Study of high-multiplicity three-prong and five-prong
decays at
B
A
B
AR
J. P. Lees,
1
V. Poireau,
1
V. Tisserand,
1
J. Garra Tico,
2
E. Grauges,
2
A. Palano,
3a,3b
G. Eigen,
4
B. Stugu,
4
D. N. Brown,
5
L. T. Kerth,
5
Yu. G. Kolomensky,
5
G. Lynch,
5
H. Koch,
6
T. Schroeder,
6
D. J. Asgeirsson,
7
C. Hearty,
7
T. S. Mattison,
7
J. A. McKenna,
7
R. Y. So,
7
A. Khan,
8
V. E. Blinov,
9
A. R. Buzykaev,
9
V. P. Druzhinin,
9
V. B. Golubev,
9
E. A. Kravchenko,
9
A. P. Onuchin,
9
S. I. Serednyakov,
9
Yu. I. Skovpen,
9
E. P. Solodov,
9
K. Yu. Todyshev,
9
A. N. Yushkov,
9
M. Bondioli,
10
D. Kirkby,
10
A. J. Lankford,
10
M. Mandelkern,
10
H. Atmacan,
11
J. W. Gary,
11
F. Liu,
11
O. Long,
11
G. M. Vitug,
11
C. Campagnari,
12
T. M. Hong,
12
D. Kovalskyi,
12
J. D. Richman,
12
C. A. West,
12
A. M. Eisner,
13
J. Kroseberg,
13
W. S. Lockman,
13
A. J. Martinez,
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
P. Ongmongkolkul,
14
F. C. Porter,
14
A. Y. Rakitin,
14
R. Andreassen,
15
Z. Huard,
15
B. T. Meadows,
15
M. D. Sokoloff,
15
L. Sun,
15
P. C. Bloom,
16
W. T. Ford,
16
A. Gaz,
16
U. Nauenberg,
16
J. G. Smith,
16
S. R. Wagner,
16
R. Ayad,
17,
*
W. H. Toki,
17
B. Spaan,
18
K. R. Schubert,
19
R. Schwierz,
19
D. Bernard,
20
M. Verderi,
20
P. J. Clark,
21
S. Playfer,
21
D. Bettoni,
22a
C. Bozzi,
22a
R. Calabrese,
22a,22b
G. Cibinetto,
22a,22b
E. Fioravanti,
22a,22b
I. Garzia,
22a,22b
E. Luppi,
22a,22b
M. Munerato,
22a,22b
L. Piemontese,
22a
V. Santoro,
22a
R. Baldini-Ferroli,
23
A. Calcaterra,
23
R. de Sangro,
23
G. Finocchiaro,
23
P. Patteri,
23
I. M. Peruzzi,
23,
†
M. Piccolo,
23
M. Rama,
23
A. Zallo,
23
R. Contri,
24a,24b
E. Guido,
24a,24b
M. Lo Vetere,
24a,24b
M. R. Monge,
24a,24b
S. Passaggio,
24a
C. Patrignani,
24a,24b
E. Robutti,
24a
B. Bhuyan,
25
V. Prasad,
25
C. L. Lee,
26
M. Morii,
26
A. J. Edwards,
27
A. Adametz,
28
U. Uwer,
28
H. M. Lacker,
29
T. Lueck,
29
P. D. Dauncey,
30
U. Mallik,
31
C. Chen,
32
J. Cochran,
32
W. T. Meyer,
32
S. Prell,
32
A. E. Rubin,
32
A. V. Gritsan,
33
Z. J. Guo,
33
N. Arnaud,
34
M. Davier,
34
D. Derkach,
34
G. Grosdidier,
34
F. Le Diberder,
34
A. M. Lutz,
34
B. Malaescu,
34
P. Roudeau,
34
M. H. Schune,
34
A. Stocchi,
34
G. Wormser,
34
D. J. Lange,
35
D. M. Wright,
35
C. A. Chavez,
36
J. P. Coleman,
36
J. R. Fry,
36
E. Gabathuler,
36
D. E. Hutchcroft,
36
D. J. Payne,
36
C. Touramanis,
36
A. J. Bevan,
37
F. Di Lodovico,
37
R. Sacco,
37
M. Sigamani,
37
G. Cowan,
38
D. N. Brown,
39
C. L. Davis,
39
A. G. Denig,
40
M. Fritsch,
40
W. Gradl,
40
K. Griessinger,
40
A. Hafner,
40
E. Prencipe,
40
R. J. Barlow,
41,
‡
G. Jackson,
41
G. D. Lafferty,
41
E. Behn,
42
R. Cenci,
42
B. Hamilton,
42
A. Jawahery,
42
D. A. Roberts,
42
C. Dallapiccola,
43
R. Cowan,
44
D. Dujmic,
44
G. Sciolla,
44
R. Cheaib,
45
D. Lindemann,
45
P. M. Patel,
45,
§
S. H. Robertson,
45
P. Biassoni,
46a,46b
N. Neri,
46a
F. Palombo,
46a,46b
S. Stracka,
46a,46b
L. Cremaldi,
47
R. Godang,
47,
k
R. Kroeger,
47
P. Sonnek,
47
D. J. Summers,
47
X. Nguyen,
48
M. Simard,
48
P. Taras,
48
G. De Nardo,
49a,49b
D. Monorchio,
49a,49b
G. Onorato,
49a,49b
C. Sciacca,
49a,49b
M. Martinelli,
50
G. Raven,
50
C. P. Jessop,
51
J. M. LoSecco,
51
W. F. Wang,
51
K. Honscheid,
52
R. Kass,
52
J. Brau,
53
R. Frey,
53
N. B. Sinev,
53
D. Strom,
53
E. Torrence,
53
E. Feltresi,
54a,54b
N. Gagliardi,
54a,54b
M. Margoni,
54a,54b
M. Morandin,
54a
M. Posocco,
54a
M. Rotondo,
54a
G. Simi,
54a
F. Simonetto,
54a,54b
R. Stroili,
54a,54b
S. Akar,
55
E. Ben-Haim,
55
M. Bomben,
55
G. R. Bonneaud,
55
H. Briand,
55
G. Calderini,
55
J. Chauveau,
55
O. Hamon,
55
Ph. Leruste,
55
G. Marchiori,
55
J. Ocariz,
55
S. Sitt,
55
M. Biasini,
56a,56b
E. Manoni,
56a,56b
S. Pacetti,
56a,56b
A. Rossi,
56a,56b
C. Angelini,
57a,57b
G. Batignani,
57a,57b
S. Bettarini,
57a,57b,
{
M. Carpinelli,
57a,57b,
{
G. Casarosa,
57a,57b
A. Cervelli,
57a,57b
F. Forti,
57a,57b
M. A. Giorgi,
57a,57b
A. Lusiani,
57a,57c
B. Oberhof,
57a,57b
E. Paoloni,
57a,57b
A. Perez,
57a
G. Rizzo,
57a,57b
J. J. Walsh,
57a
D. Lopes Pegna,
58
J. Olsen,
58
A. J. S. Smith,
58
A. V. Telnov,
58
F. Anulli,
59a
R. Faccini,
59a,59b
F. Ferrarotto,
59a
F. Ferroni,
59a,59b
M. Gaspero,
59a,59b
L. Li Gioi,
59a
M. A. Mazzoni,
59a
G. Piredda,
59a
C. Bu
̈
nger,
60
O. Gru
̈
nberg,
60
T. Hartmann,
60
T. Leddig,
60
H. Schro
̈
der,
60,
§
C. Voss,
60
R. Waldi,
60
T. Adye,
61
E. O. Olaiya,
61
F. F. Wilson,
61
S. Emery,
62
G. Hamel de Monchenault,
62
G. Vasseur,
62
Ch. Ye
`
che,
62
D. Aston,
63
D. J. Bard,
63
R. Bartoldus,
63
J. F. Benitez,
63
C. Cartaro,
63
M. R. Convery,
63
J. Dorfan,
63
G. P. Dubois-Felsmann,
63
W. Dunwoodie,
63
M. Ebert,
63
R. C. Field,
63
M. Franco Sevilla,
63
B. G. Fulsom,
63
A. M. Gabareen,
63
M. T. Graham,
63
P. Grenier,
63
C. Hast,
63
W. R. Innes,
63
M. H. Kelsey,
63
P. Kim,
63
M. L. Kocian,
63
D. W. G. S. Leith,
63
P. Lewis,
63
B. Lindquist,
63
S. Luitz,
63
V. Luth,
63
H. L. Lynch,
63
D. B. MacFarlane,
63
D. R. Muller,
63
H. Neal,
63
S. Nelson,
63
M. Perl,
63
T. Pulliam,
63
B. N. Ratcliff,
63
A. Roodman,
63
A. A. Salnikov,
63
R. H. Schindler,
63
A. Snyder,
63
D. Su,
63
M. K. Sullivan,
63
J. Va’vra,
63
A. P. Wagner,
63
W. J. Wisniewski,
63
M. Wittgen,
63
D. H. Wright,
63
H. W. Wulsin,
63
C. C. Young,
63
V. Ziegler,
63
W. Park,
64
M. V. Purohit,
64
R. M. White,
64
J. R. Wilson,
64
A. Randle-Conde,
65
S. J. Sekula,
65
M. Bellis,
66
P. R. Burchat,
66
T. S. Miyashita,
66
M. S. Alam,
67
J. A. Ernst,
67
R. Gorodeisky,
68
N. Guttman,
68
D. R. Peimer,
68
A. Soffer,
68
P. Lund,
69
S. M. Spanier,
69
J. L. Ritchie,
70
A. M. Ruland,
70
R. F. Schwitters,
70
B. C. Wray,
70
J. M. Izen,
71
X. C. Lou,
71
F. Bianchi,
72a,72b
D. Gamba,
72a,72b
S. Zambito,
72a,72b
L. Lanceri,
73a,73b
L. Vitale,
73a,73b
F. Martinez-Vidal,
74
A. Oyanguren,
74
H. Ahmed,
75
J. Albert,
75
Sw. Banerjee,
75
F. U. Bernlochner,
75
H. H. F. Choi,
75
G. J. King,
75
R. Kowalewski,
75
M. J. Lewczuk,
75
I. M. Nugent,
75
J. M. Roney,
75
R. J. Sobie,
75
N. Tasneem,
75
T. J. Gershon,
76
P. F. Harrison,
76
T. E. Latham,
76
E. M. T. Puccio,
76
H. R. Band,
77
S. Dasu,
77
Y. Pan,
77
R. Prepost,
77
and S. L. Wu
77
PHYSICAL REVIEW D
86,
092010 (2012)
1550-7998
=
2012
=
86(9)
=
092010(16)
092010-1
Ó
2012 American Physical Society
(
B
A
B
AR
Collaboration)
1
Laboratoire d’Annecy-le-Vieux de Physique des Particules (LAPP), Universite
́
de Savoie, CNRS/IN2P3,
F-74941 Annecy-Le-Vieux, France
2
Facultat de Fisica, Departament ECM, Universitat de Barcelona, E-08028 Barcelona, Spain
3a
INFN Sezione di Bari, I-70126 Bari, Italy
3b
Dipartimento di Fisica, Universita
`
di Bari, I-70126 Bari, Italy
4
Institute of Physics, University of Bergen, N-5007 Bergen, Norway
5
Lawrence Berkeley National Laboratory and University of California, Berkeley, California 94720, USA
6
Institut fu
̈
r Experimentalphysik 1, Ruhr Universita
̈
t Bochum, D-44780 Bochum, Germany
7
University of British Columbia, Vancouver, British Columbia V6T 1Z1, Canada
8
Brunel University, Uxbridge, Middlesex UB8 3PH, United Kingdom
9
Budker Institute of Nuclear Physics, Novosibirsk 630090, Russia
10
University of California at Irvine, Irvine, California 92697, USA
11
University of California at Riverside, Riverside, California 92521, USA
12
University of California at Santa Barbara, Santa Barbara, California 93106, USA
13
Institute for Particle Physics, University of California at Santa Cruz,
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, USA
18
Fakulta
̈
t Physik, Technische Universita
̈
t Dortmund, D-44221 Dortmund, Germany
19
Institut fu
̈
r Kern- und Teilchenphysik, Technische Universita
̈
t Dresden, D-01062 Dresden, Germany
20
Laboratoire Leprince-Ringuet, Ecole Polytechnique, CNRS/IN2P3, F-91128 Palaiseau, France
21
University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom
22a
INFN Sezione di Ferrara, I-44100 Ferrara, Italy
22b
Dipartimento di Fisica, Universita
`
di Ferrara, I-44100 Ferrara, Italy
23
INFN Laboratori Nazionali di Frascati, I-00044 Frascati, Italy
24a
INFN Sezione di Genova, I-16146 Genova, Italy
24b
Dipartimento di Fisica, Universita
`
di Genova, I-16146 Genova, Italy
25
Indian Institute of Technology Guwahati, Guwahati, Assam 781 039, India
26
Harvard University, Cambridge, Massachusetts 02138, USA
27
Harvey Mudd College, Claremont, California 91711, USA
28
Universita
̈
t Heidelberg, Physikalisches Institut, Philosophenweg 12, D-69120 Heidelberg, Germany
29
Institut fu
̈
r Physik, Humboldt-Universita
̈
t zu Berlin, Netwonstrausse 15, D-12489 Berlin, Germany
30
Imperial College London, London SW7 2AZ, United Kingdom
31
University of Iowa, Iowa City, Iowa 52242, USA
32
Iowa State University, Ames, Iowa 50011-3160, USA
33
Johns Hopkins University, Baltimore, Maryland 21218, USA
34
Laboratoire de l’Acce
́
le
́
rateur Line
́
aire, IN2P3/CNRS et Universite
́
Paris-Sud 11, Centre Scientifique d’Orsay,
B. P. 34, F-91898 Orsay Cedex, France
35
Lawrence Livermore National Laboratory, Livermore, California 94550, USA
36
University of Liverpool, Liverpool L69 7ZE, United Kingdom
37
Queen Mary, University of London, London E1 4NS, United Kingdom
38
Royal Holloway and Bedford New College, University of London, Egham, Surrey TW20 0EX, United Kingdom
39
University of Louisville, Louisville, Kentucky 40292, USA
40
Institut fu
̈
r Kernphysik, Johannes Gutenberg-Universita
̈
t Mainz, D-55099 Mainz, Germany
41
University of Manchester, Manchester M13 9PL, United Kingdom
42
University of Maryland, College Park, Maryland 20742, USA
43
University of Massachusetts, Amherst, Massachusetts 01003, USA
44
Massachusetts Institute of Technology, Laboratory for Nuclear Science,
Cambridge, Massachusetts 02139, USA
45
McGill University, Montre
́
al, Que
́
bec H3A 2T8, Canada
46a
INFN Sezione di Milano, I-20133 Milano, Italy
46b
Dipartimento di Fisica, Universita
`
di Milano, I-20133 Milano, Italy
47
University of Mississippi, University, Mississippi 38677, USA
48
Universite
́
de Montre
́
al, Physique des Particules, Montre
́
al, Que
́
bec H3C 3J7, Canada
49a
INFN Sezione di Napoli, I-80126 Napoli, Italy
J. P. LEES
et al.
PHYSICAL REVIEW D
86,
092010 (2012)
092010-2
49b
Dipartimento di Scienze Fisiche, Universita
`
di Napoli Federico II, I-80126 Napoli, Italy
50
NIKHEF, National Institute for Nuclear Physics and High Energy Physics,
NL-1009 DB Amsterdam, The Netherlands
51
University of Notre Dame, Notre Dame, Indiana 46556, USA
52
Ohio State University, Columbus, Ohio 43210, USA
53
University of Oregon, Eugene, Oregon 97403, USA
54a
INFN Sezione di Padova, I-35131 Padova, Italy
54b
Dipartimento di Fisica, Universita
`
di Padova, I-35131 Padova, Italy
55
Laboratoire de Physique Nucle
́
aire et de Hautes Energies, IN2P3/CNRS, Universite
́
Pierre et Marie Curie-Paris6,
Universite
́
Denis Diderot-Paris7, F-75252 Paris, France
56a
INFN Sezione di Perugia, I-06100 Perugia, Italy
56b
Dipartimento di Fisica, Universita
`
di Perugia, I-06100 Perugia, Italy
57a
INFN Sezione di Pisa, I-06100 Perugia, Italy
57b
Dipartimento di Fisica, Universita
`
di Pisa, I-06100 Perugia, Italy
57c
Scuola Normale Superiore di Pisa, I-56127 Pisa, Italy
58
Princeton University, Princeton, New Jersey 08544, USA
59a
INFN Sezione di Roma, I-00185 Roma, Italy
59b
Dipartimento di Fisica, Universita
`
di Roma La Sapienza, I-00185 Roma, Italy
60
Universita
̈
t Rostock, D-18051 Rostock, Germany
61
Rutherford Appleton Laboratory, Chilton, Didcot, Oxon OX11 0QX, United Kingdom
62
CEA, Irfu, SPP, Centre de Saclay, F-91191 Gif-sur-Yvette, France
63
SLAC National Accelerator Laboratory, Stanford, California 94309, USA
64
University of South Carolina, Columbia, South Carolina 29208, USA
65
Southern Methodist University, Dallas, Texas 75275, USA
66
Stanford University, Stanford, California 94305-4060, USA
67
State University of New York, Albany, New York 12222, USA
68
Tel Aviv University, School of Physics and Astronomy, Tel Aviv 69978, Israel
69
University of Tennessee, Knoxville, Tennessee 37996, USA
70
University of Texas at Austin, Austin, Texas 78712, USA
71
University of Texas at Dallas, Richardson, Texas 75083, USA
72a
INFN Sezione di Torino, I-10125 Torino, Italy
72b
Dipartimento di Fisica Sperimentale, Universita
`
di Torino, I-10125 Torino, Italy
73a
INFN Sezione di Trieste, I-34127 Trieste, Italy
73b
Dipartimento di Fisica, Universita
`
di Trieste, I-34127 Trieste, Italy
74
IFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spain
75
University of Victoria, Victoria, British Columbia V8W 3P6, Canada
76
Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
77
University of Wisconsin, Madison, Wisconsin 53706, USA
(Received 14 September 2012; published 27 November 2012)
We present measurements of the branching fractions of three-prong and five-prong
decay modes
using a sample of 430 million
lepton pairs, corresponding to an integrated luminosity of
468 fb
1
,
collected with the
BABAR
detector at the PEP-II asymmetric-energy
e
þ
e
storage rings at SLAC National
Accelerator Laboratory. The
!ð
3
Þ
,
!ð
3
Þ
!
, and
!
f
1
ð
1285
Þ
branching
fractions are presented, as well as a new limit on the branching fraction of the second-class current decay
!
0
ð
958
Þ
. We search for the decay mode
!
K
0
ð
958
Þ
and for five-prong decay modes
with kaons, and place the first upper limits on their branching fractions.
DOI:
10.1103/PhysRevD.86.092010
PACS numbers: 13.35.Dx, 14.60.Fg
I. INTRODUCTION
Study of the three-prong and five-prong decay modes of
the
lepton, where ‘‘prong’’ refers to the number of
charged hadrons (
or
K
) in the final state, allows one to
test the Standard Model and search for evidence of new
physics. The large
lepton data sample collected by the
BABAR
experiment provides an opportunity to perform a
comprehensive study of rare, high multiplicity decay
modes and to search for forbidden processes.
*
Now at the University of Tabuk, Tabuk 71491, Saudi Arabia.
†
Also with Universita
`
di Perugia, Dipartimento di Fisica,
Perugia, Italy.
‡
Now at the University of Huddersfield, Huddersfield HD1
3DH, UK.
§
Deceased.
k
Now at University of South Alabama, Mobile, Alabama
36688, USA.
{
Also with Universita
`
di Sassari, Sassari, Italy.
STUDY OF HIGH-MULTIPLICITY THREE-PRONG AND
...
PHYSICAL REVIEW D
86,
092010 (2012)
092010-3
We present measurements of the
!ð
3
Þ
,
!ð
3
Þ
!
, and
!
f
1
branching fractions.
We use the primary decay modes of the
,
!
ð
782
Þ
, and
f
1
ð
1258
Þ
mesons:
!
,
!
þ
0
,
!
3
0
,
!
!
þ
0
,
f
1
!
2
þ
2
, and
f
1
!
þ
.No
other narrow resonances are observed. We measure the
branching fractions of the nonresonant decays, where the
nonresonant category includes possible contributions
from broad resonances. We present a new limit on the
branching fractions of the second-class current decay
!
0
ð
958
Þ
, and the first limits on the allowed
first-class current decays
!
K
0
ð
958
Þ
and
!
0
0
ð
958
Þ
. Finally, we present the first limits on the
branching fractions of five-prong decay modes in which
one or more of the charged hadrons is a charged kaon. Note
that the branching fractions exclude the contribution of
K
0
S
!
þ
decays. Throughout this paper, charge con-
jugation is implied.
This analysis is based on data recorded with the
BABAR
detector at the PEP-II asymmetric-energy
e
þ
e
storage
rings operated at the SLAC National Accelerator
Laboratory. With an integrated luminosity (
L
) of 424
and
44 fb
1
recorded at center-of-mass (CM) energies of
10.58 and 10.54 GeV, respectively, and an
e
þ
e
!
þ
cross section of
þ
¼ð
0
:
919
0
:
003
Þ
nb
[
1
], the data
sample contains 430 million
pairs.
The
BABAR
detector is described in detail in Ref. [
2
].
Charged-particle momenta are measured with a five-layer
double-sided silicon vertex tracker and a 40-layer drift
chamber, both operating in the 1.5 T magnetic field of a
superconducting solenoid. Information from a detector of
internally reflected Cerenkov light is used in conjunction
with specific energy loss measurements from the tracking
detectors to identify charged pions and kaons [
3
]. Photons
are reconstructed from energy clusters deposited in a CsI
(TI) electromagnetic calorimeter. Electrons are identified by
combining tracking and calorimeter information. An instru-
mented magnetic flux return is used to identify muons.
The background contamination and selection efficien-
cies are determined using Monte Carlo simulation. The
-pair production is simulated with the KK2F event gen-
erator [
4
]. The
decays, continuum
q
q
events (
q
¼
udsc
),
and final-state radiative effects are modeled with the
Tauola [
5
], JETSET [
6
], and Photos [
7
] generators, respec-
tively. Dedicated samples of
þ
events are created using
the Tauola or EVTGEN [
8
] programs, with one of the
leptons allowed to decay to any mode while the other
decays to a specific final state. The detector response is
simulated with GEANT4 [
9
]. All Monte Carlo events are
processed through a full simulation of the
BABAR
detector
and are reconstructed in the same manner as the data.
II. EVENT SELECTION
The
pair is produced back-to-back in the
e
þ
e
CM
frame. The decay products of the two
leptons can thus be
separated from each other by dividing the event into two
hemispheres: the ‘‘signal’’ hemisphere and the ‘‘tag’’
hemisphere. The separation is performed using the event
thrust axis [
10
], which is calculated using all charged
particle and photon candidates in the event.
We select events where one hemisphere (tag) contains
exactly one track while the other hemisphere (signal) con-
tains exactly three or five tracks with total charge opposite
to that of the tag hemisphere. The event is rejected if any
pair of oppositely charged tracks is consistent with a
photon conversion. The component of the momentum
transverse to the beam axis for each of the tracks must be
greater than
0
:
1 GeV
=c
in the laboratory frame. All tracks
are required to have a point of closest approach to the
interaction region less than 1.5 cm in the plane transverse
to the beam axis and less than 2.5 cm in the direction along
that axis. This requirement eliminates
K
0
S
mesons that
decay to
þ
at points distant from the
e
þ
e
collision
point.
To reduce backgrounds from non-
pair events, we
require that the momentum of the charged particle in the
tag hemisphere be less than
4 GeV
=c
in the CM frame and
that the charged particle be identified as an electron or a
muon. The
q
q
background is suppressed by requiring that
there be at most one energetic (
E>
1 GeV
) electromag-
netic calorimeter cluster in the tag hemisphere that is not
associated with a track. Additional background suppres-
sion is achieved by requiring the magnitude of the event
thrust to lie between 0.92 and 0.99.
Neutral pion and eta candidates are reconstructed from
two photon candidates, each with energy greater than
30 MeV in the laboratory frame; the invariant mass of
the
0
(
) is required to be between 0.115 (0.35) and
0.150
ð
0
:
70
Þ
GeV
=c
2
. Neutral pion candidates are recon-
structed in the signal hemisphere. If a photon candidate
meets the invariant mass requirement with multiple photon
candidates, then the neutral pion candidate with invariant
mass closest to the nominal
0
mass [
11
] is selected. The
search for additional pion candidates is repeated using the
remaining photon candidates. The residual photon clusters
in the signal hemisphere are used to search for
!
candidates. In the case of multiple
candidates, the can-
didate with invariant mass closest to the nominal
mass is
selected. We reject events in which the invariant mass
M
formed from the system of charged particles,
0
, and
candidates, all in the signal hemisphere, exceeds
1
:
8 GeV
=c
2
.
The branching fractions are calculated using the expres-
sion
B
¼
N
X
=
ð
2
N"
Þ
where
N
X
is the number of candidates
after background subtraction,
N
is the number of
pairs
produced, and
"
is the selection efficiency.
N
is determined
from the product of the integrated luminosity and the
e
þ
e
!
þ
cross section. The uncertainty of
N
is
estimated to be 1%. The selection efficiencies are deter-
mined from the signal Monte Carlo samples. The
J. P. LEES
et al.
PHYSICAL REVIEW D
86,
092010 (2012)
092010-4
uncertainty on the selection efficiencies includes 0.5% per
track on the track reconstruction efficiency, as well as
particle identification (PID) selection uncertainties. From
studies conducted on real and simulated events, the uncer-
tainties on the charged particle identification selectors are
estimated to be 1% for electrons, 2.5% for muons, 0.5% for
pions, and 1.8% for kaons. The combined electron and
muon particle identification uncertainty is estimated to be
1.6% based on the composition of the event samples. The
uncertainty on the
0
!
and
!
reconstruction
efficiency is estimated to be 3% per candidate.
III. RESULTS
We present measurements of
decays to a system with
,
f
1
and
!
resonances in Secs.
III A
,
III B
, and
III C
,
respectively. Decays with these resonances do not account
for all three-prong or five-prong
decay modes, as dis-
cussed below, and we present measurements of the
branching fractions through nonresonant modes in
Sec.
III D
. Section
III E
presents a search for
decays
with an
0
(958) meson, while Sec.
III F
presents a search
for decays with either one or two charged kaons.
A.
!ð
3
Þ
The
!
2
þ
mode is studied in the
!
,
!
þ
0
, and
!
3
0
final states, while the
!
2
0
mode is studied in the
!
þ
0
final state.
The event yields are determined by fitting the
mass
peak in the
,
þ
0
, and
3
0
invariant mass distri-
butions (see Fig.
1
). The fit uses a Novosibirsk function
[
12
] (a Gaussian distribution with a tail parameter) for the
and a polynomial function for the background.
The Monte Carlo simulation indicates that some of the
entries in the
peak are from
e
þ
e
!
q
q
events. Control
samples, obtained by reversing the requirement on the
invariant mass of the observed decay products (
M>
1
:
8 GeV
=c
2
), are used to validate the background estimate.
The expected background is corrected by the ratio of data
to Monte Carlo events, and the statistical uncertainty of the
ratio is included in the background systematic uncertainty.
This method of validating the
q
q
background estimate is
used for all decays and is not mentioned in the later
sections.
The reconstruction efficiencies are determined from fits
to the signal Monte Carlo samples. The
!
2
0
sample is generated using a phase-space model for the
final-state particles. The
!
2
þ
sample is com-
posed of
!
f
1
(
f
1
!
þ
) decays and
decays without an intermediate resonance. The
!
2
þ
(excluding
f
1
) and
!
f
1
efficiencies
are the same for
!
þ
0
and
!
3
0
events,
whereas a slight difference is observed for
!
events
and a 2.5% uncertainty is added to the selection efficiency
systematic for this mode. In addition, a 4% uncertainty is
added to the
!
2
þ
selection efficiency for the
!
þ
0
mode to take into account variations
observed for different fits.
The three determinations of the
!
2
þ
branching fraction are found to be in good agreement
(see Table
I
) and we therefore calculate a weighted aver-
age. The statistical and systematic uncertainties on the
average are obtained by combining the individual uncer-
tainties in quadrature, accounting for correlations between
the systematic terms. The weighted average (inclusive of
!
f
1
) is found to be
B
ð
!
2
þ
Þ¼ð
2
:
25
0
:
07
0
:
12
Þ
10
4
:
Hereinafter, when two uncertainties are quoted, the first is
statistical and the second is systematic. The average
FIG. 1. The
,
þ
0
, and
3
0
invariant mass distribu-
tions for
!
2
þ
decay candidates, and the
þ
0
invariant mass distribution for
!
2
0
decay candi-
dates, after all selection criteria are applied. The solid lines
represent the fit to the
peak and background. The dashed lines
show the extrapolation of the background function under the
peak.
STUDY OF HIGH-MULTIPLICITY THREE-PRONG AND
...
PHYSICAL REVIEW D
86,
092010 (2012)
092010-5
branching fraction (exclusive of
!
f
1
) is deter-
mined to be
ð
0
:
99
0
:
09
0
:
13
Þ
10
4
and is obtained
using the branching fraction (inclusive of
!
f
1
),
given above, and subtracting the product branching frac-
tion
B
ð
!
f
1
Þ
B
ð
f
1
!
þ
Þ
presented in
the next section.
The
!
2
0
branching fraction is found to be
B
ð
!
2
0
Þ¼ð
2
:
01
0
:
34
0
:
22
Þ
10
4
:
Naively, the ratio of the
!
2
þ
to
!
2
0
branching fractions is expected to be two if
the decay is dominated by the
!
f
1
decay mode
(based on the
f
1
branching fractions [
11
]). The data do not
support this expectation.
Our previous measurement of the
!
2
þ
branching fraction
ð
1
:
60
0
:
05
0
:
11
Þ
10
4
[
13
],
which is based on the
!
mode only, is superseded
by this measurement. The fit used in the previous analysis
was performed using a narrower range in the invariant
mass distribution (
0
:
47
–
0
:
63 GeV
=c
2
) defined in a pre-
determined
selector. The narrow fit range resulted in
an incorrect description of the background distribution
giving the wrong number of
candidates. The current
work uses wider fit range (
0
:
30
–
0
:
70 GeV
=c
2
) and the
background distribution is well described.
The
!
2
þ
and
!
2
0
branch-
ing fractions are in good agreement with the results
from the CLEO collaboration,
ð
2
:
3
0
:
5
Þ
10
4
and
ð
1
:
5
0
:
5
Þ
10
4
, respectively [
14
]. Li predicts a larger
!
2
þ
branching fraction,
2
:
93
10
4
[
15
].
B.
!
f
1
The branching fraction of
!
f
1
and the mass
of the
f
1
meson are measured using the
f
1
!
2
þ
2
and
f
1
!
þ
decay modes, where the
f
1
!
þ
decay is reconstructed using
!
,
!
þ
0
,
and
!
3
0
events. The criteria used to select the
!
f
1
decays for the branching fraction measurement
are described earlier. We modify the selection for the mass
measurement, dropping the requirement that the track in
the tag hemisphere be a lepton and the restriction on the
number of photon candidates in the tag hemisphere, to
increase the size of the event sample.
The numbers of
!
f
1
candidates are deter-
mined by fitting the
f
1
peak in the
2
þ
2
and
þ
invariant mass distributions (see Fig.
2
). The
f
1
line shape
is expected to be a Breit-Wigner distribution, modified
by the limited phase space. Previous studies show that
the
f
1
!
a
0
þ
(
a
0
ð
980
Þ!
) channel appears to
account for all
f
1
!
þ
decays [
16
]. The mass of
the
a
0
ð
980
Þ
system and the
mass provide a lower and
upper limit, respectively, on the
f
1
line shape. We use the
four vectors of the charged pion and
a
0
ð
980
Þ
from
the EVTGEN generator to determine the simulated
f
1
line shape and find it to be a close approximation to the
Breit-Wigner expectation. The
f
1
peak is fit using this
line shape convolved with a Gaussian distribution to take
into account the effects of the detector resolution. The
results of the fits are presented in Table
II
. There is no
evidence for peaking background from
q
q
events or other
decays.
The product of the
!
f
1
and
f
1
!
2
þ
2
branching fractions, and the product of the
!
f
1
TABLE I. Results and branching fractions for
!ð
3
Þ
decays.
Decay mode
!
2
þ
!
2
þ
!
2
þ
!
2
0
!
!
þ
0
!
3
0
!
þ
0
Branching fraction (
10
4
)
2
:
10
0
:
09
0
:
13
2
:
37
0
:
12
0
:
18
2
:
54
0
:
27
0
:
25
2
:
01
0
:
34
0
:
22
Data events
2887
103
1440
68
315
34
381
45
2
=NDF
107
=
76
60
=
52
31
=
34
95
=
75
Selection efficiency
ð
3
:
83
0
:
11
Þ
%
ð
2
:
97
0
:
12
Þ
%
ð
0
:
42
0
:
01
Þ
%
ð
0
:
75
0
:
02
Þ
%
Background events
131
29
65
38
13
783
12
Systematic uncertainties (%)
Tracking efficiency
2.7
3.8
2.7
2.7
0
and
PID
3.0
3.0
9.0
9.0
Pion PID
1.5
2.5
1.5
1.5
Lepton-tag PID
1.6
1.6
1.6
1.6
N
1.0
1.0
1.0
1.0
Selection efficiency
3.9
4.0
2.8
2.7
Background
1.0
2.8
2.3
4.0
B
ð
!
Þ
1.0
B
ð
!
þ
0
Þ
1.8
1.8
B
ð
!
3
0
Þ
0.9
Total (%)
6.3
7.4
10
11
J. P. LEES
et al.
PHYSICAL REVIEW D
86,
092010 (2012)
092010-6
and
f
1
!
þ
branching fractions, are measured
to be
B
ð
!
f
1
Þ
B
ð
f
1
!
2
þ
2
Þ
¼ð
5
:
20
0
:
31
0
:
37
Þ
10
5
;
B
ð
!
f
1
Þ
B
ð
f
1
!
þ
Þ
¼ð
1
:
26
0
:
06
0
:
06
Þ
10
4
;
respectively, where the second result is the weighted
average of the three
modes. The
B
ð
!
f
1
Þ
branching fraction is determined to be
ð
4
:
73
0
:
28
0
:
45
Þ
10
4
and
ð
3
:
60
0
:
18
0
:
23
Þ
10
4
,as
obtained by dividing the product branching fractions by
B
ð
f
1
!
2
þ
2
Þ¼
0
:
110
þ
0
:
007
0
:
006
and
B
ð
f
1
!
þ
Þ¼
0
:
349
þ
0
:
013
0
:
015
[
17
], respectively.
Our two measured values for the
!
f
1
branch-
ing fraction are consistent with each other to within two
standard deviations of the combined statistical and system-
atic uncertainties. The ratio of the product branching frac-
tions is used to determine the ratio of the
f
1
!
2
þ
2
and
f
1
!
þ
branching fractions as
B
ð
f
1
!
2
þ
2
Þ
B
ð
f
1
!
Þ
¼
0
:
28
0
:
02
0
:
02
;
where
B
ð
f
1
!
Þ¼
1
:
5
B
ð
f
1
!
þ
Þ
based
on isospin symmetry. This agrees with average value of
0
:
41
0
:
14
quoted by the Particle Data Group [
11
] but
disagrees with their fit value of
0
:
63
0
:
06
[
11
].
The systematic uncertainties of the branching fractions
are listed in Table
II
. We observe that the number of events
in the
f
1
peak in the
f
1
!
2
þ
2
sample varies by 5%
for different background shapes. This variation is included
as a systematic uncertainty. We also observe that the
selection efficiency obtained from the Monte Carlo simu-
lation exhibits a slight dependence on whether the
f
1
decays via the
f
1
!
a
0
þ
or the
f
1
!
þ
mode,
and the variation is included as a systematic uncertainty
(listed under ‘‘fit model’’ in Table
II
).
The
!
f
1
branching fraction using the
f
1
!
2
þ
2
mode is consistent with the previous
BABAR
measurement (the new result supersedes the pre-
vious measurement), which is also based on the
f
1
!
2
þ
2
mode [
18
]. CLEO published a branching fraction
of
ð
5
:
8
þ
1
:
4
1
:
3
1
:
8
Þ
10
4
[
19
] and Li predicts a branching
fraction of
2
:
9
10
4
[
20
].
The
f
1
mass is determined by fitting the peak with a
nonrelativistic Breit-Wigner function, which was used in
previous measurements of the
f
1
mass [
11
]. As a cross
check, we use the energy-momentum four vectors from the
generator Monte Carlo simulation, and we find the fitted
mass value to be consistent with the input mass value.
We fit the invariant mass distribution in the fully recon-
structed Monte Carlo samples to determine whether the
result of the fit differs from the input mass of the
Monte Carlo generator. The difference is used to correct
the value of the invariant mass of each channel obtained
from the fit and the uncertainty in the difference is included
as a systematic error.
Table
III
and Fig.
3
show the results of the fits to the
data. The last column of the table presents the mass after
the application of the reconstruction correction factor.
The average of these results is
M
f
1
¼ð
1
:
28025
0
:
00039
Þ
GeV
=c
2
, where the error is statistical.
Previous
BABAR
analyses have measured the invariant
mass of resonances to be approximately
1 MeV
=c
2
less
than the values quoted by the Particle Data Group [
11
].
This shift is observed in the measurement of the mass of
the
f
1
meson [
21
] and the
lepton [
22
]. The shift is
attributed to the absolute energy and momentum calibra-
tion of the detector. We measure the calibration correction
FIG. 2. The
2
þ
2
and
þ
invariant mass distributions
for
!
2
þ
decay candidates after all selection crite-
ria are applied. The lower three plots are for the
!
,
!
þ
0
, and
!
3
0
decays. The solid lines represent the fit
to the
f
1
ð
1285
Þ
peak and background. The dashed lines show the
extrapolation of the background function under the
f
1
peak.
STUDY OF HIGH-MULTIPLICITY THREE-PRONG AND
...
PHYSICAL REVIEW D
86,
092010 (2012)
092010-7
TABLE II. Results and branching fractions for
!
f
1
decays.
Decay mode
f
1
!
þ
f
1
!
þ
f
1
!
þ
f
1
!
2
þ
2
!
!
þ
0
!
3
0
Branching fractions (
10
4
)
B
ð
!
f
1
Þ
B
ð
f
1
!
2
þ
2
Þ
0
:
520
0
:
031
0
:
037
B
ð
!
f
1
Þ
B
ð
f
1
!
þ
Þ
1
:
25
0
:
08
0
:
07 1
:
26
0
:
11
0
:
08 1
:
33
0
:
39
0
:
20
Data events
3722
222
1605
94
731
62
197
59
2
=NDF
77
=
62
50
=
43
61
=
55
39
=
43
Selection efficiency
ð
8
:
3
0
:
1
Þ
%
ð
3
:
75
0
:
04
Þ
%
ð
2
:
97
0
:
05
Þ
%
ð
0
:
53
0
:
06
Þ
%
Systematic uncertainties (%)
Tracking efficiency
3.8
2.7
3.8
2.7
0
and
PID
3.0
3.0
9.0
Pion PID
2.5
1.5
2.5
1.5
Lepton-tag PID
1.6
1.6
1.6
1.6
N
1.0
1.0
1.0
1.0
Selection efficiency
0.6
1.1
1.6
11
Fit model
5.0
2.7
B
ð
!
Þ
0.7
B
ð
!
þ
0
Þ
1.2
B
ð
!
3
0
Þ
0.9
Total (%)
7.0
5.6
6.1
15
TABLE III. Results of fits for the mass of the
f
1
resonance in
!
f
1
decays. The errors are statistical.
Decay mode
Monte Carlo
Data
Data
(generator-fit)
(fit)
(corrected)
(
GeV
=c
2
)(
GeV
=c
2
)(
GeV
=c
2
)
f
1
!
2
þ
2
0
:
00074
0
:
00008
1
:
28031
0
:
00067
1
:
28105
0
:
00067
f
1
!
þ
!
0
:
00292
0
:
00040
1
:
27775
0
:
00045
1
:
28067
0
:
00060
!
þ
0
0
:
00018
0
:
00020
1
:
27787
0
:
00080
1
:
27805
0
:
00082
!
3
0
0
:
00347
0
:
00033
1
:
28036
0
:
00335
1
:
28383
0
:
00337
FIG. 3 (color online). Compilation of our measurements of the
f
1
mass. The solid line is the weighted average and the shaded
area is the one standard deviation region.
FIG. 4. The fits to the
!
peak in the
þ
0
invariant mass
distributions for
!
2
þ
!
and
!
2
0
!
de-
cay candidates after all selection criteria are applied. The solid
lines represent the fit to the
!
peak and background. The dashed
lines show the extrapolation of the background function under
the
!
peak.
J. P. LEES
et al.
PHYSICAL REVIEW D
86,
092010 (2012)
092010-8
factor by fitting the
,
!
,
0
,
D
0
and
D
states using
data samples that have one track in the tag hemisphere
and either three or five tracks in the signal hemisphere.
No other selection criteria are applied. The peak masses
are found to be lower than the known values by
ð
0
:
91
0
:
10
Þ
MeV
=c
2
and the values are independent
of the mass of the resonance. We use the
ð
0
:
91
0
:
10
Þ
MeV
=c
2
as a correction factor that is
applied to the invariant mass and its error is included in
the systematic uncertainty.
We determine the mass of the
f
1
ð
1258
Þ
meson to be
M
f
1
¼ð
1
:
28116
0
:
00039
0
:
00045
Þ
GeV
=c
2
:
The systematic uncertainty includes the reconstruction
uncertainty and the calibration uncertainty. This result is
in good agreement with the Particle Data Group value
ð
1
:
2818
0
:
0006
Þ
GeV
=c
2
[
11
].
C.
!ð
3
Þ
!
We measure the
!
2
þ
!
and
!
2
0
!
branching fractions. The number of events is
determined by fitting the
!
peak in the
þ
0
invariant
mass distributions (see Fig.
4
) with a Breit-Wigner distri-
bution, which is convolved with a Gaussian distribution to
take into account the detector resolution. The resolution
parameter of the Gaussian distribution is determined using
a data control sample consisting of
q
q
events, and is fixed
in the fit. A polynomial function is used to fit the back-
ground. The results are presented in Table
IV
.
Approximately 10% of the events in the
!
2
þ
!
channel are backgrounds from other
decays
(primarily
!
0
!
decays) and
e
þ
e
!
q
q
events. The backgrounds are subtracted before calculating
the branching fraction.
The
!
2
0
!
sample has substantial contribu-
tions from
!
!
and
!
0
!
decays.
The background is estimated with the Monte Carlo simu-
lation and verified using data and simulation control
samples. The control samples follow the nominal selection
criteria but select one or two
0
instead of three
0
mesons.
The branching fractions are found to be
B
ð
!
2
þ
!
Þ¼ð
8
:
4
0
:
4
0
:
6
Þ
10
5
;
B
ð
!
2
0
!
Þ¼ð
7
:
3
1
:
2
1
:
2
Þ
10
5
:
The systematic uncertainties are listed in Table
IV
.
The
!
2
þ
!
and
!
2
0
!
branch-
ing fractions are consistent with the results from CLEO,
ð
1
:
2
0
:
2
0
:
1
Þ
10
4
and
ð
1
:
4
0
:
4
0
:
3
Þ
10
4
,
respectively [
14
]. Gao and Li suggest that this mode is
dominated by the (
!
) state and predict a branching
fraction in the range of
1
:
8
2
:
1
10
4
with the two
modes (
!
2
þ
!
and
!
2
0
!
) having
the same value [
23
]. The result measured in this work is
approximately 50% of the predicted rate but the ratio of the
two branching fractions is consistent with unity.
D. Nonresonant decay modes
The resonant modes, involving
,
!
and
f
1
mesons, do
not account for all of the observed decays, as discussed
below. We consider the excess in the observed decays to be
from ‘‘nonresonant’’ modes. We make no attempt to iden-
tify the contribution of resonances with larger widths
(
>
100 MeV
=c
2
) as the nature of these resonances is com-
plex and their line shapes will be modified by the limited
phase space in the
decay. The Monte Carlo simulation
describes the final states using a phase-space model
for the final-state particles. The only exception is the
TABLE IV. Results and branching fractions for
!ð
3
Þ
!
decays.
Decay mode
!
2
þ
!
!
2
0
!
!
!
þ
0
!
!
þ
0
Branching fractions (
10
5
)
8
:
4
0
:
4
0
:
67
:
3
1
:
2
1
:
2
Data events
2372
94
1135
70
2
=NDF
55
=
44
42
=
44
Selection efficiency
ð
3
:
27
0
:
03
Þ
%
ð
0
:
75
0
:
01
Þ
%
Background
257
71
709
59
Systematic uncertainties (%)
Tracking efficiency
3.8
2.7
0
and
PID
3.0
9.0
Pion PID
2.5
1.5
Lepton-tag PID
1.6
1.6
N
1.0
1.0
Selection efficiency
0.8
1.8
Background
3.4
14
B
ð
!
!
þ
0
Þ
0.8
0.8
Total (%)
6.8
17
STUDY OF HIGH-MULTIPLICITY THREE-PRONG AND
...
PHYSICAL REVIEW D
86,
092010 (2012)
092010-9