EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)
CERN-PH-EP-2015-202 LHCb-PAPER-2015-036 August 13, 2015
Search for hidden-sector bosons in
B
0
→ K
∗0
µ
+
µ
−
decays
The LHCb collaboration†
Abstract
A search is presented for hidden-sector bosons, χ, produced in the decay B0→ K∗(892)0χ, with K∗(892)0 → K+π− and χ → µ+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 ≤ m(χ) ≤ 4350 MeV, and upper limits are placed on the branching fraction product B(B0→ K∗(892)0χ)× B(χ→ µ+µ−) 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 m(χ) range, and place the most stringent constraints to date on many theories that predict the existence of additional low-mass bosons.
Published as Physical Review Letters 115 (2015) 161802.
c
CERN on behalf of the LHCb collaboration, license CC-BY-4.0.
†Authors are listed at the end of this Letter.
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 particles interact via GeV-scale bosons [9–11] (c = 1 throughout 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 hypothesizes 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 associated inflaton particle is expected to have a mass in the range 270 . m(χ) . 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 additional 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 . m(χ) . 800 MeV and an energy scale, f (χ), at which the symmetry is broken in the range 1 . f (χ) . 3 TeV. A broader range of m(χ) and f (χ) 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 B0→ K∗0χ,
with χ→ µ+µ− and K∗0→ K+π− (throughout this Letter, K∗0 ≡ K∗(892)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 2m(µ) < m(χ) < m(B0)− m(K∗0) 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 B0→ K∗0χ decay is chosen instead
of B+ → K+χ, since better χ decay time resolution is obtained due to the presence of the K+π− vertex, and because there is less background contamination. The data
used correspond to integrated luminosities of 1.0 and 2.0 fb−1 collected at center-of-mass energies of √s = 7 and 8 TeV in pp collisions with the LHCb detector. 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. Previous limits set on χ boson production in such decays
b d Vtb Vts s d µ− µ+ t W+ χ B0 K∗0
Figure 1: Feynman diagram for the decay B0→ K∗0χ, with χ→ µ+µ−.
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 mo-menta [26,27]; two ring-imaging Cherenkov detectors for distinguishing charged hadrons [28]; a calorimeter system for identifying photons, electrons, 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 B0→ K∗0χ candidates in the software trigger requires the presence of a vertex identified by a multivariate algorithm [31] as being consistent 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 (pT) and large impact parameter (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 detector, 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 outgoing particles with the detector are modelled as in Refs. [36, 37].
A search is conducted, following Ref. [38], by scanning the m(µ+µ−) distribution for an
excess of χ signal candidates over the expected background. In order to avoid experimenter bias, all aspects of the search are fixed without examining those B0→ K∗0χ candidates
which have an invariant mass consistent with the known B0 mass [39]. The step sizes
in m(χ) are σ[m(µ+µ−)]/2, where σ[m(µ+µ−)] is the dimuon mass resolution. Signal candidates satisfy |m(µ+µ−)
− m(χ)| < 2σ[m(µ+µ−)], while the background is estimated
by interpolating the yields in the sidebands starting at 3σ[m(µ+µ−)] from m(χ). With
m(K+π−µ+µ−) constrained [40] to the known B0 mass, σ[m(µ+µ−)] is less than 8 MeV over the entire m(µ+µ−) range, and is as small as 2 MeV below 220 MeV. The statistical
and without 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+µ− decay vertex is permitted, but not required, to be displaced from the
B0→ K∗0χ decay vertex. Two regions of reconstructed dimuon lifetime, τ (µ+µ−), are defined for each m(χ) considered in the search: a prompt region,|τ(µ+µ−)
| < 3σ[τ(µ+µ−)],
and a displaced region, τ (µ+µ−) > 3σ[τ (µ+µ−)]. The lifetime resolution is about 0.2 ps
for m(µ+µ−) & 250 MeV, and 1 ps near 2m(µ). The joint likelihood is formed from the product of the likelihoods for candidates populating the prompt and displaced regions, since no assumption is made about τ (χ). Narrow resonances are vetoed by excluding the regions near the ω, φ, J/ψ, ψ(2S) and ψ(3770) 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(B0→ K∗0χ(µ+µ−)) ≡ B(B0 → K∗0χ)× B(χ → µ+µ−) is measured relative to
B(B0→ K∗0µ+µ−), where the normalization sample is taken
from the prompt region and restricted to 1.1 < m2(µ+µ−) < 6.0 GeV2. This normalization
decay is chosen since the detector response is similar to that for the B0→ K∗0χ decay, and because the hidden-sector theory parameters can be obtained from the ratio B(B0→
K∗0χ(µ+µ−))/
B(B0 → K∗0µ+µ−) with reduced theoretical uncertainty. Correlations
between the yields of a possible signal in the prompt 1.1 < m2(µ+µ−) < 6.0 GeV2 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 B0, K∗0 and χ decay vertices must all be separated
from any PV and be of good quality; the B0 IP must be small, while the IP of the kaon,
pion and muons must be large; the angle between the B0 momentum vector and the vector between the associated PV and the B0 decay vertex must be small; and the kaon, pion
and muons must each satisfy loose particle identification requirements. Candidates are retained if m(K+π−) is within 100 MeV of the known K∗0 mass [39].
A multivariate selection is applied to reduce the background further. The uBoost algorithm [43] is employed to ensure that the performance is nearly independent of m(χ) and τ (χ). The inputs to the algorithm include pT(B0), various topological features of the
decay, the muon identification quality, and an isolation criterion [44] designed to suppress backgrounds from partially reconstructed decays. Data from the high-mass sideband, 150 < m(K+π−µ+µ−)− m(B0) < 500 MeV, are used to represent the background in the training, while simulated samples generated with m(χ) values of 214, 1000, and 4000 MeV, and τ (χ) large enough to populate the full reconstructible region, are used for the signal. The multivariate selection requirement is determined by maximizing the figure of merit of Ref. [45] for finding a signal with a significance of five 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 m(χ) and τ (χ) values. The performance is consistent for all samples.
Peaking backgrounds that survive the multivariate selection are vetoed explicitly. A small number of Bs0→ φ(K+K−)µ+µ− decays are removed by rejecting K+π− candidates
) [MeV] − µ + µ − π + K ( m 5200 5300 5400 Candidates / 15 MeV 0 50 100 150 200 Data − µ + µ *0 K → 0 B Background LHCb 2 ) < 6.0 GeV − µ + µ ( 2 m 1.1 <
Figure 2: Invariant mass spectrum with fit overlaid for all prompt B0→ K∗0µ+µ− candidates with 1.1 < m2(µ+µ−) < 6.0 GeV2.
that are consistent with the decay φ→ K+K− if the π− is assumed to be a misidentified K−. A similar veto is applied that removes about 250 Λ0
b→ pK
−µ+µ− decays. Candidates
are also rejected if the dimuon system is consistent with any of the following decays: KS0→ π+π−, where the pions decay in flight to muons; Λ0→ pπ−, where the pion decays in flight and the proton is misidentified as a muon; and D0→ K+π−, where the kaon and
pion decay in flight. All other particle-misidentification backgrounds are negligible. Figure 2 shows the K+π−µ+µ−mass distribution for all prompt candidates that satisfy the full selection in the region 1.1 < m2(µ+µ−) < 6.0 GeV2. An unbinned extended
maxi-mum likelihood fit is performed to obtain the B0→ K∗0µ+µ− yield. The signal model is
obtained from data using the subset of prompt candidates with m(µ+µ−) in the J/ψ region, where the background isO(10−3). A small correction, obtained from simulation, is applied to account for the difference in signal shape expected in the 1.1 < m2(µ+µ−) < 6.0 GeV2
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 (4± 4)% [42]. The yield of the normalization mode is N (B0→ K∗0µ+µ−) = 506
± 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 m(χ)-τ (χ) plane, whose local significance is 5σ, would not produce a significant excess in these wide-binned data.
Figure 3 shows the m(µ+µ−) distributions in both the prompt and displaced regions
) [MeV] − µ + µ ( m 1000 2000 3000 4000 Candidates / 10 MeV 5 10 15 20 Prompt Displaced LHCb ω φ J/ψ ψ(2S)+ψ(3770) 200
Figure 3: Distribution of m(µ+µ−) 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 , ψ(2S) and ψ(3770) peaks are suppressed to better display the search region.
significant local excess occurs for m(χ) = 253 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 m(ω). 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 onB(B0→ K∗0χ(µ+µ−)), 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 additional Gaussian terms in the likeli-hood [38]. Since no contamination from the ω or φ resonance is found in the displaced region, upper limits are set in these m(χ) regions for τ (χ) > 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 (B0→ K∗0χ(µ+µ−))/(B0→ K∗0µ+µ−), which is taken from simulation, arises due to its
dependence on τ (µ+µ−). The simulation is validated by comparing τ (π+π−) distributions
between B0→ J/ψ KS0(π+π−) decays reconstructed in simulated and experimental data in bins of K0
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 m(µ+µ−) signal window, due to mismodeling of σ[m(µ+µ−)], is determined to
be 1% based on a comparison of the J/ψ peak between B0→ J/ψ (µ+µ−)K∗0 decays in
simulated and experimental data. A similar comparison for σ[τ (µ+µ−)] 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 distribution [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%.
) [MeV] − µ + µ ( m 1000 2000 3000 4000 -2 10 -1 10 1 LHCb =1000ps τ =100ps τ =10ps τ )) − 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 -9 10 -8 10 -7 10
Figure 4: Upper limits at 95% CL for (left axis)B(B0→ K∗0χ(µ+µ−))/B(B0→ K∗0µ+µ−), with B0→ K∗0µ+µ− in 1.1 < m2(µ+µ−) < 6.0 GeV2, and (right axis)B(B0→ K∗0χ(µ+µ−)). The sparseness of the data leads to rapid fluctuations in the limits. Excluding the region near 2m(µ), the relative limits for τ < 10 ps are between 0.005–0.05 and all relative limits for τ ≤ 1000 ps are less than one.
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 as supplemental material to this Letter [48].
Figure 4 shows the upper limits onB(B0→ K∗0χ(µ+µ−)), relative to
B(B0→ K∗0µ+µ−)
in the 1.1 < m2(µ+µ−) < 6.0 GeV2 region, set at the 95% confidence level (CL) for several values of τ (χ); limits as functions of τ (χ) are provided as supplemental material to this Letter. The limits become less stringent for τ (χ) & 10 ps, as the probability of the χ boson decaying within the first charged-particle detector decreases. The branching fraction B(B0→ K∗0µ+µ−) = (1.6
± 0.3) × 10−7 [42] is used to obtain upper limits on
B(B0→ K∗0χ(µ+µ−)), which are also shown in Fig. 4. Due to 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 large ratio of Higgs-doublet vacuum expectation values, tan β & 3, for charged-Higgs masses m(h) = 1 and 10 TeV (this choice of restricted parameter space is made for ease of graphical presentation). The constraints scale as log (m(h)/ TeV) for m(h) & 800 GeV. The branching fraction of the axion into hadrons varies greatly in different models. Figure 5 shows the results for two extreme cases: B(χ→ hadrons) = 0 and 0.99. While B(χ→ µ+µ−) is 100 times larger when
B(χ→ hadrons) = 0, τ(χ) is also larger, which results in the model probing the region where the upper limits are weaker. The constraints are loose for m(χ) > 2m(τ ), since the axion preferentially decays into τ+τ− if kinematically allowed; otherwise the exclusions reach the PeV scale.
) [MeV] − µ + µ ( m 1000 2000 3000 4000 0.5 1 1 2 )=10 TeV h( m [PeV], β 2 )tan χ ( f )=1 TeV h( m [PeV], β 2 )tan χ ( f hadrons) = 0 → χ ( B hadrons) = 0.99 → χ ( B LHCb ) [MeV] − µ + µ ( m 400 600 800 1000 2 θ -8 10 -7 10 -6 10 -5 10 -4 10 LHCb Theory Theory CHARM
Figure 5: Exclusion regions at 95% CL: (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.
Figure 5 also shows exclusion regions for the inflaton model of Ref. [51], which only considers m(χ) < 1 GeV. The branching fraction into hadrons is taken directly from 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 B(B0→ K∗0χ)× B(χ→ µ+µ−). 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.
Acknowledgments
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 national agencies: CAPES, CNPq, FAPERJ and FINEP (Brazil); NSFC (China); CNRS/IN2P3 (France); BMBF, DFG, HGF and MPG (Germany); INFN (Italy); FOM and NWO (The 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 computing centres are supported by IN2P3 (France), KIT and BMBF (Germany), INFN (Italy), NWO and SURF (The 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
Sk lodowska-Curie Actions and ERC (European Union), Conseil g´en´eral de Haute-Savoie, Labex ENIGMASS and OCEVU, R´egion Auvergne (France), RFBR (Russia), XuntaGal and GENCAT (Spain), Royal Society and Royal Commission for the Exhibition of 1851 (United Kingdom).
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Supplemental Material
The limits reported in the Letter assume a spin-zero hidden-sector boson. To convert these into limits for a spin-one boson, the ratio of efficiencies for the spin-one to spin-zero cases must be accounted for. Determining this ratio involves integrals of the form
R
fj(~Ω)(~Ω, m2(µ+µ−))d~Ω
R
f1c(~Ω)(~Ω, m2(µ+µ−))d~Ω
,
where ~Ω = (θK, θ`, φ) (see Appendix A of Ref. [40] in the Letter for details on the
angular basis), (~Ω, m2(µ+µ−)) is the efficiency, f
j(~Ω) are functions of the angles, and
f1c(~Ω) = cos2θK. Figure 6 shows the values for
f1s(~Ω) = sin2θK,
f2s(~Ω) = sin2θKcos 2θ`,
f2c(~Ω) = cos2θKcos 2θ`.
All other integrals, each of which has a value of zero in the absence of inefficiency, have values O(0.01). Therefore, the following terms in the general angular distribution can be ignored when determining the limits:
f3(~Ω) = sin2θKsin2θ`cos 2φ,
f4(~Ω) = sin 2θKsin 2θ`cos φ,
f5(~Ω) = sin 2θKsin θ`cos φ,
f6s(~Ω) = sin2θKcos θ`,
f6c(~Ω) = cos2θKcos θ`,
f7(~Ω) = sin 2θKsin θ`sin φ,
f8(~Ω) = sin 2θKsin 2θ`sin φ,
f9(~Ω) = sin2θKsin2θ`sin 2φ.
Figure 6 shows an example efficiency ratio for the case of a spin-one boson produced unpolarized in the decay. Since the j = 3, 4, . . . 9 terms integrate to approximately zero, this same curve applies for any theory that predicts that the longitudinal polarization fraction of the K∗0 is FL= 1/3.
) [GeV] − µ + µ ( m 1 2 3 4 value relative to 1c -1 0 1 2 3 LHCb 1s 2s 2c ) [GeV] − µ + µ ( m 1 2 3 4
unpolarized spin-one / spin-zero 1
1.1 1.2 1.3
LHCb
Figure 6: (left) Integral values for 1s, 2s and 2c relative to the value for 1c (see text for details). The dashed lines show the values in the absence of inefficiency. (right) Ratio of the efficiency for an unpolarized spin-one boson to that of a spin-zero boson.
) [MeV] − µ + µ ( m 1000 2000 3000 4000 -2 10 -1 10 1 LHCb =1000ps τ =100ps τ =10ps τ =0ps τ τ=1ps )) − 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 -9 10 -8 10 -7 10
Figure 7: Upper limits at 95% CL for (left axis) B(B0→ K∗0χ(µ+µ−))/B(B0→ K∗0µ+µ−), with B0→ K∗0µ+µ− in 1.1 < m2(µ+µ−) < 6.0 GeV2, and (right axis) B(B0→ K∗0χ(µ+µ−)). Same as Fig. 4 in the Letter but including the τ = 0 and 1 ps limits.
B B0! K⇤0 (µ+µ ) /B(B0! K⇤0µ+µ ) [1.1,6.0] GeV2 ⌧ [ps] m(µ+µ ) [MeV] LHCb ⌧ [ps] m(µ+µ ) [MeV] B B0! K⇤0 (µ+µ ) LHCb B B0! K⇤0 (µ+µ ) /B(B0! K⇤0µ+µ ) [1.1,6.0] GeV2 B(B0! K⇤0 (µ+µ )) ⌧ [ps] m(µ+µ ) [MeV] LHCb
Figure 8: Upper limits at 95% CL for (top) B(B0→ K∗0χ(µ+µ−))/B(B0→ K∗0µ+µ−), with B0→ K∗0µ+µ− in 1.1 < m2(µ+µ−) < 6.0 GeV2, (middle) B(B0→ K∗0χ(µ+µ−)), and (bottom) both relative and absolute limits. The ω and φ resonance regions are only excluded in the prompt region. A utility is provided to obtain these limits for any (m(χ), τ (χ)) on the CERN Document Server.
LHCb collaboration
R. Aaij38, B. Adeva37, M. Adinolfi46, A. Affolder52, Z. Ajaltouni5, S. Akar6, J. Albrecht9, F. Alessio38, M. Alexander51, S. Ali41, G. Alkhazov30, P. Alvarez Cartelle53, A.A. Alves Jr57, S. Amato2, S. Amerio22, Y. Amhis7, L. An3, L. Anderlini17, J. Anderson40, G. Andreassi39, M. Andreotti16,f, J.E. Andrews58, R.B. Appleby54, O. Aquines Gutierrez10, F. Archilli38, P. d’Argent11, A. Artamonov35, M. Artuso59, E. Aslanides6, G. Auriemma25,m, M. Baalouch5, S. Bachmann11, J.J. Back48, A. Badalov36, C. Baesso60, W. Baldini16,38, R.J. Barlow54,
C. Barschel38, S. Barsuk7, W. Barter38, V. Batozskaya28, V. Battista39, A. Bay39, L. Beaucourt4, J. Beddow51, F. Bedeschi23, I. Bediaga1, L.J. Bel41, V. Bellee39, N. Belloli20, I. Belyaev31, E. Ben-Haim8, G. Bencivenni18, S. Benson38, J. Benton46, A. Berezhnoy32, R. Bernet40,
A. Bertolin22, M.-O. Bettler38, M. van Beuzekom41, A. Bien11, S. Bifani45, P. Billoir8, T. Bird54, A. Birnkraut9, A. Bizzeti17,h, T. Blake48, F. Blanc39, J. Blouw10, S. Blusk59, V. Bocci25, A. Bondar34, N. Bondar30,38, W. Bonivento15, S. Borghi54, M. Borsato7, T.J.V. Bowcock52, E. Bowen40, C. Bozzi16, S. Braun11, M. Britsch10, T. Britton59, J. Brodzicka54, N.H. Brook46, E. Buchanan46, A. Bursche40, J. Buytaert38, S. Cadeddu15, R. Calabrese16,f, M. Calvi20,j, M. Calvo Gomez36,o, P. Campana18, D. Campora Perez38, L. Capriotti54, A. Carbone14,d, G. Carboni24,k, R. Cardinale19,i, A. Cardini15, P. Carniti20, L. Carson50, K. Carvalho Akiba2,38, G. Casse52, L. Cassina20,j, L. Castillo Garcia38, M. Cattaneo38, Ch. Cauet9, G. Cavallero19, R. Cenci23,s, M. Charles8, Ph. Charpentier38, M. Chefdeville4, S. Chen54, S.-F. Cheung55, N. Chiapolini40, M. Chrzaszcz40, X. Cid Vidal38, G. Ciezarek41, P.E.L. Clarke50,
M. Clemencic38, H.V. Cliff47, J. Closier38, V. Coco38, J. Cogan6, E. Cogneras5, V. Cogoni15,e, L. Cojocariu29, G. Collazuol22, P. Collins38, A. Comerma-Montells11, A. Contu15, A. Cook46, M. Coombes46, S. Coquereau8, G. Corti38, M. Corvo16,f, B. Couturier38, G.A. Cowan50, D.C. Craik48, A. Crocombe48, M. Cruz Torres60, S. Cunliffe53, R. Currie53, C. D’Ambrosio38, E. Dall’Occo41, J. Dalseno46, P.N.Y. David41, A. Davis57, K. De Bruyn41, S. De Capua54, M. De Cian11, J.M. De Miranda1, L. De Paula2, P. De Simone18, C.-T. Dean51, D. Decamp4, M. Deckenhoff9, L. Del Buono8, N. D´el´eage4, M. Demmer9, D. Derkach55, O. Deschamps5, F. Dettori38, B. Dey21, A. Di Canto38, F. Di Ruscio24, H. Dijkstra38, S. Donleavy52, F. Dordei11, M. Dorigo39, A. Dosil Su´arez37, D. Dossett48, A. Dovbnya43, K. Dreimanis52, L. Dufour41, G. Dujany54, F. Dupertuis39, P. Durante38, R. Dzhelyadin35, A. Dziurda26, A. Dzyuba30, S. Easo49,38, U. Egede53, V. Egorychev31, S. Eidelman34, S. Eisenhardt50, U. Eitschberger9, R. Ekelhof9, L. Eklund51, I. El Rifai5, Ch. Elsasser40, S. Ely59, S. Esen11, H.M. Evans47, T. Evans55, A. Falabella14, C. F¨arber38, N. Farley45, S. Farry52, R. Fay52, D. Ferguson50, V. Fernandez Albor37, F. Ferrari14, F. Ferreira Rodrigues1, M. Ferro-Luzzi38, S. Filippov33, M. Fiore16,38,f, M. Fiorini16,f, M. Firlej27, C. Fitzpatrick39, T. Fiutowski27, K. Fohl38, P. Fol53, M. Fontana15, F. Fontanelli19,i, R. Forty38, O. Francisco2, M. Frank38, C. Frei38, M. Frosini17, J. Fu21, E. Furfaro24,k, A. Gallas Torreira37, D. Galli14,d, S. Gallorini22, S. Gambetta50, M. Gandelman2, P. Gandini55, Y. Gao3, J. Garc´ıa Pardi˜nas37, J. Garra Tico47, L. Garrido36, D. Gascon36, C. Gaspar38, R. Gauld55, L. Gavardi9, G. Gazzoni5, D. Gerick11, E. Gersabeck11, M. Gersabeck54, T. Gershon48, Ph. Ghez4, A. Gianelle22, S. Gian`ı39, V. Gibson47, O.
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1Centro Brasileiro de Pesquisas F´ısicas (CBPF), Rio de Janeiro, Brazil
2Universidade Federal do Rio de Janeiro (UFRJ), Rio de Janeiro, Brazil
3Center for High Energy Physics, Tsinghua University, Beijing, China
4LAPP, Universit´e Savoie Mont-Blanc, CNRS/IN2P3, Annecy-Le-Vieux, France
5Clermont Universit´e, Universit´e Blaise Pascal, CNRS/IN2P3, LPC, Clermont-Ferrand, France
6CPPM, Aix-Marseille Universit´e, CNRS/IN2P3, Marseille, France
7LAL, Universit´e Paris-Sud, CNRS/IN2P3, Orsay, France
8LPNHE, Universit´e Pierre et Marie Curie, Universit´e Paris Diderot, CNRS/IN2P3, Paris, France
9Fakult¨at Physik, Technische Universit¨at Dortmund, Dortmund, Germany
10Max-Planck-Institut f¨ur Kernphysik (MPIK), Heidelberg, Germany
11Physikalisches Institut, Ruprecht-Karls-Universit¨at Heidelberg, Heidelberg, Germany
12School of Physics, University College Dublin, Dublin, Ireland
13Sezione INFN di Bari, Bari, Italy
14Sezione INFN di Bologna, Bologna, Italy
15Sezione INFN di Cagliari, Cagliari, Italy
16Sezione INFN di Ferrara, Ferrara, Italy
18Laboratori Nazionali dell’INFN di Frascati, Frascati, Italy
19Sezione INFN di Genova, Genova, Italy
20Sezione INFN di Milano Bicocca, Milano, Italy
21Sezione INFN di Milano, Milano, Italy
22Sezione INFN di Padova, Padova, Italy
23Sezione INFN di Pisa, Pisa, Italy
24Sezione INFN di Roma Tor Vergata, Roma, Italy
25Sezione INFN di Roma La Sapienza, Roma, Italy
26Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of Sciences, Krak´ow, Poland
27AGH - University of Science and Technology, Faculty of Physics and Applied Computer Science,
Krak´ow, Poland
28National Center for Nuclear Research (NCBJ), Warsaw, Poland
29Horia Hulubei National Institute of Physics and Nuclear Engineering, Bucharest-Magurele, Romania
30Petersburg Nuclear Physics Institute (PNPI), Gatchina, Russia
31Institute of Theoretical and Experimental Physics (ITEP), Moscow, Russia
32Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow, Russia
33Institute for Nuclear Research of the Russian Academy of Sciences (INR RAN), Moscow, Russia
34Budker Institute of Nuclear Physics (SB RAS) and Novosibirsk State University, Novosibirsk, Russia
35Institute for High Energy Physics (IHEP), Protvino, Russia
36Universitat de Barcelona, Barcelona, Spain
37Universidad de Santiago de Compostela, Santiago de Compostela, Spain
38European Organization for Nuclear Research (CERN), Geneva, Switzerland
39Ecole Polytechnique F´ed´erale de Lausanne (EPFL), Lausanne, Switzerland
40Physik-Institut, Universit¨at Z¨urich, Z¨urich, Switzerland
41Nikhef National Institute for Subatomic Physics, Amsterdam, The Netherlands
42Nikhef National Institute for Subatomic Physics and VU University Amsterdam, Amsterdam, The
Netherlands
43NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine
44Institute for Nuclear Research of the National Academy of Sciences (KINR), Kyiv, Ukraine
45University of Birmingham, Birmingham, United Kingdom
46H.H. Wills Physics Laboratory, University of Bristol, Bristol, United Kingdom
47Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom
48Department of Physics, University of Warwick, Coventry, United Kingdom
49STFC Rutherford Appleton Laboratory, Didcot, United Kingdom
50School of Physics and Astronomy, University of Edinburgh, Edinburgh, United Kingdom
51School of Physics and Astronomy, University of Glasgow, Glasgow, United Kingdom
52Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom
53Imperial College London, London, United Kingdom
54School of Physics and Astronomy, University of Manchester, Manchester, United Kingdom
55Department of Physics, University of Oxford, Oxford, United Kingdom
56Massachusetts Institute of Technology, Cambridge, MA, United States
57University of Cincinnati, Cincinnati, OH, United States
58University of Maryland, College Park, MD, United States
59Syracuse University, Syracuse, NY, United States
60Pontif´ıcia Universidade Cat´olica do Rio de Janeiro (PUC-Rio), Rio de Janeiro, Brazil, associated to 2
61Institute of Particle Physics, Central China Normal University, Wuhan, Hubei, China, associated to3
62Departamento de Fisica , Universidad Nacional de Colombia, Bogota, Colombia, associated to8
63Institut f¨ur Physik, Universit¨at Rostock, Rostock, Germany, associated to11
64National Research Centre Kurchatov Institute, Moscow, Russia, associated to31
65Yandex School of Data Analysis, Moscow, Russia, associated to31
66Instituto de Fisica Corpuscular (IFIC), Universitat de Valencia-CSIC, Valencia, Spain, associated to36
aUniversidade Federal do Triˆangulo Mineiro (UFTM), Uberaba-MG, Brazil
bP.N. Lebedev Physical Institute, Russian Academy of Science (LPI RAS), Moscow, Russia
cUniversit`a di Bari, Bari, Italy
dUniversit`a di Bologna, Bologna, Italy
eUniversit`a di Cagliari, Cagliari, Italy
fUniversit`a di Ferrara, Ferrara, Italy
gUniversit`a di Urbino, Urbino, Italy
hUniversit`a di Modena e Reggio Emilia, Modena, Italy
iUniversit`a di Genova, Genova, Italy
jUniversit`a di Milano Bicocca, Milano, Italy
kUniversit`a di Roma Tor Vergata, Roma, Italy
lUniversit`a di Roma La Sapienza, Roma, Italy
mUniversit`a della Basilicata, Potenza, Italy
nAGH - University of Science and Technology, Faculty of Computer Science, Electronics and
Telecommunications, Krak´ow, Poland
oLIFAELS, La Salle, Universitat Ramon Llull, Barcelona, Spain
pHanoi University of Science, Hanoi, Viet Nam
qUniversit`a di Padova, Padova, Italy
rUniversit`a di Pisa, Pisa, Italy
sScuola Normale Superiore, Pisa, Italy
tUniversit`a degli Studi di Milano, Milano, Italy
![Figure 5: Exclusion regions at 95% CL: (left) constraints on the axion model of Ref. [20]; (right) constraints on the inflaton model of Ref](https://thumb-eu.123doks.com/thumbv2/123doknet/14112538.466680/9.892.145.793.150.364/figure-exclusion-regions-constraints-axion-model-constraints-inflaton.webp)
