of 7
arXiv:1502.02580v2 [hep-ex] 1 May 2015
B
A
B
AR
-PUB-14/010
SLAC-PUB-16226
Search for Long-Lived Particles in
e
+
e
Collisions
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
C. Campagnari,
12
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. Lo Vetere
ab
,
23
M. R. Monge
ab
,
23
S. Passaggio
a
,
23
C. Patrignani
ab
,
23
E. Robutti
a
,
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
G. Sciolla,
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,
∗∗
P. Sonnek,
43
D. J. Summers,
43
M. Simard,
44
P. Taras,
44
G. De Nardo
ab
,
45
G. Onorato
ab
,
45
C. Sciacca
ab
,
45
M. Martinelli,
46
G. Raven,
46
C. P. Jessop,
47
J. M. LoSecco,
47
K. Honscheid,
48
R. Kass,
48
E. Feltresi
ab
,
49
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
S. Pacetti
ab
,
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
A. Cervelli
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
A. Perez
a
,
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
L. Li Gioi
a
,
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
A. A. Salnikov,
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
R. M. White,
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
B. C. Wray,
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)
2
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
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
3
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
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 present a search for a neutral, long-lived particle
L
that is produced in
e
+
e
collisions and
decays at a significant distance from the
e
+
e
interaction point into various flavor combinations
of two oppositely charged tracks. The analysis uses an
e
+
e
data sample with a luminosity of
489
.
1 fb
1
collected by the
B
A
B
AR
detector at the
Υ
(4
S
),
Υ
(3
S
), and
Υ
(2
S
) resonances and just
below the
Υ
(4
S
). Fitting the two-track mass distribution in search of a sig
nal peak, we do not
observe a significant signal, and set 90% confidence level upp
er limits on the product of the
L
production cross section, branching fraction, and reconst
ruction efficiency for six possible two-body
L
decay modes as a function of the
L
mass. The efficiency is given for each final state as a function
of the mass, lifetime, and transverse momentum of the candid
ate, allowing application of the upper
limits to any production model. In addition, upper limits ar
e provided on the branching fraction
B
(
B
X
s
L
), where
X
s
is a strange hadronic system.
PACS numbers: 13.66.Hk, 14.80.-j, 14.80.Ec
Recent anomalous astrophysical observations [1–3]
have generated interest in GeV-scale hidden-sector states
that may be long-lived [4–12]. Searches for long-lived
particles have been performed both in the sub-GeV [13–
15] and multi-GeV [16–21] mass ranges. Dedicated ex-
periments to search for such particles have been pro-
posed [22] or are under construction [23]. However,
the
O
(1 GeV
/c
2
) mass range has remained mostly unex-
plored, especially in a heavy-flavor environment.
B
fac-
tories offer an ideal laboratory to probe this regime. Pre-
viously, the only
B
-factory results were from a search for
a heavy neutralino by the Belle collaboration [24].
We search herein for a neutral, long-lived particle
L
,
which decays into any of the final states
f
=
e
+
e
,
μ
+
μ
,
e
±
μ
,
π
+
π
,
K
+
K
, or
K
±
π
. A displaced vertex and
two-body decay kinematics constitute the main means
for background suppression, and the search is performed
by fitting the distribution of the
L
-candidate mass.
The results are presented in two ways. In the “model-
independent” presentation, no assumption is made re-
garding the production mechanism of the
L
. Rather, we
present limits on the product of the inclusive produc-
tion cross section
σ
(
e
+
e
LX
), branching fraction
B
(
L
f
), and efficiency
ǫ
(
f
) for each of the two-body
final states
f
, where
X
is any set of particles. As supple-
mental material to this letter [25], we provide tables of
the efficiency as a function of
L
mass
m
, transverse [36]
momentum
p
T
in the center-of-mass (CM) frame, and
proper decay distance
, assuming the
L
to be a spin-
zero particle. The provided upper limits, efficiencies, and
p
T
distributions of the simulated events used to obtain
the efficiencies facilitate the application of the model-
independent presentation of the results to any specific
model of
L
production. In the “model-dependent” pre-
sentation, we provide limits on the branching fraction
for the decay
B
X
s
L
, where
X
s
is a hadronic sys-
tem with strangeness
1. This presentation is motivated
by Higgs-portal models of dark matter and other hidden
sectors [8–11].
The data were collected with the
B
A
B
AR
detector at
the PEP-II asymmetric-energy
e
+
e
collider at SLAC
National Accelerator Laboratory. The sample consists
of 404
.
0
±
1
.
7 fb
1
collected at a CM energy correspond-
ing to the
Υ
(4
S
) resonance, an “off-resonance” sample
of 43
.
74
±
0
.
20 fb
1
collected about 40 MeV below the
Υ
(4
S
) peak, 27
.
85
±
0
.
18fb
1
collected at the
Υ
(3
S
), and
13
.
56
±
0
.
09fb
1
taken at the
Υ
(2
S
) [26]. The
Υ
(4
S
) sam-
ple contains (448
.
4
±
2
.
2)
×
10
6
B
B
pairs, and the
Υ
(3
S
)
and
Υ
(2
S
) samples have (121
.
3
±
1
.
2)
×
10
6
Υ
(3
S
) and
(98
.
3
±
0
.
9)
×
10
6
Υ
(2
S
) mesons, respectively [27]. An
additional
Υ
(4
S
) sample of 20
.
37
±
0
.
09 fb
1
is used to
validate the analysis procedure and is not included in the
final analysis.
The
B
A
B
AR
detector and its operation are described
4
in detail in Refs. [28] and [29]. Charged-particle mo-
menta are measured in a tracking system consisting of
a five-layer, double-sided silicon vertex detector (SVT)
and a 40-layer drift chamber (DCH), both located in a
1.5 T axial magnetic field. Electron and photon energies
are measured in a CsI(Tl) electromagnetic calorimeter
(EMC) inside the magnet coil. Charged-particle identifi-
cation (PID) is performed using an internally reflecting,
ring-imaging Cherenkov detector, as well as the energy
loss measured by the SVT, DCH and EMC. Muons are
identified mainly with the instrumented magnetic-flux re-
turn.
Using Monte Carlo (MC) simulations, we determine
both the signal mass resolution and reconstruction effi-
ciency. The events are produced with the
EvtGen
[31]
event generator, taking the
L
spin to be zero. We gen-
erate two types of signal MC samples. In the first type,
which is used to create the efficiency tables [25] for the
model-independent presentation, the
L
is produced at
11 different masses,
m
MC
0
= 0
.
5, 1, 2, 3, 4, 5, 6, 7, 8,
9, and 9.5 GeV
/c
2
. For
m
MC
0
4 GeV
/c
2
, the
L
is cre-
ated in the process
e
+
e
B
B
, with one
B
meson de-
caying to
L
+
N π
(
N
= 1, 2, or 3) and the other
B
decaying generically. At higher masses, the production
process is
Υ
(4
S
)
L
+
N π
. In both cases, the
L
is pro-
duced uniformly throughout the available phase space,
with an average transverse decay distance of 20 cm. The
events are subsequently reweighted to obtain efficiencies
for other decay lengths. Note that these specific processes
do not reflect preferred hypotheses about the production
mechanism, nor do the results depend on these processes.
Rather, they are a convenient method to populate the
kinematic range for the efficiency tables.
The second type of signal MC, used for the model-
dependent presentation of the results, contains
B
X
s
L
decays, for the seven mass values
m
MC
0
= 0
.
5, 1, 2, 3, 3.5,
4, and 4.5 GeV
/c
2
. The
X
s
is nominally taken to be 10%
K
, 25%
K
(892), and 65%
K
(1680) [30], with the high-
mass tail of the
X
s
spectrum suppressed by phase-space
limitations, especially for heavy
L
states. This choice of
X
s
composition results in an
L
-momentum spectrum as
a function of
m
MC
0
that reproduces the dimuon spectrum
for
B
X
s
μ
+
μ
in events generated with
EvtGen
using
the BTOXSLL model [31]. The other
B
meson in the
event decays generically.
In addition to the signal MC samples, background
MC samples are used for optimizing the event selec-
tion criteria and studying the signal extraction method.
The background samples are
e
+
e
B
B
(produced
with
EvtGen
[31]),
τ
+
τ
,
μ
+
μ
(
KK2f
[32]),
e
+
e
(
BHWIDE
[33]), and
q
q
events (
JETSET
[34]), where
q
is
a
u
,
d
,
s
, or
c
quark. The detector response is simulated
with
GEANT4
[35].
The
L
candidates are reconstructed from pairs of op-
positely charged tracks, identified as either
e
+
e
,
μ
+
μ
,
e
±
μ
,
π
+
π
,
K
+
K
, or
K
±
π
. The PID efficiency
depends on the track momentum, and is in the range
0
.
96
0
.
99 for electrons, 0
.
60
0
.
88 for muons, and
0
.
90
0
.
98 for kaons and pions. The pion misidentifi-
cation probability is less than 0
.
01 for the electron PID
criteria, less than 0
.
03 for the muon criteria, and aver-
ages at 0
.
06 for the kaon criteria. A track may have
different PID assignments and may appear in multiple
pairs. Each track must satisfy
d
0
d
0
>
3, where
d
0
is
the transverse distance of closest approach of the track
to the
e
+
e
interaction point (IP), and
σ
d
0
is the
d
0
un-
certainty, calculated from the SVT and DCH hit position
uncertainties during the track reconstruction. The two
tracks are fit to a common vertex, and the
χ
2
value of
the fit is required to be smaller than 10 for one degree of
freedom. The two-dimensional vector
~r
between the IP
and the vertex in the transverse plane must have length
r
≡ |
~r
|
in the range 1
< r <
50 cm, and the uncer-
tainty on
r
is required to satisfy
σ
r
<
0
.
2 cm. We require
the angle
α
between
~r
and the
L
-candidate transverse-
momentum vector to satisfy
α <
0
.
01 rad. The uncer-
tainty
σ
m
on the measured
L
-candidate mass
m
must
be less than 0
.
2 GeV
/c
2
. The
L
candidate is discarded
if either of the tracks has SVT or DCH hits located be-
tween the IP and the vertex, or if the vertex is within
the material of the beampipe wall, the DCH support
tube, or the DCH inner cylinder. Candidates must sat-
isfy the following decay-mode-specific invariant-mass cri-
teria:
m
e
+
e
>
0
.
44 GeV
/c
2
,
m
μ
+
μ
<
0
.
37 GeV
/c
2
or
m
μ
+
μ
>
0
.
5 GeV
/c
2
,
m
e
±
μ
>
0
.
48 GeV
/c
2
,
m
π
+
π
>
0
.
86 GeV
/c
2
,
m
K
+
K
>
1
.
35 GeV
/c
2
, and
m
K
±
π
>
1
.
05 GeV
/c
2
. These criteria reject background from
K
0
S
π
+
π
and
Λ
decays. In addition, other
than in the
μ
+
μ
mode, they exclude low-mass regions
in which the mass distributions of background MC events
are not smooth, and therefore incompatible with the
background description method outlined below. We re-
quire at least one of the tracks of
L
μ
+
μ
candidates
with
m
8 GeV
/c
2
to have an SVT hit. This rejects
candidates that decay into
μ
+
μ
within the material of
the final-focusing magnets, and thus have poor mass res-
olution. These selection criteria are found to yield near-
optimal signal sensitivity given the broad range of
m
and
r
values of this search.
For each decay mode, we determine the full efficiency
ǫ
, including the impact of detector acceptance, trigger,
reconstruction, and selection criteria, for different values
of
m
MC
0
,
, and
p
T
. The efficiency, which is tabulated
in Ref. [25], reaches a maximal value of
ǫ
= 52% for
L
π
+
π
decays with
m
= 2 GeV
/c
2
,
p
T
>
4 GeV
/c
,
and
= 6 cm. The dominant factor affecting
ǫ
is the
average transverse flight distance
h
r
i
=
h
p
T
i
/m
. Re-
flecting the 1
< r <
50 cm requirement,
ǫ
drops rapidly
when
h
r
i
goes below 1 cm or above 50 cm. In addition,
ǫ
has some dependence on the
L
polar-angle
θ
, mea-
sured with respect to the direction of the
e
+
e
center
of mass. For a 1 + cos
2
θ
distribution in the CM frame,