arXiv:1502.01784v1 [hep-ex] 6 Feb 2015
B
A
B
AR
-PUB-14/013
SLAC-PUB-16212
Measurement of the branching fractions of the radiative lep
tonic
τ
decays
τ
→
eγν
̄
ν
and
τ
→
μγν
̄
ν
at
B
A
B
AR
J. P. Lees,
1
V. Poireau,
1
V. Tisserand,
1
E. Grauges,
2
A. Palano
ab
,
3
G. Eigen,
4
B. Stugu,
4
D. N. Brown,
5
L. T. Kerth,
5
Yu. G. Kolomensky,
5
M. J. Lee,
5
G. Lynch,
5
H. Koch,
6
T. Schroeder,
6
C. Hearty,
7
T. S. Mattison,
7
J. A. McKenna,
7
R. Y. So,
7
A. Khan,
8
V. E. Blinov
abc
,
9
A. R. Buzykaev
a
,
9
V. P. Druzhinin
ab
,
9
V. B. Golubev
ab
,
9
E. A. Kravchenko
ab
,
9
A. P. Onuchin
abc
,
9
S. I. Serednyakov
ab
,
9
Yu. I. Skovpen
ab
,
9
E. P. Solodov
ab
,
9
K. Yu. Todyshev
ab
,
9
A. J. Lankford,
10
B. Dey,
11
J. W. Gary,
11
O. Long,
11
M. Franco Sevilla,
12
T. M. Hong,
12
D. Kovalskyi,
12
J. D. Richman,
12
C. A. West,
12
A. M. Eisner,
13
W. S. Lockman,
13
W. Panduro Vazquez,
13
B. A. Schumm,
13
A. Seiden,
13
D. S. Chao,
14
C. H. Cheng,
14
B. Echenard,
14
K. T. Flood,
14
D. G. Hitlin,
14
T. S. Miyashita,
14
P. Ongmongkolkul,
14
F. C. Porter,
14
M. R ̈ohrken,
14
R. Andreassen,
15
Z. Huard,
15
B. T. Meadows,
15
B. G. Pushpawela,
15
M. D. Sokoloff,
15
L. Sun,
15
P. C. Bloom,
16
W. T. Ford,
16
A. Gaz,
16
J. G. Smith,
16
S. R. Wagner,
16
R. Ayad,
17,
∗
W. H. Toki,
17
B. Spaan,
18
D. Bernard,
19
M. Verderi,
19
S. Playfer,
20
D. Bettoni
a
,
21
C. Bozzi
a
,
21
R. Calabrese
ab
,
21
G. Cibinetto
ab
,
21
E. Fioravanti
ab
,
21
I. Garzia
ab
,
21
E. Luppi
ab
,
21
L. Piemontese
a
,
21
V. Santoro
a
,
21
A. Calcaterra,
22
R. de Sangro,
22
G. Finocchiaro,
22
S. Martellotti,
22
P. Patteri,
22
I. M. Peruzzi,
22,
†
M. Piccolo,
22
M. Rama,
22
A. Zallo,
22
R. Contri
ab
,
23
M. R. Monge
ab
,
23
S. Passaggio
a
,
23
C. Patrignani
ab
,
23
B. Bhuyan,
24
V. Prasad,
24
A. Adametz,
25
U. Uwer,
25
H. M. Lacker,
26
U. Mallik,
27
C. Chen,
28
J. Cochran,
28
S. Prell,
28
H. Ahmed,
29
A. V. Gritsan,
30
N. Arnaud,
31
M. Davier,
31
D. Derkach,
31
G. Grosdidier,
31
F. Le Diberder,
31
A. M. Lutz,
31
B. Malaescu,
31,
‡
P. Roudeau,
31
A. Stocchi,
31
G. Wormser,
31
D. J. Lange,
32
D. M. Wright,
32
J. P. Coleman,
33
J. R. Fry,
33
E. Gabathuler,
33
D. E. Hutchcroft,
33
D. J. Payne,
33
C. Touramanis,
33
A. J. Bevan,
34
F. Di Lodovico,
34
R. Sacco,
34
G. Cowan,
35
D. N. Brown,
36
C. L. Davis,
36
A. G. Denig,
37
M. Fritsch,
37
W. Gradl,
37
K. Griessinger,
37
A. Hafner,
37
K. R. Schubert,
37
R. J. Barlow,
38,
§
G. D. Lafferty,
38
R. Cenci,
39
B. Hamilton,
39
A. Jawahery,
39
D. A. Roberts,
39
R. Cowan,
40
R. Cheaib,
41
P. M. Patel,
41,
¶
S. H. Robertson,
41
N. Neri
a
,
42
F. Palombo
ab
,
42
L. Cremaldi,
43
R. Godang,
43,
∗∗
D. J. Summers,
43
M. Simard,
44
P. Taras,
44
G. De Nardo
ab
,
45
G. Onorato
ab
,
45
C. Sciacca
ab
,
45
G. Raven,
46
C. P. Jessop,
47
J. M. LoSecco,
47
K. Honscheid,
48
R. Kass,
48
M. Margoni
ab
,
49
M. Morandin
a
,
49
M. Posocco
a
,
49
M. Rotondo
a
,
49
G. Simi
ab
,
49
F. Simonetto
ab
,
49
R. Stroili
ab
,
49
S. Akar,
50
E. Ben-Haim,
50
M. Bomben,
50
G. R. Bonneaud,
50
H. Briand,
50
G. Calderini,
50
J. Chauveau,
50
Ph. Leruste,
50
G. Marchiori,
50
J. Ocariz,
50
M. Biasini
ab
,
51
E. Manoni
a
,
51
A. Rossi
a
,
51
C. Angelini
ab
,
52
G. Batignani
ab
,
52
S. Bettarini
ab
,
52
M. Carpinelli
ab
,
52,
††
G. Casarosa
ab
,
52
M. Chrzaszcz
a
,
52
F. Forti
ab
,
52
M. A. Giorgi
ab
,
52
A. Lusiani
ac
,
52
B. Oberhof
ab
,
52
E. Paoloni
ab
,
52
G. Rizzo
ab
,
52
J. J. Walsh
a
,
52
D. Lopes Pegna,
53
J. Olsen,
53
A. J. S. Smith,
53
F. Anulli
a
,
54
R. Faccini
ab
,
54
F. Ferrarotto
a
,
54
F. Ferroni
ab
,
54
M. Gaspero
ab
,
54
A. Pilloni
ab
,
54
G. Piredda
a
,
54
C. B ̈unger,
55
S. Dittrich,
55
O. Gr ̈unberg,
55
M. Hess,
55
T. Leddig,
55
C. Voß,
55
R. Waldi,
55
T. Adye,
56
E. O. Olaiya,
56
F. F. Wilson,
56
S. Emery,
57
G. Vasseur,
57
D. Aston,
58
D. J. Bard,
58
C. Cartaro,
58
M. R. Convery,
58
J. Dorfan,
58
G. P. Dubois-Felsmann,
58
W. Dunwoodie,
58
M. Ebert,
58
R. C. Field,
58
B. G. Fulsom,
58
M. T. Graham,
58
C. Hast,
58
W. R. Innes,
58
P. Kim,
58
D. W. G. S. Leith,
58
D. Lindemann,
58
S. Luitz,
58
V. Luth,
58
H. L. Lynch,
58
D. B. MacFarlane,
58
D. R. Muller,
58
H. Neal,
58
M. Perl,
58,
¶
T. Pulliam,
58
B. N. Ratcliff,
58
A. Roodman,
58
R. H. Schindler,
58
A. Snyder,
58
D. Su,
58
M. K. Sullivan,
58
J. Va’vra,
58
W. J. Wisniewski,
58
H. W. Wulsin,
58
M. V. Purohit,
59
J. R. Wilson,
59
A. Randle-Conde,
60
S. J. Sekula,
60
M. Bellis,
61
P. R. Burchat,
61
E. M. T. Puccio,
61
M. S. Alam,
62
J. A. Ernst,
62
R. Gorodeisky,
63
N. Guttman,
63
D. R. Peimer,
63
A. Soffer,
63
S. M. Spanier,
64
J. L. Ritchie,
65
R. F. Schwitters,
65
J. M. Izen,
66
X. C. Lou,
66
F. Bianchi
ab
,
67
F. De Mori
ab
,
67
A. Filippi
a
,
67
D. Gamba
ab
,
67
L. Lanceri
ab
,
68
L. Vitale
ab
,
68
F. Martinez-Vidal,
69
A. Oyanguren,
69
P. Villanueva-Perez,
69
J. Albert,
70
Sw. Banerjee,
70
A. Beaulieu,
70
F. U. Bernlochner,
70
H. H. F. Choi,
70
G. J. King,
70
R. Kowalewski,
70
M. J. Lewczuk,
70
T. Lueck,
70
I. M. Nugent,
70
J. M. Roney,
70
R. J. Sobie,
70
N. Tasneem,
70
T. J. Gershon,
71
P. F. Harrison,
71
T. E. Latham,
71
H. R. Band,
72
S. Dasu,
72
Y. Pan,
72
R. Prepost,
72
and S. L. Wu
72
(The
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-Vie
ux, France
2
Universitat de Barcelona, Facultat de Fisica, Departament
ECM, E-08028 Barcelona, Spain
3
INFN Sezione di Bari
a
; Dipartimento di Fisica, Universit`a di Bari
b
, I-70126 Bari, Italy
4
University of Bergen, Institute of Physics, N-5007 Bergen,
Norway
2
5
Lawrence Berkeley National Laboratory and University of Ca
lifornia, Berkeley, California 94720, USA
6
Ruhr Universit ̈at Bochum, Institut f ̈ur Experimentalphys
ik 1, D-44780 Bochum, Germany
7
University of British Columbia, Vancouver, British Columb
ia, Canada V6T 1Z1
8
Brunel University, Uxbridge, Middlesex UB8 3PH, United Kin
gdom
9
Budker Institute of Nuclear Physics SB RAS, Novosibirsk 630
090
a
,
Novosibirsk State University, Novosibirsk 630090
b
,
Novosibirsk State Technical University, Novosibirsk 6300
92
c
, Russia
10
University of California at Irvine, Irvine, California 926
97, USA
11
University of California at Riverside, Riverside, Califor
nia 92521, USA
12
University of California at Santa Barbara, Santa Barbara, C
alifornia 93106, USA
13
University of California at Santa Cruz, Institute for Parti
cle Physics, Santa Cruz, California 95064, USA
14
California Institute of Technology, Pasadena, California
91125, USA
15
University of Cincinnati, Cincinnati, Ohio 45221, USA
16
University of Colorado, Boulder, Colorado 80309, USA
17
Colorado State University, Fort Collins, Colorado 80523, U
SA
18
Technische Universit ̈at Dortmund, Fakult ̈at Physik, D-44
221 Dortmund, Germany
19
Laboratoire Leprince-Ringuet, Ecole Polytechnique, CNRS
/IN2P3, F-91128 Palaiseau, France
20
University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom
21
INFN Sezione di Ferrara
a
; Dipartimento di Fisica e Scienze della Terra, Universit`a
di Ferrara
b
, I-44122 Ferrara, Italy
22
INFN Laboratori Nazionali di Frascati, I-00044 Frascati, I
taly
23
INFN Sezione di Genova
a
; Dipartimento di Fisica, Universit`a di Genova
b
, I-16146 Genova, Italy
24
Indian Institute of Technology Guwahati, Guwahati, Assam,
781 039, India
25
Universit ̈at Heidelberg, Physikalisches Institut, D-691
20 Heidelberg, Germany
26
Humboldt-Universit ̈at zu Berlin, Institut f ̈ur Physik, D-
12489 Berlin, Germany
27
University of Iowa, Iowa City, Iowa 52242, USA
28
Iowa State University, Ames, Iowa 50011-3160, USA
29
Physics Department, Jazan University, Jazan 22822, Kingdo
m of Saudia Arabia
30
Johns Hopkins University, Baltimore, Maryland 21218, USA
31
Laboratoire de l’Acc ́el ́erateur Lin ́eaire, IN2P3/CNRS et
Universit ́e Paris-Sud 11,
Centre Scientifique d’Orsay, F-91898 Orsay Cedex, France
32
Lawrence Livermore National Laboratory, Livermore, Calif
ornia 94550, USA
33
University of Liverpool, Liverpool L69 7ZE, United Kingdom
34
Queen Mary, University of London, London, E1 4NS, United Kin
gdom
35
University of London, Royal Holloway and Bedford New Colleg
e, Egham, Surrey TW20 0EX, United Kingdom
36
University of Louisville, Louisville, Kentucky 40292, USA
37
Johannes Gutenberg-Universit ̈at Mainz, Institut f ̈ur Ker
nphysik, D-55099 Mainz, Germany
38
University of Manchester, Manchester M13 9PL, United Kingd
om
39
University of Maryland, College Park, Maryland 20742, USA
40
Massachusetts Institute of Technology, Laboratory for Nuc
lear Science, Cambridge, Massachusetts 02139, USA
41
McGill University, Montr ́eal, Qu ́ebec, Canada H3A 2T8
42
INFN Sezione di Milano
a
; Dipartimento di Fisica, Universit`a di Milano
b
, I-20133 Milano, Italy
43
University of Mississippi, University, Mississippi 38677
, USA
44
Universit ́e de Montr ́eal, Physique des Particules, Montr ́
eal, Qu ́ebec, Canada H3C 3J7
45
INFN Sezione di Napoli
a
; Dipartimento di Scienze Fisiche,
Universit`a di Napoli Federico II
b
, I-80126 Napoli, Italy
46
NIKHEF, National Institute for Nuclear Physics and High Ene
rgy Physics, NL-1009 DB Amsterdam, The Netherlands
47
University of Notre Dame, Notre Dame, Indiana 46556, USA
48
Ohio State University, Columbus, Ohio 43210, USA
49
INFN Sezione di Padova
a
; Dipartimento di Fisica, Universit`a di Padova
b
, I-35131 Padova, Italy
50
Laboratoire de Physique Nucl ́eaire et de Hautes Energies,
IN2P3/CNRS, Universit ́e Pierre et Marie Curie-Paris6,
Universit ́e Denis Diderot-Paris7, F-75252 Paris, France
51
INFN Sezione di Perugia
a
; Dipartimento di Fisica, Universit`a di Perugia
b
, I-06123 Perugia, Italy
52
INFN Sezione di Pisa
a
; Dipartimento di Fisica,
Universit`a di Pisa
b
; Scuola Normale Superiore di Pisa
c
, I-56127 Pisa, Italy
53
Princeton University, Princeton, New Jersey 08544, USA
54
INFN Sezione di Roma
a
; Dipartimento di Fisica,
Universit`a di Roma La Sapienza
b
, I-00185 Roma, Italy
55
Universit ̈at Rostock, D-18051 Rostock, Germany
56
Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX
11 0QX, United Kingdom
57
CEA, Irfu, SPP, Centre de Saclay, F-91191 Gif-sur-Yvette, F
rance
58
SLAC National Accelerator Laboratory, Stanford, Californ
ia 94309 USA
59
University of South Carolina, Columbia, South Carolina 292
08, USA
60
Southern Methodist University, Dallas, Texas 75275, USA
3
61
Stanford University, Stanford, California 94305-4060, US
A
62
State University of New York, Albany, New York 12222, USA
63
Tel Aviv University, School of Physics and Astronomy, Tel Av
iv, 69978, Israel
64
University of Tennessee, Knoxville, Tennessee 37996, USA
65
University of Texas at Austin, Austin, Texas 78712, USA
66
University of Texas at Dallas, Richardson, Texas 75083, USA
67
INFN Sezione di Torino
a
; Dipartimento di Fisica, Universit`a di Torino
b
, I-10125 Torino, Italy
68
INFN Sezione di Trieste
a
; Dipartimento di Fisica, Universit`a di Trieste
b
, I-34127 Trieste, Italy
69
IFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spa
in
70
University of Victoria, Victoria, British Columbia, Canad
a V8W 3P6
71
Department of Physics, University of Warwick, Coventry CV4
7AL, United Kingdom
72
University of Wisconsin, Madison, Wisconsin 53706, USA
We perform a measurement of the
τ
→
lγν
̄
ν
(
l
=
e, μ
) branching fractions for a minimum photon
energy of 10 MeV in the
τ
rest frame, using 431 fb
−
1
of
e
+
e
−
collisions collected at the center-of-
mass energy of the
Υ
(4
S
) resonance with the
B
A
B
AR
detector at the PEP-II storage rings. We find
B
(
τ
→
μγν
̄
ν
) = (3
.
69
±
0
.
03
±
0
.
10)
×
10
−
3
, and
B
(
τ
→
eγν
̄
ν
) = (1
.
847
±
0
.
015
±
0
.
052)
×
10
−
2
, where
the first quoted error is statistical, and the second is syste
matic. These results are substantially
more precise than previous measurements.
PACS numbers: 13.30.Ce, 13.35-r, 13.40.Em, 13.40.Ks, 14.6
0.Fg
Leptonic
τ
decays are generally well suited to inves-
tigate the Lorentz structure of electroweak interactions
in a model-independent way [1]. In particular, leptonic
radiative decays
τ
→
lγν
̄
ν
, where the charged lepton (
l
)
is either an electron (
e
) or a muon (
μ
), have been studied
for a long time because they are sensitive to the anoma-
lous magnetic moment of the
τ
lepton [2]. At tree level,
these decays can proceed through three Feynman dia-
grams depending on whether the photon is emitted by
the incoming
τ
, the outgoing charged lepton, or the in-
termediate
W
boson, as shown in Fig. 1. The amplitude
for the emission of the photon by the intermediate boson
is suppressed by a factor (
m
τ
/M
W
)
2
with respect to a
photon from the incoming/outgoing fermions and is thus
negligible with respect to next-to-leading order (NLO)
QED radiative corrections [3]. Both branching fractions
have been measured by the CLEO collaboration. CLEO
obtained
B
(
τ
→
μγν
̄
ν
) = (3
.
61
±
0
.
16
±
0
.
35)
×
10
−
3
,
and
B
(
τ
→
eγν
̄
ν
) = (1
.
75
±
0
.
06
±
0
.
17)
×
10
−
2
for
a minimum photon energy of 10 MeV in the
τ
rest
frame [4]. In addition, the OPAL collaboration finds
B
(
τ
→
μγν
̄
ν
) = (3
.
0
±
0
.
4
±
0
.
5)
×
10
−
3
for a minimum
photon energy of 20 MeV in the
τ
rest frame [5].
∗
Now at: University of Tabuk, Tabuk 71491, Saudi Arabia
†
Also at: Universit`a di Perugia, Dipartimento di Fisica, I-
06123
Perugia, Italy
‡
Now at: Laboratoire de Physique Nucl ́eaire et de Hautes Ener
gies,
IN2P3/CNRS, F-75252 Paris, France
§
Now at: University of Huddersfield, Huddersfield HD1 3DH, UK
¶
Deceased
∗∗
Now at: University of South Alabama, Mobile, Alabama 36688,
USA
††
Also at: Universit`a di Sassari, I-07100 Sassari, Italy
In the present work we perform a measurement of
τ
→
lγν
̄
ν
branching fractions for a minimum photon
energy of 10 MeV in the
τ
rest frame. This analysis
uses data recorded by the
B
A
B
AR
detector at the PEP-
II asymmetric-energy
e
+
e
−
storage rings operated at the
SLAC National Accelerator Laboratory. The data sam-
ple consists of 431 fb
−
1
of
e
+
e
−
collisions recorded at at
the center-of-mass energy (CM)
√
s
= 10
.
58 GeV [6]. The
cross section for
τ
-pair production is
σ
ττ
= 0
.
919
±
0
.
003
nb [7] corresponding to a data sample of about 400
×
10
6
τ
-pairs. A detailed description of the
B
A
B
AR
detector is
given elsewhere [8, 9]. Charged particle momenta are
measured with a five-layer double-sided silicon vertex
tracker and a 40-layer helium-isobutane drift chamber
inside a 1.5 T superconducting solenoid magnet. An
electromagnetic calorimeter (EMC) consisting of 6580
CsI(Tl) crystals is used to measure electron and pho-
ton energies; a ring-imaging Cherenkov detector is used
to identify charged hadrons; the instrumented magnetic
flux return (IFR) is used for muon identification. About
half of the data were taken with the IFR embedded with
resistive plate chambers, later partially replaced by lim-
ited streamer tubes.
For this analysis, a Monte Carlo (MC) simulation is
used to estimate the signal efficiency and to optimize the
selection algorithm. Simulated
τ
-pair events are gener-
ated using
KK2f
[10] and
τ
decays are simulated with
Tauola
[11]. Final-state radiative effects for
τ
decays in
Tauola
are simulated using
Photos
[12]. A signal
τ
-pair
MC sample is generated where one of the
τ
leptons de-
cays to
τ
→
lγν
̄
ν
, and the other decays according to
known decay modes [13]. For the signal sample we re-
quire the minimum photon energy in the
τ
rest frame
to be
E
∗
γ,
min
>
10 MeV. The
τ
→
lγν
̄
ν
decays with
E
∗
γ,
min
<
10 MeV are treated as background. A separate
τ
-pair MC sample is generated requiring each
τ
lepton to
decay in a mode based on current experimental knowl-
edge; we exclude signal events in the former sample to
4
FIG. 1: Standard Model Feynman diagrams for
τ
→
lγν
̄
ν
at tree level.
obtain a
τ
-pair background sample. Other MC simu-
lated background samples include
μ
+
μ
−
,
q
̄
q
(
u
̄
u
,
d
̄
d
,
s
̄
s
,
c
̄
c
), and
B
̄
B
(
B
=
B
+
,
B
0
) events. The
μ
+
μ
−
events
are generated by
KK2f
,
q
̄
q
events are generated using
the
JETSET
generator [14] while
B
̄
B
events are simu-
lated with
EVTGEN
[15]. The detector response is sim-
ulated with
GEANT4
[16]. Background from two-photon
and Bhabha events is estimated from data.
The signature for
τ
→
lγν
̄
ν
decays is a charged par-
ticle (track), identified either as an electron or a muon,
and an energy deposit (cluster) in the EMC not associ-
ated with any track, the photon. Since
τ
leptons decay
mostly to a single charged particle, events with two well-
reconstructed tracks and zero total charge are selected,
where no track pair is consistent with being a photon
conversion in the detector material. The transverse mo-
mentum of each track is required to be
p
T
>
0
.
3 GeV/c,
the cosine of the polar angle is required to be between
−
0
.
75 and 0
.
95 within the calorimeter acceptance range
to ensure good particle identification. The total miss-
ing transverse moment of the event is required to be
p
T,
miss
>
0
.
5 GeV/
c
. All clusters in the EMC with no
associated tracks (neutral clusters) are required to have
a minimum energy of 50 MeV. We also reject events with
neutral clusters having
E <
110 MeV if they are within
25 cm of a track, where the distance is measured on the
inner wall of the EMC.
Each event is divided into hemispheres (signal and tag
hemispheres) in the CM frame by a plane perpendicu-
lar to the thrust axis, calculated using all reconstructed
charged and neutral particles [17]. For every event, the
magnitude of the thrust is required to be between 0.9
and 0.995. The lower limit on the thrust magnitude
rejects most
q
̄
q
events while the upper limit removes
e
+
e
−
→
μ
+
μ
−
and Bhabha events. The signal hemi-
sphere must contain one track and one neutral cluster.
The tag hemisphere must contain one track, identified
either as an electron, muon or pion, and possibly one
additional neutral cluster or
nπ
0
(
n
=1, 2). Each
π
0
candidate is built up from a pair of neutral clusters with
a di-photon invariant mass in the range [100
,
160] MeV.
To further suppress di-muon and Bhabha events, we re-
ject events where the leptons in the signal and tag hemi-
spheres have the same flavor. Since there are at least
three undetected neutrinos in the final state we require
the total energy to be less than 9 GeV. In the signal
hemisphere, we require that the distance (
d
lγ
) between
the track and the neutral cluster, measured on the inner
wall of the EMC, to be less than 100 cm.
Electrons are identified by applying an Error Cor-
recting Output Code (ECOC) [18] algorithm based on
Bagged Decision Tree (BDT) [19] classifiers using as in-
put the ratio of the energy in the EMC to the magnitude
of the momentum of the track (
E/p
), the ionization loss
in the tracking system (d
E/
d
x
), and the shape of the
shower in the electromagnetic calorimeter.
Muon identification makes use of a BDT algorithm, us-
ing as input the number of hits in the IFR, the number of
interaction lengths traversed, and the energy deposition
in the calorimeter. Since muons with momenta less than
500 MeV
/c
do not penetrate into the IFR, the BDT also
uses information the energy loss
dE/dx
in the tracking
system to maintain a very low
π
−
μ
misidentification
probability with high selection efficiencies. The electron
and muon identification efficiencies are 91% and 62%, re-
spectively. The probability for a
π
to be misidentified as
an
e
is below 0.1%, while the probability to be misiden-
tified as a
μ
is around 1% depending on momentum.
After the preselection, both samples are dominated
by background events. For the
τ
→
μγν
̄
ν
sample,
the main background sources are initial-state radiation
(ISR),
τ
→
ππ
0
ν
decays,
e
+
e
−
→
μ
+
μ
−
events, and
τ
→
πν
decays. For the
τ
→
eγν
̄
ν
sample, almost
all background contribution is from
τ
→
eν
̄
ν
decays in
which the electron radiates a photon in the magnetic field
of the detector (bremsstrahlung). Further background
suppression is obtained by placing requirements on the
angle between the lepton and photon in the CM frame
(cos
θ
lγ
). For
τ
→
μγν
̄
ν
we require cos
θ
lγ
>
0
.
99, while
for
τ
→
eγν
̄
ν
we require cos
θ
lγ
>
0
.
97 (see Figs. 2
and 3). To reject background from
τ
→
eν
̄
ν
decays in
the
τ
→
eγν
̄
ν
sample, we further impose a minimum
value for the invariant mass of the lepton-photon pair
M
lγ
≥
0
.
14 GeV/
c
2
for this channel. In addition to the
aforementioned quantities, the selection criteria use the
energy of the photon and
d
lγ
. The selection criteria are
optimized in order to give the smallest statistical and
systematic uncertainty on the branching fractions.
After optimization, for
τ
→
μγν
̄
ν
, we require cos
θ
lγ
≥
0
.
99, 0
.
10
≤
E
γ
≤
2
.
5 GeV, 6
≤
d
lγ
≤
30 cm, and
5
M
lγ
≤
0
.
25 GeV/
c
2
. The requirement on
M
lγ
rejects
backgrounds from non-signal
τ
decays. For the
τ
→
eγν
̄
ν
channel, we require cos
θ
lγ
≥
0
.
97, 0
.
22
≤
E
γ
≤
2
.
0 GeV,
8
≤
d
lγ
≤
65 cm in addition to
M
lγ
≥
0
.
14 GeV/
c
2
.
The signal efficiencies, the fraction of background
events, and the number of events selected in the data
are given in Table I.
TABLE I: Signal efficiencies
ǫ
(%), expected fractional back-
ground contribution
f
bkg
=
N
bkg
/
(
N
sig
+
N
bkg
), where
N
sig
is the number of signal events and
N
bkg
is the number of
background events, and number of observed events (
N
obs
) for
the two decay modes after applying all selection criteria. A
ll
quoted uncertainties are statistical.
τ
→
μγν
̄
ν
τ
→
eγν
̄
ν
ǫ
0
.
480
±
0
.
010
0
.
105
±
0
.
003
f
bkg
0
.
102
±
0
.
002
0
.
156
±
0
.
003
N
obs
15688
±
125
18149
±
135
The branching fraction is determined using
B
l
=
N
obs
(1
−
f
bkg
)
2
σ
ττ
L
ǫ
where
N
obs
is the number of observed events,
σ
ττ
is the
cross section for
τ
pair production,
L
is the total inte-
grated luminosity, and the signal efficiency
ǫ
is deter-
mined from the MC sample.
After applying all selection criteria, we find
B
(
τ
→
μγν
̄
ν
) = (3
.
69
±
0
.
03
±
0
.
10)
×
10
−
3
B
(
τ
→
eγν
̄
ν
) = (1
.
847
±
0
.
015
±
0
.
052)
×
10
−
2
where the first error is statistical and the second is sys-
tematic. The systematic uncertainties on signal efficiency
and on the number of the expected background events af-
fect the final result, and are summarized in Table II. The
most important contributions to the total uncertainty are
from the uncertainties on particle identification, and pho-
ton detection efficiency.
To estimate the uncertainty on photon detection effi-
ciency, we rely on
e
+
e
−
→
μ
+
μ
−
γ
events for the high
energy region (
E
γ
>
1 GeV), and photons from
π
0
de-
cays for the low energy region (
E
γ
<
1 GeV). Using fully
reconstructed
e
+
e
−
→
μ
+
μ
−
γ
events, we find that the
photon detection efficiency for data and MC samples are
consistent within 1% for
E
γ
>
1 GeV. For photon ener-
gies
E
γ
<
1 GeV, we measure the ratio of the branching
fractions for
τ
→
πν
and
τ
→
ρν
decays. The resulting
uncertainty on the
π
0
reconstruction efficiency is found to
be below 3%. Taking into account the 1.1% uncertainty
on the branching fractions, the resulting energy-averaged
uncertainty on the single photon detection efficiency is
1.8%. We use this value as the systematic uncertainty in
the efficiency for
τ
→
lγν
̄
ν
.
The uncertainties on particle identification efficiency
are estimated using control samples, by measuring the
deviation of the data and MC efficiencies for tracks with
the same kinematic properties. The uncertainty on the
efficiency of the electron identification is evaluated using
a control sample consisting of radiative and non-radiative
Bhabha events, while the uncertainty for muons is an
e
+
e
−
→
μ
+
μ
−
γ
control sample. The uncertainty on the
probability of misidentifying the pion as a muon or elec-
tron is evaluated using samples of
τ
→
πππν
decays. The
corresponding systematic uncertainty on the efficiency
for
τ
→
lγν
̄
ν
is 1.5% for both channels.
For the background estimation, we define control re-
gions that are enhanced with background events. For
τ
→
μγν
̄
ν
, where the major background contribution
is not peaking in cos
θ
μγ
, we invert the cut on cos
θ
μγ
.
For cos
θ
μγ
<
0
.
8, the maximum expected signal rate
is 3% of the corresponding background rate. The maxi-
mum discrepancy between the MC sample prediction and
the number of observed events is 8%, with an excess of
events in the MC sample. We take this discrepancy as es-
timate of the uncertainty on the background prediction.
For
τ
→
eγν
̄
ν
, where the major background contribu-
tions have similar cos
θ
eγ
distributions as signal, we ap-
ply a similar strategy after requiring the invariant mass
M
lγ
<
0
.
14 GeV/
c
2
; in this case we take cos
θ
eγ
<
0
.
90.
The maximum contamination of signal events in this re-
gion is 10%, and the maximum discrepancy between the
prediction and the number of observed events is 4% with
an excess of data events. We take this value as an es-
timate of the uncertainty on the background rate. The
errors on the branching fractions due to the uncertainty
on background estimates are 0.9% for
τ
→
μγν
̄
ν
, and
0.7% for
τ
→
eγν
̄
ν
, respectively (Table II). Cross-checks
of the background estimation are performed by consider-
ing the number of events expected and observed in differ-
ent sideband regions immediately neighboring the signal
region for each decay mode and found to be compatible
with the aforementioned systematic uncertainties.
All other sources of uncertainty, including current
knowledge of the
τ
branching fractions [13] (BF), to-
tal number of
τ
pairs, limited MC statistics, dependence
on selection criteria, and track momentum resolution are
found to be smaller than 1
.
0%.
In conclusion, we have made a measurement of the
branching fractions of the radiative leptonic
τ
decays
τ
→
eγν
̄
ν
and
τ
→
μγν
̄
ν
, for a minimum photon
energy of 10 MeV in the
τ
rest frame, using the full
dataset of
e
+
e
−
collisions collected by
B
A
B
AR
at the
center-of-mass energy of the
Υ
(4
S
) resonance. We find
B
(
τ
→
μγν
̄
ν
) = (3
.
69
±
0
.
03
±
0
.
10)
×
10
−
3
, and
B
(
τ
→
eγν
̄
ν
) = (1
.
847
±
0
.
015
±
0
.
052)
×
10
−
2
, where the first
error is statistical and the second is systematic. These
results are more precise by a factor of three compared
to previous experimental measurements. Our results are
in agreement with the Standard Model values at tree
level,
B
(
τ
→
μγν
̄
ν
) = 3
.
67
×
10
−
3
, and
B
(
τ
→
eγν
̄
ν
) =
1
.
84
×
10
−
2
[3], and with current experimental bounds.
6
(cm)
γ
l
d
0
10
20
30
40
50
60
70
Events/cm
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
3
10
×
(a)
ν
ν
γ
μ
→
τ
ν
ν
γ
μ
→
τ
ν
ν
μ
→
τ
ν
0
π
π
→
τ
decays
τ
Other
-
μ
+
μ
→
-
e
+
e
Data
(cm)
γ
l
d
0
10
20
30
40
50
60
70
Events/cm
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
3
10
×
γ
l
θ
cos
0.94
0.95
0.96
0.97
0.98
0.99
1.00
Events/0.002
0
1
2
3
4
5
3
10
×
(b)
γ
l
θ
cos
0.94
0.95
0.96
0.97
0.98
0.99
1.00
Events/0.002
0
1
2
3
4
5
3
10
×
)
2
(GeV/c
γ
l
M
0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50
2
Events/0.01 GeV/c
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3
10
×
(c)
)
2
(GeV/c
γ
l
M
0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50
2
Events/0.01 GeV/c
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3
10
×
(GeV)
γ
E
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
Events/0.05 GeV
1
10
2
10
3
10
(d)
(GeV)
γ
E
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
Events/0.05 GeV
1
10
2
10
3
10
FIG. 2: Selection of the
τ
→
μγν
̄
ν
: (a) distance between lepton and photon candidates on the in
ner EMC wall, (b) cosine of
the angle between momenta of the lepton and photon candidate
s in the CM frame, (c) invariant mass of the lepton photon
pair, and (d) photon candidate energy in the CM frame for radi
ative
τ
decay into a muon after applying all selection criteria
except the one on the plotted quantities. The selection crit
eria on the plotted quantities are highlighted by the vertic
al lines;
we retain the regions indicated by the horizontal arrows.
We are grateful for the extraordinary contributions of our
PEP-II colleagues in achieving the excellent luminosity
and machine conditions that have made this work pos-
sible. The success of this project also relies critically on
the expertise and dedication of the computing organiza-
tions that support
B
A
B
AR
. The collaborating institutions
wish to thank SLAC for its support and the kind hospi-
tality extended to them. This work is supported by the
US Department of Energy and National Science Foun-
dation, the Natural Sciences and Engineering Research
Council (Canada), the Commissariat `a l’Energie Atom-
ique and Institut National de Physique Nucl ́eaire et de
Physique des Particules (France), the Bundesministerium
f ̈ur Bildung und Forschung and Deutsche Forschungsge-
meinschaft (Germany), the Istituto Nazionale di Fisica
Nucleare (Italy), the Foundation for Fundamental Re-
search on Matter (The Netherlands), the Research Coun-
cil of Norway, the Ministry of Education and Science of
the Russian Federation, Ministerio de Econom ́ıa y Com-
petitividad (Spain), the Science and Technology Facili-
ties Council (United Kingdom), and the Binational Sci-
ence Foundation (U.S.-Israel). Individuals have received
support from the Marie-Curie IEF program (European
Union) and the A. P. Sloan Foundation (USA).
TABLE II: Summary of systematic contributions (%) to the
branching fraction from the different uncertainty sources f
or
the two signal channels. The total systematic uncertaintie
s
are obtained summing in quadrature the various systematic
uncertainties for each decay channel.
τ
→
μγν
̄
ν
τ
→
eγν
̄
ν
Photon efficiency
1.8
1.8
Particle identification
1.5
1.5
Background evaluation
0.9
0.7
BF [13]
0.7
0.7
Luminosity and cross section
0.6
0.6
MC statistics
0.5
0.6
Selection criteria
0.5
0.5
Trigger selection
0.5
0.6
Track reconstruction
0.3
0.3
Total
2.8
2.8
7
(cm)
γ
l
d
0
10
20
30
40
50
60
70
80
Events/1.5 cm
0.0
0.2
0.4
0.6
0.8
1.0
1.2
3
10
×
(a)
ν
ν
γ
e
→
τ
ν
ν
γ
e
→
τ
ν
ν
e
→
τ
decays
τ
Other
Data
(cm)
γ
l
d
0
10
20
30
40
50
60
70
80
Events/1.5 cm
0.0
0.2
0.4
0.6
0.8
1.0
1.2
3
10
×
γ
l
θ
cos
0.70
0.75
0.80
0.85
0.90
0.95
1.00
Events/0.005
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
3
10
×
(b)
γ
l
θ
cos
0.70
0.75
0.80
0.85
0.90
0.95
1.00
Events/0.005
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
3
10
×
)
2
(GeV/c
γ
l
M
0.10
0.12 0.14
0.16
0.18
0.20
0.22 0.24
2
Events/0.0025 GeV/c
0.0
0.5
1.0
1.5
2.0
2.5
3
10
×
(c)
)
2
(GeV/c
γ
l
M
0.10
0.12 0.14
0.16
0.18
0.20
0.22 0.24
2
Events/0.0025 GeV/c
0.0
0.5
1.0
1.5
2.0
2.5
3
10
×
(GeV)
γ
E
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
Events/0.05 GeV
1
10
2
10
3
10
(d)
(GeV)
γ
E
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
Events/0.05 GeV
1
10
2
10
3
10
FIG. 3: Selection of the
τ
→
eγν
̄
ν
sample: (a) distance between lepton and photon candidates o
n the inner EMC wall, (b)
cosine of the angle between momenta of the lepton and photon c
andidates in the CM frame, (c) invariant mass of the lepton
photon pair, and (d) photon candidate energy in the CM frame f
or radiative
τ
decay into an electron after applying all selection
criteria except the one on the plotted quantities. The selec
tion criteria on the plotted quantities are highlighted by t
he vertical
lines; we retain the regions indicated by the horizontal arr
ows.
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