of 6
B
A
B
AR
-PUB-16/003
SLAC-PUB-16549
Search for a muonic dark force at
B
A
B
AR
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
abc
,
8
A. R. Buzykaev
a
,
8
V. P. Druzhinin
ab
,
8
V. B. Golubev
ab
,
8
E. A. Kravchenko
ab
,
8
A. P. Onuchin
abc
,
8
S. I. Serednyakov
ab
,
8
Yu. I. Skovpen
ab
,
8
E. P. Solodov
ab
,
8
K. Yu. Todyshev
ab
,
8
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. R ̈ohrken,
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
a
,
16
C. Bozzi
a
,
16
R. Calabrese
ab
,
16
G. Cibinetto
ab
,
16
E. Fioravanti
ab
,
16
I. Garzia
ab
,
16
E. Luppi
ab
,
16
V. Santoro
a
,
16
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
a
,
35
N. Neri
a
,
35
F. Palombo
ab
,
35
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
a
,
42
M. Margoni
ab
,
42
M. Posocco
a
,
42
M. Rotondo
a
,
42
G. Simi
ab
,
42
F. Simonetto
ab
,
42
R. Stroili
ab
,
42
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
ab
,
44
E. Manoni
a
,
44
A. Rossi
a
,
44
G. Batignani
ab
,
45
S. Bettarini
ab
,
45
M. Carpinelli
ab
,
45,
G. Casarosa
ab
,
45
M. Chrzaszcz
a
,
45
F. Forti
ab
,
45
M. A. Giorgi
ab
,
45
A. Lusiani
ac
,
45
B. Oberhof
ab
,
45
E. Paoloni
ab
,
45
M. Rama
a
,
45
G. Rizzo
ab
,
45
J. J. Walsh
a
,
45
A. J. S. Smith,
46
F. Anulli
a
,
47
R. Faccini
ab
,
47
F. Ferrarotto
a
,
47
F. Ferroni
ab
,
47
A. Pilloni
ab
,
47
G. Piredda
a
,
47
C. B ̈unger,
48
S. Dittrich,
48
O. Gr ̈unberg,
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
ab
,
60
F. De
Mori
ab
,
60
A. Filippi
a
,
60
D. Gamba
ab
,
60
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
B. Shuve,
63
N. Tasneem,
63
T. J. Gershon,
64
P. F. Harrison,
64
T. E. Latham,
64
R. Prepost,
65
and S. L. Wu
65
(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-Vieux, France
2
Universitat de Barcelona, Facultat de Fisica, Departament ECM, E-08028 Barcelona, Spain
3
INFN Sezione di Bari and Dipartimento di Fisica, Universit`a di Bari, I-70126 Bari, Italy
4
University of Bergen, Institute of Physics, N-5007 Bergen, Norway
5
Lawrence Berkeley National Laboratory and University of California, Berkeley, California 94720, USA
6
Ruhr Universit ̈at Bochum, Institut f ̈ur Experimentalphysik 1, D-44780 Bochum, Germany
7
University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z1
8
Budker Institute of Nuclear Physics SB RAS, Novosibirsk 630090
a
,
Novosibirsk State University, Novosibirsk 630090
b
,
Novosibirsk State Technical University, Novosibirsk 630092
c
, 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
arXiv:1606.03501v1 [hep-ex] 10 Jun 2016
13
University of Cincinnati, Cincinnati, Ohio 45221, USA
14
University of Colorado, Boulder, Colorado 80309, USA
15
Laboratoire Leprince-Ringuet, Ecole Polytechnique, CNRS/IN2P3, F-91128 Palaiseau, France
16
INFN Sezione di Ferrara
a
; Dipartimento di Fisica e Scienze della Terra, Universit`a di Ferrara
b
, 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’Acc ́el ́erateur Lin ́eaire, IN2P3/CNRS et Universit ́e 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-Universit ̈at Mainz, Institut f ̈ur 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, Montr ́eal, Qu ́ebec, Canada H3A 2T8
35
INFN Sezione di Milano
a
; Dipartimento di Fisica, Universit`a di Milano
b
, I-20133 Milano, Italy
36
University of Mississippi, University, Mississippi 38677, USA
37
Universit ́e de Montr ́eal, Physique des Particules, Montr ́eal, Qu ́ebec, Canada H3C 3J7
38
INFN Sezione di Napoli and Dipartimento di Scienze Fisiche,
Universit`a 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
42
INFN Sezione di Padova
a
; Dipartimento di Fisica, Universit`a di Padova
b
, I-35131 Padova, Italy
43
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
44
INFN Sezione di Perugia
a
; Dipartimento di Fisica, Universit`a di Perugia
b
, I-06123 Perugia, Italy
45
INFN Sezione di Pisa
a
; Dipartimento di Fisica,
Universit`a di Pisa
b
; Scuola Normale Superiore di Pisa
c
, I-56127 Pisa, Italy
46
Princeton University, Princeton, New Jersey 08544, USA
47
INFN Sezione di Roma
a
; Dipartimento di Fisica,
Universit`a di Roma La Sapienza
b
, I-00185 Roma, Italy
48
Universit ̈at 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
60
INFN Sezione di Torino
a
; Dipartimento di Fisica, Universit`a di Torino
b
, I-10125 Torino, Italy
61
INFN Sezione di Trieste and Dipartimento di Fisica, Universit`a 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
65
University of Wisconsin, Madison, Wisconsin 53706, USA
Many models of physics beyond the Standard Model predict the existence of new Abelian forces
with new gauge bosons mediating interactions between “dark sectors” and the Standard Model. We
report a search for a dark boson
Z
coupling only to the second and third generations of leptons in the
reaction
e
+
e
μ
+
μ
Z
,Z
μ
+
μ
using 514 fb
1
of data collected by the
B
A
B
AR
experiment.
2
No significant signal is observed for
Z
masses in the range 0
.
212
10 GeV. Limits on the coupling
parameter
g
as low as 7
×
10
4
are derived, leading to improvements in the bounds compared to
those previously derived from neutrino experiments.
PACS numbers: 12.60.-i, 14.80.-j, 13.66.Hk, 95.35.+d
In spite of the many successes of the Standard Model
(SM), the known particles and interactions are insuffi-
cient to explain cosmological and astrophysical observa-
tions of dark matter. This motivates the possibility of
new hidden sectors that are only feebly coupled to the
SM; by analogy with the SM, such sectors may contain
their own interactions with new gauge bosons (
Z
). In
the simplest case of a hidden U(1) interaction, SM fields
may directly couple to the
Z
, or alternatively the
Z
boson may mix with the SM hypercharge boson, which
typically results from an off-diagonal kinetic term [1]. In
the latter case, the
Z
inherits couplings proportional to
the SM gauge couplings; due to large couplings to elec-
trons and light-flavor quarks, such scenarios are strongly
constrained by existing searches [2–8].
When SM fields are directly charged under the dark
force, however, the
Z
may interact preferentially with
heavy-flavor leptons, greatly reducing the sensitivity of
current searches. Such interactions could account for the
experimentally measured value of the muon anomalous
magnetic dipole moment [9], as well as the discrepancy
in the proton radius extracted from measurements of the
Lamb shift in muonic hydrogen compared to observations
in non-muonic atoms [10, 11]. Direct
Z
couplings to left-
handed leptons also lead to new interactions involving
SM neutrinos that increase the cosmological abundance
of sterile neutrinos mixing with SM neutrinos, consistent
with the observed dark matter abundance [12].
We report herein a search for dark bosons
Z
with vec-
tor couplings only to the second and third generations of
leptons [13, 14] in the reaction
e
+
e
μ
+
μ
Z
,Z
μ
+
μ
. While such a scenario can be additionally con-
strained by neutrino-nucleus scattering at neutrino beam
experiments, the measurement presented here is also sen-
sitive to models where couplings to neutrinos are ab-
sent, such as a gauge boson coupled exclusively to right-
handed muons [15]. This search is based on 514 fb
1
of data collected by the
B
A
B
AR
detector at the PEP-II
e
+
e
storage ring, mostly taken at the
Υ
(4
S
) resonance,
but also at the
Υ
(3
S
) and
Υ
(2
S
) peaks, as well as in
the vicinity of these resonances [16]. The
B
A
B
AR
detec-
tor is described in detail elsewhere [17, 18]. Dark boson
masses between the dimuon threshold and 10 GeV are
probed [19]. To avoid experimental bias, the data are
only examined after finalizing the analysis strategy. A
sample of about 5% of the dataset is used to optimize
and validate the analysis strategy, and is then discarded.
Signal events are simulated by MadGraph 5 [20] and
hadronized in Pythia 6 [21] for
Z
mass hypotheses
ranging from the dimuon mass threshold to 10
.
3 GeV.
The background arises mainly from QED processes.
The
e
+
e
μ
+
μ
μ
+
μ
reaction is generated with
Diag36 [22], which includes the full set of lowest order
diagrams, while the
e
+
e
μ
+
μ
(
γ
) and
e
+
e
τ
+
τ
(
γ
) processes are simulated with KK [23]. Other
sources of background include
e
+
e
q
q
(
q
=
u,d,s,c
)
continuum production, simulated with JETSET [24], and
e
+
e
π
+
π
J/ψ
events, generated using EvtGen [25]
with a phase-space model. The detector acceptance and
reconstruction efficiencies are determined using a Monte
Carlo (MC) simulation based on GEANT4 [26].
We select events containing two pairs of oppositely-
charged tracks, where both positively-charged or both
negatively-charged tracks are identified as muons by par-
ticle identification algorithms (PID). Identifying only two
muons maintains high signal efficiency while rejecting al-
most all background sources but
e
+
e
μ
+
μ
μ
+
μ
events. In addition, the sum of energies of electromag-
netic clusters above 30 MeV not associated to any track
must be less than 200 MeV to remove background con-
taining neutral particles. To suppress background from
the decay chain
Υ
(3
S,
2
S
)
π
+
π
Υ
(1
S
)
(1
S
)
μ
+
μ
, we reject events taken on the
Υ
(2
S
) or
Υ
(3
S
)
peaks containing any pair of oppositely charged tracks
with any dimuon invariant mass within 100 MeV of the
nominal
Υ
(1
S
) mass.
The distribution of the four-muon invariant mass af-
ter these cuts is shown in Fig. 1 for the data taken at
the
Υ
(4
S
) center-of-mass (CM) energy. The background
at low masses is fairly well reproduced by the simula-
tion, while the
e
+
e
μ
+
μ
μ
+
μ
Monte Carlo over-
estimates the full-energy peak by
30% and fails to re-
produce the radiative tail. This is expected, since Diag36
does not simulate initial state radiation (ISR). We fur-
ther select
e
+
e
μ
+
μ
μ
+
μ
events by requiring a
four-muon invariant mass within 500 MeV of the nominal
CM energy, allowing for the possibility of ISR emission.
The four-muon system is finally fitted, constraining its
CM energy to be within the beam energy spread and the
tracks to originate from the interaction point to within
its uncertainty. This kinematic fit is solely used to im-
prove the
Z
mass resolution of the bulk of events near
the full-energy peak; no further requirement is imposed
on the fit quality. We do not attempt to select a single
Z
μ
+
μ
candidate per event, but simply consider all
combinations.
The distribution of the reduced dimuon mass,
m
R
=
m
2
μ
+
μ
4
m
2
μ
, is shown in Fig. 2, together with the
predictions of various Monte Carlo simulations. The
3
reduced mass has a smoother behavior near threshold
and is easier to model than the dimuon mass.
The
spectrum is dominated by
e
+
e
μ
+
μ
μ
+
μ
pro-
duction, with additional contributions from
e
+
e
π
+
π
ρ,ρ
π
+
π
,
e
+
e
μ
+
μ
ρ,ρ
π
+
π
, and
e
+
e
π
+
π
J/ψ,J/ψ
μ
+
μ
events, where one or
several pions are misidentified as muons. A peak cor-
responding to the
ρ
meson is visible at low mass; the
second
Z
candidate reconstructed in these events gen-
erates the enhancement near 9
.
5 GeV. Other than the
J/ψ
, no significant signal of other narrow resonances is
observed.
) (GeV)
μ
m(4
6
7
8
9
10
11
Entries / 0.06 (GeV)
10
2
10
3
10
4
10
5
10
Data
-
μ
+
μ
-
μ
+
μ
-
e
+
e
-
τ
+
τ
-
e
+
e
q=u,d,s,c
q
q
-
e
+
e
)
-
μ
+
μ
(
ψ
J/
-
π
+
π
-
e
+
e
FIG. 1: The distribution of the four-muon invariant mass,
m
(4
μ
), for data taken at the
Υ
(4
S
) peak together with Monte
Carlo predictions of various processes normalized to data lu-
minosity. The
e
+
e
μ
+
μ
μ
+
μ
Monte Carlo does not
include ISR corrections.
The signal efficiency rises from
35% at low masses to
50% around
m
R
= 6
7 GeV, before dropping again
at higher masses. The signal efficiencies include a cor-
rection factor of 0.82, which primarily accounts for the
impact of ISR not included in the simulation, as well
as differences between data and simulation in trigger ef-
ficiency, charged particle identification, and track and
photon reconstruction efficiencies. This correction fac-
tor is derived from the ratio of the
m
R
distribution in
simulated
e
+
e
μ
+
μ
μ
+
μ
events to the observed
distribution in the mass region 1–9 GeV, excluding the
J/ψ
region (light blue line in Fig. 2). An uncertainty of
5% is propagated as a systematic uncertainty, covering
the small variations between data-taking periods and the
uncertainties on the
e
+
e
μ
+
μ
μ
+
μ
cross-section.
We extract the signal yield as a function of
m
Z
by
performing a series of unbinned maximum likelihood fits
to the reduced dimuon mass spectrum, covering the mass
range
m
R
<
10 GeV for the data taken near the
Υ
(4
S
)
resonance, and up to 9 GeV for the datasets collected
near the
Υ
(2
S
) and
Υ
(3
S
) resonances. The search is
(GeV)
R
m
Entries / 0.1 (GeV)
0
1000
2000
3000
4000
5000
Data
-
μ
+
μ
-
μ
+
μ
-
e
+
e
-
τ
+
τ
-
e
+
e
q=u,d,s,c
q
q
-
e
+
e
)
-
μ
+
μ
(
ψ
J/
-
π
+
π
-
e
+
e
(GeV)
R
m
0
1
2
3
4
5
6
7
8
9
10
Data/MC
0.8
1
1.2
FIG. 2: The distribution of the reduced dimuon mass,
m
R
,
together with Monte Carlo predictions of various processes
normalized to data luminosity. Four combinations per event
are included. The fit of the ratio between reconstructed and
simulated events is shown as a light blue dashed line. The
e
+
e
μ
+
μ
μ
+
μ
Monte Carlo does not include ISR or
other efficiency corrections (see text).
conducted in varying mass steps that correspond to the
dark boson mass resolution. Each fit is performed over
an interval 50 times broader than the signal resolution
at that mass for
m
R
>
0
.
2 GeV, or over a fixed interval
0
0
.
3 GeV for
m
R
<
0
.
2 GeV. We estimate the signal
resolution by Gaussian fits to several simulated
Z
sam-
ples for the purpose of determining the scan steps, and
interpolate the results to all other masses. The resolution
varies between 1
9 MeV, dominated by experimental ef-
fects. We probe a total of 2219 mass hypotheses. The
bias in the fitted values, estimated from a large ensemble
of pseudo-experiments, is negligible.
The likelihood function, described below, contains
components from signal, continuum background, and
peaking background where appropriate. The signal prob-
ability density function (pdf) is modeled directly from
the signal Monte Carlo mass distribution using a non-
parametric kernel density function. The pdf is interpo-
lated between the known simulated masses using an algo-
rithm based on the cumulative density function [27]. An
uncertainty of 0
.
1
3
.
2 events associated to this proce-
dure is estimated by taking the next-to-closest mass point
in place of the closest simulated mass point to interpolate
the signal shape. The agreement between the simulated
signal resolution and the data is assessed by fitting the
full-energy peak of the four-muon invariant mass spec-
trum in the range 10
.
3
10
.
7 GeV with a Crystal Ball
function [28]. The ratio of simulated and reconstructed
peak widths is 1
.
01
±
0
.
04, consistent with unity. The im-
pact of ISR emission on the peak widths are expected to
be small in that mass range. Similarly, the decay width
4