Search for Axionlike and Scalar Particles with the NA64 Experiment

D. Banerjee, J. Bernhard, V. E. Burtsev, A. G. Chumakov, D. Cooke, P. Crivelli , E. Depero, A. V. Dermenev, S. V. Donskov, R. R. Dusaev, T. Enik, N. Charitonidis, A. Feshchenko, V. N. Frolov, A. Gardikiotis, S. G. Gerassimov, S. N. Gninenko , M. Hösgen, M. Jeckel, V. A. Kachanov, A. E. Karneyeu, G. Kekelidze, B. Ketzer, D. V. Kirpichnikov, M. M. Kirsanov, V. N. Kolosov, I. V. Konorov, S. G. Kovalenko, V. A. Kramarenko, L. V. Kravchuk, N. V. Krasnikov, S. V. Kuleshov, V. E. Lyubovitskij, V. Lysan, V. A. Matveev, Yu. V. Mikhailov, L. Molina Bueno, D. V. Peshekhonov, V. A. Polyakov, B. Radics, R. Rojas, A. Rubbia, V. D. Samoylenko, H. Sieber, D. Shchukin, V. O. Tikhomirov, I. Tlisova, D. A. Tlisov, A. N. Toropin, A. Yu. Trifonov, B. I. Vasilishin, G. Vasquez Arenas, P. V. Volkov, V. Yu. Volkov, and P. Ulloa

The a − γγ interaction is given by the Lagrangian where g aγγ is the coupling constant, F μν is the photon field strength,F μν ¼ 1 2 ϵ μναβ F αβ , and a is the axionlike particle field. For a generic axion, the coupling constant is where E and N are the electromagnetic and color anomalies of the axial current associated with the axion [6,22,23]. In grand unified models such as DFSZ [3] and KSVZ [4], E=N ¼ 8=3 and E=N ¼ 0, respectively, while a broader range of E=N values is possible [6,23]. For the scalar case, an example of an s particle weakly coupled to two photons is the dilaton, which arises in superstring theories and interacts with matter through the trace of the energymomentum tensor [24], and its two-photon interaction is given by Eq. (1) with the replacementF μν → F μν . Usually, it is assumed that g sγγ ¼ OðM −1 Pl Þ and that the dilaton mass m s ¼ OðM Pl Þ, where M Pl is the Planck mass. However, in some models, see, e.g., [25], the dilaton could be rather light. Since there are no firm predictions for the coupling g sγγ the searches for such particles have become interesting.
Experimental bounds on g aγγ for light as in the eV/c 2 -MeV/c 2 mass range can be obtained from laser experiments [26,27], from experiments studying J=ψ and ϒ particles [28], from the NOMAD experiment by using a photonregeneration method at the CERN SPS neutrino beam [29], and from orthopositronium decays [30]. Limits on ALPs in the MeV=c 2 − GeV=c 2 mass range have been typically placed by beam-dump experiments or from searches at e þ e − colliders [6,31], leaving the large area 10 −2 ≲ g aγγ ≲ 10 −5 GeV −1 of the ðg aγγ ; m a Þ-parameter space still unprobed. Additionally, since the theory predictions for the coupling, mass scale, and decay modes of ALPs are still quite uncertain, it is crucial to perform independent laboratory tests on the existence of such particles in the mass and coupling strength range discussed above. One possible way to answer these questions is to search for ALPs in a beam dump experiment [6]. However, for the coupling lying in the range 10 −2 ≲ g aγγ ≲ 10 −4 GeV −1 traditional beam dump experiments are not very promising, because, for the masses in the sub-GeV=c 2 region, the a is expected to be a relatively short-lived particle.
In this Letter, we propose and describe a direct search for ALPs with the coupling to two photons from the ðm a ; g aγγ Þparameter space uncovered by previous searches. The application of the obtained results to the s → γγ decay case is straightforward, see, e.g., [19].
The NA64 detector located at the CERN SPS H4 electron beam [32] is schematically shown in Fig. 1. It consists of a set of beam defining scintillator counters S 1−4 and veto V 1;2 , a magnetic spectrometer consisting of two dipole magnets (MBPL1,2) and a low-material-budget tracker composed of two upstream Micromegas chambers MM 1;2 , and four downstream MM 3−6 stations [33], two straw-tube ST 1;2 [34] and GEM 1;2 chambers. A synchrotron radiation detector (SRD) is used for the identification of incoming e − s [35,36] and suppression of the hadron contamination in the beam down to the level π=e − ≲ 10 −5 . An active dump, consisting of a preshower detector (PRS) and an electromagnetic (e-m) calorimeter (ECAL), made of a matrix of 6 × 6 Shashlik-type modules, is assembled from Pb and Sc plates of ≃40 radiation lengths (X 0 ). A large high-efficiency veto counter (VETO) and a massive, hermetic hadronic calorimeter (HCAL) composed of three modules HCAL1-3 complete the setup. Each module is a 3 × 3 cell matrix with a thickness of ≃7.5 nuclear interaction lengths. The events from e − interactions in the PRS and ECAL were collected with the trigger provided by the S 1−4 requiring also an in-time cluster in the ECAL with the energy E ECAL ≲ 85 GeV. The detector is described in more detail in Ref. [37].
If ALPs exist, one would expect a flux of such high energy particles from the dump. Both scalars and pseudoscalars could be produced in the forward direction through the Primakoff effect in interactions of high energy bremsstrahlung photons, generated by 100 GeV electrons in the target, with virtual photons from the electrostatic field of the target nuclei: as illustrated in Fig. 2. If the ALP is a relatively long-lived particle, it would penetrate the first downstream HCAL1 module serving as shielding and would be observed in the NA64 detector with two distinctive signatures, either (1) via its decay into 2γ inside the HCAL2 or HCAL3 modules (denoted further as HCAL2,3), or (2) as an event with large missing energy if it decays downstream of the HCAL2,3. The selection criteria for signal and background samples have been obtained using a GEANT4 [38,39] based Monte Carlo (MC) simulation of the NA64 detector. The code for the simulation of signal events is implemented in the same program according to the general scheme described in [40,41], with the a → γγ decay width given by Γ a ¼ g 2 aγγ m 3 a =64π. The event from the incoming electron interacting in the dump was required to have the incoming track momentum in the range of 100 AE 3 GeV, the SRD signal within the range of synchrotron radiation emitted by e − s, a single PRS cluster matched to an isolated ECAL cluster with an energy greater than 0.5 GeV and an ECAL cluster with the shape expected from a single e-m shower [37,40]. As the 2γ opening angle for the a → γγ decay is very small, it was not possible to distinguish this decay from a single e-m shower in the HCAL. Therefore, the candidate events with the signature 1 were selected as a single shower in the neutral final state, i.e., no activity in the VETO and the HCAL1, with e-m-like lateral shape, the shower maximum in the HCAL2,3 central cell and the energy deposition E HCAL ≳ 15 GeV. This allowed us to reduce background to a small level, while maximizing the a yield by using the cut on the ECAL energy E ECAL ≲ 85 GeV. For events with the signature 2, we required the ECAL energy to be E ECAL ≲ 50 GeV and no activity in the VETO and the HCAL. The above event selection criteria, as well as the efficiency corrections, backgrounds and their systematic errors were similar to those used in our searches for the invisible decays of dark photons [37,42].
An additional background suppression for the case 1 was achieved by using the lateral shower shape in the HCAL module. It was characterized by a variable R, defined as where E HCAL , E c HCAL are the total HCAL energy and the energy deposited in the central cell, respectively. An example of R distributions obtained from data and MC simulations is shown in Fig. 3. As expected, the distribution for e − s is narrower than for hadrons, and can be employed for effective particle identification. Using the cut R < 0.06 rejects ≳98% of hadrons, while keeping the signal efficiency ≳95%.
The search described in this Letter uses data samples of n EOT ¼ 2.84 × 10 11 electrons on target (EOT) collected during the 2016-2018 run period with the beam intensity in the range ≃ð2 − 9Þ × 10 6 e − /spill. In Fig. 4(a), the distribution of ≃3 × 10 4 events from the reaction e − Z → anything in the ðE ECAL ; E HCAL Þ plane collected with the trigger and by requiring the presence of a beam e − identified with the SRD tag is shown. Events from the horizontal band with E HCAL ≃ 10 GeV originate from the QED dimuon pair production in the ECAL and were used to cross-check the reliability of the MC simulation and background estimate [37]. The further requirement of no activity in the VETO identified a sample of ≃7 × 10 3 events shown in Fig. 4(b). This sample corresponds to the neutral hadronic secondaries from electroproduction in the dump with full hadronic energy deposition in the HCAL1 module. The events located mostly along the diagonal satisfy the condition of energy conservation E ECAL þ E HCAL ≃ 100 GeV.
The signal events with the signature 1 are expected to exhibit themselves as an excess of e-m-like events in the ðE ECAL ; E HCAL Þ plane in the signal box 1 [ Fig. 4(c)] around the diagonal E ECAL þ E HCAL ¼ 100 AE 10 GeV satisfying the energy conservation within the energy resolution of the detectors and the cut R < 0.06, as shown in Fig. 4(c). By inverting this cut we obtain the control region, where the signal events are almost absent. The signal box 2, 0 ≲ E ECAL ≲ 55 GeV, E HCAL ≲ 1 GeV for signal events having a large missing energy is also shown [40,41].
The following processes that may fake the a → γγ decay in the HCAL2,3 were considered: (1) the production of a leading neutron (n), or (2) a leading K 0 meson in the ECAL by e − s in the reaction e − A → nðK 0 Þ þ mπ 0 þ X, that punchthrough the HCAL1 and deposited their energy E nðK 0 Þ ≃ E 0 − E ECAL in the HCAL2,3 either in hadronic interactions with a significant e-m component in the shower, or via K 0 S → π 0 π 0 or K 0 L → 3π 0 decays. The reaction can be accompanied by the production of any number m of π 0 s that decay immediately in the ECAL and a small activity X in the Veto and HCAL1 below the corresponding thresholds E Veto ≲ 0.5MIP and E HCAL1 ≲ 1 GeV. (iii) Similar reactions induced by beam π − and K − that are not rejected by the SRD. As well as the π − , K − → e − ν, or K − → π 0 e − ν decays of poorly detected punchthrough beam π − , K − downstream of the HCAL1, or production of a hard bremsstrahlung γ in the downstream part of the HCAL1. (iv) The decays and reactions induced by muons from dimuon pairs produced in the ECAL.
The main background source is expected from the reactions (ii), mostly due to K 0 S;L decays in flight. The background was then evaluated by using the simulation combined with the data themselves by two methods. In the first one, we use the sample of n n ¼ 7 × 10 3 observed neutral events shown in Fig. 4(b). A conservative number of background events originated from leading neutrons and K 0 was defined as n where f nðK 0 Þ ; P nðK 0 Þ pth , and P nðK 0 Þ em are, respectively, the fraction of leading neutrons and kaons in the sample, the probability for nðK 0 Þ to punchthrough the HCAL1, and the probability for the nðK 0 Þ induced shower to be accepted as an e-m one. Using GEANT4 simulations we found f nðK 0 Þ ¼ 0.2 AE 0.07ð0.18 AE 0.06Þ. The values P nðK 0 Þ pth ≃ 10 −3 ð4.7 × 10 −3 Þ were calculated by using measured absorption cross sections from Refs. [43,44]. The values P nðK 0 Þ em ≃ 5 × 10 −3 ð1.1 × 10 −2 Þ were evaluated from the MC distributions of Fig. 3. The systematic errors of 10% and 30% have been assigned to P nðK 0 Þ pth and P nðK 0 Þ em values, respectively, by taking into account the data-MC difference in punchthrough and transverse shapes of showers (see Fig. 3) generated by πs.
In the second method we used the number of n c ¼ 12 neutral events observed in the control region, shown in Fig. 4(c). This number was found to be in a good agreement with 9 AE 4 events expected from the sample of neutral events shown in Fig. 4(b). The background then was estimated by taking into account the relative composition of these events which was found to be ≃25% of neutrons and 75% of K 0 s. All background estimates were then summed up, taking into account the corresponding normalisation factors. These factors were calculated from beam composition, cross sections for the processes listed above, and punchthrough probabilities evaluated directly from the data and MC simulations. The total number of expected candidate  . 4. Panel (a) shows the measured distribution of all events in the (E ECAL ; E HCAL ) plane selected at the initial phase of the analysis with the loose cuts. The distribution of pure neutral hadronic secondaries is illustrated in panel (b). The shaded area shown in panel (c) represents the signal boxes 1 and 2 in the ðE ECAL ; E HCAL Þ plane for the signatures 1 and 2, respectively, where no candidates for the signal events were found after applying all selection criteria. The blue dots represent 12 events in the control region R > 0.06 from leading neutral hadrons. The size of the signal box 2 is increased by a factor of 5 along the E HCAL axis for the illustration purposes. events after applying the selection criteria are given in Table I for each background component. The total background of 0.17 AE 0.046 events, where statistical and systematic errors were added in quadrature, estimated with the first method was found to agree with the second estimate resulting in 0.19 AE 0.07 events. For the signature 2, the total background in the data sample was estimated to be 0.53 AE 0.17 events, as described in detail in Ref. [42].
After determining all the selection criteria and background levels, we unblinded the signal boxes. No event in the signal boxes shown in Fig. 4(c) were found, allowing us to obtain the m a -dependent upper limits on the coupling strength g aγγ . The exclusion limits were calculated by employing the multibin limit setting technique in the ROOSTATS package [45] with the modified frequentist approach, using the profile likelihood as a test statistic [46][47][48]. The combined 90% confidence level (C.L.) limits on the coupling strength g aγγ were obtained from the corresponding limit for the expected number of signal events, n a , which is given by the sum: ε i a n i a ðg aγγ ; m a Þ; ð4Þ where ε i a is the signal efficiency and n i a ðg aγγ ; m a Þ is the number of the a decays for the signature i. The a yield from the reaction chain (3) was obtained with the calculations described in Ref. [49] assigning ≲10% systematic uncertainty due to different form-factor parametrizations [50,51]. An additional uncertainty of ≃10% was accounted for the data-MC difference for the dimuon yield [37,52]. The signal detection efficiency for each signature in (4) was evaluated by using signal MC and was found slightly m a dependent. For instance, for the signature 1 and m a ≃ 10 MeV, the ε 1 a and its systematic error was determined from the product of efficiencies accounting for the geometrical acceptance (0.97 AE 0.02), the primary track (≃0.83 AE 0.04), SRD (≳0.95 AE 0.03), ECAL (0.95 AE 0.03), VETO (0.94 AE 0.04), HCAL1 (0.94 AE 0.04), and HCAL2,3 (0.97 AE 0.02) signal event detection. The signal efficiency loss ≲7% due to pileup was taken into account using reconstructed dimuon events [37]. The VETO and HCAL1 efficiencies were defined as a fraction of events below the corresponding energy thresholds with the main uncertainty estimated to be ≲4% for the signal events, which is caused by the pileup effect from penetrating hadrons. The trigger efficiency was found to be 0.95 with a small uncertainty of 2%. The total signal efficiency ϵ a varied from 0.51 AE 0.09 to 0.48 AE 0.08 for the a mass range of 10-50 MeV. The total systematic uncertainty on n a calculated by adding all errors in quadrature did not exceed 20% for both signatures. The attenuation of the a flux due to interactions in the HCAL1 was found to be negligible. The combined signal region excluded in the (m a ; g aγγ ) plane at 90% C.L. is shown in Fig. 5 together with the results of other experiments. Our limits are valid for both scalar and pseudoscalar cases and exclude the region in the coupling range 2 × 10 −4 ≲ g aγγ ≲ 5 × 10 −2 GeV −1 for masses m a ≲ 55 MeV.
We gratefully acknowledge the support of the CERN management and staff and the technical staff of the participating institutions for their vital contributions. We would like to thank M. W. Krasny for providing us with Ref. [54] and useful comments, B. Döbrich for providing information on the E141 and updated CHARM and NuCal exclusion curves, and G. Lanfranchi for valuable discussions.   5. The NA64 90% C.L. exclusion region for ALPs coupling predominantly to photons in the ðm a ; g aγγ Þ plane as a function of the (pseudo)scalar mass m a derived from the present analysis. The yellow band represents the parameter space for the benchmark DFSZ [3] and KSVZ [4] models extended with a broader range of E=N values [6,23]. Constraints from the BABAR [31], E137 [53], E141 [54,55], LEP [56], and PrimEx [57] experiments, as well as limits from CHARM [58] and NuCal [59], updated in Ref. [60] are also shown. For more limits from indirect searches and proposed measurements; see, e.g., Refs. [11][12][13].