Search

A search for Dark Sectors is performed using the unique M2 beam line at the CERN Super Proton Synchrotron. New particles ($X$) could be produced in the bremsstrahlung-like reaction of high energy 160 GeV muons impinging on an active target, $\mu N\rightarrow\mu NX$, followed by their decays, $X\rightarrow\text{invisible}$. The experimental signature would be a scattered single muon from the target, with about less than half of its initial energy and no activity in the sub-detectors located downstream the interaction point. The full sample of the 2022 run is analyzed through the missing energy/momentum channel, with a total statistics of $(1.98\pm0.02)\times10^{10}$ muons on target. We demonstrate that various muon-philic scenarios involving different types of mediators, such as scalar or vector particles, can be probed simultaneously with such a technique. For the vector-case, besides a $L_\mu-L_\tau$ $Z'$ vector boson, we also consider an invisibly decaying dark photon ($A'\rightarrow\text{invisible}$). This search is complementary to NA64 running with electrons and positrons, thus, opening the possibility to expand the exploration of the thermal light dark matter parameter space by combining the results obtained with the three beams., Comment: 24 pages, 22 figures

We present the first results from a proof-of-concept search for dark sectors via invisible decays of pseudoscalar $\eta$ and $\eta'$ mesons in the NA64h experiment at the CERN SPS. Our novel technique uses the charge-exchange reaction of 50 GeV $\pi^-$ on nuclei of an active target as the source of neutral mesons. The $\eta, \eta' \to invisible$ events would exhibit themselves via a striking signature - the complete disappearance of the incoming beam energy in the detector. No evidence for such events has been found with $2.9\times10^{9}$ pions on target accumulated during one day of data taking. This allows us to set a stringent limit on the branching ratio ${\rm Br}(\eta' \to invisible) < 2.1 \times 10^{-4}$ improving the current bound by a factor of $\simeq3$. We also set a limit on ${\rm Br}(\eta \to invisible) < 1.1 \times 10^{-4}$ comparable with the existing one. These results demonstrate the great potential of our approach and provide clear guidance on how to enhance and extend the sensitivity for dark sector physics from future searches for invisible neutral meson decays., Comment: 5 pages, 3 figures

We propose two generalizations of the dark photon model which predict the suppressed elastic dark matter nuclei cross section in comparison with the corresponding prediction of the dark photon model. In the first model the main difference from dark photon model is that the mixing parameter $\epsilon$ is nonlocal formfactor $\epsilon(q^2)= \frac{q^2}{\Lambda^2}V(\frac{q^2}{\Lambda^2}) $ depending on the square of the momentum transfer $q^2$. Here $V(\frac{q^2}{\Lambda^2})$ is an entire function of the growth $\rho \geq \frac{1}{2}$ and $\Lambda$ is nonlocal scale. In this model our world and dark world are described by renormalizable field theories while the communication between them is performed by nonlocal interaction. The second model is renormalizable model where besides dark photon field $A'$ additional vector boson $Z'$ interacts with $B - L$ current. The communication between our world and dark world is performed due to nonzero kinetic mixing between $Z'$ and $A'$ fields. The predictions of the models for the search for dark matter at the accelerators don't contain additional suppression factors., Comment: 12 pages

The inclusion of an additional $U(1)$ gauge $L_\mu-L_\tau$ symmetry would release the tension between the measured and the predicted value of the anomalous muon magnetic moment: this paradigm assumes the existence of a new, light $Z^\prime$ vector boson, with dominant coupling to $\mu$ and $\tau$ leptons and interacting with electrons via a loop mechanism. The $L_\mu-L_\tau$ model can also explain the Dark Matter relic abundance, by assuming that the $Z'$ boson acts as a "portal" to a new Dark Sector of particles in Nature, not charged under known interactions. In this work we present the results of the $Z'$ search performed by the NA64-$e$ experiment at CERN SPS, that collected $\sim 9\times10^{11}$ 100 GeV electrons impinging on an active thick target. Despite the suppressed $Z'$ production yield with an electron beam, NA64-$e$ provides the first accelerator-based results excluding the $g-2$ preferred band of the $Z'$ parameter space in the 1 keV $ < m_{Z'} \lesssim 2$ MeV range, in complementarity with the limits recently obtained by the NA64-$\mu$ experiment with a muon beam., Comment: 15 pages, 5 figures. New version with extended exclusion limits down to 1 keV in Z' mass

The search for new comparably light (well below the electroweak scale) feebly interacting particles is an exciting possibility to explain some mysterious phenomena in physics, among them the origin of Dark Matter. The sensitivity study through detailed simulation of projected experiments is a key point in estimating their potential for discovery. Several years ago we created the DMG4 package for the simulation of DM (Dark Matter) particles in fixed target experiments. The natural approach is to integrate this simulation into the same program that performs the full simulation of particles in the experiment setup. The Geant4 toolkit framework was chosen as the most popular and versatile solution nowadays. The simulation of DM particles production by this package accommodates several possible scenarios, employing electron, muon or photon beams and involving various mediators, such as vector, axial vector, scalar, pseudoscalar, or spin 2 particles. The bremsstrahlung, annihilation or Primakoff processes can be simulated. The package DMG4 contains a subpackage DarkMatter with cross section methods weakly connected to Geant4. It can be used in different frameworks. In this paper, we present the latest developments of the package, such as extending the list of possible mediator particle types, refining formulas for the simulation and extending the mediator mass range. The user interface is also made more flexible and convenient. In this work, we also demonstrate the usage of the package, the improvements in the simulation accuracy and some cross check validations., Comment: 17 pages, 11 figures, 1 table

We report on a search for a new $Z'$ ($L_\mu-L_\tau$) vector boson performed at the NA64 experiment employing a high energy muon beam and a missing energy-momentum technique. Muons from the M2 beamline at the CERN Super Proton Synchrotron with a momentum of 160 GeV/c are directed to an active target. A signal event is a single scattered muon with momentum $<$ 80 GeV/c in the final state, accompanied by missing energy, i.e. no detectable activity in the downstream calorimeters. For a total statistic of $(1.98\pm0.02)\times10^{10}$ muons on target, no event is observed in the expected signal region. This allows us to set new limits on part of the remaining $(m_{Z'},\ g_{Z'})$ parameter space which could provide an explanation for the muon $(g-2)_\mu$ anomaly. Additionally, our study excludes part of the parameter space suggested by the thermal Dark Matter relic abundance. Our results pave the way to explore Dark Sectors and light Dark Matter with muon beams in a unique and complementary way to other experiments., Comment: 5 pages, 4 figures

We present the results of a missing-energy search for Light Dark Matter which has a new interaction with ordinary matter transmitted by a vector boson, called dark photon $A^\prime$. For the first time, this search is performed with a positron beam by using the significantly enhanced production of $A^\prime$ in the resonant annihilation of positrons with atomic electrons of the target nuclei, followed by the invisible decay of $A^\prime$ into dark matter. No events were found in the signal region with $(10.1 \pm 0.1)~\times~10^{9}$ positrons on target with 100 GeV energy. This allowed us to set new exclusion limits that, relative to the collected statistics, prove the power of this experimental technique. This measurement is a crucial first step toward a future exploration program with positron beams, whose estimated sensitivity is here presented., Comment: Version submitted to PRL

We discuss the most sensitive constraints on Light Dark Matter (LDM) from accelerator experiments NA64 and BaBar and compare it with recent results from direct searches at XENON1T, DAMIC-M, SuperCDMS, and DarkSide-50. We show that for the dark photon ($A'$) model with scalar LDM, NA64 gives more stringent bounds for $A'$ masses $m_{A'} \leq 0.15~GeV$ than direct searches. Moreover, for the case of Majorana LDM the damping DM velocity $v$ factor, $v^2 \sim O(10^{-6})$, for the elastic LDM electron(nucleon) cross section makes direct observation of Majorana LDM extremely challenging, while the absence of this suppression in the NA64 case gives an advantage to the experiment. The similar situation takes place for pseudo-Dirac LDM. The BaBar provides the most stringent bounds for $A'$ masses $m_{A'} \geq 0.35~GeV$. For scalar LDM the direct detection experiments give more stringent bounds at $m_{A'} \geq 0.35~GeV$ while for Majorana and pseudo-Dirac LDM case, the BaBar bounds are more stringent. The complementarity of the two approaches in searching for LDM is underlined., Comment: 8 pages, 3 figures, typos corrected, references added

Thermal dark matter models with particle $\chi$ masses below the electroweak scale can provide an explanation for the observed relic dark matter density. This would imply the existence of a new feeble interaction between the dark and ordinary matter. We report on a new search for the sub-GeV $\chi$ production through the interaction mediated by a new vector boson, called the dark photon $A'$, in collisions of 100 GeV electrons with the active target of the NA64 experiment at the CERN SPS. With $9.37\times10^{11}$ electrons on target collected during 2016-2022 runs NA64 probes for the first time the well-motivated region of parameter space of benchmark thermal scalar and fermionic dark matter models. No evidence for dark matter production has been found. This allows us to set the most sensitive limits on the $A'$ couplings to photons for masses $m_{A'} \lesssim 0.35$ GeV, and to exclude scalar and Majorana dark matter with the $\chi-A'$ coupling $\alpha_D \leq 0.1$ for masses $0.001 \lesssim m_\chi \lesssim 0.1$ GeV and $3m_\chi \leq m_{A'}$., Comment: 7 pages, 7 figures. arXiv admin note: text overlap with arXiv:1906.00176

In this study, we present the measurement of the intrinsic hadronic contamination at the CERN SPS H4 beamline configured to transport electrons and positrons at 100 GeV/c momentum. The analysis was performed using data collected by the NA64-$e$ experiment in 2022. Our study is based on calorimetric measurements, exploiting the different interaction mechanisms of electrons and hadrons in the NA64-ECAL and NA64-HCAL detectors. We determined the intrinsic hadronic contamination by comparing the results obtained using the nominal electron/positron beamline configuration with those obtained in a dedicated setup, in which only hadrons impinged on the detector. The significant differences in the experimental signatures of electrons and hadrons motivated our approach, resulting in a small and well-controlled systematic uncertainty for the measurement. Our study allowed us to precisely determine the intrinsic hadronic contamination, which represents a crucial parameter for the NA64 experiment in which the hadron contaminants may result in non-trivial backgrounds. Moreover, we performed dedicated Monte Carlo simulations for the hadron production induced by the primary T2 target. We found a good agreement between measurements and simulation results, confirming the validity of the applied methodology and our evaluation of the intrinsic hadronic contamination.

In addition to vector ($V$) type new particles extensively discussed previously, both CP-even ($S$) and CP-odd ($P$) spin-0 Dark Matter (DM) mediators can couple to muons and be produced in the bremsstrahlung reaction $\mu^- + N \rightarrow \mu^- + N + S(P)$. Their possible subsequent invisible decay into a pair of Dirac DM particles, $S(P) \to \chi \overline{\chi}$, can be detected in fixed target experiments through missing energy signature. In this paper, we focus on the case of experiments using high-energy muon beams. For this reason, we derive the differential cross-sections involved using the phase space Weisz\"acker-Williams approximation and compare them to the exact-tree-level calculations. The formalism derived can be applied in various experiments that could observe muon-spin-0 DM interactions. This can happen in present and future proton beam-dump experiments such as NA62, SHIP, HIKE, and SHADOWS; in muon fixed target experiments as NA64$\mu$, MUoNE and M3; in neutrino experiments using powerful proton beams such as DUNE. In particular, we focus on the NA64$\mu$ experiment case, which uses a 160 GeV muon beam at the CERN Super Proton Synchrotron accelerator. We compute the derived cross-sections, the resulting signal yields and we discuss the experiment projected sensitivity to probe the relic DM parameter space and the $(g-2)_\mu$ anomaly favoured region considering $10^{12}$ and $10^{13}$ muons on target., Comment: 11 pages, 9 figures

A search for a new $Z'$ gauge boson associated with (un)broken B-L symmetry in the keV-GeV mass range is carried out for the first time using the missing-energy technique in the NA64 experiment at the CERN SPS. From the analysis of the data with 3.22e11 electrons on target collected during 2016-2021 runs no signal events were found. This allows to derive new constraints on the $Z'-e$ coupling strength, which for the mass range $0.3 < m_{Z'} < 100$ MeV are more stringent compared to those obtained from the neutrino-electron scattering data., Comment: 6 pages, 3 figures. Revised shorter version, Fig.3 updated, published in Physical Review Letters

The extension of Standard Model made by inclusion of additional $U(1)$ gauge $L_\mu-L_\tau$ symmetry can explain the difference between the measured and the predicted value of the muon magnetic moment and solve the tension in $B$ meson decays. This model predicts the existence of a new, light $Z^\prime$ vector boson, predominantly coupled to second and third generation leptons, whose interaction with electrons is due to a loop mechanism involving muons and taus. In this work, we present a rigorous evaluation of the upper limits in the $Z^\prime$ parameter space, obtained from the analysis of the data collected by the NA64-$e$ experiment at CERN SPS, that performed a search for light dark matter with $2.84\times10^{11}$ electrons impinging with 100 GeV on an active thick target. The resulting limits, despite being included in a region already investigated by neutrino experiments,touch the muon $g-2$ preferred band for values of the $Z^\prime$ mass of order of 1 MeV. The sensitivity projections for the future high-statistics NA64-$e$ runs demonstrate the power of the electrons/positron beam approach in this theoretical scenario., Comment: 11 pages, 9 figures. This version was accepted for publication

In this note I show that nonlocal generalization of the standard model (SM) with nonlocal scale $\Lambda_{nl} \approx 3$ TeV can explain recent CDF result on the W-mass measurement, Comment: 5 pages, several misprints corrected, 3 references added

We present a model explaining both the 4.2 $\sigma$ muon $g-2$ anomaly and the relic density of dark matter (DM) in which DM interacts with the Standard Model (SM) via a scalar portal boson $\varphi$ carrying both dark and SM leptonic numbers, and mediating a nondiagonal interaction between the electron and muon that allows $e \leftrightarrow \mu$ transitions. The $\varphi$ could be produced in high-energy electron scattering off a target nuclei in the reaction $e Z \to \mu Z\varphi$ followed by the prompt invisible decay $\varphi~\to$~DM particles and searched for in events with large missing energy accompanied by a single outgoing muon in the final state. Interestingly, several events with a similar signature have been observed in a data sample of $\simeq 3\times 10^{11}$ electrons on target collected during 2016-2018 for the search for light dark matter in the NA64 experiment at the CERN SPS [PRL {\bf 123}, 121801 (2019)]. Attributing so far these events to background allows us to set first constraints on the $\varphi$ mass and couplings while leaving at the same time decisively probing the origin of these events and a large fraction of the remaining parameter space to a near exiting future with the upgraded NA64 detector or other planned experiments., Comment: 6 pages, 3 figures. References added, matches published version

We report the results of a search for a new vector boson ($A'$) decaying into two dark matter particles $\chi_1 \chi_2$ of different mass. The heavier $\chi_2$ particle subsequently decays to $\chi_1$ and $A' \to e^- e^+$. For a sufficiently large mass splitting, this model can explain in terms of new physics the recently confirmed discrepancy observed in the muon anomalous magnetic moment at Fermilab. Remarkably, it also predicts the observed yield of thermal dark matter relic abundance. A detailed Monte-Carlo simulation was used to determine the signal yield and detection efficiency for this channel in the NA64 setup. The results were obtained re-analyzing the previous NA64 searches for an invisible decay $A'\to \chi \overline{\chi}$ and axion-like or pseudo-scalar particles $a \to \gamma \gamma$. With this method, we exclude a significant portion of the parameter space justifying the muon g-2 anomaly and being compatible with the observed dark matter relic density for $A'$ masses from 2$m_e$ up to 390 MeV and mixing parameter $\epsilon$ between $3\times10^{-5}$ and $2\times10^{-2}$.

We report the results of a search for a light pseudoscalar particle $a$ that couples to electrons and decays to $e^+e^-$ performed using the high-energy CERN SPS H4 electron beam. If such pseudoscalar with a mass $\simeq 17$ MeV exists, it could explain the ATOMKI anomaly. We used the NA64 data samples collected in the "visible mode" configuration with total statistics corresponding to $8.4\times 10^{10}$ electrons on target (EOT) in 2017 and 2018. In order to increase sensitivity to small coupling parameter $\epsilon$ we used also the data collected in 2016-2018 in the "invisible mode" configuration of NA64 with a total statistics corresponding to $2.84\times 10^{11}$ EOT. A thorough analysis of both these data samples in the sense of background and efficiency estimations was already performed and reported in our previous papers devoted to the search for light vector particles and axion-like particles (ALP). In this work we recalculate the signal yields, which are different due to different cross section and life time of a pseudoscalar particle $a$, and perform a new statistical analysis. As a result, the region of the two dimensional parameter space $m_a - \epsilon$ in the mass range from 1 to 17.1 MeV is excluded. At the mass of the ATOMKI anomaly the values of $\epsilon$ in the range $2.1 \times 10^{-4} < \epsilon < 3.2 \times 10^{-4}$ are excluded., Comment: 6 pages, 2 figures

We performed a search for a new generic $X$ boson, which could be a scalar ($S$), pseudoscalar ($P$), vector ($V$) or an axial vector ($A$) particle produced in the 100 GeV electron scattering off nuclei, $e^- Z \to e^- Z X$, followed by its invisible decay in the NA64 experiment at CERN. No evidence for such process was found in the full NA64 data set of $2.84\times 10^{11}$ electrons on target. We place new bounds on the $S, P, V, A$ coupling strengths to electrons, and set constraints on their contributions to the electron anomalous magnetic moment $a_e$, $|\Delta a_{X}| \lesssim 10^{-15} - 10^{-13}$ for the $X$ mass region $m_X\lesssim 1$ GeV. These results are an order of magnitude more sensitive compared to the current accuracy on $a_e$ from the electron $g-2$ experiments and recent high-precision determination of the fine structure constant., Comment: 6 pages, 4 figures

We present the package for the simulation of DM (Dark Matter) particles in fixed target experiments. The most convenient way of this simulation (and the only possible way in the case of beam-dump) is to simulate it in the framework of the program for tracing particles in the experimental setup. One of the most popular such programs is Geant4. Specifically, the package includes the processes of DM particles production via electron and muon bremsstrahlung off nuclei, resonant in-flight positron annihilation on atomic electrons and gamma to ALP (axion-like particles) conversion on nuclei. Four types of DM mediator particles are considered: vector, scalar, pseudoscalar and axial vector. In particular, for bremsstrahlung the total cross sections are calculated at exact tree level (ETL). The code handles both the case of invisible DM mediator decay and of visible decay into $e^+e^-$ (or into $\gamma \gamma$ in the case of ALP). The software consists of a collection of different classes, inheriting from the Geant4 framework classes, thus the expected use of this package is to include it in a Geant4-based code for the simulation of particles propagation and interaction in the detector. As an example of its usage, we discuss the results obtained from the simulation of a typical active beam-dump experiment, considering $5 \times 10^{12}$ 100 GeV electrons impinging on a lead/plastic scintillator active thick target, showing the expected sensitivity for the four types of DM mediator particles mentioned above., Comment: 10 pages, 4 figures

We show that in nonlocal generalization of standard nonsupersymmetric SU(5) GUT it is possible to solve the problems with the proton lifetime and the Weinberg angle without introduction of additional particles in the spectrum of the theory. Non-local scale responsible for ultraviolet cutoff coincides (up to some factor) with GUT scale. We find that in the simplest nonlocal modification of the SU(5) model $M_{\rm GUT} = 3 * 10^{16}$ GeV . In general case the value of M_GUT is an arbitrary and the most interesting option $M_{\rm GUT} = O(M_{\rm PL})$ could be realized., Comment: 7 pages

We carried out a model-independent search for light scalar (s) and pseudoscalar axionlike (a) particles that couple to two photons by using the high-energy CERN SPS H4 electron beam. The new particles, if they exist, could be produced through the Primakoff effect in interactions of hard bremsstrahlung photons generated by 100 GeV electrons in the NA64 active dump with virtual photons provided by the nuclei of the dump. The a(s) would penetrate the downstream HCAL module, serving as shielding, and would be observed either through their $a(s)\to\gamma \gamma$ decay in the rest of the HCAL detector or as events with large missing energy if the a(s) decays downstream of the HCAL. This method allows for the probing the a(s) parameter space, including those from generic axion models, inaccessible to previous experiments. No evidence of such processes has been found from the analysis of the data corresponding to $2.84\times10^{11}$ electrons on target allowing to set new limits on the $a(s)\gamma\gamma$-coupling strength for a(s) masses below 55 MeV., Comment: This publication is dedicated to the memory of our colleague Danila Tlisov. 7 pages, 5 figures, revised version accepted for publication in Phys. Rev. Lett

The NA64 experiment consists of two detectors which are planned to be located at the electron (NA64e) and muon (NA64$\mu$) beams of the CERN SPS and start operation after the LHC long-stop 2 in 2021. Its main goals include searches for dark sector physics - particularly light dark matter (LDM), visible and invisible decays of dark photons ($A'$), and new light particles that could explain the $^8$Be and $g_{\mu}-2$ anomalies. Here we review these physics goals, the current status of NA64 including recent results and perspectives of further searches, as well as other ongoing or planned experiments in this field. The main theoretical results on LDM, the problem of the origin of the $\gamma-A'$ mixing term and its connection to loop corrections, possible existence of a new light $Z'$ coupled to $L_\mu-L_\tau$ current are also discussed., Comment: 49 pages, 13 figures, to be published in PEPAN journal

We point out that last NA64 bound on coupling constant of hypothetical $X(16.7 MeV)$ vector boson with electrons plus the recent value of the anomalous electron magnetic moment exclude at 90 \% C.L. purely vector or axial vector couplings of $X(16.7)$ boson with electrons. Models with nonzero $V \pm A$ coupling constant with electron survive and they can explain both the electron and muon $g - 2$ anomalies., Comment: 6 pages

The improved results on a direct search for a new X(16.7 MeV) boson which could explain the anomalous excess of $e^+e^-$ pairs observed in the excited 8Be nucleus decays ("Berillium anomaly") are reported. Due to its coupling to electrons, the X boson could be produced in the bremsstrahlung reaction e-Z -> e-ZX by a high-energy beam of electrons incident on active target in the NA64 experiment at the CERN SPS and observed through its subsequent decay into $e^+e^-$ pair. No evidence for such decays was found from the combined analysis of the data samples with total statistics corresponding to 8.4\times 10^{10} electrons on target collected in 2017 and 2018. This allows to set the new limits on the $X$--$e^-$ coupling in the range 1.2 \times 10^{-4} < \epsilon_e < 6.8 \times 10^{-4}, excluding part of the parameter space favored by the Berillium anomaly. We also set new bounds on the mixing strength of photons with dark photons (A') from non-observation of the decay $A' \to e^+e^-$ of the bremsstrahlung A' with a mass below 24 MeV., Comment: 7 pages, 5 figures, 1 table. arXiv admin note: substantial text overlap with arXiv:1803.07748

A search for sub-GeV dark matter production mediated by a new vector boson $A'$, called dark photon, is performed by the NA64 experiment in missing energy events from 100 GeV electron interactions in an active beam dump at the CERN SPS. From the analysis of the data collected in the years 2016, 2017, and 2018 with $2.84\times10^{11}$ electrons on target no evidence of such a process has been found. The most stringent constraints on the $A'$ mixing strength with photons and the parameter space for the scalar and fermionic dark matter in the mass range $\lesssim 0.2$ GeV are derived, thus demonstrating the power of the active beam dump approach for the dark matter search., Comment: 6 pages, 4 figures, version accepted for publication in Phys. Rev. Lett. arXiv admin note: text overlap with arXiv:1710.00971, arXiv:1610.02988

We discuss prospects of searching for a dark photon ($A'$) which serves as mediator between Standard model (SM) particles and light dark matter (LDM) by using the combined results from the NA64 experiment at the CERN SPS running in high-energy electron (NA64e) and muon (NA64$\mu$) modes. We discuss the most natural values and upper bounds on the $A'$ coupling constant to LDM and show they are lying in the range accessible at NA64. While for the projected $ 5\times10^{12}$ electrons on target (EOT) NA64e is able to probe the scalar and Majorana LDM scenarios, the combined NA64e and NA64$\mu$ results with $\simeq 10^{13}$ EOT and a few $10^{13}$ MOT, respectively, will allow covering significant region in the parameter space of the most interesting LDM models. This makes NA64e and NA64$\mu$ extremely complementary to each other and increases significantly the discovery potential of sub-GeV DM., Comment: 16 pages, 4 figures, revised manuscript, matches to PLB version

In this note we estimate the sensitivity of the NA64 experiment to millicharged particles ($\chi$). That experimental facility is dedicated to the searching for dark sector particles in missing energy events at the CERN SPS. We consider missing momentum signatures in the $\simeq$ 100 GeV electron and muon beams and show that the later one allows to obtain more stringent bounds on the millicharge $Q_{\chi}$, which for the $\chi$ masses $100$~MeV $\leq m_{\chi} \leq 500$~MeV at the level $ Q_{\chi}/e\lesssim O(10^{-3}) - O(10^{-2})$., Comment: 9 pages, 3 figures, version accepted for publication in PRD

We report the first results on a direct search for a new 16.7 MeV boson (X) which could explain the anomalous excess of e+e- pairs observed in the excited Be-8 nucleus decays. Due to its coupling to electrons, the X could be produced in the bremsstrahlung reaction e- Z -> e- Z X by a 100 GeV e- beam incident on an active target in the NA64 experiment at the CERN SPS and observed through the subsequent decay into an e+e- pair. With 5.4\times 10^{10} electrons on target, no evidence for such decays was found, allowing to set first limits on the X-e^- coupling in the range 1.3\times 10^{-4} < \epsilon_e < 4.2\times 10^{-4} excluding part of the allowed parameter space. We also set new bounds on the mixing strength of photons with dark photons (A') from non-observation of the decay A'->e+e- of the bremsstrahlung A' with a mass <~ 23 MeV., Comment: 6 pages, 3 figures. Title changed as suggested by Journal; references added; version published in Phys. Rev. Lett

In the L_{\mu} - L_{\tau} model the 3.6$\sigma$ discrepancy between the predicted and measured values of the anomalous magnetic moment of positive muons can be explained by the existence of a new dark boson Z' with a mass in the sub-GeV range, which is coupled at tree level predominantly to the second and third lepton generations. However, at the one-loop level, the Z' coupling to electrons or quarks can be induced via the \gamma -Z' kinetic mixing, which is generated through the loop involving the muon and tau lepton. This loophole has important experimental consequences since it opens up new possibilities, in particular for the complementary searches of the Z' in the ongoing NA64 and incoming dark photon experiments with high-energy electrons. An extension of the model able to explain relic Dark Matter density is also discussed., Comment: 14 pages, 1 figure

Dark photon ($A'$) that couples to the standard model fermions via the kinetic mixing with photons and serves as a mediator of dark matter production could be observed in the high-energy electron scattering $e^- + Z ~\rightarrow e^- + Z + A'$ off nuclei followed by the $A' \to invisible $ decay. We have performed the exact, tree-level calculations of the $A'$ production cross sections and implemented them in the program for the full simulation of such events in the experiment NA64 at the CERN SPS. Using simulations results, we study the missing energy signature for the bremsstrahlung $A' \rightarrow $ invisible decay that permits the determination of the $\gamma-A'$ mixing strength in a wide, from sub-MeV to sub-GeV, $A'$ mass range. We refine and expand our earlier studies of this signature for discovering $A'$ by including corrections to the previously used calculations based on the improved Weizsaker-Williams approximation, which turn out to be significant. We compare our cross sections values with the results from other calculations and find a good agreement between them. The possibility of future measurements with high-energy electron beams and the sensitivity to $A'$ are briefly discussed., Comment: 11 pages, 6 figures, revised version, improved cross-section integrator is used, comparison with bremsstrahlung spectrum is added, final conclusions remain unchanged

A search is performed for a new sub-GeV vector boson ($A'$) mediated production of Dark Matter ($\chi$) in the fixed-target experiment, NA64, at the CERN SPS. The $A'$, called dark photon, could be generated in the reaction $ e^- Z \to e^- Z A'$ of 100 GeV electrons dumped against an active target which is followed by the prompt invisible decay $A' \to \chi \overline{\chi}$. The experimental signature of this process would be an event with an isolated electron and large missing energy in the detector. From the analysis of the data sample collected in 2016 corresponding to $4.3\times10^{10}$ electrons on target no evidence of such a process has been found. New stringent constraints on the $A'$ mixing strength with photons, $10^{-5}\lesssim \epsilon \lesssim 10^{-2}$, for the $A'$ mass range $m_{A'} \lesssim 1$ GeV are derived. For models considering scalar and fermionic thermal Dark Matter interacting with the visible sector through the vector portal the 90% C.L. limits $10^{-11}\lesssim y \lesssim 10^{-6}$ on the dark-matter parameter $y = \epsilon^2 \alpha_D (\frac{m_\chi}{m_{A'}})^4 $ are obtained for the dark coupling constant $\alpha_D = 0.5$ and dark-matter masses $0.001 \lesssim m_\chi \lesssim 0.5 $ GeV. The lower limits $\alpha_D \gtrsim 10^{-3} $ for pseudo-Dirac Dark Matter in the mass region $m_\chi \lesssim 0.05 $ GeV are more stringent than the corresponding bounds from beam dump experiments. The results are obtained by using tree level, exact calculations of the $A'$ production cross-sections, which turn out to be significantly smaller compared to the one obtained in the Weizs\"{a}cker-Williams approximation for the mass region $m_{A'} \gtrsim 0.1$ GeV., Comment: 22 pages, 17 figures, version accepted for publication in PRD

We consider isosinglet scalar extension of a model with a Higgs democracy - multihiggs extension of the SM where each quark and lepton has its own Higgs isodoublet. The addition of light isosinglet scalar allows to solve both muon $g_{\mu}-2$ anomaly and dark matter problem. Also we point out that an extension of the model with $L_{\mu} - L_{\tau}$ vector interaction allows not only explain muon $g_{\mu} - 2$ anomaly but also dark matter density., Comment: 15 pages. Two appendices and several references have been addedSeveral references added

This mini review aims to outline the main experimental and theoretical results related with the search for a new light vector boson proposed as a solution of the muon $g-2$ anomaly. Additionally, I consider a model with infinite number of light vector bosons which can explain the anomaly, while still remaining consistent with current experimental bounds., Comment: Based on talk given at the meeting celebrated Prof. V.A.Matveev jubilee, Dubna, 16 December 2016

We report on a direct search for sub-GeV dark photons (A') which might be produced in the reaction e^- Z \to e^- Z A' via kinetic mixing with photons by 100 GeV electrons incident on an active target in the NA64 experiment at the CERN SPS. The A's would decay invisibly into dark matter particles resulting in events with large missing energy. No evidence for such decays was found with 2.75\cdot 10^{9} electrons on target. We set new limits on the \gamma-A' mixing strength and exclude the invisible A' with a mass < 100 MeV as an explanation of the muon g_\mu-2 anomaly., Comment: 6 pages, 3 figures; Typos corrected, references added

This report, based on the Dark Sectors workshop at SLAC in April 2016, summarizes the scientific importance of searches for dark sector dark matter and forces at masses beneath the weak-scale, the status of this broad international field, the important milestones motivating future exploration, and promising experimental opportunities to reach these milestones over the next 5-10 years., Comment: 66 pages, 15 figures, 3 tables. Workshop website and agenda: http://www-conf.slac.stanford.edu/darksectors2016/ https://indico.cern.ch/event/507783/ Editors: J. Alexander, M. Battaglieri, B. Echenard, R. Essig, M. Graham, E. Izaguirre, J. Jaros, G. Krnjaic, J. Mardon, D. Morrissey, T. Nelson, M. Perelstein, M. Pyle, A. Ritz, P. Schuster, B. Shuve, N. Toro, R. Van De Water

We consider the SM extension with additional light real singlet scalar, right-handed neutrino and nonrenormalizable Yukawa interaction for the first two generations. We show that the proposed model can explain the observed $(g - 2)$ muon anomaly. Phenomenological consequences as flavour violating decays $\tau \rightarrow \mu\mu\mu, \mu \mu e, \mu e e $ are briefly discussed. We also propose the $U_R(1)$ gauge generalization of the SM with complex scalar singlet and nonzero right-handed charges for the first two generations., Comment: Based on the talk given by N.V.Krasnikov at the SNP PSD RAS conference, Dubna 12-15 April 2016, 10 pages

The dark photon ($A'$) production through the mixing with the bremsstrahlung photon from the electron scattering off nuclei can be accompanied by the dominant invisible $A'$ decay into dark-sector particles. In this work we discuss the missing energy signature of this process in the experiment NA64 aiming at the search for $A'\to invisible$ decays with a high-energy electron beam at the CERN SPS. We show the distinctive distributions of variables that can be used to distinguish the $A'\to invisible$ signal from background. The results of the detailed simulation of the detector response for the events with and without $A'$ emission are presented. The efficiency of the signal event selection is estimated. It is used to evaluate the sensitivity of the experiment and show that it allows to probe the still unexplored area of the mixing strength $10^{-6}\lesssim \epsilon \lesssim 10^{-2}$ and masses up to $M_{A'} \lesssim 1$ GeV. The results obtained are compared with the results from other calculations. In the case of the signal observation, a possibility of extraction of the parameters $M_{A'}$ and $\epsilon$ by using the missing energy spectrum shape is discussed. We consider as an example the $A'$ with the mass 16.7 MeV and mixing $\epsilon \lesssim 10^{-3}$, which can explain an excess of events recently observed in nuclear transitions of an excited state of $^8$Be. We show that if such $A'$ exists its invisible decay can be observed in NA64 within a month of running, while data accumulated during a few months would allow also to determine the $\epsilon$ and $M_{A'}$ parameters., Comment: 12 pages, 15 figures. Revised version

In the Standard Model (SM) the branching ratio for the decay $K_L \to \nu \bar{\nu}$ into two neutrinos is helicity suppressed and predicted to be very small $ \leq O(10^{-17})$. We consider two natural extensions of the SM, such as two-Higgs-doublet model (2HDM) and the $\nu$MSM with additional singlet scalar, those main features is that they can lead to an enhanced $Br(K_L \to invisible)$. In the 2HDM the smallness of the neutrino mass is explained due to the smallness of the second Higgs doublet vacuum expectation value. Moreover, the $\nu$MSM extension with additional singlet field can explain the $(g - 2)$ muon anomaly. The considered models demonstrate that the $K_L \to invisible $ decay is a clean probe of new physics scales well above 100 TeV, that is complementary to rare $K \to \pi+invisible$ decay, and provide a strong motivation for its sensitive search in a near future low-energy experiment., Comment: 11 pages, no figures

The decay $K_L \to invisible$ has never been experimentally tested. In the Standard Model (SM) its branching ratio for the decay into two neutrinos is helicity suppressed and predicted to be $Br(K_L \to \nu \bar{\nu}) \lesssim 10^{-10}$. We consider several natural extensions of the SM, such as two-Higgs-doublet (2HDM), 2HDM and light scalar, and mirror dark matter models, those main feature is that they allow to avoid the helicity suppression factor and lead to an enhanced $Br(K_L \to invisible)$. For the decay $K_L \to \nu \bar{\nu}$ the smallness of the neutrino mass in the considered 2HDM model is explained by the smallness of the second Higgs doublet vacuum expectation value. The small nonzero value of the second Higgs isodoublet can arise as a consequence of nonzero quark condensate. We show that taking into account the most stringent constraints from the $K \to \pi +invisible$ decay, this process could be in the region of $Br(K_L \to invisible) \simeq 10^{-8}-10^{-6}$, which is experimentally accessible. In some scenarios the $K_L \to invisible$ decay could still be allowed while the $K \to \pi +invisible$ decay is forbidden. The results obtained show that the $K_L \to invisible$ decay is a clean probe of new physics scales well above 100 TeV, that is complementary to rare $K \to \pi+invisible$ decay, and provide a strong motivation for its sensitive search in a near future experiment., Comment: 6 pages. Discussion and references added

The 3.6 \sigma discrepancy between the predicted and measured values of the anomalous magnetic moment of positive muons can be explained by the existence of a new dark boson Z_\mu with a mass in the sub-GeV range, which is coupled predominantly to the second and third lepton generations through the L_\mu - L_\tau current . After a discussion of the present phenomenological bounds on the Z_\mu coupling, we show that if the Z_\mu exists, it could be observed in the reaction \mu+Z \to \mu+Z+Z_\mu of a muon scattering off nuclei by looking for an excess of events with large missing muon beam energy in a detector due to the prompt bremsstrahlung Z_\mu decay Z_\mu \to \nu\nu into a couple of neutrinos. We describe the experimental technique and the preliminary study of the feasibility for the proposed search. We show that this specific signal allows for a the search for the Z_\mu with a sensitivity in the coupling constant \alpha_\mu > 10^{-11}, which is 3 orders of magnitude higher than the value required to explain the discrepancy. We point out that the availability of high-energy and -intensity muon beams at CERN SPS provides a unique opportunity to either discover or rule out the Z_\mu in the proposed search in the near future. The experiment is based on the missing-energy approach developed for the searches for invisible decays of dark photons and (pseudo)scalar mesons at CERN and is complementary to these experiments., Comment: 13 pages, 9 figures. Version to appear in PRD, refs. and discussions added, title modified in journal

Several models of dark matter suggest the existence of dark sectors consisting of SU(3)_C x SU(2)_L x U(1)_Y singlet fields. These sectors of particles do not interact with the ordinary matter directly but could couple to it via gravity. In addition to gravity, there might be another very weak interaction between the ordinary and dark matter mediated by U'(1) gauge bosons A' (dark photons) mixing with our photons. In a class of models the corresponding dark gauge bosons could be light and have the $\gamma$-A' coupling strength laying in the experimentally accessible and theoretically interesting region. If such A' mediators exist, their di-electron decays A' -> e+e- could be searched for in a light-shining-through-a-wall experiment looking for an excess of events with the two-shower signature generated by a single high energy electron in the detector. A proposal to perform such an experiment aiming to probe the still unexplored area of the mixing strength 10^-5 < $\epsilon$ < 10^-3 and masses M_A' < 100 MeV by using 10-300 GeV electron beams from the CERN SPS is presented. The experiment can provide complementary coverage of the parameter space, which is intended to be probed by other searches. It has also a capability for a sensitive search for A's decaying invisibly to dark-sector particles, such as dark matter, which could cover a significant part of the still allowed parameter space. The full running time of the proposed measurements is requested to be up to several months, and it could be taken at different SPS secondary beams., Comment: 42 pages, 19 figures. This work is a continuation of work started in arXiv:1308.6521

We investigate the relation between frequentist and Bayesian approaches. Namely, we find the "frequentist" Bayes prior \pi_{f}(\lambda,x_{obs}) = -\frac{\int_{-\infty}^{x_{obs}}\frac{\partial f(x,\lambda)}{\partial \lambda}dx}{f(x_{obs},\lambda)} (here f(x,\lambda) is the probability density) for which the results of frequentist and Bayes approaches to the determination of confidence intervals coincide. In many cases (but not always) the "frequentist" prior which reproduces frequentist results coincides with the Jeffreys prior., Comment: 8 pages, 1 figure

We propose modified frequentist definitions for the determination of confidence intervals for the case of Poisson statistics. We require that 1-\beta^{'} \geq \sum_{n=o}^{n_{obs}+k} P(n|\lambda) \geq \alpha^{'}. We show that this definition is equivalent to the Bayesian method with prior \pi(\lambda) \sim \lambda^{k}. Other generalizations are also considered. In particular, we propose modified symmetric frequentist definition which corresponds to the Bayes approach with the prior function \pi(\lambda) \sim 1/2(1 + \frac{n_{obs}}{\lambda}). Modified frequentist definitions for the case of nonzero background are proposed., Comment: 15 pages, 3 figures. Talk given by N.V. Krasnikov at Workshop "Calculations for modern and future colliders", Dubna, July 2012, Russia