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Table of Contents2

1 Introduction3

2 NA64 status from the 2017 run4 2.1 The detector and ongoing activities4 2.2 Data sample from 2016-2017 runs7

3 Search for the A0 → invisible decay8 3.1 Exact tree-level cross section calculations and signal simulation.9 3.2 Data analysis and selection criteria 11 3.3 Background 15 3.4 Results and calculation of limits 22 3.5 Constraints on light thermal Dark Matter 24 3.6 Preliminary results from the 2017 run 27

4 Search for a new 17 MeV gauge boson from the 8Be anomaly and dark photon decays A0 → e+e− 28 4.1 The search method and the detector 29 4.2 Event selection and background evaluation 30 4.3 First results on the X → e+e− and A0 → e+e− decays 33

5 Plans for the 2018 and 2021 runs 35 5.1 Search for the A0 → invisible decays 35 5.2 Search for the X → e+e− and A0 → e+e− decays 37 5.3 Search for the ALP decays a → γγ and a → e+e− 40

6 Detector upgrade and location at the H4 line 41 6.1 Detector upgrades for the 2021 run 41 6.2 Detector location at the H4 line 42

7 Summary 43

8 Publications 44

References 45

– 1 – SUMMARY

The measurements performed in 2017 are a part of a broad NA64 program which address the most important issues currently accessible to the dark sector: a search for the A0 → invisible decay of the dark photons, in particular in the A0 parameter space relevant for the possible existence of the sub-GeVThermal Dark Matter (TDM), and a search for the X → e+e− decay of a new 17 MeV X- boson, which may explain the 8Be anomaly - an excess of e+e− events in the excited 8Be transitions. The upcoming run in 2018, combined with the 2016-17 NA64 runs, provides us with the opportunity to meet and perhaps exceed our original goals for both programs and set a solid base for a possible new physics program for post LS2. During the 2016 run, we collected 4.3 × 1010 electron on target (EOT). Five weeks of running time in 2017 allows us to increase the data sample up to ' 1011 EOT and improve sensitivity to the mixing strength by a factor 6. Our goals for the 2018 run are: (i) to increase the full statistics for the invisible A0 decay by a factor 3; (ii) to perform the search for a new light X boson with the detector configuration similar to the one used in 2017 run, but with the beam energy of 150 GeV. The NA64 collaboration also proposes to carry out further searches of the A0 → invisible decay and other rare processes with the H4 electron beam after the LS2 in the year 2021 with the main goal to accumulate in total up to ' 5 × 1011 EOT in order to cover much of the remaining (; mA0 ) parameter space and to explore the sub-Gev TDM parameter regions not yet above those currently being constrained by the beam-dump experiments.

– 2 – 1 Introduction

Despite the intensive searches at the LHC and in non-accelerator experiments Dark Matter (DM) still is a great puzzle. Though stringent constraints obtained on DM coupling to standard model (SM) particles ruled out many DM models, little is known about the origin and dynamics of the dark sector itself. One difficulty so far is that DM can be probed only through its gravitational interaction. An exciting possibility is that in addition to gravity, a new force between the dark sector and visible matter transmitted by a new vector boson A0 (dark photon) might exist. Such A0 could have a mass mA0 . 1 GeV - associated with a spontaneously broken gauged U(1)D symmetry- and couple to the SM through kinetic mixing with the ordinary photon, 1 0µν − 2 FµνA , parametrized by the mixing strength   1. This has motivated a worldwide theoretical and experimental effort towards searches for dark forces and other portals between the visible and dark sectors, shifting the strategy from the high energy to the high intensity frontier, see Refs. [1,2] for a review. An additional motivation for existence of the A0 has been provided by hints on astrophysical signals of dark matter [3], which can be explained by a sub-GeV A0 with the coupling  ' 10−3. Such small values of  could naturally be obtained from loop effects of particles charged under both the dark and SM U(1) interactions with a typical 1-loop value  = eg /16π2 [4], where g is the coupling constant of the D D √ U(1)D gauge interactions. A dark photon mass in the sub-GeV range, mA0 ' MZ , can be generated in several physics scenarios. Thus, if U(1)D is embedded in a Grand Unifed Theory (GUT), the mixing can be generated by a one-(two-)loop interaction and naturally results in values of  ' 10−3 − 10−1(10−5 − 10−3)[3–5]. If the A0 is the lightest state in the dark sector, then it would decay mainly vis- ibly, i.e., typically to SM leptons l = e, µ or hadrons, which could be used to detect it. Previous beam dump, fixed target, collider, and rare meson decay experiments have already put stringent constraints on the mass mA0 and  of such dark photons excluding, in particular, the parameter region favored by the gµ − 2 anomaly [2]. However, in the presence of light dark states, in particular dark matter, with the 0 masses . mA0 , the A would predominantly decay invisibly into those particles pro- 0 vided that gD > e. Models introducing such invisible A offer new intriguing possi- bilities to explain the gµ − 2 and various other anomalies and are subject to different experimental constraints. Compared to the visible decay mode, the invisible decay is constrained in significantly smaller (; mA0 ) parameter space living large area still unexplored. The NA64 was designed as a hermetic general purpose detector to search for dark sector physics in missing energy events from electron, hadron, and muon scattering off nuclei. Because of the higher energy of the incident beam, the centre-of-mass system is boosted relative to the laboratory system. Taking this boost into account results in enhanced hermeticity of the detector providing a nearly full solid angle

– 3 – coverage. This NA64 report to the SPSC focuses mostly on the status of the analysis of data accumulated during the runs in 2016 and 2017. The results from these sets of measurements were taken into account also for the detector preparation for the run 2018 which is currently underway as planned. The detector has been completely commissioned. For the success of NA64 the precise identification of the initial state, i.e. the knowledge of the incoming particle ID and its momentum is crucial. The important milestone in development of such tagging system in 2017 was the production and run- ning of the improved Synchrotron Radiation Detector(SRD) consisting of three fully functioning modules. Another important step was the deployment of the completely commissioned Micromegas and GEM chamber tracker. In 2017 data taking was per- formed at high intensities. The results from the run data analysis are as expected confirming that the NA64 is be able to run at high intensities up to ' 5 − 8 × 106 e− / spill. We should underline that at this stage of the experiment in order to probe the previously discussed (, mA0 ) parameter space it will be necessary to accumulate 12 & 5 × 10 EOT with good data quality and efficiency. This requires taking data at the ultimate sustainable rate of ' 107 e− / spill. The document is organized as follows. Sec.2 provides an overview of the NA64 method of search, the summary of the data collected in 2016-17, and the detector performance. Sec.3 presents the status of the A0 → invisible decay analysis. In Sec.4 the first results on the search for the X → e+e− decay of a new 17 MeV X- boson, which could explain the 8Be anomaly, as well as on the A0 → e+e− decays of dark photons are reported. In Sec.5 the continuation of the ongoing program is described. It includes plans for 2018 and beyond the LS2. Detector upgrade and request for its permanent location at the H4 line are presented in Sec.6, while conclusion and finally the status of the NA64 publications are presented in Sect.7,8 respectively.

2 NA64 status from the 2017 run

The NA64 experiment first ran five weeks with the H4 electron beam from August 30 to October 2 2017. Previously, following a brief period of commissioning and repairs, the experiment began to collect physics quality data during four weeks in the October 2016 run. In the following sections, we briefly summarize the performance of the detector during the 2017 run, and give the current status of data analysis for NA64.

2.1 The detector and ongoing activities The experiment uses the optimized CERN SPS H4 e− beam, which is produced in the target T2 of the CERN SPS and transported to the detector in an evacuated beam-line tuned to a freely ajustable beam momentum from 10 up to 300 GeV/c. In 2017 the maximal obtained beam intensity at ' 100 GeV, was of the order of

– 4 – TOP VIEW GOLIATH

μM1-2 S0 SRD S GEM ECAL HCAL0-3 MBPL1 MBPL2 1 1-2

θ= 20mrad

S St V μM 2 VETO 1-2 0 3-4 0.8 m Vacuum pipe DESY Goliath table table St3-4 1,5 m 6 m 10.2 m 2,7 m 1.1m 6,6 m

SIDE VIEW GOLIATH μM V S SRD 1-2 0 0 GEM S 1-2 ECAL HCAL0-3 MBPL1 MBPL2 1 VETO

Vacuum pipe

m m

c

c

Goliath DESY

7

7 Concrete 2 St 2

1-2 table Table 1-2 table 1 1 blocks table0

Figure 1. Schematic illustration of the setup to search for A0 → invisible decays of the bremsstrahlung A0s produced in the reaction eZ → eZA0 of 100 GeV e− incident on the active ECAL target.

2 × 107 e− for one typical SPS spill with about 70 Units of protons on target. Note, that a typical SPS cycle for Fixed Target (FT) operation lasts 14.8 s, including 4.8 s spill duration. The number of FT cycles is typically 2 per minute. The NA64 detector is schematically shown in Fig.1. The experiment employed the optimized 100 GeV electron beam from the H4 beam line. The beam has a maximal intensity ' 5 − 7 × 106 per SPS spill of 4.8 s produced by the primary 400 GeV proton beam with an intensity of a few 1012 protons on target. The detector utilized the beam defining scintillator (Sc) counters S1-S3 and veto V1, and magnetic spectrometer consisting of two successive dipole magnets 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 (T1, T2) and two downstream sets of (MM+GEM) stations (T3, T4) allowing the measurements of the e− momentum with the precision δp/p ' 1% [8,9]. The magnets also served as an effective filter rejecting low energy component of the beam. To enhance the electron identification the synchrotron radiation (SR) emitted by electrons was used for their efficient tagging. A 15 m long vacuum vessel between the magnets and the ECAL was installed to minimize absorption of the SR photons detected immediately at the downstream end of the

– 5 – vessel with a SR detector (SRD), which was either an array of B4Ge3O12(BGO) crystals or a PbSc sandwich calorimeter of a very fine segmentation [10]. By using − −2 the SRD the initial level of the hadron contamination in the beam π/e . 10 was further suppressed by a factor ' 103. The detector was also equipped with an active target, which is an electromagnetic calorimeter (ECAL) for measurement of the √ electron energy deposition EECALwith the accuracy δEECAL/EECAL ' 0.1/ EECAL. The ECAL was a matrix of 6 × 6 Shashlik-type modules assembled from Pb and Sc plates with wave length shifting fiber read-out. Each module was ' 40 radiation lengths. Downstream the ECAL the detector was equipped with a high-efficiency veto counter VETO, and a massive, hermetic hadronic calorimeter (HCAL) of ' 30 nuclear interaction lengths. The HCAL served as an efficient veto to detect muons or hadronic secondaries produced in the e−A interactions in the target. The HCAL √ energy resolution was δEHCAL/EHCAL ' 0.6/ EHCAL. Four muon plane counters, MU1-MU4, located between the HCAL modules were used for the muon identification in the final state. The HCAL is used to enhance the longitudinal setup hermeticity for the sensitive search for the invisible decay A0 → χχ¯ into the lighter dark matter particles. The Hadron Calorimeter (HCAL) is intended to detect charged and neutral hadrons and to provide a measurement of the energy leak from the ECAL complementary to that derived from momentum measurements in the tracker chambers and the ECAL it- self. Knowledge of neutral hadrons energy is important when constructing kinematic variable such as missing energy, as Veto cannot reject events with a neutral hadronic final stat. HCAL calorimetric measurements of charged particles can be also used both as a consistency check on the momentum measurement of the incoming charged particles and as an aid in distinguishing between muons and charged hadrons. The HCAL consists of 4 modules, each of 9 cells arranged in a matrix 3x3. Each cell consists of 48 iron/scintillator layers with 25 mm and 4 mm thickness, respec- tively. The iron plates are spot-welded together providing appropriate mechanical rigidity. Each module has transverse dimension of 60 × 60 cm2, weight 3500 kg and corresponds to about 7 λint (nuclear interaction lengths). In 2017 the last HCAL module installed downstream was used as a Zero-degree calorimeter to detect high- energy (undeflected) neutrals such as bremsstrahlung photons or neutrons, and thus help to reject background of electrons from the low energy tail of the primary beam. The HCAL modules have been calibrated individually by putting each on a mov- able platform with a subsequent irradiation of the HCAL cells with 100 GeV electron and 80 GeV pion beams. The dependence of obtained energy resolution on beam energy in the energy range 10 - 100 GeV is given by σE = 0√.57 + 0.037. The peak of E E the minimum-ionizing distribution, which has the expected Landau shape is at '2.5 GeV in agreement with MC prediction and calibration measurements. For events from hadron electro-production or when hadrons begin to shower in the approxi- mately 1.2 λint of ECAL upstream of the hadron calorimeter, the total hadronic

– 6 – energy deposited in the ECAL+HCAL system is taken to be a weighted sum of the energies deposited separately in the hadron and electromagnetic calorimeters. The new straw-tube tracker, shown in Fig.2, is manufactured with 6 mm in diameter straw tubes covered by Cu layer. Each of coordinate plane consist of two layers of straw shifted each other to the size of the radius. Two mother board for different layers. New 6 Amplifier AST-1-1 (32channels) for each coordinate which has to operate with 3 TDC units, are located directly on the each chamber stand. Cables are 17 twisted pairs, each of 60 cm in length. Since the test run 2016, the reconstruction of events in the straw tube tracker has been significantly improved. The Straw tubes will be equipped with preamplifier-discriminator cards devel- oped for CBM experiment and based on OKA-1 ASIC. A new TDC card for NA64 experiment based on an FPGA has been developed. The first prototype was success- fully tested, and the all NA64 TDC are currently produced and delivered at CERN.

Figure 2. Photograph of the new Straw-tube tracker

2.2 Data sample from 2016-2017 runs The events were collected with the hardware trigger of (3.2) (see below) requiring an in-time cluster in the ECAL with the energy EECAL . 80 GeV. The results reported 10 here came mostly from a set of data in which nEOT = 4.3 × 10 of electrons on target (EOT) were collected with the beam intensity ranging from ' 1.5 × 106 to 6 − 10 ' 5 × 10 e per spill. A similar sample of nEOT = 5.2 × 10 EOT at the intensity

– 7 – 6 − Ie = (5 − 8) × 10 e was also recorded in 2017. Data of these two runs were analyzed with similar selection criteria and finally summed up, taking into account the corresponding normalization factors. The combined analysis is still in progress.

3 Search for the A0 → invisible decay

The method of the search is as follows [6,7]. If the A0 exists it could be produced via the kinetic mixing with bremsstrahlung photons in the reaction of high-energy electrons scattering off nuclei of an active target of a hermetic detector, followed by the prompt A0 → invisible decay into dark matter particles (χ):

e−Z → e−ZA0; A0 → invisible (3.1)

A fraction f of the primary beam energy EA0 = fE0 is carried away by χ’s which penetrate the detector without interactions resulting in an event with zero-energy deposition. While the remaining part Ee = (1 − f)E0 is deposited in the target by the scattered electron. Thus, the occurrence of A0 produced in the reaction (4.1) would appear as an excess of events whose signature is a single electromagnetic (e- m) shower in the target with energy Ee accompanied by a significant missing energy Emiss = EA0 = E0 − Ee above those expected from backgrounds. Here we assume that the χs have to traverse the detector without decaying visibly in order to give a missing energy signature. No other assumptions on the nature of the A0 → invisible decay are made. The occurrence of A0 produced in the reaction (3.1) would appear as an excess of events whose signature is a single electromagnetic (e-m) shower in the target with energy Ee accompanied by a significant missing energy Emiss = EA0 = E0 −Ee above those expected from backgrounds. Here we assume that the χs have to traverse the detector without decaying visibly in order to give a missing energy signature. No other assumptions on the nature of the A0 → invisible decay are made. The signal candidate events have the signature:

SA0 = ΠSi × PS × ECAL × Veto × HCAL, (3.2) and should satisfy the following selection criteria:

• The starting point of the shower should be localized within few first X0 in PS.

• The fraction of the total energy deposition in the ECAL is f . 0.8. The lateral and longitudinal shapes of both showers in ECAL are consistent with an electromagnetic one.

• No energy deposition in the Veto.

• No activity in the HCAL.

– 8 – 3.1 Exact tree-level cross section calculations and signal simulation. Throughout this experiment, we have relied on two codes: NA64 [11] for simulation of dark photon production and decays, and GEANT4 [12] for propagation of produced secondaries and decay particles through the detector. In this report, we base our comparison with data on these two codes, and we also anticipate that comparison of dimuon results will follow in the near future. In order to determine the acceptance of the experiment we perform the signal Monte Carlo simulation as described in details in Ref.[11]. We simulate the electro- magnetic shower development in the ECAL with GEANT4 using the following steps (i) calculate the total and differential cross-sections of the A0 bremsstrahlung pro-

duction as a function of the electron energy E0,

(ii) at each step of an electron propagation in the lead converters of the ECAL, the emission of the A0 is randomly generated,

(iii) if the emission is accepted, then we generate values of x, cos θ, and the azimuthal

angle φA0 ,

(iv) finally, the 4-momentum of the recoil electron is calculated. At the final simulation stage, the cross section is multiplied by an additional factor so that about 0.1 A0 per one event is produced. This factor is later used for the final normalization. It has been recently pointed out, that for a certain kinematic region of the pa- 0 rameters mA0 ,EA0 , the A yield derived in the Weizs¨acker-Williams (WW) calculation framework could differ significantly from the one obtained with the exact tree-level (ETL) calculations [13, 14]. Therefore, it is instructive to perform an accurate cal- culation of the A0 cross-section based on precise phase space integration over the final state particles in the reaction e−Z → e−ZA0. A reliable theoretical prediction for the A0 yield is essential for the proper interpretation of the experimental results in order to obtain robust exclusion limits in the A0 parameter space or the possible observation of the A0 signal. In order to derive more accurately the A0 yield, we have used the A0 production cross sections of (3.1) obtained without the WW approximation, but with ETL cal- culations of Ref. [15]. These cross sections were cross checked with those calculated by Liu et al. [13, 14] and were found to be in agreement. The comparison showed that the difference between the two calculations in the wide A0 mass range does not exceed ' 10% (see Fig. 1 in Ref.[15]), which will be further used as a systematic uncertainty in the calculation of the A0 yield. This difference is, presumably, due to the different accuracy of computation programs used for integration over the phase space and, possibly due to the different parameterisation of the form factors used as an input for the cross section calculations.

– 9 – In order to implement the ETL cross-section formula into Geant4 [17] based NA64 simulation package, we introduce a correction k-factor defined by the following ratio A0 σWW 0 k(mA ,E0,Z,A) = A0 . (3.3) σEXACT A0 Here, the cross-section σEXACT takes into account the phase space integration over the final states of the particles and represents the overall uncertainties in the cross- section (3.1) calculated in simplified WW approach. The A0 yield was calculated with the replacement A0 −1 A0 σWW → k(mA0 ,E0,Z,A) σWW (3.4) We refer to this method as k-factor approach throughout the paper. For heavy target nuclei k depends rather weakly on Z and A, i.e. for tungsten and lead the deviation is about 0.5%. In Fig.3 (left panel) , k values are shown as a function of the electron beam energy E0 for various mA0 . One can see that for mA0 = 100 MeV and E0 = 100 GeV, the ETL cross sections of the A0 production are smaller by a factor 1.7 than the corresponding WW cross-sections. On the other hand, σEXACT exceeds σWW for the masses mA0 below 5 MeV, so that one can slightly improve the limits on the mixing strength for this mass region. An example of differential A0 spectra from the electron beam interactions in the thin,  X0, Pb target (here X0 is the radiation length) calculated for the mass mA0 = 100 MeV as a function of x = EA0 /Ee for different electron energies is shown in Fig.3.

mA'=1 MeV = 2.5 mA' 5 MeV mA'=10 MeV mA'=20 MeV mA'=50 MeV = 2.0 mA' 100 MeV EXACT Σ  1.5 WW

Σ 1.0

20 40 60 80 100

E0HGeVL

Figure 3. Left panel: The k-factor for the A0 production in the reaction e−Z → e−ZA0 0 as a function of the electron energy E0 for different values of the A masses. Right panel: 0 The differential A spectra from the electron beam interactions in the thin ( X0) Pb target calculated for the mass mA0 = 100 MeV as a function of x = EA0 /Ee. The spectra are computed for different electron energies as indicated in the legend. The spectra are normalized to the same number of EOT.

– 10 – Exact x20: M =100 MeV 0.9 A' IWW x20: MA'=100 MeV

0.8 Exact: MA'=10 MeV IWW: M =10 MeV 0.7 A' 0.6 0.5 0.4 0.3 Signal counts/1GeV 0.2 0.1 0 50 60 70 80 90 100 EA' [GeV]

Figure 4. The A0 emission spectra from the 100 GeV electron beam interactions in the thick Pb target (t  X0, see Sec.III)) calculated for the masses mA0 = 10 and 100 MeV without and with the improved WW (IWW) approximation. The spectra are normalized to the same number of EOT.

Once the A0 flux was defined, the next step was to simulate the A0 emission spectrum from the target. The decay electrons and positrons were tracked through the dump medium including bremsstrahlung photons, their conversion and multiple scattering in the target. The A0 reconstruction efficiency in the target was computed and convoluted with the target details and detector geometrical acceptance based on the NA64 Monte Carlo (MC) simulation package used in our previous search [103]. The comparison of the energy distributions of A0s emitted from the thick target (t  X0) with the energy EA0 & 0.5E0 calculated for masses mA0 = 10 and 100 MeV with and without WW approximation for the 100 GeV beam energy is shown in Fig.4. The spectra have the similar shape and differ mostly in the overall nomalization factor. Note that these distributions represent also the spectra of the missing energy in the detector.

3.2 Data analysis and selection criteria The search for the A0 → invisible decay described in this paper uses the full data sample collected during July and October runs in 2016 corresponding to nEOT = 4.3 × 1010 EOT. The results reported here are obtained using three sets of data in 10 10 10 which nEOT = 2.3 × 10 , 1.1 × 10 and 0.9 × 10 EOT were collected with the beam intensities ' (1.4 − 2) × 106, ' (3 − 3.5) × 106 and ' (4.5 − 5) × 106 e− per spill, respectively. Data of these three runs (hereafter called respectively the run I,II, and III) were processed with selection criteria similar to the one used in our

– 11 – previous analysis [103] and finally combined as described in Sec. 3.4. Compared to Ref.[103], a number of improvements in the event reconstruction, e.g., adding the pileup algorithm, were made in order to increase the reconstruction efficiency. The strategy of the analysis was to identify A0 → invisible candidates by precise reconstruction of the initial e− state and an isolated low energy e-m shower in the

ECAL that are accompanied by no other activity in the V2 and HCAL detectors. The measured rate of such events was then supposed to be compared to that ex- pected from known sources. The spectra of A0s produced in the ECAL target by primary electrons were calculated using the approach reported in Ref.[11]. A de- tailed Geant4 based MC simulation was used to study the detector performance and acceptance losses, to simulate background sources, and to select cuts and estimate the reconstruction efficiency. The candidate events were pre-selected with the criteria chosen to maximize the acceptance for simulated signal events and to minimize the numbers of events ex- pected from background sources discussed in Sec.3.3. The following selection criteria were applied:

• There must be one and only one incoming particle track having a small angle with respect to the beam axis. This cut rejects low momentum electrons as they were typically correlated with a large-angle incoming tracks originating presumably from the upstream e− interactions. The reconstructed momentum

of the particle was required to be Pe = 100 ± 2 GeV.

• The track should be identified as an electron with the SRD detector. The energy deposited in each of the three SRD modules should be within the SR range emitted by e−s and in time with the trigger. This was the key cut identifying the pure initial e− state, with the pion suppression factor < 10−5 and electron efficiency > 95% [10].

• The lateral and longitudinal shower shape in the ECAL should be consistent with the one expected for the signal shower [11, 18]. It is also used to distinguish hadrons from electrons providing an additional hadron rejection factor of ' 10 [19].

• There should be no activity in the veto counter VETO.

In total ' 7 × 104 events passed these criteria from the combined 2016 data sample. The final selection is a cut-based and uses the cuts on the ECAL missing energy Emiss = Ebeam − EECAL and on the energy deposition in the HCAL. In order to avoid biases in the choice of selection criteria for A0 events, a blind analysis was performed, with a preliminary definition of the signal box as Emiss > 50 GeV th and EHCAL < 1 GeV. The HCAL zero-energy threshold EHCAL = 1 GeV in (3.2) was determined mostly by the noise of the read-out electronics. Events from the

– 12 – 120 120 120 10

105 100 100 100 103 104 80 III 80 80

3 B 10 2

, GeV , GeV 10 , GeV 60 II 60 60 HCAL HCAL HCAL E E E 102 A 40 40 40 10

20 10 20 20 I C 0 1 0 1 0 1 0 20 40 60 80 100 0 20 40 60 80 100 0 20 40 60 80 100

EECAL, GeV EECAL, GeV EECAL, GeV

120 120 120 10 105 100 100 100 103 4 III 10 80 80 80

3 B 10 2 , GeV 60 , GeV 60 10 , GeV 60 HCAL HCAL HCAL

E II E E 102 A 40 40 40 10

20 10 20 20 I C 0 1 0 1 0 1 0 20 40 60 80 100 0 20 40 60 80 100 0 20 40 60 80 100

EECAL, GeV EECAL, GeV EECAL, GeV

Figure 5. Event distribution in the (EECAL;EHCAL) plane from the runs II(top row) and III (bottom row) data. The left panels show the measured distribution of events at the earlier phase of the analysis. Plots in the middle show the same distribution after applying all selection criteria, but the cut against upstream interactions. The right plots present the final event distributions after all cuts applied. The dashed area is the signal box region which is open. The side bands A and C are the one used for the background estimate inside the signal box. For illustration purposes the size of the signal box along EHCAL-axis is increased by a factor five. preliminary signal box were excluded from the analysis of the data until the validity of the background estimate in this region was established. The cut on Emiss was optimized as described in Sec.3.4. In Fig.5 the left panels show an example of the distributions of events from − the reaction e Z → anything in the (EECAL; EHCAL) plane measured in the runs II(top) and III(bottom) with moderate selection criteria requiring only the presence of the SRD tag identifying the beam electrons. Here, EHCAL is the sum of the energy deposited in the HCAL1 and HCAL2. The distributions of events from the run I with low intensity are similar to the one shown in Ref.[103]. Events from the areas I in Fig.5 originate from the QED dimuon production, dominated by the the muon pair photoproduction by a hard bremsstrahlung photon conversion on a target nucleus:

e−Z → e−Zγ; γ → µ+µ−. (3.5) with some contribution from γγ → µ+µ− fusion process. The µ+µ− pairs were characterised by the HCAL energy deposition of ' 10 GeV. This rare process whose

– 13 – −5 fraction of events with EECAL . 60 GeV was . 10 /EOT served as a benchmark allowing to verify the detector performance and as a reference for the background prediction. The regions II shows the events from the SM hadron electroproduction in the ECAL which satisfy the energy conservation EECAL + EHCAL ' 100 GeV within the detector energy resolution. The leak of these events to the signal region mainly due to the HCAL energy resolution was found to be negligible. The fraction of events from the region III was due to pileup of e− and beam hadrons. It was beam rate dependent with a typical value from about a few % up to ' 20%. An example of the summary of corrected efficiencies used for calculations of the limits for the run III data sample obtained with a beam intensity ' 5 × 106 e−/spill is presented in Table1. These efficiencies were slightly different for the data samples from runs I and II, mostly because of the different pileup algorithm efficiencies which were rate dependent and also determined from measurements in calibration runs at different beam rates. The quantities e, ECAL were the most rate-dependent detec- tion efficiencies of the tracker chambers and SRD, and ECAL cluster reconstruction, respectively. The DAQ deadtime was a function of the beam rate and was 7.4% averaged over the full data-taking period.

item Efficiency sample − primary e , e 0.58 Data, Dimuons ECAL, ECAL 0.93(0.90) Data, Dimuons V2, V 0.94 Data, MC HCAL, HCAL 0.98 Data, MC Total 0.50(0.48)

Table 1. Summary of efficiencies for the signal event selection for the mass mA0 = 10(100) MeV in the data sample obtained for the high intensity run III.

The total number of collected EOT in 2016 was obtained from the recorded number of events from the e-m e−Z interactions in the ECAL target by taking 2 into account the trigger suppression factor (& 10 ) and DAQ dead time which was beam rate dependent. The e− beam loss due to interactions with the beam line materials was estimated to be small. The trigger and SRD efficiency obtained by using unbiased samples of events that bypass the selection criteria was found to be ' 0.95 and ' 0.97 with a small uncertainty 2%. The probability of A0 events to pass all selection criteria, A0 was evaluated by processing the simulated signal events through the same reconstruction program as data, with the same cuts. The A0 yield calculated in accordance with Ref.[11, 15] was corrected for the production cross section. The overall signal efficiency was in the range tot ' (0.7 − 0.5) decreasing for the higher intensity run.

– 14 – The systematic uncertainties are determined to stem from the overall normal- ization, signal cross section computations, reweighting the EAL signal energy dis- tribution, description of the dimuon spectrum, and the uncertainty in the signal efficiencies in the Veto and HCAL. Systematic uncertainties are determined by vary- ing cuts and taking the largest change in the calculated rate as the systematic error. Details of the systematic checks are given below. The 10% additional uncertainty, estimated from the comparison of the cross sections calculated in [14] and [15] was taken into account as the systematic error for the A0 production in the target. Note, that possible contributions from the purity of 207 the target (& 99.9%) and ' 22% admixture of spin1/2 isotope Pb are estimated to be small. Another contributions are due to the events selection in the ECAL and the reweighting procedure of the ECAL signal spectrum. The former was estimated as a difference in the signal yield with respect to the nominal value due to the PS energy threshold variation during the run. This contribution increases for large A0 masses. The systematic uncertainty from the reweighting procedure was estimated by varying the parameters of the empirical fitting functions and considering differences in the number of obtained signal events. In this case the quoted systematic uncertainty is taken to be the quadratic sum of the observed shift and the statistical error of 4% on the shift. The reweighting correction is slightly A0 mass dependent and has the total uncertainty 7% for the highest intensity run III. Other contributions to the systematic uncertainty on the A0 signal efficiency come from the choice of the cut threshold and definition of the signal efficiency for the V2 and HCAL. The uncertainties of the corrections for the V2 and HCAL signal efficiency were studied by varying the corresponding energy threshold within the range determined from the data. The calculated variations were assigning to the systematic errors, which were estimated to be 3% and 2% for the V2 and HCAL, respectively. An example of sources and the corresponding magnitudes of the systematic errors for the A0 masses 10 and 100 MeV, estimated for the run III is shown in Table2.

3.3 Background The search for the A0 → invisible decays requires particular attention to back- grounds, because every process with a single track and an e-m cluster in the ECAL can potentially fake the signal. In this Section we consider all background sources, which were also partly studied in Refs. [6, 20]. There are several backgrounds resulting in the signature of Eq.(3.2) which can be classified as being due to detector-, physical- and beam-related sources. The selection cuts to reject these backgrounds have been chosen such that they do not affect the shape of the true Emiss spectrum. The estimation of background levels and the calculation of signal acceptance were both based on the MC simulation, as well as direct measurement with the beam. Because of the small A0 coupling strength value, performing a complete detector

– 15 – Table 2. Summary of systematic uncertainties for the mass mA0 = 10(100) MeV in the high intensity run III. Source of the error Estimated error

Normalization

number of collected EOT, nEOT 2 %

A0 Yield signal cross section 10%

A0 efficiency primary e− selection 4 % ECAL selection 2% (3.5%) ECAL spectrum reweighting 7 % (5%)

V2 cut threshold 3 % HCAL cut threshold 2 % Total 9 %(8%)

simulation in order to investigate these backgrounds down to the level of a single −11 event sensitivity . 10 would require a very large amount of computing time. Consequently, we have estimated with MC simulations all known backgrounds to the extent that it is possible. Events from particle interactions or decays in the beam line, pileup activity created from them, hadron punchthrough from the target and the HCAL were included in the simulation of background events. Small event- number backgrounds such as the decays of the beam µ, π, K or µs from the reaction of dimuon production were simulated with the full statistics of the data. Large event- number processes, e.g. from e− interactions in the target or beam line, punchthrough of secondary hadrons were also studied, although simulated samples with statistics comparable to the data were not feasible. To eliminate possible instrumental effects not present in the MC calculations, the uniformity scan of the central part of the ECAL target was performed with e− by using the MM3 and MM4. We also examined the number of events observed in several regions around the signal box, which were statistically consistent with the estimates. The main detector background sources are related to

• Instrumental effects. The leak of energy throughout the possible holes, cracks, etc. in the downstream coverage of the detector which allows secondary parti- cles to pass through without interactions. To study this effect a X − Y scan over the transverse area of the ECAL and HCAL detector has been performed

– 16 – with a particular attention to the boundaries between cells, fibers positions, and dead materials. No significant leak of energy has been observed.

• Detector hermeticity. The fake signature of Eq.(3.2) could also arise when either: i) a high-energy bremsstrahlung photon from the reaction eZ → eZγ, or ii) leading hadron h from the reaction eZ → eZX + h in the target escape detection due to punchthrough in the HCAL. The reaction i) may occur if an energetic photon induces a photo-nuclear reaction accompanied by the emission of a leading neutral particle(s), such as e.g. a neutron. The neutron then could be undetected in the rest of the detector. Taking into account the estimated non-hermeticity of the detector, the probability of the reaction is found to be −14 . 10 . For the charged secondaries the punchthrough is highly suppressed by the observation of energy deposition in the HCAL modules. As the number of photoelectrons per MIP crossing the HCAL module was measured to be in

the range nph.e. ' 150−200/ MIP the inefficiency of the punchtrough detection −10 is . 10 making the overall background negligible. For the case ii) the punchthrough probability of a leading neutral hadron, 0 such as a neutron and/or KL, is defined by exp(−Ltot/λint), where Ltot is the (ECAL+HCAL) length sum. It has been estimated separately with a pion beam and compared with simulations [20] . It has been found that the overall hadron punchthrough probability is below 10−12 for the total thickness of the

ECAL and HCAL of about 30 λint. This value should be multiplied by a −4 factor . 10 , which is the probability of a leading hadron electroproduction in the ECAL target. Taking this into account the final estimate results to the negligible level of this background per incoming electron. The HCAL non- hermeticity for high energy neutral hadrons was cross-checked with Geant4- th based MC simulations [11]. For the energy threshold EHCAL ' 1 GeV the −9 non-hermeticity is expected to be at the level . 10 . Taking into account the probability to produce a single leading hadron per incoming electron as −4 −13 Ph . 10 , an overall level of this background of . 10 is obtained. This is in agreement with the above rough estimate.

• Large transverse fluctuations. Another possible source of background was caused by the large transverse fluctuations of hadronic showers from the re- action eZ → eZ+ ≥ 2 neutrals induced by electrons in the ECAL. In such 0 events all secondary long-lived neutral particles (such as neutrons and/or KL’s) could be produced in the target at a large angle, the HCAL and escape the detector without depositing energy through the lateral surface, thus resulting in the fake signal event. Taking into account results from the previous study −14 [11, 21, 22], a conservative estimate for this background gives the level . 10 per incoming electron.

– 17 – Figure 6. Energy distribution of events in the side band C collected in the run II with intensity ' 3.5 × 106 e−/spill and obtained with pileup algorithm. The curve shows single exponential fit to the data, while the dashed one represents extrapolation to the signal region which predicts nb = 0.041 ± 0.02 background events.

The beam backgrounds can be subdivided into two categories: upstream inter- actions and particle decays.

• Upstream interactions. The main background sources is caused by the upstream beam interactions with beamline materials, such e.g. as entrance windows of the beam lines, residual gas, S1, MM1,2 etc., resulting in an admixture of low energy electrons with a large incoming angle in the beam. Those may fake a missing energy signal as they still could be within acceptance of the the spectrometer, while some or all of the accompanying produced secondaries fall outside the acceptance of the downstream ECAL and HCAL calorimeters. The limited detection acceptance of the secondaries along the downstream beam axis enhances this background. In 2017 run a zero-angle detector, as well as the lead-glass counters were installed to improve the downstream coverage and detection efficiency. The fraction of upstream scattered events is estimated to −5 be at the level . 10 per EOT. An uncertainty arises also from the lack of accurate knowledge of the dead material composition in the beam line and is potentially the largest source of systematic uncertainty for accurate calculations of the fraction and energy distribution of these events. As it is not clear whether such rare large angle scattering could be reproduced with MC simulations the amount of background events from the beam upstream interactions was mainly estimated from the data itself.

In addition to the SRD cut which helps to reject low energy electrons and V2 cut,

– 18 – which rejects most of the charged secondaries up to 35 cm away from the de- flected beam axis, two additional cuts were used to study possible contribution from this source. The first one eliminated charged secondaries with multiple hits in the upstream tracker chambers more than expected from a single track event. The second one, used information on lateral reconstructed energy and time spread in the HCAL cells from charged and neutral secondaries. It was used to reject mostly events accompanied by low energy neutrals and charged secondaries with typically more activity in the HCAL than expected from in- teraction in the ECAL target. In Fig.5 the comparison of events distribution before (central panels) and after using the HCAL cut (right panels) is shown. One can clearly see that the amount of background events in the vicinity of the masked signal region is substantially reduced. Finally the background level in the signal box was estimated from the extrapo- lation of the number of data events observed in dedicated control regions to the signal region using the fitting procedure described below. Namely, we looked at the ECAL energy distribution in the control region EECAL > 50; EHCAL < 1 GeV for the runs I-III and estimated the contamination level in the signal box by fitting the EECAL distribution with the function f(EECAL) = exp[p1 + p2 · EECAL(GeV )], where p1 is a constant, and p2 is the slope. In order to validate the exponential shape of the extrapolation function from control to signal region, dedicated validation region 1 < EECAL < 80 GeV, EHCAL > 10 GeV containing a bigger data sample of events from hadronic interactions of the beam electrons with nuclei of the ECAL target was defined, see right pan- els in Fig.5. The exponential shape of the distribution of energy deposited by the scattered electrons in the ECAL observed in the validation region was cross checked with MC simulations, see Fig. 5 in Ref. [11], and found to be in agreement for the full energy range. Therefore, the amount of background in the signal region was estimated from the extrapolation procedure assuming that the energy distribution of beam electrons scattered in hadronic reactions the upstream part of the beamline has exponential shape similar to the one observed in hadronic interactions of beam electrons in the ECAL target. Note that background of electrons from the upstream QED bremsstrahlung scatter- ing is strongly suppressed as they typically follow the beam direction after the scattering, and fall outside of the detector acceptance after being deflected in the magnets. The yield of the background events was estimated by extrapolating the fit functions from the side band C to the signal box, see Fig.5, assessing the systematic uncertainties by varying the background fit functions within the corresponding errors. An example of the fit extrapolation for the side C of the ECAL energy distribution is shown in Fig.6 for the run II. The slopes

– 19 – in the exponential fitting of the EECAL distributions for the runs I-III were 0.315±0.0021, 0.396±0.0072, 0.49±0.0026 in unit of 1/(GeV/c), and the num-

ber of nb events in the signal region were expected to be 0.043 ± 0.017, 0.041 ± 0.02, 0.01 ± 0.003, respectively. Possible variation of the HCAL zero-energy threshold during data taking were also taken into account. The fit was also performed for both sideband A shown in the right panel of Fig.5. Events in

the region A (EECAL < 50 GeV ; EHCAL > 1 GeV ) are pure neutral hadronic secondaries produced by electrons in the ECAL target, while events from the − region C (EECAL & 50 GeV ; EHCAL < 1 GeV ) are likely from the e interac- tions in the upstream part of the beam line. As a result, . 0.001 events in total are expected in the signal box from the side band A for all runs, and was further neglected.

Table 3. Summary of estimated numbers of background events inside the signal box for 4.3 × 1010 EOT.

Background source Estimated number of events, nb hermeticity: punchthrough γ’s, cracks, holes < 0.001 loss of hadrons from e−Z → e− + hadrons < 0.001 loss of muons from e−Z → e−Zγ; γ → µ+µ− 0.005 ± 0.001

µ → eνν, π, K → eν, Ke3 decays 0.02 ± 0.004 e− interactions in the beam line materials 0.09 ± 0.03 µ, π, K interactions in the target 0.008 ± 0.002 accidental SR tag and e− from µ, π, K decays < 0.001

Total nb 0.12 ± 0.04

Finally, the contamination of backgrounds to the signal region due to beam interactions was estimated to be 0.09 ± 0.03 events. The uncertainty in the background estimate due to upstream scattered events was dominated by the systematic uncertainty of the upstream veto V1 and tracker efficiency, precise knowledge of the material in the beam line, and statistics of the data samples. This systematic uncertainty was estimated by performing measurements on several samples of upstream scattered events tagged by a signature of scattering in the HCAL. The uncertainties in this background estimate are evaluated by considering differences in the estimates of the event number by varying the electron identification probabilities and changing the parameters of the extrapolation functions.

• Particle decays. Other backgrounds were expected from the decays of µ, π, K → e + .... in flight in the beamline accompanied by emission of an energetic neu- trino. These backgrounds were highly suppressed by requiring the presence of

– 20 – the SRD tag. However, there might be cases when, e.g. a pion could knock electrons off the downstream window of the vacuum vessel, which hit the SRD creating a fake tag for a 100 GeV e−. The pion could then decay into eν in the upstream ECAL region thus producing the fake signal.

The main background source in this category was Ke3 decays where the electron overlapped with photons from π0 decay thus producing a single-like e-m shower in the ECAL. In addition to the SRD cut and the probability of decay in the downstream part of the setup, this process was further suppressed by requiring shower energy to be < 50 GeV and the incoming track azimuthal angle to be below 5 mrad. The transverse and longitudinal shower shape at the ECAL was also used to distinguish the single electron shower from the overlapped one. Similar background was caused by a random superposition of uncorrelated low- energy, 50 - 70 GeV, electron from the low-energy beam tail and 100 GeV beam µ, π, K occurring during the detector gate-time. The electron could emit the amount of SR energy above the threshold which is detected in the SRD as a tag of 100 GeV e− and then is deflected by the spectrometer magnets out of the detector’s acceptance angle. While the accompanying mistakenly tagged µ, π or K could either decays in-flight in front of the ECAL into the e− + X state with the decay electron energy less then the beam energy, or could also interact in the target producing an e-m like cluster below 50 GeV though the µZ → µZγ or π, K charge-exchange reactions, accompanied by the poorly detected scattered µ, or secondary hadrons, thus resulting in both cases to the signal signature of Eq.(3.2). These background components were simulated with a statistics higher or comparable to the number of events expected from the data and was found to be small.

The remaining physical backgrounds were

• Dimuon, τ, charm decays. The process (3.5) could mimic the signal either i) due to muons decay in flight inside the ECAL target into eνν state, or ii) if

the muons escape detection in the V2 and HCAL modules due to fluctuations of the energy (number of photoelectrons) deposited in these detectors. In the case i) the relatively long muon lifetime results in a small probability to decay inside the ECAL. For the case ii) the background is suppressed by the high-

efficiency veto system V2+HCAL. The V2 was a ∼ 4 cm thick high-sensitivity scintillator array whose inefficiency for a single muon detection was estimated −4 to be . 10 . Therefore, the level of dimuon background is expected to be < 10−13 per EOT. The fake signal could also arise from the reactions of τ, e.g., + − eZ → eZτ τ ; τ → eνν, or charm, e.g., eZ → eZ + Ds + anything; DS → e + ν + anything, production and their subsequent prompt decays into an

– 21 – electron accompanied by emission of neutrinos. The estimate show that these backgrounds are also expected to be negligible.

• Finally, the electroproduction of a neutrino pair eZ → eZνν resulting in the invisible final state accompanied by energy deposition in the ECAL1 from the recoil electron can occur. An estimate showed that the ratio of the cross sections for this reaction to the bremsstrahlung cross section is well below 10−13 [6].

In Table3 the contributions from all background processes estimated by using the MC simulations, exept for those from beam interactions in the upstream part of the setup, are summarized. The final number of background events estimated 10 from the combined MC and data events is nb = 0.12 ± 0.04 events for 4.3 × 10 EOT. The estimated uncertainty of about 30% was due mostly to the uncertainty in background level from upstream beam interactions. It also includes the uncertainties in the amount of passive material for e− interactions, in the cross sections of the hadron charge-exchange reactions on lead (30%), and systematic errors related to the extrapolation procedure. The total systematic uncertainty was calculated by adding all errors in quadrature.

Figure 7. The sensitivity, defined as an average expected limit, as a function of the ECAL 0 energy cut for the case of the A detection with the mass mA0 ' 20 (blue) and 2 (green) MeV.

3.4 Results and calculation of limits In the final statistical analysis the three runs I-III were analysed simultaneously using the multi-bin limit setting technique. The corresponding code is based on the RooSt- ats package [23]. First of all, the above obtained background estimates, efficiencies, and their corrections and uncertainties were used to optimize more accurately the main cut defining the signal box by comparing sensitivities, defined as an average

– 22 – expected limit calculated using the profile likelihood method, with uncertainties used as nuisance parameters. Log-normal distribution was assumed for the nuisance pa- rameters [24]. The most important inputs for this optimization were the expected values from the background extrapolation into the signal box for the data samples of the runs I,II,III. The uncertainties for background prediction were estimated by varying the extrapolation functions, as previously discussed. An example of the op- timization curves obtained for the mA0 = 2 and 20 MeV is shown in Fig.7. It was found that the optimal cut value depends very weakly on the A0 mass choice and can be safely set to EECAL < 50 GeV for the whole mass range. Overall optimization and improvement of the signal selection and background rejection criteria resulted in roughly more than a factor 10 reduction of the expected backgrounds per EOT and an increase of a factor 2 in the efficiency of A0 → invisible decay at higher beam rate for the run III compared to those obtained in the analysis reported in Ref.[103]. For the full 2016 exposure, the estimate of the number of background events expected from the sources discussed above per 1010 EOT was nb = 0.03, while for the run of Ref.[103] it was nb = 0.5.

E787, E949 −2 10 BaBar 휇 favored 푎

휇 −3 푎 10

휖

푒 푎 NA64

−4 10

1 10 −5 10 −3 −2 −1 10 10 10 퐴′ 푚 , 퐺푒푉 Figure 8. The NA64 90% C.L. exclusion region in the (mA0 , ) plane. Constraints from the BaBar [25], E787 and E949 experiments [26, 27], as well as the muon αµ favored area gµ−2 are also shown. Here, αµ = 2 . For more limits obtained from indirect searches and planned measurements see e.g. Ref. [28].

After determining and optimizing all the selection criteria and estimating back- ground levels, we examined the events in the signal box and found no candidates, as shown in Fig.5. We proceeded then with the calculation of the upper limits on the A0 production. The combined 90% confidence level (C.L.) upper limits for the corresponding mixing strength  were determined from the 90% C.L. upper limit for 90% the expected number of signal events, NA0 by using the modified frequentist ap- proach for confidence levels (C.L.), taking the profile likelihood as a test statistic in

– 23 – mA0 , MeV 90% C.L. upper limit 90% C.L. upper limit on , 10−4 , no k-factors on , 10−4with k-factors 1.1 0.22 0.19 2 0.23 0.24 5 0.43 0.49 16.7 1.25 1.33 20 1.29 1.6 100 5.5 8.2 200 13.0 22.6 500 38.7 97.8 950 94.20 362.0

Table 4. Comparison of upper bounds on mixing  at 90 % CL obtained with WW and

ETL calculations for the Pb-Sc ECAL target for Emiss > 0.5E0 at E0 = 100 GeV. the asymptotic approximation [29–31]. The total number of expected signal events in the signal box was the sum of expected events from the three runs:

3 3 X i X i i i NA0 = NA0 = nEOT totnA0 (, mA0 , ∆Ee) (3.6) i=1 i=1

i i where tot is the signal efficiency in the run i, and the nA0 (, mA0 , ∆EA0 ) value is the signal yield per EOT generated by a single 100 GeV electron in the ECAL target in the energy range ∆Ee. Each i-th entry in this sum was calculated by simulating the signal events for 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 expected backgrounds and estimated systematic errors were also taking into account in the limits calculation. The combined 90% C.L. exclusion limits on the mixing strength as a function of the A0 mass can be seen in Fig.8. In Table4 the limits obtained with the ETL and WW calculations for different mA0 values are also shown for comparison. One can see that the corrections are mostly relevant in the higher mass region mA0 & 100 MeV. The derived bounds are the best for the mass range 0.001 . mA0 . 0.1 GeV obtained from direct searches of A0 → invisible decays [39].

3.5 Constraints on light thermal Dark Matter The possibility of the existence of light (sub-GeV) thermal Dark Matter (LTDM) has been the subject of intense theoretical activity over the past several years [28], see also [32, 33]. The LTDM models can be classified by the spins and masses of the DM particles and mediators. The scalar dark matter mediator models are severely restricted or even excluded by non-observation of rare B-meson decays [28, 39], so we

– 24 – Direct Direct −6 Detection −8 Detection MiniBooNE 10 Nucleon 10 Nucleon −7 BaBar MiniBooNE −9 10 BaBar

4 4

) −8 ) 10

퐴′ 퐴′ 10 NA64 −10

/푚 −9 /푚

휒 휒 10 10 E137 (푚 (푚 −11 E137

퐷 −10 퐷

훼 훼

2 2 10 Majorana Relic 10 Elastic & Inelastic Scalar Relic −11 NA64 LSND −12 Majorana Relic 푦 = 휖 10 Elastic & Inelastic Scalar Relic 푦 = 휖 10 −12 Pseudo-Dirac Fermion Relic 10 −13 LSND Pseudo-Dirac Fermion Relic −13 10

10 −14 −14 10 10 1 1 −15 −15 10 −3 −2 −1 10 −3 −2 −1 10 10 10 10 10 10 휒 휒 푚 , 퐺푒푉 푚 , 퐺푒푉 Figure 9. The NA64 limits in the (y;mχ) plane obtained for αD = 0.5 (left panel) and αD = 0.005 (right panel) from the full 2016 data set shown in comparison with limits obtained in Refs.[28, 41–43] from the results of the BaBar [25], LSND [40, 45], E137 [46], MiniBooNE [49] and direct detection [35]experiments. The favoured parameters to account for the observed relic DM density for the scalar, pseudo-Dirac and Majorana type of light thermal DM are shown as the lowest solid line. consider here only the case of a vector mediator. The most popular vector mediator model is the one with additional massive dark photon A0 which couples with DM 0 µ √ particle currents via interaction L = eDAµJχ , where coupling eD = 4παD. The µ ¯ µ µ + µ µ + currents Jχ = ψχγ ψχ and Jχ = i(φχ ∂ φχ −φχ∂ φχ ) for spin 1/2 and 0, respectively. Here, χ denotes both, either scalar or fermion LTDM particle. The γ−A0 mixing leads 0 to nonzero interaction of dark photon Aµ with the electrically charged SM particles with the charges e0 = e. As a result of the mixing the cross-section of DM particle annihilation into SM particles, which determines the relic DM density, is proportional to 2. Hence using constraints on the cross section of the DM annihilation freeze out (resulting in Eq.(3.7)), and obtained limits on mixing strength of Fig.8, one can derive constraints in the (y;mχ) plane, which can also be used to restrict models predicting existence of LTDM for the masses mχ . 1 GeV. These limits obtained from the full data sample of the 2016 run are shown in the left panel of Fig.9 together with the favoured parameters for scalar, pseudo-Dirac (with a small splitting) and Majorana scenario of LTDM taking into account the observed relic DM density [28]. The limits are calculated under the conventional assumption αD = 0.5, and mA0 = 3mχ, here mχ stands for the LTDM particle’s masses, either scalars or fermions. The plot shows also the comparison of our results with limits from other experiments. Note, that some of these limits were obtained by using WW approximation for the cross section calculation and therefore might require revision. The choice of αD = 0.5 is compatible with the bounds derived in Ref. [34] based on the running of the dark gauge coupling. However, it should be noted that differently form the results of beam dump experiments, such as LSND [40, 45], E137 2 4 [46], MiniBooNE [49], the χ-yield in our case scales as  , not as  αD. Therefore, for

– 25 – 10 4 10 4 1 TeV Landau Pole 1 TeV Landau Pole π π 1 1 0.5 0.5 Majorana Thermal DM Pseudo Dirac Thermal DM

퐷 퐷 LSND −1 −1 BaBar

훼 훼 10 10

NA64 −2 BaBar −2 MiniBooNE 퐸푀 퐸푀 10 NA64 훼 10 훼 E137

−3 LSND −3 10 10 1 1 −4 −4 10 −3 −2 −1 10 −3 −2 −1 10 10 10 10 10 10 휒 휒 푚 , 퐺푒푉 푚 , 퐺푒푉 Figure 10. The NA64 constraints in the (αD;mA0 ) plane on the pseudo-Dirac (the left panel) and Majorana ( right panel) type light thermal DM shown in comparison with bounds obtained in Ref. [28] from the results of the BaBar [25], LSND [40, 45], E137 [46], and MiniBooNE [49] experiments.

sufficiently small values of αD our limits will be much stronger. This is illustrated in the right panel of Fig.9, where the NA64 limits and bounds from other experiments are shown for αD = 0.005. One can see, that for this, or smaller, values of αD, the direct search for the A0 → invisible decay in NA64 excludes model of scalar and Majorana DM production via vector mediator for the remaining mass region mχ . 0.05 GeV. While being combined with the BaBar limit [25], the result excludes the model for the entire mass region mχ . 1 GeV. The experimental upper bounds on  also allow to obtain lower bounds on cou- pling constant αD which are shown in Fig. 10 in the (αD;mχ) plane. For the case of pseudo-Dirac fermions and small splitting, the limits in the left panel of Fig. 10 were calculated by taking the value f = 0.25 in Eq.(3.7).

−3 2 4 2 10   mA0  10 MeV  αD ' 0.02f (3.7)  100 MeV mχ 2 where αD = eD/4π, f . 10 for a scalar [40], and f . 1 for a fermion [41]. For the mass range mχ . 0.05 GeV the obtained bounds are more stringent than the limits obtained from the results of LSND [40, 45] and E137 [46]. The limits for the Majorana case shown in the right panel of Fig. 10 were calculated by setting f = 3. To cross check our calculations, we also derived limits on αD by using BaBar bounds on  [25], see Fig.8, Eq.(3.7) and the previous f values for the pseudo-Dirac and Majorana cases. The obtained BaBar limits were found to be in good agreement with those shown in Fig. 10 for the mass region mχ . 0.1 GeV. Note, that new constraints for the large pseudo-Dirac fermion splitting can also be derived. They will be more stringent than for the case of the small splitting and similar to the one obtained for the Majorana case.

– 26 – Figure 11. Left panel: Event distribution in the (EECAL;EHCAL) plane from the 2017 run data after all cuts applied. The dashed area is the signal box region which is open. The side bands A and C are the one used for the background estimate inside the signal box. For illustration purposes the size of the signal box along EHCAL-axis is increased by a factor five. Right panel: Energy distribution of events in the side band C collected in the run II with intensity ' 5 × 106 e−/spill and obtained with pileup algorithm. The curve shows single exponential fit to the data, while the dashed one represents extrapolation to the signal region which predicts nb = 0.07 ± 0.03 background events.

3.6 Preliminary results from the 2017 run The event selection and analysis of the data sample from the 2017 run was similar to the one described previously. The background level in the signal box 2017 was estimated from the extrapolation of the number of data events observed in dedicated control regions to the signal region using the fitting procedure described previously for the analysis of 2016 data sample. Namely, we looked at the ECAL energy distribution in the control region EECAL > 50; EHCAL < 1 GeV for the run 2017 and estimated the contamination level in the signal box by fitting the EECAL distribution with the function f(EECAL) = exp[p1 + p2 · EECAL(GeV )], where p1 is a constant, and p2 is the slope. The yield of the background events was estimated by extrapolating the fit functions from the side band C to the signal box, see Fig. 11, assessing the systematic uncertainties by varying the background fit functions within the corresponding errors. An example of the fit extrapolation for the side C of the ECAL energy distribution is shown in Fig. 11 for the 2017 run. The slope in the exponential fitting of the EECAL distributions for the run was 0.26 ± 0.0021 in unit of 1/(GeV/c), and the number of nb events in the signal region were expected to be 0.07 ± 0.03. Possible variation of the HCAL zero-energy threshold during data taking were also taken into account. The combined analysis of 2016 and 2017 data sample is still ongoing. We believe it will be worth to publish it only being combined with the data sample accumulated

– 27 – in 2018, as it will represent a sample of ' (2 − 3) × 1011 EOT, and thus, will be an essential improvement of already published results from the year 2016.

Figure 12. The 8Be signal region, along with current constraints and projected sensitiv- ities of future experiments in the (mx : e) plane as discussed in Ref.[56, 57]. The white points indicate expected 90% C.L. exclusion areas in the (mX ; e) plane from NA64 for the accumulated statistics of 1011 eot at 100 GeV. For the 8Be signal, the coupling to −4 −3 electrons can be in the range 2 × 10 < |e| < 1.4 × 10 , while the excluded area is −5 −3 7 × 10 < |e| < 0.9 × 10 .

4 Search for a new 17 MeV gauge boson from the 8Be anomaly and dark photon decays A0 → e+e−

The ATOMKI experiment of Krasznahorkay et al. [55] 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 8Be∗ 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 −4 non-universal coupling to quarks, coupling to electrons in the range 2 × 10 . e . −3 −14 −12 1.4 × 10 , see Fig. 12 and the lifetime 10 . τX . 10 s [56, 57]. It has motivated worldwide theoretical and experimental efforts towards light and weakly coupled vector bosons, see, e.g. [58–65]. Another strong motivation to the search for a new light boson decaying into e+e− pair is provided by the Dark Matter puzzle. An intriguing possibility is that in

– 28 – addition to gravity a new effective force between the dark sector and visible matter, transmitted by a new vector boson, A0 (dark photon), might exist [66, 67]. Such A0 could have a mass mA0 . 1 GeV, associated with a spontaneously broken gauged U(1)D symmetry, and would couple to the Standard Model (SM) through kinetic 1 0µν mixing with the ordinary photon, − 2 FµνA , parametrized by the mixing strength   1 [4,5, 68]. For a review see, e.g. [1,2, 58]. A number of previous beam dump

MU4

MU3 HCAL4 MU2 HCAL3 MU1 V3 HCAL2 HCAL1 S4 S3 T4 T3 ECAL V2 S2 e−

Vacuum vessel WCAL e+ SRD X

γ Magnet2 e− Magnet1 T2 T1 V1 S1

e−, 100 GeV

Figure 13. Schematic illustration of the NA64 setup to search for the A0,X → e+e− decays.

[69–83], fixed target [84–86], collider [87–89] and rare particle decay [90–94, 96–

102, 102] experiments have already put stringent constraints on the mass mA0 and  of such dark photons excluding, in particular, the parameter space region favored −4 −3 by the gµ − 2 anomaly. However, the range of mixing strengths 10 .  . 10 corresponding to a short-lived A0 still remains unexplored. Below, we report the first results from the NA64 experiment specifically designed for a direct search of the e+e− decays of new short-lived particles in the sub-GeV mass range at the CERN SPS [6, 20, 103–105].

4.1 The search method and the detector The method of the search for A0 → e+e− decays is described in [6, 20]. Its application to the case of the X → e+e− decay is straightforward. Briefly, a high-energy electron beam is sent into an electromagnetic (e-m) calorimeter that serves as an active beam dump. Typically the beam electron loses all its shower energy in the dump. If the A0 exists, due to the A0(X) − e− coupling it would occasionally be produced by a shower electron (or positron) in its scattering off a nuclei of the dump:

e− + Z → e− + Z + A0(X); A0(X) → e+e−. (4.1)

Since the A0 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

– 29 – (ECAL). Thus, the signature of the A0(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. 13. The upstream part of the detector and the 100 GeV beam were similar to those used for the A0 → invisible decay search ( see Fig.1). The use of SR detectors (SRD) was a key point for the improvement of the sensitivity compared to the previous electron beam dump searches [73, 74]. Differently from the invisible decay search, an active beam dump was installed immediately downstream the vacuum vessel. 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 [104]. The ECAL has ' 40 radiation lengths (X0) and is located at a distance ' 3.5 m from the WCAL. Downstream the ECAL the detector was equipped with a high-efficiency veto counter, V3, and a hermetic hadron calorimeter (HCAL) [104] used as a hadron veto and for muon identification. The results reported here were obtained from data samples in which 2.4×1010 electrons on 10 target (EOT) and 3×10 EOT were collected with the WCAL of 40 X0 (with a length of 290 mm) and of 30 X0 (220 mm), respectively. The events were collected with a hardware trigger requiring in-time energy deposition in the WCAL and EW CAL . 70 GeV. Data of these two runs (hereafter called the 40 X0 and 30 X0 run) were analyzed with similar selection criteria and finally summed up, taking into account the corresponding normalization factors. For the mass range 1 ≤ mA0 ≤ 25 MeV and energy EA0 & 20 GeV, the opening angle Θe+e− ' 2mA0 /EA0 . 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.

4.2 Event selection and background evaluation The candidate events were selected with the following criteria chosen to maximize the signal acceptance and minimize background, using both Geant4 [16, 17] based simulations and data: (i) There should be only one track entering the dump. No cuts on reconstructed outgoing tracks were used; (ii) No energy deposition in the V2 counter exceeding about half of the energy deposited by 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, Etot = EW CAL +EECAL, 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 [106, 107]; (v) The showers in the WCAL and ECAL should start to develop within a few first X0; (vi) The lateral and longitudinal shape of the shower in the ECAL 0 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

– 30 – 120

100

80 Energy in ECAL [GeV]

60

40

20

0 0 20 40 60 80 100 120 Energy in WCAL [GeV]

Figure 14. Distribution of selected e-m neutral (presumably photon) and signal events in the (EW CAL; EECAL) plane from the combined 30 X0 and 40 X0 runs. Neutral e-m events are shown as blue squares. The only signal-like event is shown as a red square. The dashed band represents the signal box.

cut EECAL > 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 [103, 104] a clean sample of ' 105 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 < Etot < 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 A0 → e+e− signal. Among them the two most important were expected the e+e− pair production either from decay 0 0 0 0 + − 0 + − chain KS → π π ; π → γe e of KS produced in the WCAL or from the γ → e e 0 0 0 0 conversion of photons from KS → π π → π → γγ decays in the T3 plane or 0 + − earlier in the beamline. Another background could come from the KS → π π hadronic decays that could be misidentified as an e-m event in the ECAL at the level −5 . 2.5 × 10 evaluated from the measurements with the pion beam. The leading K0 can be produced in the dump either by misidentified beam π−,K− or directly 0 by electrons. The background from the KS decay chain was estimated by using the 0 direct measurements of the KS flux from the dump with the following method. It is well known that the K0 produced in hadronic reactions is a linear combination √ 0 0 0 of the short- and long-lived components |K >= (|KS > +|KL >)/ 2. The flux of K0 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 0 3 account corrections due to the KS decays in-flight. The main fraction of ' 10 events observed in the HCAL were neutrons produced in the same processes as K0 in the

– 31 – WCAL. According to simulations, . 10% of them were predicted to be other neutral hadrons, i.e. Λ and K0, that were also included in the data sample. The conservative 0 0 assumption that ' 100 K were produced allows us to calculate the number of KS 0 + − from the dump and simulate the corresponding background from the KS → π π 0 0 0 0 + − and KS → π π ; π → γe e decay chain, which was found to be . 0.04 events per 5.4 × 1010 EOT. To cross-check 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. 14. Using simulations we calculated that there were ' 150 leading K0 produced in the dump, which is in a reasonable 0 agreement with the previous estimate resulting in a conservative KS background of 0.06 events. The µ, π and K mistakenly tagged as e−s [10] 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 misidentified pion could

Table 5. Expected numbers of background events in the signal box estimated for 5.4×1010 EOT. Source of background Events e+e− pair production by punchthrough γ < 0.001 0 0 0 + − + − 0 + − KS → 2π ; π → γe e ;γ → e e ; KS → π π 0.06 ± 0.034 πN → (≥ 1)π0 + n + ...; π0 → 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 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 charge-exchange reaction π−p → (≥ 1)π0 + 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 ∼ Z2/3, measured on different nuclei [108]. The contribution from the beam kaon decays in-flight − − + − − − + − K → e νπ π (Ke4) and dimuon production in the dump e Z → e Zµ µ with

– 32 – 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 × 1010 EOT. The dominant 0 contribution to background is 0.06 events from the KS decays, with the uncertainty dominated by the statistical error. In Fig. 14 the final distribution of e-m neutral, presumably photons, and signal candidate events from the reaction e−Z → anything in the (EECAL; EW CAL) plane that passed the selection criteria (i)-(iii), (v)-(vii) is shown. No candidates are found in the signal box. The conclusion that the background is small is confirmed by the data.

4.3 First results on the X → e+e− and A0 → e+e− decays 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, 90% NA0 , by using the modified frequentist approach, taking the profile likelihood as a test statistic [29–31]. The NA0 value is given by the sum :

2 2 X i X i i i NA0 = NA0 = nEOT totnA0 (, mA0 ) (4.2) i=1 i=1

i i where tot is the signal efficiency in the run i (30 X0 or 40 X0), and nA0 (, mA0 ) is the 0 + − number of the A → e e decays in the decay volume with energy EA0 > 30 GeV per EOT, calculated under assumption that this decay mode is predominant, see e.g. Eq.(3.7) in Ref. [20]. 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 A0 efficiency and its systematic error were determined to stem from the overall normalization, A0 yield and decay probability, which were the A0 mass dependent, and also from efficiencies and their uncertainties − in the primary e (0.85 ± 0.02), WCAL(0.93 ± 0.05), V2(0.96 ± 0.03), ECAL(0.93 ± 0.05), V3(0.95 ± 0.04), and HCAL(0.98 ± 0.02) event detection. The later, shown as − an example values for the 40 X0 run, were determined from measurements with e beam cross-checked with simulations. A detailed simulation of the e-m shower in the dump [106] with A0 cross sections was used to calculate the A0 yield [13, 14, 107]. The . 10% difference between the calculations in Ref.[107] and Ref.[13, 14] was accounted for as a systematic uncertainty in nA0 (, mA0 ). In the overall signal efficiency for each run the acceptance loss due to pileup (' 7% for 40 X0 and ' 10% for 30 X0 runs) was taken into account and cross-checked using reconstructed dimuon events [104]. The dimuon efficiency corrections (. 20%) were obtained with uncertainty of 10% and 15%, for the 40 X0 and 30 X0 runs, respectively. The total systematic uncertainty on NA0 calculated by adding all errors in quadrature did not exeed 25% for both

– 33 – 10−2 KLOE-2013

HADES PHENIX

−3

휖 10 NA48 BaBar

8 NA64 퐵푒

E774 푒

(푔 − 2)

10−4 E141 10−2 10−1

푚퐴′ , 퐺푒푉

Figure 15. Left panel: The 90% C.L. exclusion areas in the (mX ; ) plane from the NA64 experiment (blue area). For the mass of 16.7 MeV, the X − e− coupling region excluded −4 −4 8 by NA64 is 1.3 × 10 < e < 4.2 × 10 . The allowed range of e explaining the Be* anomaly (red area) [56, 57], constraints on the mixing  from the experiments E141 [71], E774 [74], BaBar [89], KLOE [94], HADES [97], PHENIX [98], NA48 [100], and bounds from the electron anomalous magnetic moment (g − 2)e [26] are also shown. Right panel: The 90% C.L. exclusion areas in the (mX ; ) plane from the NA64 experiment (blue curves) for the different numbers of EOT indicated near the curves accumulated at 150 GeV with the A0 decay length ' 7 m after removal of the Goliath dump at H4. runs. The combined 90% C.L. exclusion limits on the mixing  as a function of the A0 mass is shown in Fig. 15 together with the current constraints from other experiments. Our results exclude X-boson as an explanation for the 8Be* anomaly − −4 for the X − e coupling e . 4.2 × 10 and mass value of 16.7 MeV, leaving the −4 −3 still unexplored region 4.2 × 10 . e . 1.4 × 10 as quite an exciting prospect for further searches. In Fig. 15 the right panel shows the 90% C.L. exclusion areas in the (mX ; ) plane from the NA64 experiment (blue curves) for the different numbers of EOT indicated near the curves accumulated at 150 GeV. The A0 decay length is ' 7 m after removal of the Goliath dump at H4. Note that for 5 × 1012 EOT the NA64 experiment constraints significant part of the exclusion area of the planned HPS experiment. The statistical limit on the sensitivity of the proposed experiment 2 is proportional to e. Thus, it is important to accumulate a large number of events. As one can see from Eq. (4.2), the obtained exclusion regions are also sensitive to the choice of the length L0 of the calorimeter WCAL, which should be as short as

– 34 – possible.

5 Plans for the 2018 and 2021 runs

The main goals for the running in 2018 and 2021 is to address several areas of great interest in dark sector physics:

1. to continue the search for the A0 → invisible decay of the vector mediator of light thermal dark matter production and to reach sensitivity level allowing to probe significant fraction of the theoretically interesting parameter space −6 −3 (10 .  . 10 ; mA0 . 1 GeV), 2. to continue the search for the X → e+e− decay of a new 17 MeV gauge boson which could explain the 8Be anomaly,

3. to perform a new search for the ALPs decaying either into a pair of photons, a → γγ, or invisibly,

4. continue our studies of Zµ → invisible decay of the Lµ − Lτ dark boson, which will include the first prototype detector operating in a realistic muon beam environment.

As discussed in this report, the few issues encountered during the last run are being addressed, so that the 2018-2021 data sample should have better properties than the 2016-2017 data. As the offline analysis proceeds, we also continue to learn how to take better data in 2018. Experience gained in the 2017-2018 run will be an important and necessary step towards a program to set a stringent constraints on the dark sector models or, possibly, detect and measure some decay in NA64. We believe realization of the full potential of NA64 proposed program will require at least 25 weeks of running. It should be noted that this estimate of the running period does not include time needed for detector assembly for each run, time for commissioning and tuning, and assumes about 120 good hours of a H4 beam per week. Although physics programs with H4 beam nominally can be realized in a 25 week run, it seems likely that more than 30 calendar weeks, instead of 25, will be required to collect the data samples described in this report. The allocation of a permanent place for NA64 at H4 would give more running time and provide important contingency against unforeseen losses of the beam time.

5.1 Search for the A0 → invisible decays For the A0 → invisible decay mode we plan to accumulate during 2016-2018 and 11 2021 in total about & 5 × 10 EOT. The successful run in 2016-17 and experience 6 in 2018 with about 4 -spill structure during ' 1 min cycle and intensity & 5 × 10 EOT/spill gave us significant increase in the A0 yield and show this is quite realistic.

– 35 – 11 An extrapolation from this year run shows that we can collect & 2 × 10 EOT in a two-week of running in 2018 and the same amount in 2021. The combined 2016-2018 and 2021 data sample thus will include more than 5 × 1011 EOT resulting also in a significant projected coverage of the (; mA0 ) and (αD; mχ) parameter space shown in Figs.16 and 17, respectively.

10−2 E787, E949

푎휇 BaBar 푎휇 favored 10−3

푎 푒

−4 NA64 휖 10

10−5

10−6 10−3 10−2 10−1 1 10

푚퐴′ , 퐺푒푉

Figure 16. The projective NA64 90% C.L. exclusion region in the (mA0 , ) plane obtained for 5 × 1011 EOT. Constraints from the BaBar [25], E787 and E949 experiments [26, 27], gµ−2 as well as the muon αµ favored area are also shown. Here, αµ = 2 . For more limits obtained from indirect searches and planned measurements see e.g. Ref. [28].

10 4 π 10 4 π 1 TeV Landau Pole 1 TeV Landau Pole 1 1 0.5 0.5 Majorana Thermal DM Pseudo-Dirac Thermal DM −1 10−1 10 LSND BaBar

퐷 퐷

훼 훼 10−2 10−2 훼퐸푀 NA64 훼퐸푀 BaBar MiniBooNE NA64 10−3 E137 10−3 LSND 10−4 10−4 10−3 10−2 10−1 1 10−3 10−2 10−1 1

푚휒, 퐺푒푉 푚휒, 퐺푒푉

Figure 17. The projective NA64 constraints in the (αD;mA0 ) plane on the pseudo-Dirac (the left panel) and Majorana ( right panel) type light thermal DM obtained for 5 × 1011 EOT and shown in comparison with bounds obtained in Ref. [28] from the results of the BaBar [25], LSND [40, 45], E137 [46], and MiniBooNE [49] experiments.

– 36 – 5.2 Search for the X → e+e− and A0 → e+e− decays For the further tests of the 8Be- anomaly through the search for the X → e+e− decay, and the search for the dark photon A0 → e+e− decays the plan is to run at 150 GeV with the decay volume length extended up to 7 m by removing the GOLIATH dump at the H4 beam. The intensity test in 2017 showed that the running at 150 GeV 6 with & 3 · 10 e-/spill is possible. In order to cover further the most of the X and 0 11 A parameter space the number of nEOT & 10 EOT at 150 GeV are planned to be collected, provided that & 50 units will be deliver by the SPS at the T2 target during period of one month. Assuming that the combined 2018 and 2021 data sample will include ' 2 × 1011 EOT collected at 150 GeV results in significant coverage of −5 the (; mA0 ) parameter space up to  ' 10 for the mass mA0 . 0.1 GeV and −4 −4 10 . e . 8 × 10 for the mass 17 MeV, as shown in Fig.8. There are several ways to further increase sensitivity of NA64: either increase 12 the number of EOT up to nEOT & 5 × 10 EOT at 150 GeV, boosting the decay of the X boson by increasing the primary beam energy, or increasing the decay volume by reducing significantly the length of the active dump. Since the intensity drops with increasing the beam energy, e.g. at 150 GeV it drops by a factor two, this alone requires a few months run to gain the desired coverage and it motivates the reduction of the WCAL length in the new setup. Here, we briefly address the challenges of a shorter calorimeter with a simplified but realistic Monte Carlo study performed by adapting the existing Geant4 package developed for the NA64 simulation. Pixel sen- sor with 256 µm thickness were chosen as tracking detector for this study, as their ability to deal with large occupancy and their very good spatial resolution makes them the good choice for this search. Two pixel sensor attached to an FE-I4 are currently being tested in the 2018 beam time to further explore the integration of such detector in the NA64 experiment. The main challenge of a short calorime- ter is the loss of the hermeticity compared to the previous setup. This degrades the capability to identify an event in the signal region EECAL1+EECAL2 ∼EBEAM with exactly to tracks detected between the calorimeters. The punchtrough particles would leave multiple-hits in the trackers and therefore one will not be able anymore to reconstruct the vertex compatible with a decay of a dark matter gauge boson. The strategy being currently explored is to use a strong magnetic field in the area of the decay volume. The first advantage of this approach will be to filter out all low energy particles. This is expected to reduce the occupancy in the tracking detec- tors and, therefore, reduce the combinatorics through backward propagation of the tracks which allows for precise vertex reconstruction. Moreover, the use of the mag- net enables momentum reconstruction of the candidate tracks, which can be used to reconstruct the invariant mass of the decay products. This is a powerful tool to reject the main background coming from pair conversion of gamma in the last layer of the tungsten calorimeter.

– 37 – Number of charged particle detected at different distances from ECAL1 Invariant mass 170 mm −1 470 mm 10 Background tracks 106 1170 mm

1470 mm −2 Frequency 10 X-boson tracks

105

10−3

104 10−4

103 10−5

0 10 20 30 40 50 60 70 80 90 0 100 200 300 400 500 600 700 800 900 Nparticles MeV

Figure 18. On the left: Occupancy experienced by a tracker placed at different distance from a 5X0 tungsten calorimeter impacted by a 100 GeV electron in a field of 2.5 Tesla On the right:Invariant mass reconstructed from tracks produced by an X-boson decay (black) and tracks produced by a standard event from a 100 GeV electron dumped to a 5X0 tungsten calorimeter (red)

The simulation was performed with the same geometry used in the visible mode setup of 2017 [105]. A vacuum tube of 2m length closed with two Mylar window was placed immediately after the end of the Tungsten calorimeter, inside the tube 4 tracking detectors were placed, consisting of a layer of silica with a thickness of 256 µm. Inside the tube a uniform magnetic field with strength varying from 1.7 T of 2.5 T was applied for the particle bending. To simulate events with X-bosons production, the worst case scenario of a coupling  ∼1.5×10−3 was assumed, and the interaction was added in Geant4 using cross sections computed using tree level corrections discussed in Sec.3. Finally the size of the calorimeter was set to be

5X0, as preliminary calculations show this length to be effective in covering the desired parameter space with a reasonable statistics of 1011 EOT. The evolution of the occupancy distribution for different distance traveled in the field is shown in Fig.18. This result highlights that the occupancy rapidly decrease in the magnetic field, roughly by a factor 2 for every 30 cm. After 1 m only ∼60% of events will have more than 1 particle required for the signal definition, with a mean of ∼ 3 particle registered per event. These numbers depend only weakly from the exact field values, it was observed that the difference between the mean values of occupancy is roughly 2 between a 2.5 T and 1.7 T field. This difference can be easily compensated by optimizing the detector position as a function of applied magnetic field. For a field strength of 0.5 Tesla an average of 5 more particles per detector compared to a magnetic field of 2.5 T, a shift of detectors of approximately 1 m could compensate for the larger occupancy. The analysis of such setup will be the focus of our next studies. Although the magnetic field already act by its own as a powerful tool to reduce background the number of surviving tracks is still high. The most powerful cut to

– 38 – MX=16.7 MeV, LWCAL= 5X0 3 10 12

efficiency = 80 % EOT=10 2 10 11

EOT=10 10 1

signal 10 90% CL Poiss. Upp. Lim.

N Nsign < N90% CL=2.3 EOT=10

8 0 Be* anomaly: -4 ε -3 10 2*10 < X <1.5*10

10-1 10-6 10-5 10-4 10-3 ε X

Figure 19. Upper limit in the parameter space of a dark boson with Mass 16.7 MeV produced in the reaction e + N → e + X + N using a 100 GeV electron as particle and a 5X0 tungsten calorimeter as target. The exclusion curve is computed assuming Poisson statistics with zero background and 80% efficiency of detection for three different number of EOTS reject them was found to be the reconstruction of the invariant mass of each ver- tex candidate. The tracks of different momentum sign were selected and combined requiring that the χ2 of their reconstructed momenta was smaller than 1.5. After that the invariant mass was computed by propagating their estimated momentum at the vertex position and using as assumption the two particles to have the electron mass. The invariant mass, both coming from simulated standard model events and from extra tracks in an event with X-boson production, was computed this way and compared to the invariant mass from the true tracks of an X-boson decay. The re- sults are shown in Fig.18, the separation is immediately apparent: while the tracks coming from dark matter decay correctly recover the invariant mass of the original particle the one reconstructed by background tracks typically return a reconstructed invariant mass much larger, creating a very effective background rejection tool. The distribution of the background particle was determined by bremsstrahlung distribu- tion coming from the electromagnetic shower creating vertices by pair conversion. Conveniently the distribution is cut by the presence of the magnetic field, which rejects the pairs created from photon which are low energy, corresponding in our range of searches to the one generating most of the background. After a range of vertex candidates with reconstructed invariant mass between 15 MeV and 19 MeV was selected, 11 background events were still observed after a statistics of 107 EOTS with a nearly perfect (>99%) efficiency for the simulated X-boson. The benchmark setup used for the simulation was with a field of 2.5 Tesla and the trackers placed at a distance of 30 cm between each other. To further suppress these events the

– 39 – following cuts were applied:

• Minimum reconstructed momentum of 1 GeV for each track

• Vertex reconstructed between end of Tungsten calorimeter and first tracker

• Energy deposit in the cell outside the center of the shower larger than 3 GeV

The last cut is justified from the fact that an events with X-boson production typically has larger energy deposit in the ECAL’s cells surrounding the one where most of the shower takes place, given by the photons traveling stright to the ECAL without any bending. This is explained by the fact that a large portion of energy of the incoming particle is carried away from the two charged particle produced in the X-boson decay that will therefore tend to be deposited on the periphery of the calorimeter due to the bending experienced. This cut could be improved by raising the distance between the two calorimeter, which would increase the separation be- tween the two showers. The three cuts combined suppressed 10 of the 11 background events observed reducing the background to a single event in a statistic of 107 EOTS. The combined efficiency of X-boson detection was found to be 80%, roughly half of it is caused by the acceptance of the setup, which reject events where one of the two decay product of the X-boson is too low energetic to travel trough the field, while the other half is caused by the limited efficiency of the applied cuts. Using this preliminary estimate of efficiency the parameter space covered by on hypothetical 11 experiment with 5X0 is shown in Fig.19. A statistics of 10 in such setup could in principle cover completely the parameter space that explains the origin of the Beryllium anomaly as due to the new protophobic gauge boson decay.

5.3 Search for the ALP decays a → γγ and a → e+e− The first results from the 2017 run shows that NA64 is also capable to search for the axion-like particles (ALP) couple predominantly to two photons. The idea is to use the detector shown in Fig.13 for the new physics search in events with the pure neutral e.m. final state detected in the ECAL. The methods for the suppression of background from hadronic decays, discussed in Sec. 4.2, are currently under development, and in mostly relay on the use of a new variable, called collinearity (C) which is determined by the angle of the observed candidate event with a primary beam electron axis. As far as projected sensitivity is concerned, one can see from Fig. 20 that NA64 could cover the niche of short-lived APLs decaying into two photons, −4 −2 a → γγ, corresponding to the parameter space 10 . gaγγ . 10 for the a-mass 12 range 10 . ma . 500 MeV assuming accumulation of nEOT ' 5 × 10 .

– 40 – Figure 20. Left panel: the existing constraints of ALP coupling gγγ vs ma (from Ref.[50]). The ellipse represents the unexplored niche in the parameter space that can be filled by

NA64. Right panel: The projective NA64 constraints in the (gq;ma) plane on the ALP decaying as a → γγ obtained for 5 × 1011, 5 × 1012 EOT and shown in comparison with bounds obtained in Ref. [28] from the results of the BaBar [25], LSND [40, 45], E137 [46], and MiniBooNE [49] experiments.

6 Detector upgrade and location at the H4 line

Although the first NA64 runs overall were quite successful, several difficulties were encountered which will be addressed for the 2021 run. These items are listed and briefly discussed below in this report.

6.1 Detector upgrades for the 2021 run In the sections below, we describe several detector issues which must be addressed for NA64 to collect data as efficiently as possible in the 2021 run. The upgrades proposed are designed to improve the reliability of the detector and to improve the trigger/DAQ livetime. The improvement in data-taking efficiency will come mainly from the replacement of DAQ components partly described in section 2.12. Several modifications to the trigger and front-end readout are required to achieve the live- time improvement; these modifications are described in Section 4.5. We estimate that the combined improvement will reduce the experiment’s overall deadtime (i.e., total beam time for which the experiment is not live) by 10%, equivalent to adding potentially 0.5 weeks to a 5 week run.

– 41 – To increase the overall signal efficiency and improve background rejection the following upgrade of the setup will be installed:

(i) additional number of the MM, GEM, ST stations. A possible use of Si pixels as the tracker for the X → e+e− decay search is also considered. The corre- sponding feasibility study is currently underway in the 2018 run.

(ii) two fast beam hodoscopes in the upstream part of the setup

(iii) transversely segmented SRD detector with improved readout

(iv) zero-angle veto to suppress bremsstrahlung photons

(v) large Veto in front of the ECAL to reject low energy electrons

(vi) upstream small size Sc counter to improve beam divergency.

(vii) Further developments of the DAQ and the analysis program are in progress to 12 ensure a substantial data collection of neot ' 10 events in 2021.

6.2 Detector location at the H4 line As mentioned above, in order to probe the theoretically interesting parameter space −5 −3  ' 10 − 10 and mA0 . 1 GeV the number of accumulated electrons on target 12 is required to be around neot & 10 or more, and a very low background rate. Assuming the beam rate to be around 5 × 106 e−/spill around 6 months of data taken are required. Therefore, in order to use more effectively the H4 line, two current drawbacks that we faced for the moment, should be solved:

• Installation of the detector at H4 line from the scratch and its debugging takes already about one week. Alighment, detector calibration and tuning takes additional week more. In 2018 more complex setup is expected to be used, resulting in possible increase of time needed for installation, alignment and calibration. As the complexity of the detector increased that time for debugging of the detector is also increased and already reached the level of a weeks.

• Tuning of the setup from the scratch up to the steadily increased complexity level of the trigger level is also very time consuming procedure. In particular tuning of the SRD detector, beam location, trim scanning due to low thresh- old,..

Therefore, a permanent location at H4 would be extremely useful to avoid loss of the beam time. We cannot fully take advantage of the H4 beamline until both above issues are solved.

– 42 – 7 Summary

In 2016 and 2017 runs the NA64 detector was fully operational and working. Good quality data of ' 1011 EOT were collected in total. Although NA64’s runs were quite successful and produce significant physics results, we believe we have only begun to exploit the physics potential of the proposed experimental technique and detector. The further runs will provide us with the opportunity to continue this program to meet our original goals for the proposal.

(i) Results from 2016-2017 runs on the invisible mode - the results of 2016 run corresponding to 4.3 × 1010 EOT have been published in Phys. Rev. D, Ref.[104]. - in 2017 run ' 5.5·1010 EOT were accumulated and the combined data sample from 2016+17 reaches the milestone of ' 1011 EOT . - the 2017 data analysis is close to completion. Currently the further back- ground rejection and signal efficiency improvement are under study, as well as the development of an improved track reconstruction combining information from MM and GEM for the overall track efficiency.

(ii) Results from 2017 run on the 8Be-anomaly and A0 → e+e− decay search. - ' 5.4 · 1010 EOT were accumulated - the data analysis is completed. With 5.4×1010 electrons on target no evidence for such decays was found, allowing to set first limits on the X − e− coupling in −4 −4 the range 1.3 × 10 . e . 4.2 × 10 excluding part of the parameter space. - new bounds are set on the mixing strength of photons with dark photons (A0) from non-observation of the decay A0 → e+e− of the bremsstrahlung A0 with a mass . 23 MeV. - The corresponding paper [105] is accepted for publication in Phys. Rev. Lett. - Promising results from the feasibility study of ALP decays search are obtained.

(iii) Lessons from the 2017 run 6 − - The detector worked well at the intensity & 5 · 10 e / spill. - Accumulation of ' (4 − 5) · 1011 EOT during a month of running is realistic. - For further runs beyond LS2 an intensity up to a few 107 e−/ spill can be obtained, assuming & 60 units on T2.

(iv) The 2018 and 2021 runs - data taking still in progress - 2 · 1011 EOT are collected for invisible mode 10 - & 5 · 10 EOT are expected to be collected for visible mode at 150 GeV - Plan for the 2018 and 2021 runs is to accumulate in total ' 6 · 1011 EOT

– 43 – in order to cover yet unexplored areas in the sub-GeV Thermal Dark Matter parameter space and to perform a more sensitive search for the A0(X) → e+e− decays The analysis of the data sample collected before LS2 in 2016-2018 should provide a significant contribution to the update of the European Strategy for Particle Physics and can also play an essential role in helping to plan for a future dark sector experi- ments at the SPS.

8 Publications

Since the last NA64 SPSC report in 2017 the collaboration has completed the physics analyses of the 2016 data sample on the search for the A0 → invisible decay and analysis of the 2017 data on the search for the X → e+e− of the 17 MeV X-boson from the 8Be anomaly and the A0 → e+e− decays of dark photons, and also have published a few results on further extension of the research program of NA64: (i) NA64 collaboration: D. Banerjee et al. ”Search for vector mediator of Dark Matter production in invisible decay mode”, Phys. Rev. D 97 no.7, 072002 (2018).

(ii) NA64 collaboration: D. Banerjee et al. ”Search for a new X(16.7) boson and dark photons in the NA64 experiment at CERN”, CERN-EP-2018-043, arXiv:1803.07748[heh-ex], to be published in Phys. Rev. Lett. (2018).

(iii) NA64 collaboration: D. Banerjee et al., ”Performance of Multiplexed XY Re- sistive Micromegas detectors in a high intensity beam”, Nucl. Instrum. Meth. Phys. Res., Sect. A 881 (2018) 72-81.

(iv) NA64 collaboration: E. Depero et al., ”High purity 100 GeV electron identifi- cation with synchrotron radiation”, Nucl. Instrum. Methods Phys. Res., Sect. A 866, 196 (2017).

(v) S.N. Gninenko, N.V. Krasnikov, M.M. Kirsanov, D.V. Kirpichnikov, ” The ex- act tree-level calculation of the dark photon production in high-energy electron scattering at the CERN SPS”, arXiv:1712.05706 [hep-ph], to be published in Phys. Lett. B (2018).

(vi) S.N. Gninenko, N.V. Krasnikov ” Probing the muon gµ − 2 anomaly, Lµ − Lτ gauge boson and Dark Matter in dark photon experiments” arXiv:1801.10448[hep- ph].

(vii) S. Gninenko, S. Kovalenko, S. Kuleshov, V. E. Lyubovitskij, A. S. Zhevlakov, ”Deep inelastic e−τ and µ−τ conversion in the NA64 experiment at the CERN SPS”, arXiv:1804.05550 [hep-ph].

– 44 – More analyses are in preparation for review within the NA64 Collaborations and timely publication.

(i) NA64 collaboration: ”Search for invisible decays of sub-GeV dark scalars and ALPs at the CERN SPS”, based on 2017 and 2018 data sample.

The NA64 Collaboration contributed to several topical Workshops with NA64 De- tector contributions and recently published or preliminary physics results from data analyses. During the period form June 2017 to June 2018, the NA64 speakers pre- sented 4 talks. More contributions including the International Conferences, are also planned in 2018.

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– 50 –