the
sum of a template derived from smoothed background MC
histograms and a first-order polynomial, with the normali-
zation determined from the fit. At higher masses, only the
first-order polynomial is needed to model the background.
The data-to-MC ratio is approximately constant over each
fit interval, and the residual differences are accommodated
by the linear polynomial. The shapes of the
π
0
,
η
, and
η
0
resonances are also modeled from background MC, while
the
η
c
is modeled using the signal MC mass distribution
with a width broadened to match the
η
c
natural linewidth.
For the
π
0
,
η
, and
η
0
background components, the nor-
malization is determined from the fit to data, while the
normalization of the
η
c
component is fixed to the product of
the world-average value of
B
ð
B
→
K
η
c
Þ
B
ð
η
c
→
γγ
Þ
and
the signal efficiency evaluated at this mass. This allows us
to measure an ALP signal rate for
m
a
≈
m
η
c
while simul-
taneously accounting for events from
B
→
K
η
c
;
η
c
→
γγ
decays. We have verified that our signal extraction pro-
cedure is robust against changes in the background model
by varying the order of the polynomial component of the
continuum background.
To assess systematic uncertainties in the MC-derived
continuum and peaking background components, we fit the
relative normalizations of different background compo-
nents (continuum
q
̄
q; B
þ
B
−
;B
0
̄
B
0
) to data rather than
fixing each component
’
s normalization to match the lumi-
nosity of the total dataset, and we repeat our signal
extraction procedure with the reweighted MC-derived
templates. We also propagate the uncertainties in the
resolution of the peaking components and in the uncer-
tainties in the world-average value of the
η
c
linewidth. For
the
η
c
model, we assess a systematic uncertainty originating
from uncertainties in
B
ð
B
→
K
η
c
Þ
B
ð
η
c
→
γγ
Þ
by vary-
ing the
η
c
normalization within the uncertainties in the
world-average value. The systematic uncertainty in the
signal yield resulting from variations in the continuum
(peaking) background shape due to refitting the component
normalizations is estimated to be, on average, 1% (2%) of
the corresponding statistical uncertainty.
We further assess systematic uncertainties associated
with our signal model. We derive a systematic uncertainty
in the signal yield resulting from our extrapolation of the
signal pdf between simulated mass points. We assess this
uncertainty by comparing the extracted signal from fits
using nearest and next-to-nearest neighbor extrapolation of
the signal shape. This uncertainty is estimated to be, on
average, 4% of the corresponding statistical uncertainty. We
assess a signal resolution systematic uncertainty by repeat-
ing our fits with a signal shape whose width is varied within
the mass resolution uncertainty, leading to a signal reso-
lution systematic uncertainty that is, on average, 3% of the
statistical uncertainty. We determine a systematic uncer-
tainty in the signal efficiency by taking the data/MC ratio
for events within 50 MeVof the
η
0
resonance. Events in this
interval are predominantly signal-like
B
→
K
η
0
,
η
0
→
γγ
decays. The data to MC ratio is consistent with unity within
statistical errors, and we take the deviation from unity (6%)
as a relative systematic uncertainty in the efficiency.
The fitted signal yields and statistical significances are
shown in Fig.
2
. The largest local significance of
3
.
3
σ
is
observed near
m
a
¼
3
.
53
GeV with a global significance
of
1
.
1
σ
after including trial factors
[50]
, consistent with the
null hypothesis. Background-only fits to the
m
γγ
spectrum
are shown over the whole mass range in Ref.
[45]
.
To further validate the signal extraction procedure, we
measure the
B
→
K
h
0
,
h
0
→
γγ
(
h
0
¼
π
0
;
η
;
η
0
;
η
c
)
product branching fractions by treating the peaks as signal,
extracting the number of events in the peak using the fitting
procedure described above, and subtracting nonpeaking
background whose magnitude is determined from MC. The
results are found to be compatible with the current world
averages
[47]
within uncertainties.
In the absence of significant signal, Bayesian upper
limits at 90% confidence level (CL) on
B
ð
B
→
K
a
Þ
×
B
ð
a
→
γγ
Þ
are derived with a uniform positive prior in the
product branching fraction. We have verified that the limits
PHYSICAL REVIEW LETTERS
128,
131802 (2022)
131802-5