of 19
Study of the reactions
e
+
e
π
+
π
π
0
π
0
π
0
π
0
and
π
+
π
π
0
π
0
π
0
η
at center-of-mass energies from threshold to 4.5 GeV using
initial-state radiation
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
,
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
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
1
Laboratoire d
Annecy-le-Vieux de Physique des Particules (LAPP), Universit ́
e de Savoie, CNRS/IN2P3,
F-74941 Annecy-Le-Vieux, France
2
Departament ECM, Facultat de Fisica, Universitat de Barcelona, E-08028 Barcelona, Spain
3
INFN Sezione di Bari, I-70126 Bari, Italy
4
Institute of Physics, University of Bergen, N-5007 Bergen, Norway
5
Lawrence Berkeley National Laboratory and University of California, Berkeley, California 94720, USA
6
Institut für Experimentalphysik 1, Ruhr Universität Bochum, D-44780 Bochum, Germany
7a
Institute of Particle Physics, Vancouver, British Columbia V6T 1Z1, Canada
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
11
Institute for Particle Physics, University of California at Santa Cruz, 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
PHYSICAL REVIEW D
104,
112004 (2021)
2470-0010
=
2021
=
104(11)
=
112004(19)
112004-1
Published by the American Physical Society
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 Ferrara, 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
Institut für Physik, Humboldt-Universität zu Berlin, 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
CNRS/IN2P3, IJCLab, Universit ́
e Paris-Saclay, 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
Institut für Kernphysik, Johannes Gutenberg-Universität Mainz, D-55099 Mainz, Germany
32
University of Manchester, Manchester M13 9PL, United Kingdom
33
University of Maryland, College Park, Maryland 20742, USA
34
Laboratory for Nuclear Science, Massachusetts Institute of Technology,
Cambridge, Massachusetts 02139, USA
35a
Institute of Particle Physics, Montr ́
eal, Qu ́
ebec H3A 2T8, Canada
35b
McGill University, Montr ́
eal, Qu ́
ebec H3A 2T8, Canada
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
Physique des Particules, Universit ́
e de Montr ́
eal, Montr ́
eal, Qu ́
ebec H3C 3J7, Canada
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, 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 B2G 2W5, Canada
56
Stanford University, Stanford, California 94305, USA
57
State University of New York, Albany, New York 12222, USA
58
School of Physics and Astronomy, Tel Aviv University, 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
J. P. LEES
et al.
PHYS. REV. D
104,
112004 (2021)
112004-2
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 V8W 3P6, Canada
65b
University of Victoria, Victoria, British Columbia V8W 3P6, Canada
66
Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
67
University of Wisconsin, Madison, Wisconsin 53706, USA
(Received 4 October 2021; accepted 16 November 2021; published 14 December 2021)
We study the processes
e
þ
e
π
þ
π
π
0
π
0
π
0
π
0
γ
and
π
þ
π
π
0
π
0
π
0
ηγ
in which an energetic photon is
radiated from the initial state. The data were collected with the
BABAR
detector at the SLAC National
Accelerator Laboratory. About 7300 and 870 events, respectively, are selected from a data sample
corresponding to an integrated luminosity of
469
fb
1
. The invariant mass of the hadronic final state
defines the effective
e
þ
e
center-of-mass energy. The center-of-mass energies range from threshold to
4.5 GeV. From the mass spectra, the first ever measurements of the
e
þ
e
π
þ
π
π
0
π
0
π
0
π
0
and the
e
þ
e
π
þ
π
π
0
π
0
π
0
η
cross sections are performed. The contributions from
ωπ
0
π
0
π
0
,
ηπ
þ
π
π
0
,
ωη
, and
other intermediate states are presented. We observe the
J=
ψ
and
ψ
ð
2
S
Þ
in most of these final states and
measure the corresponding branching fractions, many of them for the first time.
DOI:
10.1103/PhysRevD.104.112004
I. INTRODUCTION
Many precision Standard Model (SM) predictions require
the hadronic vacuum polarization (HVP) terms to be taken
into account. At a relatively large momentum transfer, these
terms are measured by studying the inclusive hadron pro-
duction in
e
þ
e
annihilation and arerelativelywellcalculated
by perturbative quantum chromodynamics. However, in the
energy region from the hadronic threshold to about 2 GeV,
the inclusive hadronic cross section cannot be measured or
calculated reliably, and a sumof exclusive states must be used.
It is particularly important for the calculation of the muon
anomalous magnetic moment (
g
μ
2
), which is most sensi-
tive to the low-energy region. Despite large datasets of
e
þ
e
cross sections, accumulated in the past years, and the studies
performed
[1,2]
, there still is a discrepancy between the SM
calculation and the experimental value. With the latest result
of the (
g
μ
2
) experiment at Fermilab
[3]
,thisdiscrepancy
increased to 4.2 sigma.
Electron-positron annihilation events with initial-state
radiation (ISR) can be used to study processes over a wide
range of energies below the nominal
e
þ
e
c.m. energy
(
E
c
:
m
:
), as proposed in Ref.
[4]
. The possibility of exploit-
ing ISR to make precise measurements of low-energy cross
sections at high-luminosity
φ
and
B
factories is discussed in
Refs.
[5
7]
and motivates the studies described in this
paper. Not all accessible states have yet been measured;
thus new measurements will improve the reliability of the
HVP calculation. In addition, studies of ISR events at
B
factories are interesting in their own right, because they
provide information on resonance spectroscopy for masses
up to the charmonium region.
Studies of hadron (
h
) production in the ISR processes
e
þ
e
h
γ
using data from the
BABAR
experiment at
SLAC have been previously reported
[8
22]
. Initial-state
radiation events with detection of the ISR photon are
characterized by good reconstruction efficiency and by
well-understood kinematics, demonstrated in the references
given above. The
BABAR
detector performance (tracking,
particle identification,
π
0
,
K
0
S
, and
K
0
L
reconstruction) is
well suited to the study of ISR processes.
This paper reports on analyses of the
π
þ
π
4
π
0
and
π
þ
π
3
π
0
η
final states produced in conjunction with an
energetic photon, assumed to result from ISR. While
BABAR
data cover effective c.m. energies up to
10.58 GeV, this analysis is restricted to energies below
4.5 GeV because of backgrounds from
Υ
ð
4
S
Þ
decays.
There are no previous measurements of the
e
þ
e
π
þ
π
4
π
0
and
e
þ
e
π
þ
π
3
π
0
η
cross sections. The
*
Deceased.
Present address: Wuhan University, Wuhan 430072, China.
Present address: Universit`
a di Bologna and INFN Sezione di
Bologna, I-47921 Rimini, Italy.
§
Present address: King
s College, London WC2R 2LS, United
Kingdom.
Present address: Western Kentucky University, Bowling
Green, Kentucky 42101, USA.
Present address: University of Huddersfield, Huddersfield
HD1 3DH, United Kingdom.
**
Present address: University of South Alabama, Mobile,
Alabama 36688, USA.
††
Also at Universit`
a di Sassari, I-07100 Sassari, Italy.
‡‡
Also at Gran Sasso Science Institute, I-67100 LAquila, Italy.
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
.
STUDY OF THE REACTIONS
...
PHYS. REV. D
104,
112004 (2021)
112004-3
six-pion cross sections have a sizable value below 2 GeV
[11]
and the two-charged plus four-neutral pion processes
are currently included in the HVP calculation by assuming
isospin relations
[1]
. The direct measurement of this
channel can reduce the calculation uncertainty. It is also
important to extract the contribution of the intermediate
resonances, because the total cross section calculation
depends on their decay rate to the measured final states.
Below, we present the measurements of
e
þ
e
ωπ
0
π
0
π
0
,
e
þ
e
ηπ
þ
π
π
0
, and
e
þ
e
ωη
cross sections, with
η
π
0
π
0
π
0
, that contribute to the
e
þ
e
π
þ
π
4
π
0
final state.
A clear
J=
ψ
signal is observed for both the
π
þ
π
4
π
0
and
π
þ
π
3
π
0
η
channels, and the corresponding
J=
ψ
branching
fractions are measured.
II. THE
BABAR
DETECTOR AND DATASET
The data used in this analysis were collected with the
BABAR
detector at the PEP-II2 asymmetric-energy
e
þ
e
storage ring. The total integrated luminosity used is
468
.
6
fb
1
[23]
, which includes data collected at the
Υ
ð
4
S
Þ
resonance (
424
.
7
fb
1
) and at a c.m. energy
40 MeV below this resonance (
43
.
9
fb
1
).
The
BABAR
detector is described in detail elsewhere
[24]
. Charged particles are reconstructed using the
BABAR
tracking system, which comprises the silicon vertex tracker
(SVT) and the drift chamber (DCH), both located inside a
1.5 T solenoid. Separation of pions and kaons is accom-
plished by means of the detector of internally reflected
Cherenkov light and energy-loss measurements in the SVT
and DCH. Photons and
K
0
L
mesons are detected in the
electromagnetic calorimeter (EMC). Muon identification is
provided by the instrumented flux return.
To evaluate the detector acceptance and efficiency, we
have developed a special package of Monte Carlo (MC)
simulation programs for radiative processes based on the
approach of Czy
ż
and Kühn
[25]
. Multiple collinear soft-
photon emission from the initial
e
þ
e
state is imple-
mented with the structure function technique
[26,27]
,
while additional photon radiation from final-state particles
is simulated using the
PHOTOS
package
[28]
. The precision
of the radiative simulation is such that it contributes
less than 1% to the uncertain
ty in the measured hadronic
cross sections.
We simulate
e
þ
e
π
þ
π
π
0
π
0
π
0
π
0
γ
events assuming
production through the
ω
ð
782
Þ
η
intermediate channel, with
decay of the
ω
to three pions and decay of the
η
to all its
measured decay modes
[29]
.
A sample of 460 000 simulated events is generated for
the signal reaction and processed through the detector
response simulation, based on the
GEANT
4
package
[30]
.
These events are reconstructed using the same software
chain as the data. Most of the experimental events contain
additional soft photons due to machine background or
interactions in the detector material. Variations in the
detector and background conditions are included in the
simulation.
For the purpose of background estimation, large samples
of events from the main relevant ISR processes (
5
πγ
,
ρηγ
,
π
þ
π
π
0
π
0
γ
, etc.) are simulated. To evaluate the background
from the relevant non-ISR processes, namely
e
þ
e
q
̄
q
(
q
¼
u
,
d
,
s
) and
e
þ
e
τ
þ
τ
, simulated samples with
integrated luminosities about that of the data are generated
using the
JETSET
[31]
and
KORALB
[32]
programs, respec-
tively. The cross sections for the above processes are known
with an accuracy slightly better than 10%, which is
sufficient for the present purposes.
III. EVENT SELECTION AND KINEMATIC FIT
A relatively clean sample of
π
þ
π
4
π
0
γ
and
π
þ
π
3
π
0
ηγ
events is selected by requiring that there be two tracks
reconstructed in the DCH, SVT, or both, and nine or more
photons (sometimes up to 20), with an energy above
0.02 GeV in the EMC. We assume the photon with the
highest energy to be the ISR photon, and we require its c.m.
energy to be larger than 3 GeV.
Wealloweithertwoorthreetracksinanevent,withexactly
oneopposite-signpairthatextrapolateswithin0.25cmofthe
beamaxisand3.0cmofthenominalcollisionpointalongthat
axis. The reason a third track is allowed is to capture a
relatively small fraction of signal events that contain a
background track. The two tracks that satisfy the extrapola-
tion criteria are fit to a vertex, which is used as the point of
origin in the calculation of the photon directions.
We subject each candidate event to a set of constrained
kinematic fits and use the fit results, along with charged-
particle identification, to select the final states of interest
and evaluate backgrounds from other processes. The
kinematic fits make use of the four-momenta and covari-
ance matrices of the initial
e
þ
,
e
, and the set of selected
tracks and photons. The fitted three-momenta of each track
and photon are then used in further calculations.
Excluding the photon with the highest c.m. energy,
which is assumed to arise from ISR, we consider all
independent sets of eight other photons and combine them
into four pairs. For each set of eight photons, we test all
possible independent combinations of four photon pairs.
We consider those combinations in which the diphoton
mass of at least three pairs lies within

35
MeV
=c
2
(

3
σ
of the resolution) of the
π
0
mass
m
π
0
[29]
. The selected
combinations are subjected to a fit in which the diphoton
masses of the three pairs with
j
m
ð
γγ
Þ
m
π
0
j
<
35
MeV
=c
2
are constrained to
m
π
0
. For the signal hypothesis
e
þ
e
π
þ
π
3
π
0
γγγ
ISR
with the constraints due to four-momentum
conservation, there are thus seven constraints (7C) in the fit.
The photons in the remaining (
fourth
) pair are treated as
being independent. If all four photon pairs in the combi-
nation satisfy
j
m
ð
γγ
Þ
m
π
0
j
<
35
MeV
=c
2
, we rotate the
J. P. LEES
et al.
PHYS. REV. D
104,
112004 (2021)
112004-4