Particles, Volume 4, Issue 2 (June 2021) – 16 articles

In this article, the general solution of the tachyonic Klein–Gordon equation is obtained as a Fourier integral performed on a suitable path in the complex $\omega$-plane. In particular, it is proved that this solution does not contain any superluminal components under the given boundary conditions. On the basis of this result, we infer that all possible spacelike wave equations describe the dynamics of subluminal particles endowed with imaginary mass. This result is validated for the Chodos equation, used to describe the hypothetical superluminal behaviour of the neutrino. In this specific framework, it is proved that the wave packet propagates in spacetime with subluminal group velocities and that it behaves as a localized wave for sufficiently small energies. Full article

Hall Effect Thrusters (HETs) are nowadays widely used for satellite applications because of their efficiency and robustness compared to other electric propulsion devices. Computational modelling of plasma in HETs is interesting for several reasons: it can be used to predict thrusters’ operative life; moreover, it provides a better understanding of the physical behaviour of this device and can be used to optimize the next generation of thrusters. In this work, the discharge within the accelerating channel and near-plume of HETs has been modelled by means of an axisymmetric hybrid approach: a set of fluid equations for electrons has been solved to get electron temperatures, plasma potential and the discharge current, whereas a Particle-In-Cell (PIC) sub-model has been developed to capture the behaviour of neutrals and ions. A two-region electron mobility model has been incorporated. It includes electron–neutral/ion collisions and uses empirical constants, that vary as a continuous function of axial coordinates, to take into account electron–wall collisions and Bohm diffusion/SEE effects. An SPT-100 thruster has been selected for the verification of the model because of the availability of reliable numerical and experimental data. The results of the presented simulations show that the code is able to describe plasma discharge reproducing, with consistency, the physics within the accelerating channel of HETs. A small discrepancy in the experimental magnitude of ions’ expansion, due probably to boundary condition effects, has been found. Full article

We present the current status of the performance studies of $\mathsf{\Lambda }$ hyperon directed flow measurement with the CBM experiment at the future FAIR facility in Darmstadt. Kalman Filter mathematics is used to reconstruct $\mathsf{\Lambda }\to p{\pi }^{-}$ weak decay kinematics, while the Particle Finder Simple package is used to optimize criteria for $\mathsf{\Lambda }$ hyperon candidate selection. Directed flow of $\mathsf{\Lambda }$ hyperons is studied as a function of rapidity, transverse momentum and collision centrality. The effects on flow measurement due to non-uniformity of the CBM detector response in the azimuthal angle, transverse momentum and rapidity are corrected using the QnTools analysis framework. Full article

The size and evolution of the matter created in relativistic heavy-ion collisions strongly depend on collision geometry, defined by the impact parameter. However, the impact parameter cannot be measured directly in an experiment but might be inferred from final state observables using the centrality procedure. We present the procedure of centrality determination for the Multi-Purpose Detector (MPD) at the NICA collider and its performance using the multiplicity of produced charged particles at midrapidity. The validity of the procedure is assessed using the simulated data for Au + Au collisions at $\sqrt{s_{NN}}$ = 4–11 GeV. Full article

This paper reviews the main experimental techniques and the most significant results in the searches for the $2ϵ$, $ϵ{\beta }^{+}$ and $2{\beta }^{+}$ decay modes. Efforts related to the study of these decay modes are important, since they can potentially offer complementary information with respect to the cases of $2{\beta }^{-}$ decays, which allow a better constraint of models for the nuclear structure calculations. Some positive results that have been claimed will be mentioned, and some new perspectives will be addressed shortly. Full article

Two approaches related to the centrality determination in heavy-ion Multi-Purpose Detector (MPD) experiments, using charge-particles multiplicity in Time Projection Chamber (TPC) and the energy deposition in Forward Hadron Calorimeter (FHCal) are discussed. The main features of the FHCal are the fine transverse segmentation and the beam holes in the center of the calorimeters. Leaking the heavy non-interacting fragments (spectators) leads to ambiguity in the dependence of energy deposition in the FHCal on the collision centrality. However, the calorimeter transverse segmentation allows one to measure the energy distributions in each of the FHCal modules and to construct combined observables to resolve the problems associated with the beam hole. The comparison of these approaches in the collision centrality measurements is discussed. Full article

One of the common methods to measure the centrality of nucleus-nucleus collision events consists of detecting forward spectator neutrons. Because of non-monotonic dependence of neutron numbers on centrality, other characteristics of spectator matter in ${}^{197}$Au–${}^{197}$Au collisions at NICA must be considered to improve the centrality determination. The numbers of spectator deuterons and $\alpha$-particles and the forward–backward asymmetry of the numbers of free spectator nucleons were calculated with the Abrasion–Ablation Monte Carlo for Colliders (AAMCC) model as functions of event centrality. It was shown that the number of charged fragments per spectator nucleon decreases monotonically with an increase of the impact parameter, and thus can be used to estimate the collision centrality. The conditional probabilities that a given event with specific spectator characteristics belongs to a certain centrality class were calculated by means of AAMCC. Such probabilities can be used as an input to Bayesian or other machine-learning approaches to centrality determination in ${}^{197}$Au–${}^{197}$Au collisions. Full article

The “Facility for Antiproton and Ion Research” (FAIR) in Darmstadt, Germany, and the “Nuclotron-based Ion Collider Facility” (NICA) in Dubna, Russia, are two accelerator centers under construction. FAIR will provide beams and experimental setups to perform forefront research in hadron, nuclear, atomic, and plasma physics, as well as in radiation biology and material science. At NICA, a unique research program on nuclear matter and spin physics will be conducted. Both facilities will execute experiments to explore the properties of QCD matter at neutron star core densities, in order to study the high-density equation of state, and to shed light on the quark degrees-of-freedom emerging in QCD matter at high densities. The research programs will be performed at FAIR with the CBM experiment, and at NICA with the MPD setup at the collider, and with the BM@N experiment at the Nuclotron. These three experiments are complementary, with respect to the beam energy. The physics programs and the relevant experimental observables will be discussed. Full article

The Compressed Baryonic Matter (CBM) experiment at the future Facility for Antiproton and Ion Research (FAIR) in Darmstadt is designed to investigate the properties of high-density QCD matter with multi-differential measurements of hadrons and leptons, including rare probes such as multi-strange anti-hyperons and charmed particles. The research program covers the study of the high-density equation-of-state of nuclear matter and the exploration of the QCD phase diagram at large baryon chemical potentials, including the search for quark matter and the critical endpoint of a hypothetical 1st order phase transition. The CBM setup comprises detector systems for the identification of charged hadrons, electrons, and muons; for the determination of collision centrality and the orientation of the reaction plane; and a free-streaming data read-out and acquisition system, which allows online reconstruction and selection of events up to reaction rates of 10 MHz. In this article, emphasis is placed on the measurement of muon pairs in Au-Au collisions at FAIR beam energies, which are unique probes used to determine the temperature of the fireball, and hence to search for a caloric curve of QCD matter. Simultaneously, the subthreshold production of charmonium can be studied via its dimuon decay in order to shed light on the microscopic structure of QCD matter at high baryon densities. The CBM setup with focus on dimuon measurements and the results of the corresponding physics performance studies will be presented. Full article

Experimental studies of hypernuclear dynamics, besides being essential for the understanding of strong interactions in the strange sector, have important astrophysical implications. The observation of neutron stars with masses exceeding two solar masses poses a serious challenge to the models of hyperon dynamics in dense nuclear matter, many of which predict a maximum mass incompatible with the data. In this paper, it is argued that valuable new insight can be gained from the forthcoming extension of the experimental studies of kaon electro production from nuclei to include the ${}^{208}\mathrm{Pb}(e,e^{\prime }{K}^{+}){}_{\Lambda }^{208}\mathrm{Tl}$ process. A comprehensive framework for the description of kaon electro production, based on factorization of the nuclear cross section and the formalism of the nuclear many-body theory, is outlined. This approach highlights the connection between the kaon production and proton knockout reactions, which will allow us to exploit the available ${}^{208}\mathrm{Pb}(e,e^{\prime }p){}^{207}\mathrm{Tl}$ data to achieve a largely model-independent analysis of the measured cross section. Full article

As a part of the future upgrade program of the Multi-Purpose Detector (MPD) experiment at the Nuclotron-Based Ion Collider Facility (NICA) complex, an Inner Tracking System (ITS) made of Monolitic Active Pixel Sensors (MAPSs) is proposed between the beam pipe and the Time Projection Chamber (TPC). It is expected that the new detector will enhance the experimental potential for the reconstruction of short-lived particles—in particular, those containing the open charm particle. To study the detector performance and select its best configuration, a track reconstruction approach based on a constrained combinatorial search was developed and implemented as a software toolkit called Vector Finder. This paper describes the proposed approach and demonstrates its characteristics for primary and secondary track finding in ITS, ITS-to-TPC track matching and hyperon reconstruction within the MPD software framework. The results were obtained on a set of simulated central gold–gold collision events at $\sqrt{s_{NN}}=9$ GeV with an average multiplicity of ∼1000 charged particles in the detector acceptance produced with the Ultra-Relativistic Quantum Molecular Dynamics (UrQMD) generator. Full article

Study of the strangeness production in heavy-ion collisions is one of the most important parts of the physics program of the MPD experiment at the NICA collider. Therefore, the problem of a reliable and efficient reconstruction of strange objects should be addressed with a high priority during the preparation to the experiment. The paper describes the approach to this task which was developed and implemented as a part of the MPD software. Some results of its application during the detector Monte Carlo feasibility studies are presented. Full article

A holographic model of probe quarkonia is presented, where the dynamical gravity–dilaton background was adjusted to the thermodynamics of 2 + 1 flavor QCD with physical quark masses. The quarkonia action was modified to account for the systematic study of the heavy-quark mass dependence. We focused on the $J/\psi$ and ${\rm Y}$ spectral functions and related our model to heavy quarkonia formation as a special aspect of hadron phenomenology in heavy-ion collisions at LHC. Full article

The primary scientific mission of the Multi-Purpose Detector (MPD) at the accelerator Nuclotron-based Ion Collider facility (NICA) (Dubna) is to investigate the properties of strongly interacting matter at high net-baryon densities. The goal of this work is to study the performance of the MPD detector for directed and elliptic flow measurements of identified hadrons by using the realistic Monte Carlo simulations of heavy-ion collisions at energies $\sqrt{s_{NN}}$ = 4.5 − 11 GeV. Full article

We present a systematic review of the basic features that were adopted for different electron models and show, in a brief overview, that, for electromagnetic spinning solitons in nonlinear electrodynamics minimally coupled to gravity (NED-GR), all of these features follow directly from NED-GR dynamical equations as model-independent generic features. Regular spherically symmetric solutions of NED-GR equations that describe electrically charged objects have obligatory de Sitter center due to the algebraic structure of stress–energy tensors for electromagnetic fields. By the Gürses-Gürsey formalism, which includes the Newman–Janis algorithm, they are transformed to axially symmetric solutions that describe regular spinning objects asymptotically Kerr–Newman for a distant observer, with the gyromagnetic ratio $g=2$. Their masses are determined by the electromagnetic density, related to the interior de Sitter vacuum and to the breaking of spacetime symmetry from the de Sitter group. De Sitter center transforms to the de Sitter vacuum disk, which has properties of a perfect conductor and ideal diamagnetic. The ring singularity of the Kerr–Newman geometry is replaced with the superconducting current, which serves as the non-dissipative source for exterior fields and source of the intrinsic magnetic momentum for any electrically charged spinning NED-GR object. Electromagnetic spinning soliton with the electron parameters can shed some light on appearance of a minimal length scale in the annihilation reaction $e^{+}{e}^{-}\to \gamma \gamma \left(\gamma \right)$. Full article

We derive a set of coupled equations for the gravitational and electromagnetic perturbation in the Reissner–Nordström geometry using the Newman–Penrose formalism. We show that the information of the physical gravitational signal is contained in the Weyl scalar function ${\Psi }_4$, as is well known, but for the electromagnetic signal, the information is encoded in the function $\chi$, which relates the perturbations of the radiative Maxwell scalars ${\phi }_2$ and the Weyl scalar ${\Psi }_3$. In deriving the perturbation equations, we do not impose any gauge condition and as a limiting case, our analysis contains previously obtained results, for instance, those from Chandrashekhar’s book. In our analysis, we also include the sources for the perturbations and focus on a dust-like charged fluid distribution falling radially into the black hole. Finally, by writing the functions on the basis of spin-weighted spherical harmonics and the Reissner–Nordström spacetime in Kerr–Schild type coordinates, a hyperbolic system of coupled partial differential equations is presented and numerically solved. In this way, we completely solve a system that generates a gravitational signal as well as an electromagnetic/gravitational one, which sets the basis to find correlations between them and thus facilitates gravitational wave detection via electromagnetic signals. Full article