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.

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. The analysis, performed using data collected by the NA64-e experiment in 2022, is based on calorimetric measurements, exploiting the different interaction mechanisms of electrons and hadrons in the NA64 detector. We determined the contamination by comparing the results obtained using the nominal electron/positron beamline configuration with those from a dedicated setup, in which only hadrons impinged on the detector. We also obtained an estimate of the relative protons, anti-protons and pions yield by exploiting the different absorption probabilities of these particles in matter. We cross-checked our results with a dedicated Monte Carlo simulation for the hadron production at the primary T2 target, finding a good agreement with the experimental measurements.

The general construction of the Cauchy problem solution for the one-dimensional nonlocal population Fisher–KPP equation is briefly described in terms of semiclassical asymptotics based on the complex WKB-Maslov method. For the particular case of the equation under consideration, a family of leading terms of the semiclassical asymptotics is constructed in an explicit form, and their qualitative behavior is investigated. The behavior of the asymptotic solutions and of the corresponding numerical solutions constructed using the software package Comsol Multiphysics is compared.

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.

The extension of Standard Model made by inclusion of additional $U(1)$ gauge ${L}_{\ensuremath{\mu}}\ensuremath{-}{L}_{\ensuremath{\tau}}$ 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 ${Z}^{\ensuremath{'}}$ 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 ${Z}^{\ensuremath{'}}$ 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 $2.84\ifmmode\times\else\texttimes\fi{}{10}^{11}$ electrons impinging with 100 GeV on an active thick target. The resulting limits touch the muon $g\ensuremath{-}2$ preferred band for values of the ${Z}^{\ensuremath{'}}$ mass of order of 1 MeV, while the sensitivity projections for the future high-statistics NA64-$e$ runs demonstrate the power of the electrons/positron beam approach in this theoretical scenario.

We propose the approach to constructing semiclassical spectral series for the generalized multidimensional stationary Gross–Pitaevskii equation with a nonlocal interaction term. The eigenvalues and eigenfunctions semiclassically concentrated on a curve are obtained. The curve is described by the dynamic system of moments of solutions to the nonlocal Gross–Pitaevskii equation. We solve the eigenvalue problem for the nonlocal stationary Gross–Pitaevskii equation basing on the semiclassical asymptotics found for the Cauchy problem of the parametric family of linear equations associated with the time-dependent Gross–Pitaevskii equation in the space of extended dimension. The approach proposed uses symmetries of equations in the space of extended dimension.

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→e^{-}ZX, followed by its invisible decay in the NA64 experiment at CERN. No evidence for such a process was found in the full NA64 dataset of 2.84×10^{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}, |Δa_{X}|≲10^{-15}-10^{-13} for the X mass region 1  MeV≲m_{X}≲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.

The current most stringent constraints for the existence of sub-GeV dark matter coupling to Standard Model via a massive vector boson A 0 were set by the NA64 experiment for the mass region m A 0 ≲ 250 MeV, by analyzing data from the interaction of 2 . 84 × 10 11 100-GeV electrons with an active thick target and searching for missing-energy events. In this work, by including A 0 production via secondary positron annihilation with atomic electrons, we extend these limits in the 200 – 300 MeV region by almost an order of magnitude, touching for the first time the dark matter relic density constrained parameter combinations. Our new results demonstrate the power of the resonant annihilation process in missing energy dark-matter searches, paving the road to future dedicated e þ beam efforts.

Yu. M. Andreev, D. Banerjee, J. Bernhard, V. E. Burtsev, N. Charitonidis, A. G. Chumakov, 14 D. Cooke, P. Crivelli, E. Depero, A. V. Dermenev, S. V. Donskov, R. R. Dusaev, T. Enik, A. Feshchenko, V. N. Frolov, A. Gardikiotis, S. G. Gerassimov, 8 S. N. Gninenko, M. Hösgen, M. Jeckel, V. A. Kachanov, A. E. Karneyeu, G. Kekelidze, B. Ketzer, D. V. Kirpichnikov, M. M. Kirsanov, V. N. Kolosov, I. V. Konorov, 8 S. G. Kovalenko, V. A. Kramarenko, 9 L. V. Kravchuk, N. V. Krasnikov, 7 S. V. Kuleshov, V. E. Lyubovitskij, 14, 15 V. Lysan, V. A. Matveev, Yu. V. Mikhailov, L. Molina Bueno, 17 D. V. Peshekhonov, V. A. Polyakov, B. Radics, R. Rojas, A. Rubbia, V. D. Samoylenko, H. Sieber, D. Shchukin, V. O. Tikhomirov, I. Tlisova, A. N. Toropin, A. Yu. Trifonov, 14 B. I. Vasilishin, G. Vasquez Arenas, P. V. Volkov, 9 V. Yu. Volkov, and P. Ulloa

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 a shield, and would be observed either through their a(s)→γγ decay in the rest of the HCAL detector, or as events with a large missing energy if the a(s) decays downstream of the HCAL. This method allows for the probing of 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 2.84×10^{11} electrons on target, allowing us to set new limits on the a(s)γγ-coupling strength for a(s) masses below 55 MeV.

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.

Recently, the ATOMKI experiment has reported new evidence for the excess of e+e- events with a mass ∼ 17 MeV in the nuclear transitions of 4 He, that they previously observed in measurements with 8 Be. These observations could be explained by the existence of a new vector X17 boson. So far, the search for the decay X17→e+e- with the NA64 experiment at the CERN SPS gave negative results. Here, we present a new technique that could be implemented in NA64 aiming to improve the sensitivity and to cover the remaining X17 parameter space. If a signal-like event is detected, an unambiguous observation is achieved by reconstructing the invariant mass of the X17 decay with the proposed method. To reach this goal an optimization of the X17 production target, as well as an efficient and accurate reconstruction of two close decay tracks, is required. A dedicated analysis of the available experimental data making use of the trackers information is presented. This method provides independent confirmation of the NA64 published results [1], validating the tracking procedure. The detailed Monte Carlo study of the proposed setup and the background estimate show that the goal of the proposed search is feasible.

We propose an approach to constructing semiclassical solutions for the generalized multidimensional Gross–Pitaevskii equation with a nonlocal interaction term. The key property of the solutions is that they are concentrated on a one-dimensional manifold (curve) that evolves over time. The approach reduces the Cauchy problem for the nonlocal Gross–Pitaevskii equation to a similar problem for the associated linear equation. The geometric properties of the resulting solutions are related to Maslov’s complex germ, and the symmetry operators of the associated linear equation lead to the approximation of the symmetry operators for the nonlocal Gross–Pitaevskii equation.

We propose an approximate analytical approach to a ( 1 + 1 ) dimensional two-component system consisting of a nonlocal generalization of the well-known Fisher–Kolmogorov–Petrovskii– Piskunov (KPP) population equation and a diffusion equation for the density of the active substance solution surrounding the population. Both equations of the system have terms that describe the interaction effects between the population and the active substance. The first order perturbation theory is applied to the system assuming that the interaction parameter is small. The Wentzel–Kramers–Brillouin (WKB)–Maslov semiclassical approximation is applied to the generalized nonlocal Fisher–KPP equation with the diffusion parameter assumed to be small, which corresponds to population dynamics under certain conditions. In the framework of the approach proposed, we consider symmetry operators which can be used to construct families of special approximate solutions to the system of model equations, and the procedure for constructing the solutions is illustrated by an example. The approximate solutions are discussed in the context of the released activity effect variously debated in the literature.

Recently we derived a soft-wall AdS-Schwarzschild approach at small temperatures for the description of hadrons with integer spin and adjustable number of constituents (mesons, tetraquarks, dibaryons, etc.). In the present paper we extend our formalism to states with half-integer spin (baryons, pentaquarks, etc.), presenting analytical results for the temperature dependence of their masses and form factors.

We consider an approach to constructing approximate analytical solutions for the one-dimensional twocomponent reaction-diffusion model describing the dynamics of population interacting with the active substance surrounding the population. The system of model equations includes the nonlocal generalized Fisher–Kolmogorov–Petrovsky–Piskunov equation for the population density and the diffusion equation for the density of the active substance. Both equations contain additional terms describing the mutual influence of the population and the active substance. To find approximate solutions of the system of model equations, we first use the perturbation method with respect to the small parameter of interaction between the population and the active substance. Then we apply the well-known iterative method developed by G. Adomian to solve equations for terms of perturbation series. In the method proposed, the solution is presented as a series whose terms are determined by the corresponding iterative procedure. In this work, the diffusion operator is taken as the operator for which the inverse operator is expressed in terms of the diffusion propagator. This allows one to find the approximate solutions in the class of functions decreasing at infinity. As an illustration, we consider an example of solving the Cauchy problem for the initial functions of a Gaussian form.

The Adomian decomposition method is applied to construct an approximate solution of the generalized one-dimensional Fisher–Kolmogorov–Petrovsky–Piskunov equation describing the population dynamics with nonlocal competitive losses. An approximate solution is constructed in the class of decreasing functions. The diffusion operator is taken as a reversible linear operator. The inverse operator is presented in terms of the diffusion propagator. An example of the approximate solution of the Cauchy problem for the function of competitive losses and for the initial function of the Gaussian type is considered.

A search for sub-GeV dark matter production mediated by a new vector boson A^{'}, called a 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 2.84×10^{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 ≲0.2  GeV are derived, thus demonstrating the power of the active beam dump approach for the dark matter search.

The NA64 collaboration proposes to carry out further searches for dark sector and other rare processes in missing energy events from high energy muon interactions in the hermetic detector at the CERN SPS starting from the run in 2021. The dark sector of particles predominantly weakly-coupled to the second and possibly third generations of the Standard Model is motivated by several theoretically interesting models. Additional to gravity this new very weak interaction between the visible and dark sector could be mediated either by a scalar (Sμ) or U ′(1) gauge bosons (Zμ) interacting with ordinary muons. In a class of Lμ − Lτ models the corresponding Zμ could be light and have the coupling strength laying in the experimentally accessible region. If such Zμ mediator exists it could also explain the muon (g−2)μ anomaly the discrepancy between the predicted and measured values of the muon anomalous magnetic moment. We propose an extension of the experiment NA64 called NA64μ to search for invisible decays of the Zμ either to neutrinos or light DM aiming to probe the still unexplored area of the coupling strengths and masses MZμ . 200 MeV with the ' 100 − 160 GeV M2 beam. The NA64μ has the capability of a sensitive search for Sμs decaying invisibly to dark-sector particles, such as dark matter and millicharged particles and will cover a part of the parameter space complementary to what is intended to be probed by other searches Morevoer, the experiment will probe completely the Zμ parameter space (coupling vs mass) that could explain the muon (g− 2)μ anomaly and could be used to search lepton flavour violation process of the μ− τ conversion.

A semiclassical approximation approach based on the Maslov complex germ method is considered in detail for the one-dimensional nonlocal Fisher–Kolmogorov–Petrovskii–Piskunov (Fisher–KPP) equation under the supposition of weak diffusion. In terms of the semiclassical formalism developed, the original nonlinear equation is reduced to an associated linear partial differential equation and some algebraic equations for the coefficients of the linear equation with a given accuracy of the asymptotic parameter. The solutions of the nonlinear equation are constructed from the solutions of both the linear equation and the algebraic equations. The solutions of the linear problem are found with the use of symmetry operators. A countable family of the leading terms of the semiclassical asymptotics is constructed in explicit form. The semiclassical asymptotics are valid by construction in a finite time interval. We construct asymptotics which are different from the semiclassical ones and can describe evolution of the solutions of the Fisher–KPP equation at large times. In the example considered, an initial unimodal distribution becomes multimodal, which can be treated as an example of a space structure.