Search for Hidden-Sector Bosons in B
0
→ K
0
μ
þ
μ
−
Decays
R. Aaij et al.
*
(LHCb Collaboration)
(Received 18 August 2015; published 16 October 2015)
A search is presented for hidden-sector bosons, χ, produced in the decay B
0
→ K
ð892Þ
0
χ,
with K
ð892Þ
0
→ K
þ
π
−
and χ → μ
þ
μ
−
. The search is performed using pp-collision data corresponding
to 3.0 fb
−1
collected with the LHCb detector. No significant signal is observed in the accessible mass
range 214 ≤ mðχÞ ≤ 4350 MeV, and upper limits are placed on the branching fraction product
B(B
0
→ K
ð892Þ
0
χ) × Bðχ → μ
þ
μ
−
Þ as a function of the mass and lifetime of the χ boson. These limits
are of the order of 10
−9
for χ lifetimes less than 100 ps over most of the mðχÞ range, and place the most
stringent constraints to date on many theories that predict the existence of additional low-mass bosons.
DOI: 10.1103/PhysRevLett.115.161802 PACS numbers: 13.85.Rm, 12.60.-i, 13.20.He, 14.80.Va
Interest has been rekindled in hidden-sector theories [1],
motivated by the current lack of evidence for a dark matter
particle candidate and by various cosmic-ray anomalies
[2–8]. These theories postulate that dark matter particles
interact feebly with all known particles, which is why they
have escaped detection. Such interactions can be generated
in theories where hidden-sector particles are singlet states
under the standard model (SM) gauge interactions. Coupling
between the SM and hidden-sector particles may then arise
via mixing between the hidden-sector field and any SM field
with an associated particle that is not charged under the
electromagnetic or strong interaction (the Higgs and Z
bosons, the photon, and the neutrinos). This mixing could
provide a so-called portal through which a hidden-sector
particle, χ, may be produced if kinematically allowed.
Many theories predict that TeV-scale dark matter par-
ticles interact via GeV-scale bosons [9–11] (c ¼ 1 through-
out this Letter). Previous searches for such GeV-scale
particles have been performed using large data samples
from many types of experiments (see Ref. [12] for a
summary). These searches have placed stringent constraints
on the properties of the hidden-sector photon and neutrino
portals; however, the constraints on the axial-vector and
scalar portals are significantly weaker.
One class of models involving the scalar portal hypothe-
sizes that such a χ field was responsible for an inflationary
period in the early Universe [13], and may have generated
the baryon asymmetry observed today [14,15]. The asso-
ciated inflaton particle is expected to have a mass in the
range 270 ≲ mðχÞ ≲ 1800 MeV [13]. Another class of
models invokes the axial-vector portal in theories of dark
matter that seek to address the cosmic-ray anomalies, and to
explain the suppression of charge-parity (CP) violation in
strong interactions [16]. These theories postulate an addi-
tional fundamental symmetry, the spontaneous breaking of
which results in a particle called the axion [17]. To couple
the axion portal to a hidden sector containing a TeV-scale
dark matter particle, while also explaining the suppression
of CP violation in strong interactions, Ref. [18] proposes
an axion with 360 ≲ mðχÞ ≲ 800 MeV and an energy
scale, fðχÞ, at which the symmetry is broken in the range
1 ≲ fðχÞ
≲ 3 TeV. A broader range of mðχÞ and fð χÞ
values is allowed in other dark matter scenarios involving
axion(-like) states [19–21].
This Letter reports a search for a hidden-sector boson
produced in the decay B
0
→ K
0
χ, with χ → μ
þ
μ
−
and
K
0
→ K
þ
π
−
[throughout this Letter, K
0
≡ K
ð892Þ
0
and
the inclusion of charge-conjugate processes is implied].
Enhanced sensitivity to hidden-sector bosons arises
because the b → s transition is mediated by a top quark
loop at leading order (see Fig. 1). Therefore, a χ boson with
2mðμÞ <mðχÞ <mðB
0
Þ − mðK
0
Þ and a sizable top quark
coupling, e.g., obtained via mixing with the Higgs sector,
could be produced at a substantial rate in such decays. The
B
0
→ K
0
χ decay is chosen instead of B
þ
→ K
þ
χ, since
better χ decay time resolution is obtained due to the
presence of the K
þ
π
−
vertex, and because there is less
background contamination. The data used correspond to
FIG. 1. Feynman diagram for the decay B
0
→ K
0
χ, with
χ → μ
þ
μ
−
.
*
Full author list given at the end of the article.
Published by the American Physical Society under the terms of
the Creative Commons Attribution 3.0 License. Further distri-
bution of this work must maintain attribution to the author(s) and
the published article’s title, journal citation, and DOI.
PRL 115, 161802 (2015)
PHYSICAL REVIEW LETTERS
week ending
16 OCTOBER 2015
0031-9007=15=115(16)=161802(10) 161802-1 © 2015 CERN, for the LHCb Collaboration
integrated luminosities of 1.0 and 2.0 fb
−1
collected at
center-of-mass energies of
ffiffiffi
s
p
¼ 7 and 8 TeV in pp
collisions with the LHCb detector. This is the first dedi-
cated search over a large mass range for a hidden-sector
boson in a decay mediated by a b → s transition at leading
order, and the most sensitive search to date over the entire
accessible mass range. Previous limits set on χ boson
production in such decays have either focused on a limited
mass range [22], or have been obtained from more general
searches for long-lived particles [23].
The LHCb detector is a single-arm forward spectrometer
covering the pseudorapidity range 2 < η < 5, designed for
the study of particles containing b or c quarks [24,25]. The
detector includes a high-precision charged-particle tracking
system for measuring momenta [26,27]; two ring-imaging
Cherenkov detectors for distinguishing charged hadrons
[28]; a calorimeter system for identifying photons, elec-
trons, and hadrons; and a system for identifying muons
[29]. The trigger consists of a hardware stage, based on
information from the calorimeter and muon systems,
followed by a software stage, which applies a full event
reconstruction [30]. The selection of B
0
→ K
0
χ candidates
in the software trigger requires the presence of a vertex
identified by a multivariate algorithm [31] as being con-
sistent with the decay of a b hadron. Alternatively,
candidates may be selected based on the presence of a
displaced dimuon vertex, or the presence of a muon with
large transverse momentum (p
T
) and large impact param-
eter (IP), defined as the minimum track distance with
respect to any pp-interaction vertex (PV). Only tracks with
segments reconstructed in the first charged-particle detec-
tor, which surrounds the interaction region and is about 1 m
in length [26], can satisfy these trigger requirements;
therefore, the χ boson is required to decay well within
this detector. In the simulation, pp collisions are generated
following Refs. [32–35], and the interactions of the out-
going particles with the detector are modeled as in
Refs. [36,37].
A search is conducted, following Ref. [38], by scanning
the mðμ
þ
μ
−
Þ distribution for an excess of χ signal candi-
dates over the expected background. In order to avoid
experimenter bias, all aspects of the search are fixed
without examining those B
0
→ K
0
χ candidates which
have an invariant mass consistent with the known B
0
mass
[39]. The step sizes in mðχÞ are σ½mðμ
þ
μ
−
Þ=2, where
σ½mðμ
þ
μ
−
Þ is the dimuon mass resolution. Signal candi-
dates satisfy jmðμ
þ
μ
−
Þ − mðχÞj < 2σ½mðμ
þ
μ
−
Þ, while the
background is estimated by interpolating the yields in
the sidebands starting at 3σ½mðμ
þ
μ
−
Þ from mðχÞ . With
mðK
þ
π
−
μ
þ
μ
−
Þ constrained [40] to the known B
0
mass,
σ½mðμ
þ
μ
−
Þ is less than 8 MeV over the entire mðμ
þ
μ
−
Þ
range, and is as small as 2 MeV below 220 MeV . The
statistical test at each mðχÞ is based on the profile like-
lihood ratio of Poisson-process hypotheses with and with-
out a signal contribution [41]. The uncertainty on the
background interpolation is modeled by a Gaussian term in
the likelihood (see Ref. [38] for details).
The χ → μ
þ
μ
−
decay vertex is permitted, but not
required, to be displaced from the B
0
→ K
0
χ decay vertex.
Two regions of reconstructed dimuon lifetime, τðμ
þ
μ
−
Þ, are
defined for each mðχÞ considered in the search: a prompt
region, jτðμ
þ
μ
−
Þj < 3σ½τðμ
þ
μ
−
Þ, and a displaced region,
τðμ
þ
μ
−
Þ > 3σ½τðμ
þ
μ
−
Þ. The lifetime resolution is about
0.2 ps for mðμ
þ
μ
−
Þ ≳ 250 MeV, and 1 ps near 2mðμÞ. The
joint likelihood is formed from the product of the like-
lihoods for candidates populating the prompt and displaced
regions, since no assumption is made about τðχÞ . Narrow
resonances are vetoed by excluding the regions near the ω,
ϕ, J=ψ, ψð2SÞ, and ψð3770Þ resonances. These regions
are removed in both the prompt and displaced samples to
avoid contamination from unassociated dimuon and K
0
resonances.
The branching fraction product B(B
0
→ K
0
χðμ
þ
μ
−
Þ)≡
BðB
0
→ K
0
χÞ × Bðχ → μ
þ
μ
−
Þ is measured relative to
BðB
0
→ K
0
μ
þ
μ
−
Þ, where the normalization sample is
taken from the prompt region and restricted to
1.1 <m
2
ðμ
þ
μ
−
Þ < 6.0 GeV
2
. This normalization decay
is chosen since the detector response is similar to that
for the B
0
→ K
0
χ decay, and because the hidden-sector
theory parameters can be obtained from the ratio B(B
0
→
K
0
χðμ
þ
μ
−
Þ)=BðB
0
→ K
0
μ
þ
μ
−
Þ with reduced theoretical
uncertainty. Correlations between the yields of a possible
signal in the prompt 1.1 <m
2
ðμ
þ
μ
−
Þ < 6.0 GeV
2
region
and the normalization decay are at most a few percent and
are ignored.
The selection is similar to that of Ref. [42] with the
exception that the K
0
and dimuon candidates are not
required to share a common vertex. Signal candidates are
required to satisfy a set of loose requirements: the B
0
, K
0
,
and χ decay vertices must all be separated from any PV
and be of good quality; the B
0
IP must be small, while the
IP of the kaon, pion, and muons must be large; the angle
between the B
0
momentum vector and the vector between
the associated PV and the B
0
decay vertex must be
small; and the kaon, pion, and muons must each satisfy
loose particle identification requirements. Candidates are
retained if mðK
þ
π
−
Þ is within 100 MeV of the known K
0
mass [39].
A multivariate selection is applied to reduce the back-
ground further. The uBoost algorithm [43] is employed to
ensure that the performance is nearly independent of mðχÞ
and τ ðχÞ . The inputs to the algorithm include p
T
ðB
0
Þ,
various topological features of the decay, the muon
identification quality, and an isolation criterion [44]
designed to suppress backgrounds from partially recon-
structed decays. Data from the high-mass sideband,
150 <mðK
þ
π
−
μ
þ
μ
−
Þ − mðB
0
Þ < 500 MeV, are used to
represent the background in the training, while simulated
samples generated with mðχÞ values of 214, 1000, and
4000 MeV, and τðχÞ large enough to populate the full
PRL 115, 161802 (2015)
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161802-2
reconstructible region, are used for the signal. The multi-
variate selection requirement is determined by maximizing
the figure of merit of Ref. [45] for finding a signal with a
significance of 5 standard deviations. This results in a
signal selection efficiency of 85% with a background
rejection of 92% on average. The uBoost algorithm is
validated using ten additional signal samples generated
with various other mðχÞ and τðχÞ values. The performance
is consistent for all samples.
Peaking backgrounds that survive the multivariate selec-
tion are vetoed explicitly. A small number of B
0
s
→
ϕðK
þ
K
−
Þμ
þ
μ
−
decays are removed by rejecting K
þ
π
−
candidates that are consistent with the decay ϕ → K
þ
K
−
if
the π
−
is assumed to be a misidentified K
−
. A similar veto
is applied that removes about 250 Λ
0
b
→ pK
−
μ
þ
μ
−
decays.
Candidates are also rejected if the dimuon system is
consistent with any of the following decays: K
0
S
→
π
þ
π
−
, where the pions decay in flight to muons;
Λ
0
→ pπ
−
, where the pion decays in flight and the
proton is misidentified as a muon; and
¯
D
0
→ K
þ
π
−
, where
the kaon and pion decay in flight. All other particle-
misidentification backgrounds are negligible.
Figure 2 shows the K
þ
π
−
μ
þ
μ
−
mass distribution for
all prompt candidates that satisfy the full selection in
the region 1.1 <m
2
ðμ
þ
μ
−
Þ < 6.0 GeV
2
. An unbinned
extended maximum likelihood fit is performed to obtain
the B
0
→ K
0
μ
þ
μ
−
yield. The signal model is obtained
from data using the subset of prompt candidates with
mðμ
þ
μ
−
Þ in the J=ψ region, where the background is
Oð10
−3
Þ. A small correction, obtained from simulation, is
applied to account for the difference in signal shape
expected in the 1.1 <m
2
ðμ
þ
μ
−
Þ < 6.0 GeV
2
region. The
background model is an exponential function. Several
alternative background models are considered, with the
largest shift observed in the signal yield (1%) assigned as a
systematic uncertainty. The S-wave fraction (i.e., not a K
0
meson) of the Kπ system within the selected Kπ mass range
is ð4 4Þ% [42]. The yield of the normalization mode is
NðB
0
→ K
0
μ
þ
μ
−
Þ¼506 33, where the uncertainty
includes both statistical and systematic contributions.
Probability density functions, obtained from the data
using splines, are used to generate simulated data sets under
the no-signal hypothesis from which the global significance
of any χ signal is obtained [38]. For this the data are
collected in the prompt region into wide bins with a width
of 200 MeV , and into a total of three bins in the displaced
region. Simulated events show that the presence of a narrow
χ signal anywhere in the mðχÞ-τðχÞ plane, whose local
significance is 5σ, would not produce a significant excess
in these wide-binned data.
Figure 3 shows the mðμ
þ
μ
−
Þ distributions in both the
prompt and displaced regions for candidates whose invari-
ant mass is within 50 MeVof the known B
0
mass. The most
significant local excess occurs for mðχÞ¼253 MeV,
where in the prompt region 11 (6.2) candidates are
observed (expected), while the displaced region contains
a single candidate which is the only displaced candidate
below mðωÞ. The p value of the no-signal hypothesis is
about 80%, showing that no evidence is found for a hidden-
sector boson.
To set upper limits on B(B
0
→ K
0
χðμ
þ
μ
−
Þ), various
sources of systematic uncertainty are considered. The limits
are set using the profile likelihood technique [46], in which
systematic uncertainties are handled by including addi-
tional Gaussian terms in the likelihood [38]. Since no
contamination from the ω or ϕ resonance is found in the
displaced region, upper limits are set in these mðχÞ regions
for τðχÞ > 1 ps.
Many uncertainties cancel to a good approximation
because the signal and normalization decays share the
same final state. The dominant uncertainty on the efficiency
ratio ϵ(B
0
→ K
0
χðμ
þ
μ
−
Þ)=ϵðB
0
→ K
0
μ
þ
μ
−
Þ, which is
taken from simulation, arises due to its dependence on
τðμ
þ
μ
−
Þ. The simulation is validated by comparing τðπ
þ
π
−
Þ
distributions between B
0
→ J=ψK
0
S
ðπ
þ
π
−
Þ decays recon-
structed in simulated and experimental data in bins of K
0
S
momentum. The distributions in data and simulation are
consistent in each bin, and the per-bin statistical precision
(5%) is assigned as systematic uncertainty.
The uncertainty on the efficiency for a signal candidate
to be reconstructed within a given mðμ
þ
μ
−
Þ signal window,
due to mismodeling of σ½mðμ
þ
μ
−
Þ, is determined to be 1%
based on a comparison of the J=ψ peak between B
0
→
J=ψðμ
þ
μ
−
ÞK
0
decays in simulated and experimental data.
A similar comparison for σ½τðμ
þ
μ
−
Þ shows that the
uncertainty on the fraction of signal candidates expected
to be reconstructed in the prompt and displaced regions is
negligible. Finally, the efficiency for the normalization
mode is determined using the measured angular distribu-
tion [47], which is varied within the uncertainties yielding
an uncertainty in the normalization-mode efficiency of 1%.
The individual contributions are summed in quadrature
giving a total systematic uncertainty of 8%.
5200 5300 5400
0
50
100
150
200
Data
−
μ
+
μ
*0
K
→
0
B
Background
LHCb
2
) < 6.0 GeV
−
μ
+
μ
(
2
m1.1 <
Candidates / 15 MeV
) [MeV]
−
μ
+
μ
−
π
+
K(m
FIG. 2 (color online). Invariant mass spectrum with fit
overlaid for all prompt B
0
→ K
0
μ
þ
μ
−
candidates with
1.1 <m
2
ðμ
þ
μ
−
Þ < 6.0 GeV
2
.
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The spin of the hidden-sector boson determines the
angular distribution of the decay and, therefore, affects the
efficiency. The upper limits are set assuming spin zero. For
a spin-one χ boson produced unpolarized in the decay, the
sensitivity is about 10%–20% better than for the spin-zero
case. The dependence on the polarization in the spin-one
case is provided in the Supplemental Material [48].
Figure 4 shows the upper limits on
B(B
0
→ K
0
χðμ
þ
μ
−
Þ), relative to BðB
0
→ K
0
μ
þ
μ
−
Þ in
the 1.1 <m
2
ðμ
þ
μ
−
Þ < 6.0 GeV
2
region, set at the 95%
confidence level (C.L.) for several values of τðχÞ; limits as
functions of τðχÞ are provided in the Supplemental Material
[48]. The limits become less stringent for τðχÞ ≳ 10 ps, as
the probability of the χ boson decaying within the first
charged-particle detector decreases. The branching fraction
BðB
0
→ K
0
μ
þ
μ
−
Þ¼ð1.6 0.3Þ × 10
−7
[42] is used to
obtain upper limits on B(B
0
→ K
0
χðμ
þ
μ
−
Þ), which are
also shown in Fig. 4. Because of the uncertainty on the
normalization-mode branching fraction, there is not a one-
to-one mapping between the two axes in the figure;
however, the absolute limits shown are accurate to
about 2%.
Figure 5 shows exclusion regions for the DFSZ [49,50]
axion model of Ref. [20] set in the limit of the large ratio of
Higgs-doublet vacuum expectation values, tan β ≳ 3, for
charged-Higgs masses mðhÞ¼1 and 10 TeV (this choice
of restricted parameter space is made for ease of graphical
presentation). The constraints scale as log ½mðhÞ=TeV for
mðhÞ ≳ 800 GeV. The branching fraction of the axion into
hadrons varies greatly in different models. Figure 5 shows
the results for two extreme cases: Bðχ → hadronsÞ¼0 and
0.99. While Bðχ → μ
þ
μ
−
Þ is 100 times larger when
Bðχ → hadronsÞ¼0, τðχÞ is also larger, which results in
the model probing the region where the upper limits are
weaker. The constraints are loose for mðχÞ > 2mðτ Þ, since
the axion preferentially decays into τ
þ
τ
−
if kinematically
allowed; otherwise the exclusions reach the PeV scale.
Figure 5 also shows exclusion regions for the inflaton
model of Ref. [51], which only considers mðχÞ < 1 GeV.
The branching fraction into hadrons is taken directly from
1000 2000 3000 4000
5
10
15
20
Prompt
Displaced
LHCb
ω
φψJ/ (3770)ψ(2S)+ψ
200
Candidates / 10 MeV
) [MeV]
−
μ
+
μ
(m
FIG. 3 (color online). Distribution of mðμ
þ
μ
−
Þ in the (black) prompt and (red) displaced regions. The shaded bands denote regions
where no search is performed due to (possible) resonance contributions. The J=ψ, ψð2SÞ, and ψð3770Þ peaks are suppressed to better
display the search region.
) [MeV]
−
μ
+
μ
(m
1000 2000 3000 4000
-2
10
-1
10
1
LHCb
=1000ps
τ
=100ps
τ
=10ps
τ
-9
10
-8
10
-7
10
))
−
μ
+
μ
(
χ
*0
K→
0
B(B
2
)[1.1,6.0]GeV
−
μ
+
μ
*0
K→
0
B(B
))
−
μ
+
μ
(
χ
*0
K
→
0
B
(B
FIG. 4 (color online). Upper limits at 95% C.L. for (left axis) B(B
0
→ K
0
χðμ
þ
μ
−
Þ)=BðB
0
→ K
0
μ
þ
μ
−
Þ, with B
0
→ K
0
μ
þ
μ
−
in
1.1 <m
2
ðμ
þ
μ
−
Þ < 6.0 GeV
2
, and (right axis) B(B
0
→ K
0
χðμ
þ
μ
−
Þ). The sparseness of the data leads to rapid fluctuations in the
limits. Excluding the region near 2mðμÞ, the relative limits for τ < 10 ps are between 0.005 – 0.05 and all relative limits for τ ≤ 1000 ps
are less than 1.
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Ref. [51] and, as in the axion model, is highly uncertain but
this does not greatly affect the sensitivity of this search.
Constraints are placed on the mixing angle between the
Higgs and inflaton fields, θ, which exclude most of the
previously allowed region.
In summary, no evidence for a signal is observed, and
upper limits are placed on BðB
0
→ K
0
χÞ × Bðχ → μ
þ
μ
−
Þ.
This is the first dedicated search over a large mass range for
a hidden-sector boson in a decay mediated by a b → s
transition at leading order, and the most sensitive search to
date over the entire accessible mass range. Stringent
constraints are placed on theories that predict the existence
of additional scalar or axial-vector fields.
We express our gratitude to our colleagues in the CERN
accelerator departments for the excellent performance of
the LHC. We thank the technical and administrative staff at
the LHCb institutes. We acknowledge support from CERN
and from the following national agencies: CAPES, CNPq,
FAPERJ, and FINEP (Brazil); NSFC (China); CNRS/
IN2P3 (France); BMBF, DFG, HGF, and MPG
(Germany); INFN (Italy); FOM and NWO
(Netherlands); MNiSW and NCN (Poland); MEN/IFA
(Romania); MinES and FANO (Russia); MinECo
(Spain); SNSF and SER (Switzerland); NASU (Ukraine);
STFC (United Kingdom); NSF (USA). The Tier1 comput-
ing centers are supported by IN2P3 (France), KIT and
BMBF (Germany), INFN (Italy), NWO and SURF
(Netherlands), PIC (Spain), GridPP (United Kingdom).
We are indebted to the communities behind the multiple
open source software packages on which we depend. We
are also thankful for the computing resources and the
access to software R&D tools provided by Yandex LLC
(Russia). Individual groups or members have received
support from EPLANET, Marie Skłodowska-Curie
Actions, and ERC (European Union), Conseil général de
Haute-Savoie, Labex ENIGMASS and OCEVU, Région
Auvergne (France), RFBR (Russia), XuntaGal and
GENCAT (Spain), Royal Society and Royal Commission
for the Exhibition of 1851 (United Kingdom).
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1000 2000 3000 4000
0.5
1
1
2
)=10 TeVh(m
[PeV],
β
2
)tan
χ(f
)=1 TeV
h
(
m
[PeV],
β
2
)tanχ
(f
hadrons) = 0→
χ
(B
hadrons) = 0.99→
χ
(B
LHCb
400 600 800 1000
-8
10
-7
10
-6
10
-5
10
-4
10
LHCb
Theory
Theory
CHARM
) [MeV]
−
μ
+
μ
(m
2
θ
) [MeV]
−
μ
+
μ
(m
FIG. 5 (color online). Exclusion regions at 95% C.L.: (left) constraints on the axion model of Ref. [20]; (right) constraints on the
inflaton model of Ref. [51]. The regions excluded by the theory [51] and by the CHARM experiment [52] are also shown.
PRL 115, 161802 (2015)
PHYSICAL REVIEW LETTERS
week ending
16 OCTOBER 2015
161802-5