of 7
Precision Measurement of the Ratio
B
ð
Υ
ð
3
S
Þ
τ
+
τ
Þ
=
B
ð
Υ
ð
3
S
Þ
μ
+
μ
Þ
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
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
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
I. M. Nugent,
65b
J. M. Roney,
65b
A. Sibidanov ,
65b
,
R. J. Sobie,
65a,65b
N. Tasneem,
65b
T. J. Gershon,
66
P. F. Harrison,
66
T. E. Latham,
66
R. Prepost,
67
and S. L. Wu
67
(
BABAR
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 and Dipartimento di Fisica, Universit`
a 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
11
University of California at Santa Cruz, Institute for Particle Physics, Santa Cruz, California 95064, USA
PHYSICAL REVIEW LETTERS
125,
241801 (2020)
0031-9007
=
20
=
125(24)
=
241801(7)
241801-1
Published by the American Physical Society
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 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
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, 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
62a
INFN Sezione di Torino, I-10125 Torino, Italy
PHYSICAL REVIEW LETTERS
125,
241801 (2020)
241801-2
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 13 May 2020; accepted 20 October 2020; published 8 December 2020)
We report on a precision measurement of the ratio
R
Υ
ð
3
S
Þ
τμ
¼
B
ð
Υ
ð
3
S
Þ
τ
þ
τ
Þ
=
B
ð
Υ
ð
3
S
Þ
μ
þ
μ
Þ
using data collected with the
BABAR
detector at the SLAC PEP-II
e
þ
e
collider. The measurement is based
on a
28
fb
1
data sample collected at a center-of-mass energy of 10.355 GeV corresponding to a sample of
122 million
Υ
ð
3
S
Þ
mesons. The ratio is measured to be
R
Υ
ð
3
S
Þ
τμ
¼
0
.
966

0
.
008
stat

0
.
014
syst
and is in
agreement with the standard model prediction of 0.9948 within 2 standard deviations. The uncertainty in
R
Υ
ð
3
S
Þ
τμ
is almost an order of magnitude smaller than the only previous measurement.
DOI:
10.1103/PhysRevLett.125.241801
In the standard model (SM) the width of a spin-1 quark-
antiquark bound state decaying into a charged lepton-
antilepton pair is well known
[1]
. The ratio of widths to
final-state leptons with different flavors is free of hadronic
uncertainties, and for heavy spin-1 resonances, such as the
family of the
b
̄
b
bound-state
Υ
ð
nS
Þ
mesons, differs from
unity only by a small mass correction. Consequently,
leptonic decays of the
Υ
ð
nS
Þ
mesons are excellent
candidates to test SM predictions and search for phenom-
ena beyond the SM. For example, the Non-SM Higgs
boson
A
0
proposed in Ref.
[2]
couples more strongly
to heavier fermions and thus a larger value of the ratio
R
Υ
ð
3
S
Þ
τμ
¼
B
(
Υ
ð
3
S
Þ
τ
þ
τ
)
=
B
(
Υ
ð
3
S
Þ
μ
þ
μ
)
than that
predicted by lepton-flavor universality in the SM might
be observed. Recent measurements of
B
(
B
D
ðÞ
τν
)
=
B
(
B
D
ðÞ
ð
e=
μ
Þ
ν
)
[3]
suggest a tension with the SM
associated with lepton-flavor universality involving the
τ
lepton. It has been remarked
[4]
that new physics models
providing an explanation for that tension also unavoidably
affect the
R
Υ
ð
3
S
Þ
τμ
ratio. The only measurement to date of
that ratio was made by the CLEO Collaboration,
R
Υ
ð
3
S
Þ
τμ
¼
1
.
05

0
.
08

0
.
05
[5]
. A new precise measurement will
further constrain new physics models.
We present a precision measurement of the ratio
R
Υ
ð
3
S
Þ
τμ
using a novel technique to discriminate between
resonant and nonresonant (i.e., continuum) dimuon pro-
duction based on differences in the dimuon mass distribu-
tions associated with initial-state radiation (ISR). In the
resonant process,
e
þ
e
Υ
ð
3
S
Þ
μ
þ
μ
, ISR is heavily
suppressed compared to the nonresonant,
e
þ
e
μ
þ
μ
,
process. How we estimate the non-
Υ
ð
3
S
Þ
contribution to
the dimuon sample using this technique is detailed below.
This method ensures that the measured ratio is fully
inclusive of radiation effects and does not require a precise
luminosity determination.
We use data collected with the
BABAR
detector at the
PEP-II asymmetric-energy
e
þ
e
collider at the SLAC
National Accelerator Laboratory. The
BABAR
experiment
collected data at center-of-mass energies of the
Υ
ð
4
S
Þ
,
Υ
ð
3
S
Þ
, and
Υ
ð
2
S
Þ
resonances, as well as at nonresonant
energies. The PEP-II positron beam energy was 3.1 GeV,
while the electron beam energy was 8.6 GeV at the
Υ
ð
3
S
Þ
and 9.0 GeV at the
Υ
ð
4
S
Þ
, resulting in different boosts of
the final-state system and different detector acceptances in
the center-of-mass frame. We measure the ratio
R
Υ
ð
3
S
Þ
τμ
using a sample of 122 million
Υ
ð
3
S
Þ
decays corresponding
to an integrated luminosity of
27
.
96
fb
1
[6]
collected at
ffiffiffi
s
p
¼
10
.
355
GeV during 2008 (referred to as Run-7),
where
ffiffiffi
s
p
is the center-of-mass energy. We also employ
three data control samples: data collected at the
Υ
ð
4
S
Þ
in
2007 (referred to as Run-6) corresponding to
78
.
3
fb
1
,
data taken 40 MeV below the
Υ
ð
4
S
Þ
resonance (termed
off-resonance
) corresponding to
7
.
75
fb
1
, and data
taken 30 MeV below the
Υ
ð
3
S
Þ
resonance corresponding
to
2
.
62
fb
1
. All data used in this analysis were collected
with the same detector configuration after the last major
upgrade in 2007. These data control samples are used to
evaluate properties of the background, to study systematic
effects, and to calculate corrections to Monte Carlo (MC)
based efficiencies. A small subset of
2
.
41
fb
1
of the total
Υ
ð
3
S
Þ
sample is used at a pre-unblinding stage to optimize
the selections.
The
BABAR
detector is described in detail elsewhere
[7,8]
. Charged particles are reconstructed as tracks with a
5-layer silicon vertex tracker and 40-layer drift chamber
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
125,
241801 (2020)
241801-3
inside a 1.5 T solenoidal magnet. An electromagnetic
calorimeter (EMC) is used to identify electrons and
photons. A ring-imaging Cherenkov detector is used to
identify charged hadrons and provides additional electron
identification information. Muons are identified by an
instrumented magnetic-flux return (IFR).
The major irreducible background process is continuum
dilepton production. The
KKMC
event generator
[9]
is used
to simulate continuum
μ
þ
μ
and
τ
þ
τ
production taking
into account radiative effects. For the Bhabha process the
BHWIDE
[10]
event generator is employed. The
E
vt
G
en
generator
[11]
is used to simulate hadronic continuum
events and generic
Υ
ð
3
S
Þ
decays, with the final-state
radiation effects modeled by means of the
PHOTOS
package
[12]
. The simulated
μ
þ
μ
,
τ
þ
τ
, and generic
Υ
ð
3
S
Þ
samples correspond to roughly twice the number of events
in the
Υ
ð
3
S
Þ
dataset, while the Bhabha sample corresponds
to roughly half the number of events. In addition, the
Υ
ð
3
S
Þ
μ
þ
μ
and
Υ
ð
3
S
Þ
τ
þ
τ
signal decays are
simulated using the
KKMC
generator with the ISR turned
off. Thus the same MC generator,
KKMC
, is employed for
both the signal and continuum, which enables a consistent
evaluation of the corrections to the discrepancies between
data and MC samples. This signal MC sample is about 3
times the size of the data sample. Particle interactions with
the detector and its response are modeled within the
GEANT
4
framework
[13]
.
Dimuon candidates have two and only two reconstructed
high momentum collinear (opening angle
>
160
°) charged
particles in the center-of-mass frame with opposite charges
and with associated EMC energy depositions consistent
with the muon hypothesis. We use a polar angle acceptance
in the center-of-mass frame that ensures the selection
efficiency is independent of the center-of-mass energy
and boost. Misidentified Bhabha events are suppressed
by requiring that at least one of the muon candidates in an
event has a response in the IFR. The scaled invariant
mass
M
μμ
=
ffiffiffi
s
p
of the two muons must be in the range
0
.
8
<M
μμ
=
ffiffiffi
s
p
<
1
.
1
. This selection provides a dimuon
sample of 18818699 events with a 99.9% purity, according
to MC studies.
The
τ
þ
τ
candidate selection proceeds by requiring two
and only two reconstructed tracks with opposite charges in
the event. One of the tracks is required to be identified as an
electron based on particle identification (PID) using all
detector systems, whereas the other track must fail the same
electron selection requirements. Backgrounds are further
suppressed by requiring the angle between the two tracks to
be greater than 110° in the center-of-mass frame. The total
energy registered in the EMC must be less than 70% of the
initial
e
þ
e
energy in the laboratory frame. The acolli-
nearity between the two tracks in the azimuthal plane must
be greater than 3°. We require
j
M
2
miss
=s
j
>
0
.
01
, where the
missing mass,
M
miss
, is calculated from the tracks and up to
the ten most energetic EMC clusters identified as photons.
The missing momentum vector must point to the sensitive
part of the detector, defined as
j
cos
θ
miss
j
<
0
.
85
in the
center-of-mass frame. To further suppress the Bhabha
background, the acollinearity angle between the nonelec-
tron track and the combination of the identified electron
track and the most energetic photon must be greater than 2°
in both azimuthal and polar angles in the center-of-mass
frame. Two-photon backgrounds are suppressed by apply-
ing cuts that exploit correlations between the transverse
momenta of the two charged particles. The selected
τ
þ
τ
sample has 2173122 events with a 98.9% purity, estimated
by MC studies.
The
2
.
62
fb
1
Υ
ð
3
S
Þ
off-resonance and
7
.
75
fb
1
Υ
ð
4
S
Þ
off-resonance samples are used to correct for differences
between MC and data
τ
þ
τ
=
μ
þ
μ
selection efficiency
ratios. For the data and their corresponding MC samples,
the number of dilepton candidates (MC sample scaled to
the data luminosity) and corresponding efficiency correc-
tions are shown in Table
I
. For the
Υ
ð
3
S
Þ
and
Υ
ð
4
S
Þ
off-
resonance data samples, the
N
ττ
=N
μμ
dilepton candidate
ratios are
0
.
11665

0
.
00029
and
0
.
11647

0
.
00017
,
respectively. These are in excellent agreement, demonstrat-
ing that the efficiency ratio does not depend on the center-
of-mass energy or the different boosts. The correspond-
ing MC samples show the same behavior and the
average data-driven correction to the MC efficiency ratio
is
C
MC
¼ð
ε
ττ
=
ε
μμ
Þ
data
=
ð
ε
ττ
=
ε
μμ
Þ
MC
¼
1
.
0146

0
.
0016
.
The method to discriminate between
Υ
ð
3
S
Þ
μ
þ
μ
decays and the continuum production
e
þ
e
μ
þ
μ
is
based on the fact that the
Υ
ð
3
S
Þ
resonance is very narrow
and thus the ISR effects are highly suppressed for the signal,
but not for the continuum background. If the ISR photons
have an energy greater than a few MeV (an amount
associated with the spread in the PEP-II center-of-mass
energy of 4 MeV coming from the spread in beam energies),
then the
e
þ
e
interaction energy is too low to form the
b
̄
b
bound state. This effect results in a significant difference in
the radiative tail of the
M
μμ
distribution for the continuum
and resonance production processes for reconstructed
TABLE I. The numbers of dilepton candidates in
2
.
62
fb
1
Υ
ð
3
S
Þ
and
7
.
75
fb
1
Υ
ð
4
S
Þ
off-resonance data and MC samples and the
correction for data and MC efficiency discrepancies. The numbers of MC events are scaled according to the measured luminosity.
Off-resonance sample
N
data
μμ
N
MC
μμ
N
data
ττ
N
MC
ττ
½ð
N
data
ττ
=N
data
μμ
Þ
=
ð
N
MC
ττ
=N
MC
μμ
Þ
Υ
ð
3
S
Þ
1 538 569
1 554 208
179 466
178 569
1
.
015

0
.
003
Υ
ð
4
S
Þ
4 422 407
4 398 983
515 067
505 133
1
.
014

0
.
002
PHYSICAL REVIEW LETTERS
125,
241801 (2020)
241801-4
dimuon candidates, as shown in Fig.
1
. About 23% of the
continuum candidates are in the low-mass radiative tail
region (
M
μμ
=
ffiffiffi
s
p
<
0
.
98
), whereas for the resonance decays
this number is 7%, and is associated with final-state radiation.
In Fig.
2
the selected events are shown for simulated
Υ
ð
3
S
Þ
decays. For the dimuon events, the
M
μμ
=
ffiffiffi
s
p
variable
is plotted whereas for the
τ
þ
τ
events the total recon-
structed event energy scaled to the center-of-mass energy,
E
ττ
=
ffiffiffi
s
p
, is plotted. The total energy is evaluated using the
measured momenta of the charged particles and up to the
ten most energetic photons not associated with them. In
the dimuon events, decays of the
Υ
ð
3
S
Þ
to lower mass
Υ
ð
1
S
Þ
or
Υ
ð
2
S
Þ
resonances via radiative and hadronic
transitions, where the
Υ
ð
1
S
Þ
or
Υ
ð
2
S
Þ
then decay into a
dimuon pair, are clearly seen and separated. We refer to
such processes, including analogous
τ
þ
τ
final-state proc-
esses, as
cascade decays.
The
M
μμ
=
ffiffiffi
s
p
distribution
provides not only an estimate of the number of
Υ
ð
3
S
Þ
μ
þ
μ
events but also a direct evaluation of the contributions
from the cascade decays. In the
τ
þ
τ
channel, however,
these cascade decay channels are nearly indistinguishable.
In order to extract the ratio
R
Υ
ð
3
S
Þ
τμ
a binned maximum-
likelihood fit procedure based on the
M
μμ
=
ffiffiffi
s
p
and
E
ττ
=
ffiffiffi
s
p
distributions is employed using the method of Ref.
[14]
. The
Υ
ð
3
S
Þ
μ
þ
μ
and
Υ
ð
3
S
Þ
τ
þ
τ
templates are taken
from the
KKMC
-based MC simulation without ISR. The
templates for
Υ
ð
2
S
Þ
l
þ
l
and
Υ
ð
1
S
Þ
l
þ
l
via
cascade decays, as well as the remaining small contributions
from
Υ
ð
nS
Þ
hadronic decays, are taken from the
E
vt
G
en
-
based MC simulation. The continuum templates use data
control samples, as described in the following paragraph.
The amount of
BABAR
data collected on-resonance is
about 10 times larger than off-resonance. Consequently,
when the continuum template is based only on the
off-resonance data, the small size of that sample dominates
the statistical uncertainty of the ratio. To overcome this
limitation,
Υ
ð
4
S
Þ
on-resonance Run-6 data, with an inte-
grated luminosity of
78
.
3
fb
1
and the same detector con-
figuration as Run-7, is used for the continuum template in the
fit. The leptonic width of the
Υ
ð
4
S
Þ
is
1
.
57
×
10
5
of its total
width, which results in a negligible number of resonance-
produced dilepton events being present in the sample
compared to the number of continuum events. However,
other
Υ
ð
nS
Þ
l
þ
l
decays appear in the data continuum
template via ISR. The radiative return processes have been
extensively studied by
BABAR
(see, e.g., Ref.
[15]
) and based
onthis approach, theamountofISR-produced
Υ
ð
nS
Þ
mesons
is estimated and subtracted from the continuum template.
The number of
Υ
ð
3
S
Þ
μ
þ
μ
events
N
μμ
and the raw
ratio
̃
R
τμ
¼
N
ττ
=N
μμ
are free parameters of the fit. In the
nonsignal templates, this ratio is fixed either as in data for
the continuum background or to the simulation prediction
for the other templates.
A graphical representation of the fit result is shown in
Figs.
3
and
4
. The fit yields a raw ratio of
̃
R
τμ
¼
N
ττ
=N
μμ
¼
0
.
10778

0
.
00091
and
N
μμ
¼ð
2
.
014

0
.
015
Þ
×
10
6
0.8
0.85
0.9
0.95
1
1.05
1.1
s
/
μ
μ
M
0
100
200
300
400
500
600
700
800
Entries(a.u.)/0.0015
μ
+
μ
S)
3
(
Υ
μ
+
μ
e
+
e
Radiative tail
B
A
B
AR
FIG. 1. Comparison of
M
μμ
=
ffiffiffi
s
p
distributions for the continuum
production
e
þ
e
μ
þ
μ
in data at the
Υ
ð
4
S
Þ
off-resonance
energy and
Υ
ð
3
S
Þ
μ
þ
μ
decays in MC simulation, where only
final-state radiation is expected. The distributions are normalized
to the same number of events. The vertical dashed line shows the
border
M
μμ
=
ffiffiffi
s
p
¼
0
.
98
.
0.8
0.85
0.9
0.95
1
1.05
1.1
s
/
μ
μ
M
2
10
3
10
4
10
5
10
6
10
Entries/0.0015
μ
+
μ
)
3S
(
Υ
μ
+
μ
)
2S
(
Υ
Cascade
μ
+
μ
)
1S
(
Υ
Cascade
) decays
3S
(
Υ
Other
B
A
B
AR
0
0.2
0.4
0.6
0.8
1
s
/
τ
τ
E
2
10
3
10
4
10
5
10
6
10
Entries/0.0200
τ
+
τ
)
3S
(
Υ
τ
+
τ
)
2S
(
Υ
Cascade
τ
+
τ
)
1S
(
Υ
Cascade
) decays
3S
(
Υ
Other
B
A
B
AR
FIG. 2. Distributions of
M
μμ
=
ffiffiffi
s
p
(top plot) and
E
ττ
=
ffiffiffi
s
p
(bottom
plot) variables in MC simulation. Cascade decays are clearly
separated in dimuon events and nearly indistinguishable in
τ
þ
τ
events.
PHYSICAL REVIEW LETTERS
125,
241801 (2020)
241801-5
events. The MC-based selection efficiencies and their ratio,
required to obtain the ratio
R
τμ
, are shown in Table
II
.
Low multiplicity
Υ
ð
4
S
Þ
B
̄
B
decays can mimic
τ
-pair
events and pass the selection criteria. According to MC
studies, the
B
̄
B
contribution to the muon template is
negligible whereas the
B
̄
B
background in the
τ
þ
τ
template
translates into a correction of
δ
B
̄
B
¼
0
.
42%
to the expected
number of
Υ
ð
3
S
Þ
τ
þ
τ
candidates and is applied to the
ratio
R
τμ
.
Combining the fit result
̃
R
τμ
, the ratio of MC efficiencies
ε
μμ
=
ε
ττ
, the data/MC correction
C
MC
, and the correction
from
B
̄
B
events
δ
B
̄
B
, the ratio is
R
Υ
ð
3
S
Þ
τμ
¼
̃
R
τμ
1
C
MC
ε
μμ
ε
ττ
ð
1
þ
δ
B
̄
B
Þ¼
0
.
9662

0
.
0084
;
where uncertainties from the data/MC correction and MC
efficiencies are included in the statistical uncertainty.
The sources of the systematic uncertainty in
R
Υ
ð
3
S
Þ
τμ
are
summarized in Table
III
. The PID uncertainty is assessed by
studying three additional
τ
þ
τ
classifiers. The first used
tighter electronselectors for both the
τ
to electron and the
τ
to
nonelectron selection. The second applied a tighter electron
selector only for the
τ
to nonelectron selection. The third
replaced the
τ
to nonelectron selection with an explicit
requirement that the nonelectron particle be identified as a
muon or a pion. Even though the data-driven corrections
associated with each of these separate
τ
þ
τ
classifiers were
applied, and despite the highly correlated statistics in these
samples, there remains a 0.9% difference between one of
these test classifiers and the default classifier, which we
assign as the PID systematic uncertainty.
The ratio of the number of dimuon and
τ
þ
τ
events from
the cascade decays in the MC fit templates is fixed
according to lepton-flavor universality. This ratio was
varied according to the current experimental uncertainties
in branching fractions for
Υ
ð
1
S
Þ
and
Υ
ð
2
S
Þ
to dimuon and
τ
þ
τ
final states, resulting in a maximum difference in
̃
R
τμ
of 0.6%, which is taken as the systematic uncertainty.
0
500
1000
3
10
×
Entries/0.0015
0
50
100
150
0
5
10
15
0.8
0.85
0.9
0.95
1
1.05
1.1
s
/
μ
μ
M
(a)
(b)
(c)
Data
μ
+
μ
e
+
e
μ
+
μ
)
3S
(
Υ
μ
+
μ
)
2S
(
Υ
Cascade
μ
+
μ
)
1S
(
Υ
Cascade
B
A
B
AR
FIG. 3. The result of the template fit to the
Υ
ð
3
S
Þ
data in the
M
μμ
=
ffiffiffi
s
p
variable. In (a) all events are shown, in (b) and (c) the
dominant continuum
e
þ
e
μ
þ
μ
background is subtracted,
and (c) is a magnified view of (b) to better show cascade decays
and the radiative-tail region.
0
0.2
0.4
0.6
0.8
1
s
/
τ
τ
E
0
2
4
6
8
10
12
14
3
10
×
Entries/0.02
B
A
B
AR
FIG. 4. The result of the template fit to the
Υ
ð
3
S
Þ
data in the
E
ττ
=
ffiffiffi
s
p
variable after the continuum background is subtracted.
Data are depicted as points with error bars. The legend is the same
as in the corresponding plot in Fig.
2
.
TABLE II. MC selection efficiencies in percent for
Υ
ð
3
S
Þ
l
þ
l
. The quoted uncertainties reflect MC statistics.
ε
μμ
(%)
ε
ττ
(%)
ε
ττ
=
ε
μμ
69
.
951

0
.
018
7
.
723

0
.
010
0
.
11041

0
.
00015
TABLE III. The summary of systematic uncertainties.
Source
Uncertainty (%)
Particle identification
0.9
Cascade decays
0.6
Two-photon production
0.5
Υ
ð
3
S
Þ
hadrons
0.4
MC shape
0.4
B
̄
B
contribution
0.2
ISR subtraction
0.2
Total
1.4
PHYSICAL REVIEW LETTERS
125,
241801 (2020)
241801-6
The systematic uncertainty associated with two-photon
background is estimated by varying the selection on the
transverse momenta to reduce the
τ
þ
τ
selection efficiency
to almost half its nominal value. These variations result in a
maximal deviation in
̃
R
τμ
of 0.5%.
The simulation of other generic
Υ
ð
3
S
Þ
decays shows that
a small fraction of background events (about 0.1% of
dimuon and 1% of
τ
þ
τ
samples) still pass the selection
criteria. The amount of this background is fixed to the MC
prediction in the fit and a 0.4% systematic uncertainty
assessed by varying these backgrounds by

50%
.
The systematic uncertainty from the MC template shape
modeling associated with the radiative and resolution
effects is estimated to be 0.4% based on varying the
M
μμ
resolution and from changing the templates based
on
KKMC
with those using
E
vt
G
en
with
PHOTOS
.
A systematic uncertainty of 0.2% is associated with the
B
̄
B
background in the continuum template, estimated by
varying the expected amount of the background by

50%
.
The systematic uncertainty associated with
Υ
ð
nS
Þ
mes-
ons produced by the radiative return process in the
continuum template is estimated by accounting for exper-
imental uncertainties of total widths and leptonic branching
fractions of these mesons and by varying the overall
amount of these produced mesons by 10% in order to
conservatively account for radiator function uncertainties.
We assign a value of 0.2% as the associated systematic
uncertainty.
Systematic uncertainties described in the preceding
paragraphs are combined in quadrature, giving a total
systematic uncertainty of 1.4%.
In conclusion, based on the data collected by the
BABAR
detector near the
Υ
ð
3
S
Þ
and
Υ
ð
4
S
Þ
resonances, the ratio of
the leptonic branching fractions of the
Υ
ð
3
S
Þ
meson is
measured to be
R
Υ
ð
3
S
Þ
τμ
¼
0
.
966

0
.
008
stat

0
.
014
syst
:
This is 6 times more precise than the only previous
measurement
[5]
and is within 2 standard deviations of
the SM prediction of 0.9948
[4]
.
We are grateful for the excellent luminosity and
machine conditions provided by our PEP-II colleagues,
and for the substantial dedicated effort from the computing
organizations that support
BABAR
. The collaborating
institutions wish to thank SLAC for its support and
kind hospitality. This work is supported by DOE and
NSF (USA), NSERC (Canada), CEA and CNRS-IN2P3
(France), BMBF and DFG (Germany), INFN (Italy),
FOM (Netherlands), NFR (Norway), MES (Russia),
MINECO (Spain), STFC (United Kingdom), BSF
(USA-Israel). Individuals have received support from the
Marie Curie EIF (European Union) and the A. P. Sloan
Foundation (USA).
*
Deceased.
Corresponding author.
sibid@uvic.ca
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: 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 L'Aquila,
Italy.
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