Dark matter search in missing energy events with NA64

A search for sub-GeV dark matter production mediated by a new vector boson $A'$, called dark photon, is performed by the NA64 experiment in missing energy events from 100 GeV electron interactions in an active beam dump at the CERN SPS. From the analysis of the data collected in the years 2016, 2017, and 2018 with $2.84\times10^{11}$ electrons on target no evidence of such a process has been found. The most stringent constraints on the $A'$ mixing strength with photons and the parameter space for the scalar and fermionic dark matter in the mass range $\lesssim 1$ GeV are derived. Thus, demonstrating the power of the active beam dump approach for the dark matter search.

The idea that in addition to gravity a new force between the dark and visible matter transmitted by a vector boson, A , called dark photon, might exist is quite exciting [1][2][3][4]. The A can have a mass in the sub-GeV mass range, and couple to the standard model (SM) via kinetic mixing with the ordinary photon, described by the term 2 F µν F µν and parameterized by the mixing strength . An example of the Lagrangian of the SM extended by the dark sector (DS) is given by: where the massive A µ field is associated with the spontaneously broken U D (1) gauge group, F µν = ∂ µ A ν − ∂ ν A µ , and m A , m χ are, respectively, the masses of the A and dark matter (DM) particles, χ, which are treated as Dirac fermions coupled to A µ with the dark coupling strength e D of the U (1) D gauge interactions. The mixing term of (1) results in the interaction L int = eA µ J µ em of dark photons with the electromagnetic current J µ em with a strength e, where e is the electromagnetic coupling and 1 [5][6][7]. Such small values of can be obtained in Grand Unified Theories from loop effects of particles charged under both the dark U D (1) and SM U (1) interactions with a typical 1-loop value = ee D /16π 2 10 −2 − 10 −4 [7], or from 2-loop contributions resulting in 10 −3 − 10 −5 . The accessibility of these values at accelerator experiments has motivated a worldwide effort towards dark forces and other portals between the visible and dark sectors, see Refs. [4,[8][9][10][11][12][13][14][15][16][17] for a review. If the A is the lightest state in the dark sector, then it would decay mainly visibly to SM leptons l (or hadrons) [17]. In the presence of light DM states χ with the masses m χ < m A /2, the A would predominantly decay invisibly into those particles provided that e D > e. Various dark sector models motivate the existence of sub-GeV scalar and Majorana or pseudo-Dirac DM coupled to the A [13,14,[17][18][19][20][21]. To interpret the observed abundance of DM relic density, the requirement of the thermal freeze-out of DM annihilation into visible matter through γ − A mixing allows one to derive a relation where α D = e 2 D /4π and the parameter f depends on m A ' and m χ [22]. For m A ' mχ = 3, f 10 for a scalar [18], and f 1 for a fermion [19]. This prediction provides an important target for the ( , m A ) parameter space which can be probed at the CERN SPS energies. Models introducing the invisible A also allow to explain various astrophysical anomalies [23] and are subject to various experimental constraints leaving, however, a large area that is still unexplored [18,[24][25][26][27][28][29][30][31][32][33].
In this work we report new results on the search for the A mediator and light dark matter (LDM) in the fixed-target experiment NA64 at the CERN SPS. In the following we assume that the A invisible decay mode is predominant, i.e. Γ(A →χχ)/Γ tot 1. If such invisible A exists, many crucial questions about its coupling constants, mass scale, decay modes, etc. arise. One possible way to answer these questions is to search for the A in fixed-target experiments. The A s could be produced by a high intensity beam in a dump and generate a flux of DM particles through the A →χχ decay, which can be detected through the scattering off electrons in the far target [18,19,24,27,34,35].
The signal event rate in the detector in this case, scales as 2 y ∝ 4 α D , with one 2 associated with the A production in the dump and 2 α D coming from the χ particle scattering in the detector, and with the parameter y is defined as Another method, discussed in this work and proposed in Refs. [36,37], is based on the detection of the missing energy, carried away by the hard bremsstrahlung A produced in the process e − Z → e − ZA ; A → invisible of high-energy electrons scattering in the active beam dump target. The advantage of this type of experiment compared to the beam dump ones is that its sensitivity is proportional to 2 , associated with the A production and its subsequent prompt invisible decay. The NA64 detector is schematically shown in Fig. 1. The experiment employed the optimized H4 electron beam. The beam has a maximal intensity 10 7 electrons per SPS spill of 4.8 s produced by the primary 400 GeV proton beam with an intensity of few 10 12 protons on target. The detector utilized the beam defining scintillator (Sc) counters S 1−4 and veto V 1,2 , a magnetic spectrometer consisting of two successive dipole magnets MBPL 1,2 with the integral magnetic field of 7 T·m and a low-material-budget tracker. The tracker was a set of two upstream Micromegas chambers MM 1,2 , and four MM 3−6 , downstream stations, as well as two straw-tube ST 1,2 and GEM 1,2 chambers allowing the measurements of e − momenta with the precision δp/p 1% [38]. To enhance electron identification, synchrotron radiation (SR) emitted in the MBPL magnetic field was used for their efficient tagging with a SR detector (SRD), which was an array of PbSc sandwich calorimeter of a very fine segmentation [36,39]. By using the SRD the initial admixture of the hadron contamination in the beam π/e − 10 −2 was further suppressed by a factor 10 3 . The detector was also equipped with an active dump target, which is an electromagnetic calorimeter (ECAL), a matrix of 6 × 6 Shashlik-type modules assembled from Pb and Sc plates for measurement of the electron energy E ECAL . Each module has 40 radiation lengths (X 0 ) with the first 4X 0 serving as a pre-shower detector. Downstream of the ECAL, the detector was equipped with a large high-efficiency veto counter VETO, and a massive, hermetic hadronic calorimeter (HCAL) of 30 nuclear interaction lengths in total. The modules HCAL 1−3 provided an efficient veto to detect muons or hadronic secondaries produced in the e − A interactions in the target, while the zero-degree calorimeter HCAL 0 was used to reject events accompanied by hard neutrals from the upstream e − interactions. The events were collected with the hardware trigger requiring an in-time cluster in the ECAL with the energy E ECAL 80 GeV. The results reported here were obtained from the combined analysis of n EOT = 2.84 × 10 11 electrons on target (EOT) collected with the beam energy E 0 = 100 GeV and intensity up to 10 7 e − per spill during the years 2016-2018, hereafter called respectively the run I,II,III.
In order to avoid biases in the determination of selection criteria for signal events, a blind analysis was performed. Candidate events were requested to have the missing energy E miss = E 0 − E ECAL > 50 GeV. The signal box (E ECAL < 50 GeV ; E HCAL < 1 GeV ) was defined based on the energy spectrum calculations for A s emitted by e ± from the electromagnetic (e-m) shower generated by the primary e − s in the target [40,41]. A Geant4 [42,43] based Monte Carlo (MC) simulation used to study the detector performance, signal acceptance, and background level, as well as the analysis procedure including selection of cuts and estimate of the sensitivity are described in detail in Ref. [31].
The left panel in Fig. 2 shows the distribution of 3 × 10 4 events from the reaction e − Z → anything in the (E ECAL ; E HCAL ) plane measured with loose selection criteria requiring mainly the presence of a beam e − identified with the SR tag. Events from the area I originate from the QED dimuon production, dominated by the reaction e − Z → e − Zγ; γ → µ + µ − with a hard bremsstrahlung photon conversion on a target nucleus and characterized by the energy of 10 GeV deposited by the dimuon pair in the HCAL. This rare process was used as a benchmark allowing to verify the reliability of the MC simulation, correct the signal acceptance, cross-check systematic uncertainties and background estimate [31]. The region II shows the SM events from the hadron electroproduction in the target which satisfy the energy conservation E ECAL + E HCAL 100 GeV within the energy resolution of the detectors.
Finally, the following selection criteria were chosen to maximize the acceptance for signal events and to minimize background: (i) The incoming particle track should have the momentum 100 ± 3 GeV and a small angle with respect to the beam axis to reject large angle tracks from the upstream e − interactions. (ii) The energy deposited in the SRD detector should be within the SR range emitted by e − s and in time with the trigger. (iii) The lateral and longitudinal shape of the shower in the ECAL should be consistent with the one expected for the signal shower [40]. (iv) There should be no multiple hits activity in the Straw-tube chambers, which was an effective cut against hadron electroproduction in the beam material upstream of the dump, and no activity in VETO. Only 1.6 × 10 4 events passed these criteria from combined runs. The two largest sources of background which may fake the A → invisible signal are expected from i) mistakenly tagged beam µ, π, K decays in flight, and ii) the energy loss in events from nuclear e-interactions in the beam line due to the insufficient downstream detector coverage. The selection cuts to eliminate these backgrounds have been chosen such that they do not affect the shape of the true E miss spectrum. Two complementary methods based on the MC simulations and data themselves were used for the background estimation in the signal region. The relatively small event-number backgrounds such as the decays of the beam µ, π, K or µ from the reaction of dimuon production were simulated with the full statistics of the data. Large event-number processes from e − interactions in the target or beam line, punchthrough of secondary hadrons were also studied extensively, although simulated samples with statistics similar to the data were not feasible. The background estimate in this case was mainly extracted from data by the extrapolation of events from sidebands A and C shown in the right panel of Fig. 2 into the signal region, assessing the systematic uncertainties by varying the background fit functions [31]. We also examined the number of events observed in several regions around the signal box, which were statistically consistent with the estimates. Events in the region A (E ECAL < 50 GeV ; E HCAL > 1 GeV ) are pure neutral hadronic secondaries produced by electrons in the ECAL target, while events from the region C (E ECAL > 50 GeV ; E HCAL < 1 GeV ) are likely from the e − hadronic interactions in the downstream part of the beam line accompanied by the large transverse fluctuations of hadronic secondaries that missed the HCAL. Table I summarizes the conservatively estimated background inside the signal region, which is expected to be 0.53 ± 0.17 events. After determining all the selection criteria and estimating background levels, we unblind the data. No event in the signal box was found, as shown in Fig. 2.
This allows us to obtain the m A -dependent upper limits on the mixing . In the final combined statistical analysis, the three runs I-III were analysed simultaneously using the multi-bin limit setting technique [31] based on the RooStats package [44]. First, the background estimate, efficiencies, and their corrections and uncertainties were used to optimize the main cut defining the signal box, by comparing sensitivities, defined as an average expected limit calculated using the profile likelihood method. The calculations were done with uncertainties used as nuisance parameters, assuming their log-normal distributions [45]. For this optimization, the most important inputs were the expected values from the background extrapolation into the signal region from the data samples of the runs I,II,III  [25,26], BaBar [32] and recent NA62 [33] experiments, as well as the muon αµ favored area are also shown. For more limits from indirect searches and planned measurements see e.g. Ref. [12][13][14].
with their errors estimated from the variation of the extrapolation functions. The optimal cut was found to be weakly dependent on the A mass choice and can be safely set to E ECAL 50 GeV for the whole mass range. The combined 90% confidence level (CL) upper limits for were determined by using the modified frequentist approach for confidence levels, taking the profile likelihood as a test statistic in the asymptotic approximation [46][47][48]. The total number of expected signal events in the signal box was the sum of expected events from the three runs: where i tot is the signal efficiency in the run i, and n i A ( , m A , ∆E A ) is the signal yield per EOT generated in the energy range ∆E e . Each i-th entry in this sum was calculated with simulations of signal events 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 expected backgrounds and estimated systematic errors were also taken into account in the limits calculation. The combined 90% C.L. exclusion limits on the mixing strength as a function of the A mass can be seen in Fig. 3. The derived bounds are currently the best for the mass range 0.001 m A 0.1 GeV obtained from direct searches of A → invisible decays [17].
The overall signal efficiency, A is slightly m A , E A dependent and is given by the product of efficiencies accounting for the geometrical acceptance (0.97), the track ( 0.83), SRD ( 0.95), VETO ( 0.94) and HCAL (0.94) signal reconstruction, the acceptance loss due to pileup ( 8%) for high-intensity runs, and the DAQ dead time (0.93). The VETO and HCAL efficiency was defined as a fraction of events below the corresponding zero-energy thresholds. The spectrum of the energy distributions in these detectors from the leak of the signal shower energy in the ECAL was simulated for different A masses [40] and cross-checked with measurements at the e − beam. The uncertainty in the VETO and HCAL efficiency for the signal events, dominated mostly by the pileup effect from penetrating hadrons in the high intensity run III, was estimated to be 4%. The trigger efficiency was found to be 0.95 with a small uncertainty 2%. The A acceptance was evaluated by taking into account the selection efficiency for the lateral and longitudinal shape of e-m showers in the ECAL from signal events [40]. The A production cross section in the primary reaction was obtained with the exact tree-level calculations as described in Refs. [41]. An additional uncertainty in the A yield prediction 10% was conservatively accounted for the difference between the predicted and measured dimuon yield [29,31], which was the dominant source of systematic uncertainties on the expected number of signal events n A ( , m A , ∆E A ). The overall signal efficiency A for high-intensity runs varied from 0.53± 0.09 to 0.48±0.08 decreasing for the higher A masses.
Using constraints on the cross section of the DM annihilation freeze out (see Eq. (2)), and obtained limits on mixing strength, one can derive constraints on the LDM models, which are shown in the (y;m χ ) and (α D ;m χ ) planes in Fig. 4 for masses m χ 1 GeV. On the same plot one can also see the favoured y parameter curves for scalar, pseudo-Dirac (with a small splitting) and Majorana scenario of LDM obtained by taking into account the observed relic DM density [13]. The limits on the variable y are calculated by using Eq.  [12,13,[19][20][21] from the results of the LSND [18,27], E137 [28], MiniBooNE [30], BaBar [32], and direct detection [49] experiments. The favoured parameters to account for the observed relic DM density for the scalar, pseudo-Dirac and Majorana type of light DM are shown as the lowest solid line in top plots.
m A = 3m χ [13,14] and shown also for comparison with bounds from other experiments. This choice of the α D region is compatible with the bounds derived based on the running of the dark gauge coupling arguments of Ref. [41,50]. It should be noted that for smaller values of α D the NA64 limits will be stronger, due to the fact that the signal rate in our case scales as 2 , instead of 4 α D as for beam dump searches. The bounds on α D for the case of pseudo-Dirac fermions shown in Fig. 4 (left panel in the bottom row) were calculated by taking the value f = 0.25, while for the Majorana case (right panel) the value f = 3 in Eq.(2) [31] was used [51]. One can see that using the active beam dump approach allows us to obtain more stringent bounds on , y, α D for the mass range m χ 0.1 GeV than the limits obtained from the results of classical beam dump experiments, thus, demonstrating its power for the dark matter search. Further improving of the sensitivity and background rejection is expected after the NA64 detector upgrade.
We gratefully acknowledge the support of the CERN management and staff and the technical staffs of the participating institutions for their vital contributions. This work was supported by the HISKP, University of Bonn