Search for a Hypothetical 16.7 MeV Gauge Boson and Dark Photons in the NA64 Experiment at CERN

We report the first results on a direct search for a new 16.7 MeV boson (X) which could explain the anomalous excess of e+e- pairs observed in the excited Be-8 nucleus decays. Due to its coupling to electrons, the X could be produced in the bremsstrahlung reaction e- Z ->e- Z X by a 100 GeV e- beam incident on an active target in the NA64 experiment at the CERN SPS and observed through the subsequent decay into an e+e- pair. With 5.4\times 10^{10} electrons on target, no evidence for such decays was found, allowing to set first limits on the X-e^- coupling in the range 1.3\times 10^{-4}<\epsilon_e<4.2\times 10^{-4} excluding part of the allowed parameter space. We also set new bounds on the mixing strength of photons with dark photons (A') from non-observation of the decay A'->e+e- of the bremsstrahlung A' with a mass<~ 23 MeV.

We report the first results on a direct search for a new 16.7 MeV boson (X) which could explain the anomalous excess of e + e − pairs observed in the excited 8 Be * nucleus decays. Due to its coupling to electrons, the X could be produced in the bremsstrahlung reaction e − Z → e − ZX by a 100 GeV e − beam incident on an active target in the NA64 experiment at the CERN SPS and observed through the subsequent decay into a e + e − pair. With 5.4×10 10 electrons on target no evidence for such decays was found, allowing to set first limits on the X −e − coupling in the range 1.3×10 −4 e 4.2×10 −4 excluding part of the allowed parameter space. We also set new bounds on the mixing strength of photons with dark photons (A ) from non-observation of the decay A → e + e − of the bremsstrahlung A with a mass 23 MeV. The ATOMKI experiment of Krasznahorkay et al. [1] has reported the observation of a 6.8 σ excess of events in the invariant mass distributions of e + e − pairs produced in the nuclear transitions of excited 8 Be * to its ground state via internal pair creation. This anomaly can be interpreted as the emission of a new protophobic gauge X boson with a mass of 16.7 MeV followed by its X → e + e − decay assuming that the X has non-universal coupling to quarks, coupling to electrons in the range 2×10 −4 e 1.4 × 10 −3 and the lifetime 10 −14 τ X 10 −12 s [2,3]. It has motivated worldwide theoretical and experimental efforts towards light and weakly coupled vector bosons, see, e.g. [4][5][6][7][8][9][10][11][12].
The method of the search for A → e + e − decays is described in [54,55]. Its application to the case of the X → e + e − decay is straightforward. Briefly, a highenergy electron beam is sent into an electromagnetic (em) calorimeter that serves as an active beam dump. Typically the beam electron loses all its shower energy in the dump. If the A exists, due to the A (X) − e − coupling it would occasionally be produced by a shower electron (or positron) in its scattering off a nuclei of the dump: Since the A is penetrating and longer lived, it would escape the beam dump, and subsequently decays into an e + e − pair in a downstream set of detectors. The pair energy would be equal to the energy missing from the dump. The apparatus is designed to identify and measure the energy of the e + e − pair in another calorimeter (ECAL). Thus, the signature of the A (X) → e + e − decay is an event with two e-m-like showers in the detector: one shower in the dump, and another one in the ECAL with the sum energy equal to the beam energy.
The NA64 setup is schematically shown in Fig. 1. The experiment employs the optimized 100 GeV electron beam from the H4 beam line in the North Area (NA) of the CERN SPS. Two scintillation counters, S1 and S2 were used for the beam definition, while the other two, S3 and S4, were used to detect the e + e − pairs. The detector was equipped with two dipole magnets and a tracker, which was a set of four upstream Micromegas (MM) chambers (T1, T2) for the incoming e − angle selection and two sets of downstream MM, gas electron multiplier (GEM) stations and scintillator hodoscopes (T3, T4) for measurements of the outgoing tracks [58,59]. To enhance the electron identification the synchrotron radiation (SR) emitted by electrons was used for their tagging allowing to suppress the initial hadron contamination in the beam π/e − 10 −2 down to the level 10 −6 [57,60]. The use of SR detectors (SRD) was a key point for the improvement of the sensitivity compared to the previous electron beam dump searches [24,25]. The dump was a compact e-m calorimeter WCAL made as short as possible to maximize the sensitivity to short lifetimes while keeping the leakage of particles at a small level. It was followed by the ECAL to measure the energy of the decay e + e − pair, which was a matrix of 6 × 6 shashlik-type modules [57]. The ECAL has 40 radiation lengths (X 0 ) and is located at a distance 3.5 m from the WCAL. Downstream of the ECAL the detector was equipped with a high-efficiency veto counter, V3, and a hermetic hadron calorimeter (HCAL) [57] used as a hadron veto and for muon identification with a help of four muon counters, MU1-MU4, located between the HCAL modules. The results reported here were obtained from data samples in which 2.4 × 10 10 electrons on target (EOT) and 3 × 10 10 EOT were collected with the WCAL of 40 X 0 (with a length of 290 mm) and of 30 X 0 (220 mm), respectively. The events were collected with a hardware trigger requiring in-time energy deposition in the WCAL and E W CAL 70 GeV. Data of these two runs (hereafter called the 40 X 0 and 30 X 0 run) were analyzed with similar selection criteria and finally summed up, taking into account the corresponding normalization factors. For the mass range 1 ≤ m A ≤ 25 MeV and energy E A 20 GeV, the opening angle Θ e + e − 2m A /E A 2 mrad of the decay e + e − pair is too small to be resolved in the tracker T3-T4, and the pairs are mostly detected as a single-track e-m shower in the ECAL.
The candidate events were selected with the following criteria chosen to maximize the signal acceptance and minimize background, using both Geant4 [61,62]  the minimum ionizing particle (MIP); (iii) The signal in the decay counter S4 is consistent with two MIPs; (iv) The sum of energies deposited in the WCAL and ECAL, E tot = E W CAL + E ECAL , is equal to the beam energy within the energy resolution of these detectors. According to simulations, at least 30% of the total energy should be deposited in the ECAL [63,64]; (v) The showers in the WCAL and ECAL should start to develop within a few first X 0 ; (vi) The lateral and longitudinal shape of the shower in the ECAL are consistent with a single e-m one. However, for A s with the energy 5 GeV the ECAL shower is poorly described by the single shower shape, hence the additional cut E ECAL > 5 GeV was applied; (vii) No significant energy deposited in the V3 and/or HCAL. These cuts were used for rejection of events with hadrons in the final state. As in the previous analyses [56,57] a clean sample of 10 5 rare µ + µ − events produced in the dump was used for the efficiency corrections in the simulations, which do not exceed 20%. A blind analysis of data was performed, with the signal box defined as 90 < E tot < 110 GeV and by using 20%(100%) of the data for the selection criteria optimization (background estimate).
There are several processes that can fake the A → e + e − signal. Among them, the two most important were expected either from decay chain K 0 S → π 0 π 0 ; π 0 → γe + e − of K 0 S produced in the WCAL or from the γ → e + e − conversion of photons from K 0 S → π 0 π 0 → π 0 → γγ decays in the T3 plane or earlier in the beamline. Another background could come from the K 0 S → π + π − hadronic decays that could be misidentified as an e-m event in the ECAL at the level 2.5 × 10 −5 evaluated from the measurements with the pion beam. The leading K 0 can be produced in the dump either by misidentified beam π − , K − or directly by electrons. The background from the K 0 S decay chain was estimated by us-ing the direct measurements of the K 0 S flux from the dump with the following method. It is well known that the K 0 produced in hadronic reactions is a linear combination of the short-and long-lived components |K 0 >= (|K 0 S > +|K 0 L >)/ √ 2. The flux of K 0 was evaluated from the measured ECAL+HCAL energy spectrum of long-lived neutral hadrons selected with the requirement of no signal in V2 and S4, taking into account corrections due to the K 0 S decays in-flight. The main fraction of 10 3 events observed in the HCAL were neutrons produced in the same processes as K 0 in the WCAL. According to simulations, 10% of them were predicted to be other neutral hadrons, i.e. Λ and K 0 , that were also included in the data sample. The conservative assumption that 100 K 0 were produced allows us to calculate the number of K 0 S from the dump and simulate the corresponding background from the K 0 S → π + π − and K 0 S → π 0 π 0 ; π 0 → γe + e − decay chain, which was found to be 0.04 events per 5.4 × 10 10 EOT. To crosscheck this result another estimate of this background was used. The true neutral e-m events, which are presumably photons, were selected with requirements of no charged tracks, i.e. no signals in V2 and S4 counters, plus a single e-m like shower in the ECAL defined by cuts cuts (v)-(vii). Three such events were found in the signal box as shown in Fig. 2. Using simulations we calculated that there were 150 leading K 0 produced in the dump, which is in a reasonable agreement with the previous estimate resulting in a conservative K 0 S background of 0.06 events. The µ, π and K mistakenly tagged as e − s [60] could also interact in the dump though the µZ → µZγ or π, K charge-exchange reactions, accompanied by the poorly detected scattered µ, or secondary hadrons. The

Source of background
Events e + e − pair production by punchthrough γ < 0.001 K 0 S → 2π 0 ; π 0 → γe + e − ;γ → e + e − ; K 0 S → π + π − 0.06 ± 0.034 πN → (≥ 1)π 0 + n + ...; π 0 → γe + e − ;γ → e + e − 0.01 ± 0.004 π − bremsstrahlung in the WCAL , γ → e + e − < 0.0001 π, K → eν, Ke4 decays < 0.001 eZ → eZµ + µ − ; µ ± → e ± νν < 0.001 punchthrough π < 0.003 Total 0.07 ± 0.035 misidentified pion could mimic the signal either directly (small fraction of showers that look like an e-m one) or by emitting a hard bremsstrahlung photon in the last layer of the dump, which then produces an e-m-shower in the ECAL, accompanied by the scattered pion track. Another background can appear from the beam π → eν decays downstream the WCAL. The latter two backgrounds can pass the selection only due to the V2 inefficiency ( 10 −4 ), which makes them negligible. The chargeexchange reaction π − p → (≥ 1)π 0 + n + ... which can occur in the last layers of the WCAL with decay photons escaping the dump without interactions and accompanied by poorly detected secondaries is another source of fake signal. To evaluate this background we used the extrapolation of the charge-exchange cross sections, σ ∼ Z 2/3 , measured on different nuclei [65]. The contribution from the beam kaon decays in-flight K − → e − νπ + π − (K e4 ) and dimuon production in the dump e − Z → e − Zµ + µ − with either π + π − or µ + µ − pairs misidentified as e-m event in the ECAL was found to be negligible. Table I summarizes the conservatively estimated background inside the signal box, which is expected to be 0.07 ± 0.034 events per 5.4 × 10 10 EOT. The dominant contribution to background is 0.06 events from the K 0 S decays, with the uncertainty dominated by the statistical error. In Fig. 2 the final distributions of e.m. neutral events, which are presumably photons, and signal candidate events that passed the selection criteria (i)-(iii) and (v)-(vii) are shown in the (E ECAL ; E W CAL ) plane. No candidates are found in the signal box. The conclusion that the background is small is confirmed by the data.
The combined 90% confidence level (C.L.) upper limits for the mixing strength were obtained from the corresponding limit for the expected number of signal events, N 90% A , by using the modified frequentist approach, taking the profile likelihood as a test statistic [66][67][68]. The N A value is given by the sum : where i tot is the signal efficiency in the run i (30 X 0 or 40 X 0 ), and n i A ( , m A ) is the number of the A → e + e − decays in the decay volume with energy E A > 30 GeV per EOT, calculated under assumption that this decay mode is predominant, see e.g. Eq.(3.7) in Ref. [55]. Each i -th entry in this sum was calculated by simulating signal events for the corresponding beam running conditions and processing them through the reconstruction program with the same selection criteria and efficiency corrections as for the data sample from the run-i. The A efficiency and its systematic error were determined to stem from the overall normalization, A yield and decay probability, which were the A mass dependent, and also from efficiencies and their uncertainties in the primary e − (0.85 ± 0.02), WCAL(0.93 ± 0.05), V 2 (0.96 ± 0.03), ECAL(0.93 ± 0.05), V 3 (0.95 ± 0.04), and HCAL(0.98 ± 0.02) event detection. The later, shown as an example values for the 40 X 0 run, were determined from measurements with e − beam cross-checked with simulations. A detailed simulation of the e-m shower in the dump [63] with A cross sections was used to calculate the A yield [64,69,70]. The 10% difference between the calculations in Ref. [64] and Ref. [69,70] was accounted for as a systematic uncertainty in n A ( , m A ). In the overall signal efficiency for each run the acceptance The allowed range of e explaining the 8 Be* anomaly (red area) [2,3], constraints on the mixing from the experiments E141 [22], E774 [25], BaBar [40], KLOE [45], HADES [48], PHENIX [49], NA48 [51], and bounds from the electron anomalous magnetic moment (g − 2)e [71] are also shown.
loss due to pileup ( 7% for 40 X 0 and 10% for 30 X 0 runs) was taken into account and cross-checked using reconstructed dimuon events [57]. The dimuon efficiency corrections ( 20%) were obtained with uncertainty of 10% and 15%, for the 40 X 0 and 30 X 0 runs, respectively. The total systematic uncertainty on N A calculated by adding all errors in quadrature did not exeed 25% for both runs. The combined 90% C.L. exclusion limits on the mixing as a function of the A mass is shown in Fig. 3 together with the current constraints from other experiments. Our results exclude X-boson as an explanation for the 8 Be* anomaly for the X − e − coupling We gratefully acknowledge the support of the CERN management and staff and the technical staffs of the participating institutions for their vital contributions. We also thank Attila Krasznahorkay for useful discussions about the Atomki experiment. This work was supported by the HISKP, University of Bonn (Germany), JINR (Dubna), MON and RAS (Russia), SNSF grant 169133 and ETHZ (Switzerland), and grants FONDE-