Search for
B
þ
→
K
þ
τ
þ
τ
−
at the
B
A
B
AR
Experiment
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
H. Koch,
6
T. Schroeder,
6
C. Hearty,
7
T. S. Mattison,
7
J. A. McKenna,
7
R. Y. So,
7
V. E. Blinov,
8a,8b,8c
A. R. Buzykaev,
8a
V. P. Druzhinin,
8a,8b
V. B. Golubev,
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
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
T. S. Miyashita,
12
P. Ongmongkolkul,
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
A. Zallo,
17
S. Passaggio,
18
C. Patrignani,
18
,
†
B. Bhuyan,
19
U. Mallik,
20
C. Chen,
21
J. Cochran,
21
S. Prell,
21
H. Ahmed,
22
A. V. Gritsan,
23
N. Arnaud,
24
M. Davier,
24
F. Le Diberder,
24
A. M. Lutz,
24
G. Wormser,
24
D. J. Lange,
25
D. M. Wright,
25
J. P. Coleman,
26
E. Gabathuler,
26
D. E. Hutchcroft,
26
D. J. Payne,
26
C. Touramanis,
26
A. J. Bevan,
27
F. Di Lodovico,
27
R. Sacco,
27
G. Cowan,
28
Sw. Banerjee,
29
D. N. Brown,
29
C. L. Davis,
29
A. G. Denig,
30
M. Fritsch,
30
W. Gradl,
30
K. Griessinger,
30
A. Hafner,
30
K. R. Schubert,
30
R. J. Barlow,
31
,
‡
G. D. Lafferty,
31
R. Cenci,
32
A. Jawahery,
32
D. A. Roberts,
32
R. Cowan,
33
R. Cheaib,
34
S. H. Robertson,
34
B. Dey,
35a
N. Neri,
35a
F. Palombo,
35a,35b
L. Cremaldi,
36
R. Godang,
36
,§
D. J. Summers,
36
P. Taras,
37
G. De Nardo,
38
C. Sciacca,
38
G. Raven,
39
C. P. Jessop,
40
J. M. LoSecco,
40
K. Honscheid,
41
R. Kass,
41
A. Gaz,
42a
M. Margoni,
42a,42b
M. Posocco,
42a
M. Rotondo,
42a
G. Simi,
42a,42b
F. Simonetto,
42a,42b
R. Stroili,
42a,42b
S. Akar,
43
E. Ben-Haim,
43
M. Bomben,
43
G. R. Bonneaud,
43
G. Calderini,
43
J. Chauveau,
43
G. Marchiori,
43
J. Ocariz,
43
M. Biasini,
44a,44b
E. Manoni,
44a
A. Rossi,
44a
G. Batignani,
45a,45b
S. Bettarini,
45a,45b
M. Carpinelli,
45a,45b
,
∥
G. Casarosa,
45a,45b
M. Chrzaszcz,
45a
F. Forti,
45a,45b
M. A. Giorgi,
45a,45b
A. Lusiani,
45a,45b
B. Oberhof,
45a,45b
E. Paoloni,
45a,45b
M. Rama,
45a
G. Rizzo,
45a,45b
J. J. Walsh,
45a
A. J. S. Smith,
46
F. Anulli,
47a
R. Faccini,
47a,47b
F. Ferrarotto,
47a,47b
F. Ferroni,
47a,47b
A. Pilloni,
47a,47b
G. Piredda,
47a
C. Bünger,
48
S. Dittrich,
48
O. Grünberg,
48
M. Heß,
48
T. Leddig,
48
C. Voß,
48
R. Waldi,
48
T. Adye,
49
F. F. Wilson,
49
S. Emery,
50
G. Vasseur,
50
D. Aston,
51
C. Cartaro,
51
M. R. Convery,
51
J. Dorfan,
51
W. Dunwoodie,
51
M. Ebert,
51
R. C. Field,
51
B. G. Fulsom,
51
M. T. Graham,
51
C. Hast,
51
W. R. Innes,
51
P. Kim,
51
D. W. G. S. Leith,
51
S. Luitz,
51
V. Luth,
51
D. B. MacFarlane,
51
D. R. Muller,
51
H. Neal,
51
B. N. Ratcliff,
51
A. Roodman,
51
M. K. Sullivan,
51
J. Va
’
vra,
51
W. J. Wisniewski,
51
M. V. Purohit,
52
J. R. Wilson,
52
A. Randle-Conde,
53
S. J. Sekula,
53
M. Bellis,
54
P. R. Burchat,
54
E. M. T. Puccio,
54
M. S. Alam,
55
J. A. Ernst,
55
R. Gorodeisky,
56
N. Guttman,
56
D. R. Peimer,
56
A. Soffer,
56
S. M. Spanier,
57
J. L. Ritchie,
58
R. F. Schwitters,
58
J. M. Izen,
59
X. C. Lou,
59
F. Bianchi,
60a,60b
F. De Mori,
60a,60b
A. Filippi,
60a
D. Gamba,
60a,60b
L. Lanceri,
61
L. Vitale,
61
F. Martinez-Vidal,
62
A. Oyanguren,
62
J. Albert,
63
A. Beaulieu,
63
F. U. Bernlochner,
63
G. J. King,
63
R. Kowalewski,
63
T. Lueck,
63
I. M. Nugent,
63
J. M. Roney,
63
N. Tasneem,
63
T. J. Gershon,
64
P. F. Harrison,
64
T. E. Latham,
64
R. Prepost,
65
and S. L. Wu
65
(
B
A
B
AR
Collaboration)
1
Laboratoire d
’
Annecy-le-Vieux de Physique des Particules (LAPP), Université de Savoie, CNRS/IN2P3,
F-74941 Annecy-Le-Vieux, France
2
Universitat de Barcelona, Facultat de Fisica, Departament ECM, E-08028 Barcelona, Spain
3
INFN Sezione di Bari and Dipartimento di Fisica, Università di Bari, I-70126 Bari, Italy
4
University of Bergen, Institute of Physics, N-5007 Bergen, Norway
5
Lawrence Berkeley National Laboratory and University of California, Berkeley, California 94720, USA
6
Ruhr Universität Bochum, Institut für Experimentalphysik 1, D-44780 Bochum, Germany
7
University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z1
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
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
PRL
118,
031802 (2017)
PHYSICAL REVIEW LETTERS
week ending
20 JANUARY 2017
0031-9007
=
17
=
118(3)
=
031802(8)
031802-1
© 2017 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, Università 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
Indian Institute of Technology Guwahati, Guwahati, Assam 781 039, India
20
University of Iowa, Iowa City, Iowa 52242, USA
21
Iowa State University, Ames, Iowa 50011, USA
22
Physics Department, Jazan University, Jazan 22822, Kingdom of Saudi Arabia
23
Johns Hopkins University, Baltimore, Maryland 21218, USA
24
Laboratoire de l
’
Accélérateur Linéaire, IN2P3/CNRS et Université Paris-Sud 11, Centre Scientifique d
’
Orsay,
F-91898 Orsay Cedex, France
25
Lawrence Livermore National Laboratory, Livermore, California 94550, USA
26
University of Liverpool, Liverpool L69 7ZE, United Kingdom
27
Queen Mary, University of London, London E1 4NS, United Kingdom
28
University of London, Royal Holloway and Bedford New College, Egham, Surrey TW20 0EX, United Kingdom
29
University of Louisville, Louisville, Kentucky 40292, USA
30
Johannes Gutenberg-Universität Mainz, Institut für Kernphysik, D-55099 Mainz, Germany
31
University of Manchester, Manchester M13 9PL, United Kingdom
32
University of Maryland, College Park, Maryland 20742, USA
33
Massachusetts Institute of Technology, Laboratory for Nuclear Science, Cambridge, Massachusetts 02139, USA
34
McGill University, Montréal, Québec, Canada H3A 2T8
35a
INFN Sezione di Milano, I-20133 Milano, Italy
35b
Dipartimento di Fisica, Università di Milano, I-20133 Milano, Italy
36
University of Mississippi, University, Mississippi 38677, USA
37
Université de Montréal, Physique des Particules, Montréal, Québec, Canada H3C 3J7
38
INFN Sezione di Napoli and Dipartimento di Scienze Fisiche, Università di Napoli Federico II, I-80126 Napoli, Italy
39
NIKHEF, National Institute for Nuclear Physics and High Energy Physics, NL-1009 DB Amsterdam, The Netherlands
40
University of Notre Dame, Notre Dame, Indiana 46556, USA
41
Ohio State University, Columbus, Ohio 43210, USA
42a
INFN Sezione di Padova, I-35131 Padova, Italy
42b
Dipartimento di Fisica, Università di Padova, I-35131 Padova, Italy
43
Laboratoire de Physique Nucléaire et de Hautes Energies, IN2P3/CNRS, Université Pierre et Marie Curie-Paris6,
Université Denis Diderot-Paris7, F-75252 Paris, France
44a
INFN Sezione di Perugia, I-06123 Perugia, Italy
44b
Dipartimento di Fisica, Università di Perugia, I-06123 Perugia, Italy
45a
INFN Sezione di Pisa, I-56127 Pisa, Italy
45b
Dipartimento di Fisica, Università di Pisa, I-56127 Pisa, Italy
45c
Scuola Normale Superiore di Pisa, I-56127 Pisa, Italy
46
Princeton University, Princeton, New Jersey 08544, USA
47a
INFN Sezione di Roma, I-00185 Roma, Italy
47b
Dipartimento di Fisica, Università di Roma La Sapienza, I-00185 Roma, Italy
48
Universität Rostock, D-18051 Rostock, Germany
49
Rutherford Appleton Laboratory, Chilton, Didcot, Oxon OX11 0QX, United Kingdom
50
CEA, Irfu, SPP, Centre de Saclay, F-91191 Gif-sur-Yvette, France
51
SLAC National Accelerator Laboratory, Stanford, California 94309 USA
52
University of South Carolina, Columbia, South Carolina 29208, USA
53
Southern Methodist University, Dallas, Texas 75275, USA
54
Stanford University, Stanford, California 94305, USA
55
State University of New York, Albany, New York 12222, USA
56
Tel Aviv University, School of Physics and Astronomy, Tel Aviv 69978, Israel
57
University of Tennessee, Knoxville, Tennessee 37996, USA
58
University of Texas at Austin, Austin, Texas 78712, USA
59
University of Texas at Dallas, Richardson, Texas 75083, USA
60a
INFN Sezione di Torino, I-10125 Torino, Italy
60b
Dipartimento di Fisica, Università di Torino, I-10125 Torino, Italy
61
INFN Sezione di Trieste and Dipartimento di Fisica, Università di Trieste, I-34127 Trieste, Italy
62
IFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spain
63
University of Victoria, Victoria, British Columbia, Canada V8W 3P6
64
Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
PRL
118,
031802 (2017)
PHYSICAL REVIEW LETTERS
week ending
20 JANUARY 2017
031802-2
65
University of Wisconsin, Madison, Wisconsin 53706, USA
(Received 17 June 2016; published 20 January 2017)
We search for the rare flavor-changing neutral current process
B
þ
→
K
þ
τ
þ
τ
−
using data from the
BABAR
experiment. The data sample, collected at the center-of-mass energy of the
Υ
ð
4
S
Þ
resonance,
corresponds to a total integrated luminosity of
424
fb
−
1
and to
471
×
10
6
B
̄
B pairs. We reconstruct one
B
meson, produced in the
Υ
ð
4
S
Þ
→
B
þ
B
−
decay, in one of many hadronic decay modes and search for
activity compatible with a
B
þ
→
K
þ
τ
þ
τ
−
decay in the rest of the event. Each
τ
lepton is required to decay
leptonically into an electron or muon and neutrinos. Comparing the expected number of background events
with the data sample after applying the selection criteria, we do not find evidence for a signal. The resulting
upper limit, at the 90% confidence level, is
B
ð
B
þ
→
K
þ
τ
þ
τ
−
Þ
<
2
.
25
×
10
−
3
.
DOI:
10.1103/PhysRevLett.118.031802
The flavor-changing neutral current process
B
þ
→
K
þ
τ
þ
τ
−
[1]
is highly suppressed in the standard model (SM),
with a predicted branching fraction in the range
1
–
2
×
10
−
7
[2,3]
. This decay is forbidden at tree level and only occurs,
at lowest order, via one-loop diagrams. The SM contribu-
tions, shown in Fig.
1
, include the electromagnetic penguin,
the
Z
penguin, and the
W
þ
W
−
box diagrams. Rare semi-
leptonic
B
decays such as
B
þ
→
K
þ
τ
þ
τ
−
can provide a
stringent test of the SM and a fertile ground for new physics
searches. Virtual particles can enter in the loop and thus
allow us to probe, at relatively low energies, new physics at
large mass scales. Measurements of the related decays
B
þ
→
K
þ
l
þ
l
−
, where
l
¼
e
or
μ
, have been previously
published by
BABAR
[4]
and other experiments
[5
–
8]
, and
exhibit some discrepancy with the SM expectation
[9]
.
The decay
B
þ
→
K
þ
τ
þ
τ
−
is the third family equivalent
of
B
þ
→
K
þ
l
þ
l
−
and hence may provide additional
sensitivity to new physics due to third-generation couplings
and the large mass of the
τ
lepton
[10]
. An important
potential contribution to this decay is from neutral Higgs
boson couplings, where the lepton-lepton-Higgs vertices
are proportional to the mass squared of the lepton
[11]
.
Thus, in the case of the
τ
, such contributions can be
significant and could alter the total decay rate. Additional
sources of new physics and their effect on the
B
þ
→
K
þ
τ
þ
τ
−
branching fraction and the kinematic distributions
of the
τ
þ
τ
−
pair are also discussed in Refs.
[12
–
24]
. These
new physics scenarios do not necessarily have the same
impact on the
B
þ
→
K
þ
ψ
ð
2
S
Þ
,
ψ
ð
2
S
Þ
→
τ
þ
τ
−
decay, and
thus the latter will only be considered if a visible signal is
present.
We report herein a search for
B
þ
→
K
þ
τ
þ
τ
−
with data
recorded by the
BABAR
detector
[25]
at the
e
þ
e
−
PEP-II
collider at the SLAC National Accelerator Laboratory. This
search is based on
424
fb
−
1
of data
[26]
collected at the
center-of-mass (c.m.) energy of the
Υ
ð
4
S
Þ
resonance,
where
Υ
ð
4
S
Þ
decays into a
B
̄
B
pair. We use hadronic
B
meson tagging techniques, where one of the two
B
mesons,
referred to as the
B
tag
, is reconstructed exclusively via its
decay into one of several hadronic decay modes. The
remaining tracks, clusters, and missing energy in the event
are attributed to the signal
B
, denoted as
B
sig
, on which the
search for
B
þ
→
K
þ
τ
þ
τ
−
is performed. We consider only
leptonic decays of the
τ
∶
τ
þ
→
e
þ
ν
e
̄
ν
τ
and
τ
þ
→
μ
þ
ν
μ
̄
ν
τ
,
which results in three signal decay topologies with a
charged
K
, multiple missing neutrinos, and either
e
þ
e
−
,
μ
þ
μ
−
,or
e
þ
μ
−
in the final state. The neutrinos are
accounted for as missing energy in any signal event where
a charged kaon and lepton pair are identified and extra
neutral activity, including
π
0
candidates, is excluded.
Simulated Monte Carlo (MC) signal and background
events, generated with
E
vt
G
en
[27]
, are used to develop
signal selection criteria and to study potential backgrounds.
The detector response is simulated using
GEANT
4
[28]
.
Signal MC events are generated as
Υ
ð
4
S
Þ
→
B
þ
B
−
, where
one
B
decays according to its measured SM branching
fractions
[29]
and the other
B
decays via
B
þ
→
K
þ
τ
þ
τ
−
according to the model described in Ref.
[30]
. Within this
model, a light-cone sum rule approach, referred to as LCSR
is used to determine the form factors that enter into the
parametrization of the matrix elements describing this
decay. Signal events are also reweighted to a model based
on the unquenched lattice QCD calculations of the
B
→
K
l
þ
l
−
form factors
[2]
for the determination of the signal
efficiency, and the two theoretical approaches are then
compared to evaluate the model dependence of our meas-
urement. Because of the low efficiency of the hadronic
B
tag
reconstruction,
“
dedicated
”
signal MC samples are also
generated for this analysis, where one
B
decays exclusively
through
B
→
D
0
π
,
D
0
→
K
−
π
þ
while the other
B
meson decays via the signal channel. This ensures that
more events pass the hadronic
B
tag
reconstruction and
q
q
bs
t,c,u
W
, Z
l
+
l
q
q
bs
t,c,u
W
+
W
l
l
+
FIG. 1. Lowest order SM Feynman diagrams of
b
→
s
l
þ
l
−
.
PRL
118,
031802 (2017)
PHYSICAL REVIEW LETTERS
week ending
20 JANUARY 2017
031802-3
allows for increased statistics in the distributions of
discriminating variables in the signal sample. Only varia-
bles that are independent of the
B
tag
decay mode are
considered with the dedicated signal MC sample. To avoid
potential bias, this dedicated sample is not used to evaluate
the final signal selection efficiency. Background MC
samples consist of
B
þ
B
−
and
B
0
̄
B
0
decays and continuum
events,
e
þ
e
−
→
f
̄
f
, where
f
is a lepton or a quark. The
B
̄
B
and
e
þ
e
−
→
c
̄
c
MC-simulated samples are produced with
an integrated luminosity 10 times that of data, whereas the
remaining continuum samples have an integrated luminos-
ity that is 4 times larger.
The signal selection of
B
þ
→
K
þ
τ
þ
τ
−
events is pre-
ceded by the full hadronic reconstruction of the
B
tag
meson,
via
B
→
SX
[31]
. Here,
S
is a seed meson,
D
ðÞ
0
,
D
ðÞ
,
D
s
,or
J=
ψ
, and
X
is a combination of at most five charged
or neutral kaons and pions with at most two neutral
π
0
or
K
0
S
candidates. The
D
seeds are reconstructed in the decay
modes
D
þ
→
K
0
S
π
þ
,
K
0
S
π
þ
π
0
,
K
0
S
π
þ
π
−
π
þ
,
K
−
π
þ
π
þ
,
K
−
π
þ
π
þ
π
0
,
K
þ
K
−
π
þ
,
K
þ
K
−
π
þ
π
0
;
D
0
→
K
−
π
þ
,
K
−
π
þ
π
0
,
K
−
π
þ
π
−
π
þ
,
K
0
S
π
þ
π
−
,
K
0
S
π
þ
π
−
π
0
,
K
þ
K
−
,
π
þ
π
−
,
π
þ
π
−
π
0
, and
K
0
S
π
0
;
D
þ
→
D
0
π
þ
,
D
þ
π
0
;
D
0
→
D
0
π
0
,
D
0
γ
. The
D
þ
s
and
J=
ψ
seeds are recon-
structed as
D
þ
s
→
D
þ
s
γ
;
D
þ
s
→
φπ
þ
,
K
0
S
K
þ
; and
J=
ψ
→
e
þ
e
−
,
μ
þ
μ
−
, respectively.
K
0
S
and
φ
candidates
are reconstructed via their decay to
π
þ
π
−
and
K
þ
K
−
,
respectively.
We select
B
tag
candidates using two kinematic variables:
m
ES
¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ð
E
c
:
m
:
=
2
Þ
2
−
~
p
2
B
tag
q
and
Δ
E
¼ð
E
c
:
m
:
=
2
Þ
−
E
B
tag
,
where
E
B
tag
and
~
p
B
tag
are the c.m. energy and three-
momentum vector of the
B
tag
, respectively, and
ð
E
c
:
m
:
=
2
Þ
is the c.m. beam energy. A properly reconstructed
B
tag
has
m
ES
consistent with the mass of a
B
meson and
Δ
E
consistent with 0 GeV. We require
5
.
20
<m
ES
<
5
.
30
GeV
=c
2
and
−
0
.
12
<
Δ
E<
0
.
12
GeV, where the
m
ES
range includes a sideband region for background
studies. On average, about two
B
tag
candidates per event
satisfy these requirements, where the multiplicity is usually
related to whether or not a soft
π
0
is included in the
exclusive reconstruction. If there are multiple
B
tag
candi-
dates per event, the
B
tag
candidate in the highest purity
mode is chosen. The purity of a
B
tag
decay mode is
determined from MC studies and is defined as the fraction,
ranging from 0 to 1, of
B
tag
candidates with
m
ES
>
5
.
27
GeV
=c
2
that are properly reconstructed within the
given mode. If more than one
B
tag
candidate with the same
purity exists, the one with the smallest
j
Δ
E
j
is chosen.
The hadronic
B
tag
reconstruction results in both charged
and neutral
B
mesons. Since the
B
tag
is fully reconstructed,
its four-vector is fully determined and thus that of the
B
sig
can be calculated. The latter is obtained using
j
~
p
B
sig
j¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ð
E
c
:
m
:
=
2
Þ
2
−
m
2
B
p
, where
~
p
B
sig
is the three-
momentum vector of
B
sig
in the c.m. frame and
m
B
is
the mass of the
B
meson, with the direction of
~
p
B
sig
opposite
to that of
~
p
B
tag
. The missing momentum four-vector
p
miss
is
determined by subtracting the c.m. four-momentum of all
“
signal-side
”
tracks and clusters from that of the
B
sig
.
B
þ
→
K
þ
τ
þ
τ
−
signal events are required to have a
charged
B
tag
candidate with
m
ES
>
5
.
27
GeV
=c
2
and
missing energy,
E
miss
given by the energy component of
p
miss
, greater than zero. Furthermore, to reduce contami-
nation from misreconstructed events with high-multiplicity
B
tag
decay modes, the purity of
B
tag
candidates is recalcu-
lated at this point after also requiring that there remain only
three charged tracks in the event not used in the
B
tag
reconstruction (corresponding to the track multiplicity in
signal events). This purity is more relevant to the signal
selection, since only charged
B
tag
decay modes recon-
structed with low multiplicity
B
sig
events are considered.
Signal events with a purity greater than 40% are retained.
Continuum events are further suppressed using a multi-
variate likelihood selector, which consists of six event-
shape variables. These include the magnitude of the
B
tag
thrust, defined as the axis that maximizes the sum of the
longitudinal momenta of an event
’
s decay products, and its
component along the beam axis and the ratio of the second-
to-zeroth Fox-Wolfram moment
[32]
. The remaining var-
iables are the angle of the missing momentum vector
~
p
miss
with the beam axis, the angle between
~
p
B
tag
and the beam
axis, and the angle between the thrust axis of the
B
tag
and
that of the
B
sig
in the c.m. frame. The six event-shape
variables discriminate between
B
̄
B
events, where the spin-
zero
B
mesons are produced almost at rest and the decay
daughters consequently produce an isotropic distribution,
and continuum events. In the latter, fermions are initially
produced with higher momentum, resulting in a more
collinear distribution of the final decay products. We
require the likelihood ratio
L
¼
Q
i
P
B
ð
x
i
Þ
Q
i
P
B
ð
x
i
Þþ
Q
i
P
q
ð
x
i
Þ
>
0
.
50
;
ð
1
Þ
where
P
ð
x
i
Þ
are probability density functions, determined
from MC samples, that describe the six event shape
variables for
B
̄
B
,
P
B
ð
x
i
Þ
, and continuum,
P
q
ð
x
i
Þ
, events.
This requirement removes more than 75% of the continuum
events while retaining more than 80% of (signal and
background)
B
̄
B
MC events.
A signal selection is then applied on the charged tracks
and neutral clusters that are not used in the
B
tag
reconstruction.
B
þ
→
K
þ
τ
þ
τ
−
candidates are required to
possess exactly three charged tracks satisfying particle
identification (PID) requirements consistent with one
charged
K
and an
e
þ
e
−
,
μ
þ
μ
−
,or
e
þ
μ
−
pair. The PID
selection algorithms for charged tracks are based on
multivariate analysis techniques that use information from
the
BABAR
detector subsystems
[25]
. The
K
is required to
have a charge opposite to that of
B
tag
. Furthermore, events
with
3
.
00
<m
l
þ
l
−
<
3
.
19
GeV
=c
2
are discarded to
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remove backgrounds with a
J=
ψ
resonance. The invariant
mass of the combination of the
K
with the oppositely
charged lepton must also lie outside the region of the
D
0
mass, i.e.,
m
K
−
l
þ
<
1
.
80
GeV
=c
2
or
m
K
−
l
þ
>
1
.
90
GeV
=c
2
, to remove events where a pion coming from
the
D
0
decay is misidentified as a muon. Moreover, events
with
γ
→
e
þ
e
−
are removed by requiring the invariant mass
of each electron with any other oppositely charged track
in the event to be greater than
50
MeV
=c
2
. Background
events with
π
0
candidates, reconstructed from a pair of
photons with individual energies greater than 50 MeV, a
total c.m. energy greater than 100 MeV, and an invariant
mass ranging between 100 and
160
MeV
=c
2
, are rejected.
Additional calorimeter clusters not explicitly associated
with
B
tag
daughter particles may originate from other low-
energy particles in background events. We therefore define
E
extra
to be the energy sum of all neutral clusters with
individual energy greater than 50 MeV that are not used in
the
B
tag
reconstruction.
The normalized squared mass of the
τ
þ
τ
−
pair is given
by
s
B
¼ð
p
B
sig
−
p
K
Þ
2
=m
2
B
, where
p
B
sig
and
p
K
are the
four-momentum vectors of
B
sig
and of the kaon, respec-
tively, in the laboratory frame. The large mass of the
τ
leptons in signal events kinematically limits the
s
B
dis-
tribution to large values. A requirement of
s
B
>
0
.
45
is
applied. A peaking distribution about the
ψ
ð
2
S
Þ
s
B
value is
not observed, and thus the contribution of this background
is considered negligible.
At this point in the selection, remaining backgrounds are
primarily
B
̄
B
events in which a properly reconstructed
B
tag
is accompanied by
B
sig
→
D
ðÞ
l
̄
ν
l
with
D
ðÞ
→
K
l
0
̄
ν
l
0
and
thus have the same detected final-state particles as signal
events. A multilayer perceptron (MLP) neural network
[33]
, with eight input variables and one hidden layer, is
employed to suppress this background. The input variables
are (i) the angle between the kaon and the oppositely
charged lepton; (ii) the angle between the two leptons;
(iii) the momentum of the lepton with charge opposite to
the
K
, all in the
τ
þ
τ
−
rest frame, which is calculated as
p
B
sig
−
p
K
; (iv) the angle between the
B
sig
and the oppo-
sitely charged lepton; (v) the angle between the
K
and the
low-momentum lepton; and (vi) the invariant mass of the
K
þ
l
−
pair, all in the c.m. frame. Furthermore, the final
input variables to the neural network are (vii)
E
extra
and
(viii) the residual energy
E
res
, which here is effectively the
missing energy associated with the
τ
þ
τ
−
pair and is
calculated as the energy component of
p
τ
residual
¼
p
τ
B
sig
−
p
τ
K
−
p
τ
l
þ
l
−
, where
p
τ
B
sig
,
p
τ
K
, and
p
τ
l
þ
l
−
are the four-
momenta vectors in the
τ
þ
τ
−
rest frame of the
B
sig
,
K
,
and lepton pair in the event, respectively.
E
res
has, in
general, higher values for signal events than generic
B
̄
B
and
continuum events due to the higher neutrino multiplicity. A
neural network is trained and tested using randomly split
dedicated signal MC and
B
þ
B
−
background events, for
each of the three channels:
e
þ
e
−
,
μ
þ
μ
−
, and
e
þ
μ
−
. The
results are shown in Fig.
2
for the three modes combined.
The last step in the signal selection is to require that the
output of the neural network be
>
0
.
70
for the
e
þ
e
−
and
μ
þ
μ
−
channels and
>
0
.
75
for the
e
þ
μ
−
channel. This
requirement is optimized to yield the most stringent upper
limit in the absence of a signal.
The branching fraction for each of the signal modes
i
is
calculated as
B
i
¼
N
i
obs
−
N
i
bkg
ε
i
sig
N
B
̄
B
;
ð
2
Þ
where
N
B
̄
B
¼
471
×
10
6
is the total number of
B
̄
B
pairs in
the data sample, assuming equal production of
B
þ
B
−
and
B
0
̄
B
0
pairs in
Υ
ð
4
S
Þ
decays, and
N
i
obs
is the number of data
events passing the signal selection. The signal efficiency
ε
i
sig
and the background estimate
N
i
bkg
are determined for
each mode from the signal and background MC yields after
all selection requirements.
For each mode,
N
bkg
consists of two components:
background events that have a properly reconstructed
B
tag
and thus produce a distribution in
m
ES
that peaks at
the
B
mass, and combinatorial background events com-
posed of continuum and
B
̄
B
events with misreconstructed
B
tag
candidates that do not produce a peaking structure in
the
m
ES
signal region. After the MLP output requirement,
peaking background events comprise 84% of the total
N
bkg
for all three modes. To reduce the dependence on MC
simulation, the combinatorial background is extrapolated
directly from the yield of data events in the
m
ES
“
sideband
”
region (
5
.
20
<m
ES
<
5
.
26
GeV
=c
2
), after the full signal
selection. The yield of sideband data events is scaled by the
ratio, determined from MC calculations, of combinatorial
background in the
m
ES
signal region to that in the
m
ES
sideband region, and used to estimate the combinatorial
background component of data in the signal region.
The peaking background is determined using
B
þ
B
−
background MC calculations, while data in the final signal
region is kept blinded to avoid experimentalist bias.
Because of the large uncertainties on the branching
fractions of many of the
B
tag
decay modes as well as their
associated reconstruction effects, there is a discrepancy in
the
B
tag
yield of approximately 10% between MC calcu-
lations and data, independent of the signal selection. A
B
tag
yield correction is therefore determined by calculating the
ratio of data to
B
þ
B
−
MC events before the final MLP
requirement. The data sample after this requirement con-
tains a sufficiently large background contribution after the
s
B
requirement, which consists mainly of
B
þ
B
−
events
(
>
96%
) according to MC simulation, to allow for a data-
driven correction without unblinding the final signal region.
This correction factor is determined to be
0
.
913
0
.
020
,
where the uncertainty is statistical only, and is applied to
the MC reconstruction efficiency for both signal and
background events.
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The
B
tag
yield is also cross-checked using a
B
þ
→
D
0
l
þ
ν
l
,
D
0
→
K
−
π
þ
control sample, which is
selected using the same signal selection discussed above,
but with requiring one track to satisfy pion instead of
lepton PID and reversing the
D
0
veto, such that
1
.
80
<m
K
−
π
þ
<
1
.
90
GeV
=c
2
. These criteria are also
applied to the full background MC sample and the resulting
sample is found to consist mainly of peaking
B
þ
B
−
events,
which the MLP neural network is trained to classify as
background. Before the MLP requirement, good agreement
between data and MC calculations is found in all the
distributions of the input variables of the
B
þ
→
D
0
l
þ
̄
ν
l
,
D
0
→
K
−
π
þ
samples, as shown in Fig.
3
for
the
m
K
−
π
þ
distribution. These samples are then run through
the MLP neural network and a detailed comparison of the
MLP output and the input variables, after the full signal
selection, is performed.
The results for each signal channel are then combined to
determine
B
ð
B
þ
→
K
þ
τ
þ
τ
−
Þ
. This is done using a fre-
quentist approach by finding the value of
B
that maximizes
the product of the Poisson likelihoods of observing
N
i
obs
in
each of the signal channels. Branching fraction uncertain-
ties and limits are determined using the method described
in Ref.
[34]
, taking into account the statistical and sys-
tematic uncertainties on
N
bkg
and
ε
sig
.
Systematic uncertainties associated with the level of data
–
MC calculation agreement are determined for most of the
variables used in the signal selection. The determination of
the
B
tag
yield correction is anticorrelated with the extrapo-
lation of the combinatorial background from the
m
ES
side-
band, as both use the combinatorial background shape from
MCcalculations. Therefore,onlyonesystematicuncertainty
on the
B
tag
yield and combinatorial background estimate is
evaluated, using a simulated MC sample composed of
background events with the same luminosity as the data
sample. Accounting for the anticorrelation, the effect of
varying the value of the
B
tag
yield correction on the final
signal efficiency and background estimate is determined to
be 1.2% and 1.6%, respectively. The uncertainty associated
with the theoretical model is evaluated by reweighting the
s
B
distribution of the dedicated signal MC sample to the LCSR
[30]
theoretical model and to that of Ref.
[35]
and determin-
ing the difference in signal efficiency, which is calculated to
be 3.0%. The resonant
B
→
K
þ
ψ
ð
2
S
Þ
,
ψ
ð
2
S
Þ
→
τ
þ
τ
−
decay has a negligible background contribution and thus
only nonresonant models are used to estimate the theoretical
uncertainty, especially since the kinematics of any new
physics sources are not well known. Additional uncertain-
ties on
ε
sig
and
N
bkg
arise due to the modeling of PID
selectors (4.8% for
e
þ
e
−
, 7.0% for
μ
þ
μ
−
, and 5.0% for
e
þ
μ
−
) and the
π
0
veto (3.0%). The level of agreement
between data and MC calculations is evaluated using the
B
þ
→
D
0
l
þ
ν
l
,
D
0
→
K
−
π
þ
control sample before and
FIG. 2. MLP output distribution for the three signal channels
combined. The
B
þ
→
K
þ
τ
þ
τ
−
signal MC distribution is shown
(dashed) with arbitrary normalization. The data (points) are
overlaid on the expected combinatorial (hatched) plus
m
ES
-
peaking (solid line) background contributions.
FIG. 3. Invariant-mass distribution of the
K
−
π
þ
pair in the
B
þ
→
D
0
l
þ
̄
ν
l
,
D
0
→
K
−
π
þ
samples after all signal selection
criteria are applied, except for the final requirement on the MLP
output. The data (points) are overlaid on the expected combina-
torial (hatched) plus
m
ES
-peaking (solid line) background
contributions.
TABLE I. Expected background yields
N
i
bkg
, signal efficiencies
ε
i
sig
, number of observed data events
N
i
obs
, and
signed significance for each signal mode. Quoted uncertainties are statistical and systematic.
e
þ
e
−
μ
þ
μ
−
e
þ
μ
−
N
i
bkg
49
.
4
2
.
4
2
.
945
.
8
2
.
4
3
.
259
.
2
2
.
8
3
.
5
ε
i
sig
ð
×
10
−
5
Þ
1
.
1
0
.
2
0
.
11
.
3
0
.
2
0
.
12
.
1
0
.
2
0
.
2
N
i
obs
45
39
92
Significance (
σ
)
−
0
.
6
−
0
.
9
3.7
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after the MLP requirement. Comparison of both the overall
yields as well as the distributions of the input and output
variable results in a systematic uncertainty of 2.6%. Other
potential sources of systematic uncertainties have been
investigated, including those associated with the assumption
that charged and neutral
B
candidates are produced at equal
rates, the continuum likelihood suppression, the
B
tag
purity,
the track multiplicity,
E
miss
, and the
s
B
selection criteria, and
are all implicitly accounted for in the
B
tag
yield correction
uncertainty. Correlations between the signal efficiency and
the background estimate due to common systematic errors
are included, but are found to have a negligible effect on the
final branching fraction results.
The final signal efficiencies, background estimates, and
observed yields of each signal mode are shown in Table
I
,
with the associated branching fraction significance. The
yields in the
e
þ
e
−
and
μ
þ
μ
−
channels show consistency
with the expected background estimate. The signal yield in
the
e
þ
μ
−
channel is approximately equal to the sum of the
other two channels, since it also includes the charge
conjugate decay with
e
−
μ
þ
in the final state. We observe
40
e
þ
μ
−
and 52
e
−
μ
þ
events in this channel, which
corresponds to an excess of
3
.
7
σ
over the background
expectation. Examination of kinematic distributions in the
e
þ
μ
−
channel does not give any clear indication either of
signal-like behavior or of systematic problems with back-
ground modeling. When combined with the
e
þ
e
−
and
μ
þ
μ
−
modes, the overall significance of the
B
þ
→
K
þ
τ
þ
τ
−
signal is less than
2
σ
, and hence we do not interpret this
as evidence of signal. If the excess is interpreted as signal,
the branching fraction for the combined three modes
is
B
ð
B
þ
→
K
þ
τ
þ
τ
−
Þ¼½
1
.
31
þ
0
.
66
−
0
.
61
ð
stat
Þ
þ
0
.
35
−
0
.
25
ð
sys
Þ
×
10
−
3
.
The upper limit at the 90% confidence level is
B
ð
B
þ
→
K
þ
τ
þ
τ
−
Þ
<
2
.
25
×
10
−
3
.
In conclusion, this is the first search for the decay
B
þ
→
K
þ
τ
þ
τ
−
, using the full
BABAR
data set collected
at the c.m. energy of the
Υ
ð
4
S
Þ
resonance. No significant
signal is observed and the upper limit on the final branching
fraction is determined to be
2
.
25
×
10
−
3
at the 90% con-
fidence level.
We are grateful for the excellent luminosity and machine
conditions provided by our PEP-II2 colleagues, and for the
substantial dedicated effort from the computing organiza-
tions that support
BABAR
. The collaborating institutions
wish to thank SLAC for its support and kind hospitality.
This work is supported by DOE and NSF (U.S,), Natural
Sciences and Engineering Research Council of Canada
(Canada), Commissariat à l'Énergie Atomique et aux
Énergies Alternatives and Centre National de la
Recherche
Scientifique-IN2P3
(France),
Bundesministerium für Bildung ind Forschung and
Deutsche Forschungsgemeinschaft (Germany), Instituto
Nazionale di Fisica Nucleare (Italy), Stichting voor
Fundamenteel Onderzoek der Materie (The Netherlands),
Norges forskningsråd (Norway), Ministry of education and
science (Russia), Ministerio de Economía y Competitividad
(Spain), and Science and Technology Facilities Council
(United Kingdom). Individuals have received support from
the Marie Curie EIF (European Union) and the A. P. Sloan
Foundation (U.S.).
*
Present address: Wuhan University, Wuhan 43072, China.
†
Present address: Università di Bologna and INFN Sezione
di Bologna, I-47921 Rimini, Italy.
‡
Present address: University of Huddersfield, Huddersfield
HD1 3DH, United Kingdom.
§
Present address: University of South Alabama, Mobile,
Alabama 36688, USA.
∥
Also at Università di Sassari, I-07100 Sassari, Italy.
[1] Charge conjugation is implied throughout the entire
Letter.
[2] C. Bouchard, G. P. Lepage, C. Monahan, H. Na, and
J. Shigemitsu,
Phys. Rev. Lett.
111
, 162002 (2013)
.
[3] J. L. Hewitt,
Phys. Rev. D
53
, 4964 (1996)
.
[4] J. P. Lees
et al.
(
BABAR
Collaboration),
Phys. Rev. D
86
,
032012 (2012)
.
[5] R. Aaij
et al.
(LHCb Collaboration),
Phys. Rev. Lett.
113
,
151601 (2014)
.
[6] R. Aaij
et al.
(LHCb Collaboration),
J. High Energy Phys.
07 (2012) 133.
[7] R. Aaij
et al.
(LHCb Collaboration),
J. High Energy Phys.
02 (2013) 105.
[8] J. T. Wei
et al.
(Belle Collaboration),
Phys. Rev. Lett.
103
,
171801 (2009)
.
[9] R. Barbieri, G. Isidori, and A. Pattori,
Eur. Phys. J. C
76
,67
(2016)
.
[10] L. Calibbi, A. Crivellin, and T. Ota,
Phys. Rev. Lett.
115
,
181801 (2015)
.
[11] T. M. Aliev, M. Savci, and A. Ozpineci,
J. Phys. G
24
,49
(1998)
.
[12] F. Munir, S. Ishaq, and I. Ahmed, Prog. Theor. Exp. Phys.
013
, B02 (2016).
[13] S. Ishaq, A. Faisal, and I. Ahmed, J. High Energy Phys. 7
(2013) 1.
[14] S. R, Choudhry, N. Gaur, A. S. Cornell, and G. C. Joshi,
Phys. Rev. D
69
, 054018 (2004)
.
[15] S. R. Choudhry, N. Gaur, A. S. Cornell, and G. C. Joshi,
Phys. Rev. D
68
, 054016 (2003)
.
[16] A. Ali, P. Ball, L. T. Handoko, and G. Hiller,
Phys. Rev. D
61
, 074024 (2000)
.
[17] Q. S. Yan, C. S. Huang, W. Liao, and S. H. Zhu,
Phys. Rev.
D
62
, 094023 (2000)
.
[18] C. Huang and Y. Qi-Shu,
Phys. Lett. B
442
, 209 (1998)
.
[19] J. L. Hewett and J. D. Wells,
Phys. Rev. D
55
, 5549 (1997)
.
[20] Y. Dai, C. Huang, and H. Huang,
Phys. Lett. B
390
, 257 (1997)
.
[21] D. Guetta and E. Nardi,
Phys. Rev. D
58
, 012001 (1998)
.
[22] S. R. Choudhury, N. Guar, and A. Gupta,
Phys. Rev. D
60
,
115004 (1999)
.
[23] Y. Kim, P. Ko, and J. Lee,
Nucl. Phys.
B544
, 64 (1999)
.
[24] Z. Xiong and J. M. Yang,
Phys. Lett. B
317
179 (1993)
.
[25] B. Aubert
et al.
(
BABAR
Collaboration),
Nucl. Instrum.
Methods Phys. Res., Sect. A
479
, 1 (2002)
;
729
, 615 (2013)
.
PRL
118,
031802 (2017)
PHYSICAL REVIEW LETTERS
week ending
20 JANUARY 2017
031802-7
[26] J. P. Lees
et al.
(
BABAR
Collaboration),
Nucl. Instrum.
Methods Phys. Res., Sect. A
726
, 203 (2013)
.
[27] D. J. Lange,
Nucl. Instrum. Methods Phys. Res., Sect. A
462
, 152 (2001)
.
[28] S. Agostinelli
et al.
(
GEANT
4 Collaboration),
Nucl. Instrum.
Methods Phys. Res., Sect. A
506
, 250 (2003)
.
[29] K. A. Olive
et al.
(Particle Data Group),
Chin. Phys. C
38
,
090001 (2014)
.
[30] A. Ali, E. Lunghi, C. Greub, and G. Hiller,
Phys. Rev. D
66
,
034002 (2002)
.
[31] J. P. Lees
et al.
(
BABAR
Collaboration),
Phys. Rev. D
87
,
112005 (2013)
.
[32] G. Fox and S. Wolfram,
Nucl. Phys.
B149
, 413 (1979)
.
[33] B. Denby,
Neural Comput.
5
, 505 (1993)
.
[34] R. Barlow,
Comput. Phys. Commun.
149
, 97 (2002)
.
[35] D. Melikhov, N. Nikiten, and S. Simula,
Phys. Rev. D
57
,
6814 (1998)
.
PRL
118,
031802 (2017)
PHYSICAL REVIEW LETTERS
week ending
20 JANUARY 2017
031802-8