The multi-messenger exploration of dark matter and physics beyond the Standard Model has emerged as a central direction in modern astro-particle physics, particularly following the discovery of gravitational waves. In this work, we present a comprehensive review and forward-looking perspective on machine-learning-enhanced multi-messenger approaches, combining information from gravitational waves, cosmic rays, gamma rays, neutrinos, and collider experiments. We summarize the current state of the field, discuss recent methodological developments, and outline a coherent research program aimed at integrating heterogeneous datasets within a unified inference framework. Our collaboration proposes here a plan for forthcoming analyses aiming at extracting information on the properties and interactions of dark matter, and finally on its genesis, combining multi-messenger astronomy techniques and inputs from laboratory physics. The main objectives planned in this line of research comprise: i) the multi-messenger analysis of new physics in cosmology, including mainly, but not only, several different models of dark matter; ii) the phenomenology of new physics signatures in ground-based cosmic rays experiments, with cross-correlation to the corresponding physical, astrophysical and cosmological observations; iii) the development of machine learning methods for data analysis in ground-based cosmic rays experiments, in light of the new physics signatures. We note that several groups have explored the use of multi-messenger observations, including gravitational waves, to probe alternative dark matter candidates. The present work builds on these developments by focusing on the role of machine learning in integrating heterogeneous datasets. We foresee that such a cross-fertilizing approach will represent the right path to extract information about the main questions left in fundamental physics.

We present GT simulation, an open-source package for modeling the propagation of cosmic rays in arbitrary electromagnetic fields and media. The calculation proceeds by numerically integrating the equations of motion and iteratively reconstructing the trajectories of individual particles. During trajectory computation, GT simulation can optionally account for concomitant energy losses due to radiative braking and interactions with the medium, as well as the production of secondary particles and their subsequent propagation. The package architecture allows users to employ arbitrary models of the electromagnetic field and medium, and it also includes implementations of several widely used models for the magnetosphere, heliosphere, and the Galaxy. The correctness of the package components and the validity of the resulting physical outcomes are demonstrated through several application examples that reproduce fundamental physical effects. GT simulation is publicly available Github for community use and contribution.

This paper extensively explores the concept of dark atoms, hypothetical stable lepton-like particles with a charge of −2n (where n is any natural number) that form neutral bound states with n primordial helium nuclei. The discussion begins with the introduction of multiply charged stable particles. Next, the formation and evolution of dark atoms are examined, followed by a review of related constraints. The capture of dark atoms by the Earth and implications for direct dark matter search are subsequently discussed. Then, the quantum-mechanical description of bound states between dark atoms and ordinary nuclei is addressed. Moreover, procedures for systematic comparisons with this model, which have general interest, are presented considering the DAMA published results on the dark matter annual and diurnal modulation signatures as a benchmark.

We present a framework that reconstructs time-resolved galactic cosmic-ray (GCR) proton and helium energy spectra from the global neutron monitor network, providing data about GCR flux without direct satellite observations. Two methods are utilized and compared: a calibrated yield function plus force-field scheme and artificial neural networks trained on multi-station neutron monitor count rates coupled with heliophysical indices. The reconstructed spectral time series reproduce both large-scale solar-cycle modulation and short-term disturbances and extend to periods lacking daily spacecraft data, including 2006-2011 (consistent with PAMELA) and 2019-2022 (consistent with AMS-02 Bartels rotation averages). Artificial neural networks deliver excellent performance across energies, with markedly lower mean absolute percentage error and χ^2/dof near unity. A thorough validation confirms robustness and establishes neutron monitors as an effective real-time GCR spectrometer that can be utilized for various purposes.

Within the framework of the XHe hypothesis, the positive results of the DAMA/NaI and DAMA/LIBRA experiments on the direct search for dark matter particles can be explained by the annual modulation of the radiative capture of dark atoms into low-energy bound states with sodium nuclei. Since this effect is not observed in other underground WIMP (weakly interacting massive particle) search experiments, it is necessary to explain these results by investigating the possibility of the existence of low-energy bound states between dark atoms and the nuclei of matter. Numerical modeling is used to solve this problem, since the study of the XHe–nucleus system is a three-body problem and leaves no possibility of an analytical solution. To understand the key properties and patterns underlying the interaction of dark atoms with the nuclei of baryonic matter, we develop the quantum mechanical description of such an interaction. In the numerical quantum mechanical model presented, takes into account the effects of quantum physics, self-consistent electromagnetic interaction, and nuclear attraction. This approach allows us to obtain a numerical model of the interaction between the dark atom and the nucleus of matter and interpret the results of direct experiments on the underground search for dark matter, within the framework of the dark atom hypothesis. Thus, in this paper, for the first time, steps are taken towards a consistent quantum mechanical description of the interaction of dark atoms, with unshielded nuclear attraction, with the nuclei of atoms of matter. The total effective interaction potential of the OHe–Na system has therefore been restored, the shape of which allows for the preservation of the integrity and stability of the dark atom, which is an essential requirement for confirming the validity of the OHe hypothesis.

In the PAMELA experiment, precipitation of electrons from the Earth’s radiation belt was detected at moments of recording gamma ray bursts of extraterrestrial origin, leading to a hypothesis about the relationship between these phenomena. This work provides estimates of the number of electrons that have interacted with gamma quanta through the Compton effect and changed their energy and trajectories in the so-called toy model approximation. A formula is obtained for determining the cross section of the interaction between a gamma quantum and a stationary electron, depending on the angle of electron emission and the energy spectrum of the emitted electrons. A narrow peak is observed near the maximum energy in the energy distribution of secondary electrons, which is close to the energy of the initial gamma quantum. An estimate is obtained for the upper limit of the contribution from the considered process to the excess of the electron count rate over the background value recorded in the PAMELA experiment. It is found that the proposed mechanism does not explain the observed effect because the calculated electron count rate is several orders of magnitude lower and can be explained by the small Compton scattering cross section.

Due to the structural features of the geomagnetic field, Earth’s subpolar regions are the most affected by cosmic ray variations and other space weather phenomena. High grounds located in these regions are especially promising in terms of space weather research. Nowadays, there are only two high-altitude subpolar space weather observatories highly sensitive to solar activity, both located in Antarctica. In the Russian Arctic, we have several mountainous regions with geophysical conditions similar to that of the Antarctic ice sheet. In this paper, we calculate physical quantities that determine conditions for space weather observation in these regions and explore the expediency of building new scientific stations there. We show that establishment of the stations would enhance sensitivity of space weather observatory network and increase the number of detectable solar proton events.

Neutron monitors (NMs), located at different points on the planet, allow us to study the time, energy, and angular characteristics of galactic and solar particle fluxes. Since NMs are located inside Earth's magnetosphere, their response depends on their location on the planet's surface, which can be characterized by the geomagnetic cutoff rigidity. Its calculation depends on the magnetic field model, the date, and even on numerical methods. The paper presents calculated geomagnetic cutoff rigidities at the locations of some neutron monitors and compares the cutoff values with the calculation results obtained by other authors, including a comparison of the time dynamics over the past decade. We show that the geomagnetic cutoff rigidities obtained for 2020 by the IGRF-14 model differ from those derived by IGRF-13; however, for 2015 the difference between the models is negligible. We demonstrate a tendency for the geomagnetic cutoff rigidity to decrease over time, especially at midlatitudes. Comparison of the obtained geomagnetic cutoff rigidities with those obtained by other authors has shown that in most cases the difference does not exceed 0.2 GV. Such discrepancies are significant only in the circumpolar region, where particles are mostly shielded by Earth’s atmosphere rather than by the geomagnetic field. We show that the accuracy of the algorithm in use is comparable to that of other existing instruments and is sufficient for calculating neutron monitor responses.

The article develops a method for determining the geomagnetic cutoff rigidity based on tracing of charged particles in Earth’s magnetic field using the particle-in-cell method implemented in the Buneman–Boris scheme. In order to test the method, the geomagnetic cutoff rigidity in the field of an ideal dipole and in the field given by the IGRF model are calculated. In the first case, the obtained data are compared with analytical values. The calculation accuracy in this case is 3 MV. In the second case, the penumbra pattern is reproduced in different geographical locations, for different periods, and the stability of the method to small perturbations of the initial parameters is investigated. As the main results, the article constructs and analyzes geomagnetic cutoff rigidity maps at low-orbit satellite altitudes for different directions in space as well as their variations from 1900 to 2015.

A simple and robust method of reconstruction of the geomagnetically trapped proton fluxes detected with the PAMELA spectrometer is proposed. Instead of multiple calculations of the effective area for different pitch-angles and different orientations of the instrument relative to the geomagnetic field vector, a value of an effective geometrical factor (GF) is estimated using one simulation sample with additional information about the instrument’s orientation relative to the vector of the Earth magnetic field. In this procedure, the additivity of the geometrical factor for different parts of the instrument’s field of view (FOV) is used. The simulation data sample is obtained in a standard way using Monte Carlo calculations of the isotropic flux. The method was tested on the task of reconstruction of the angular distribution of the Galactic proton flux. The fluxes in the Earth’s Inner Radiation Belt (IRB) recovered with this method were compared with the measurements of the NOAA-17 experiment and showed a good agreement.

A model is created of the motion of galactic cosmic ray particles in the Earth’s magnetosphere, as defined by the IGRF and CHAOS models of the magnetic field. A second model contains a lithospheric field component that is missing from the first model. Power spectra are obtained for the flux of galactic cosmic rays at a fixed height above the Earth’s surface, and a difference is discovered at high orders of multipole expansion l > 7 . When l > 20 , the result can be explained by the contribution from the lithospheric component of the magnetic field in the CHAOS model, relative to the IGRF. When l ⩽ 20 , it can be explained by the difference in the accuracy of describing the main field, since the IGRF is limited to the 13th order of expansion.

This work presents the results of the analysis of 27-day variations in the flux of galactic protons registered by STEREO, SOHO, and AMS-02 in 2015–2016. We calculate variations’ amplitude using several different approaches and propose a description of its energy dependence in the range of magnetic rigidity from approximately 0.3 to 100 GV. We also analyse variations of the solar modulation potential, which is the only parameter of force-field model, and consider the possibility of describing the 27-day variations of galactic cosmic rays within the framework of this model. It is shown that rigidity dependence of the 27-day variations amplitude cannot be properly described using this simple approximation.

High anisotropy of geomagnetically trapped particles’ fluxes requires utilization of a complex methodology for their reconstruction from in-flight measurements. For precise position-sensitive instruments operating in the event-by-event mode, a standard approach is the one originally developed for the SAMPEX/MAST experiment. It consists in calculation of the instrument’s effective areas averaged over gyro-phase angle as a function of pitch angle of detected particles for detector’s different orientations relative to the geomagnetic field vector. This orientation normally changes as the instrument moves in space. Moreover, some space vehicles bearing a measuring instrument may and do change their orientation during flight by rotation of the instrument or as a whole. Each possible orientation needs an independent calculation of effective areas for each possible pitch angle, which is usually done by means of Monte-Carlo simulation. Therefore, especially for sophisticated devices, the calculation of an accurate and representative response function (consisting of a set of effective areas) may involve a vast amount of computation.In this paper, we propose a simplified approach, which is based on the assumption that for an anisotropic flux, the angular sphere the particles come to the detector from can be split into solid angle domains, within which the flux can be treated as isotropic. This allows one to use much easier computed geometrical factor or acceptance of the instrument as the proportionality factor. This method suggests that it can be calculated with respect to registration of the particles from these domains (we call it partial acceptance). The main advantage of the presented method is that the whole set of partial acceptances for each instrument orientation relative to the geomagnetic field vector and for all available values of (equatorial) pitch-angle for this orientation can be obtained from one simulation sample (for the given energy) of isotropic flux.

The lack of positive evidence for Weakly Interacting Massive Particles (WIMPs) as well as the lack of discovery of supersymmetric (SUSY) particles at the LHC may appeal to a non-supersymmetric solution for the Standard Model problem of the Higgs boson mass divergence, the origin of the electroweak energy scale and the physical nature of the cosmological dark matter in the approach of composite Higgs boson. If the Higgs boson consists of charged constituents, their binding can lead to stable particles with electroweak charges. Such particles can take part in sphaleron transitions in the early Universe, which balance their excess with baryon asymmetry. Constraints on exotic charged species leave only stable particles with charge −2n possible, which can bind with n nuclei of primordial helium in neutral dark atoms. The predicted ratio of densities of dark atoms and baryonic matter determines the condition for dark atoms to dominate in the cosmological dark matter. To satisfy this condition of the dark-atom nature of the observed dark matter, the mass of new stable −2n charged particles should be within reach of the LHC for their searches. We discuss the possibilities of dark-atom binding in multi-atom systems and present state-of-the-art quantum mechanical descriptions of dark-atom interactions with nuclei. Annual modulations in such interactions with nuclei of underground detectors can explain the positive results of DAMA/NaI and DAMA/LIBRA experiments and the negative results of the underground WIMP searches.

The method for determining the geomagnetic cutoff rigidity is presented, based on tracing charged particles in the Earth’s magnetic field using the particle-in-cell model implemented in the Buneman–Boris method. The method verification results are given, along with comparisons to theoretical calculations in the ideal dipole field and existing calculations in the real field. The developed procedure shows high reliability through the replication of known effects. In a dipolar approximation, it is much more accurate than theoretical calculations. A typical pattern of the geomagnetic cutoff penumbra is reproduced.

The future space-based GAMMA-400 scientific observatory is being developed under the Federal Space Program of Russian Federation in the period from 2016-2025. This observatory includes a γ-ray telescope, which will detect gamma rays in the energy range from ~20 MeV to several TeV with high angular and energy resolutions and cosmic-ray electrons + positrons up to several tens of TeV using main and lateral appertures. Recent experimental observations indicate a possible existence of a break in the electrons + positrons spectrum at around TeV energies. A number of speculations to explain this phenomenon have arisen. This article presents the method of high-energy electrons detection from the lateral aperture of the GAMMA-400 gamma-ray telescope. This method implements the machine learning analysis and provides the high-energy proton background rejection at the level of 10$^4$ in the energy range from 100 GeV to 10 TeV. The effective acceptance for electron detection with such proton rejection is about 0.52 m$^2$×sr for the four lateral sides of the GAMMA-400 gamma-ray telescope. This effective acceptance exceeds by several times that of CALET and DAMPE experiments. This capability of our instrument will allow to improve significantly the measurements of electron + positron flux above 1 TeV and, hence, understand better the debatable spectrum break.

The space observatory GAMMA-400 is processed currently in accordance with the Federal Space Program of the Russian Federation for 2016–2025. The observatory includes a gamma-ray telescope for experimental studies of gamma rays in the energy range from ~20 MeV to ~1 TeV with high angular and energy resolution, as well as for research of electrons + positrons at energies above 100 GeV in both the main (top-down), and lateral apertures. At present time, there are experimental indications concerning the possibility of existing of spectrum break in electrons + positrons intensities about TeV energies. This point stimulates several speculations to explain such phenomena. In this paper we examined capabilities of GAMMA-400 telescope to explore this problem. The methods for electron detection in the energy range from 100 GeV up to 10 TeV from the lateral aperture of a gamma-ray telescope are presented. Also, the results of calculation for proton rejection factor and for electron acceptance are revealed.

A new way of estimating the effective energy of neutron monitors is proposed. The technique is based on direct observations of 27-day variations of galactic cosmic rays in the AMS-02 experiment at the maximum of solar cycle 24 (2014–2015). The dependence of the amplitude of 27-day variations on particle rigidity is plotted with subsequent determination of the energy at which the amplitude of the neutron monitor’s variations in the count rate during the same time interval becomes equal to the one obtained in space observations. The dependence of the recovered neutron-monitor effective energy on the rigidity of the geomagnetic cutoff obtained by processing the data from several neutron monitors is studied.

A Forbush decrease (FD) is a sudden drop of cosmic-ray intensity arising as an effect of coronal mass ejection (CME) propagation in interplanetary space. The different physical properties of each CME cause variability in the FDs observed by scientific instruments. A comprehensive study of both phenomena is required to properly understand the processes involved in FDs. Most of the current studies in this field use experimental data obtained by ground-based apparatus that measure the flux of cosmic rays via their interaction with Earth’s atmosphere. Direct measurements in space of FDs are rather rare. In this work, we present the results obtained by the spacecraft-borne experiment Payload for Antimatter Matter Exploration and Light-nuclei Astrophysics (PAMELA). The experiment took data from 15 June 2006 until January 2016. A series of FDs during the period 2006 – 2013 were studied. Only significant events with amplitude ≥ 10 R = 1.1 – 2.9 GV were taken into account. The dependencies of the recovery times on the particle rigidity were obtained for FD events generated by halo-type CMEs.