Momentum Distributions Of Particles Research Articles

Individual particle approach to diffusive shock acceleration. Effect of the non-uniform flow velocity downstream of the shock

The momentum distribution of particles accelerated at strong non-relativistic shocks may be influenced by the spatial distribution of the flow speed around the shock. This phenomenon becomes evident in the cosmic-ray-modified shock, where the particle spectrum itself determines the profile of the flow velocity upstream. However, the effects of a non-uniform flow speed downstream are unclear. Hydrodynamics indicates that the spatial variation of flow speed over the length scales involved in the acceleration of particles in supernova remnants (SNRs) could be noticeable. In the present paper, we address this question. We initially followed Bell's approach to particle acceleration and then also solved the kinetic equation. We obtained an analytical solution for the momentum distribution of particles accelerated at the cosmic-ray-modified shock with spatially variable flow speed downstream. We parameterised the downstream speed profile to illustrate its effect on two model cases: the test particle and non-linear acceleration. The resulting particle spectrum is generally softer in Sedov SNRs because the distribution of the flow speed reduces the overall shock compression accessible to particles with higher momenta. On the other hand, the flow structure in young SNRs could lead to harder spectra. The diffusive properties of particles play a crucial role as they determine the distance the particles can return from to the shock, and, as a consequence, the flow speed that they encounter downstream. We discuss a possibility that the plasma velocity gradient could be (at least partially) responsible for the evolution of the radio index and for the high-energy break visible in gamma rays from some SNRs. We expect the effects of the gradient of the flow velocity downstream to be prominent in regions of SNRs with higher diffusion coefficients and lower magnetic field, that is, where acceleration of particles is not very efficient.

Enhanced vacuum pair production by combination of two spatially separated electric fields

The effective enhancement of the pair production rate using a subcritical electromagnetic field is an active area of interest in quantum electrodynamics. Enhanced pair production was investigated using the Dirac–Heisenberg–Wigner (DHW) formalism with spatially separated electric fields. Symmetric and asymmetric combinations of two separate electric fields with the same temporal shape were considered. The interplay and dynamical assistance between the fields were examined from a numerical perspective to elucidate the effects of the spatial distance and asymmetry of the field on the pair production efficiency. For the symmetric combination, the total particle number was reduced with an increase in the distance between the two fields up to one Compton length and then remained constant with distance. For the asymmetric combination, the total number of created pairs increased significantly up to a distance of one Compton length. It was also determined that not only was the separation distance crucial for enhancing pair production, but the spatial field asymmetries were also important, both of which had nontrivial effects on the particle momentum distribution. Finally, we have studied the validity of the DHW and analytical approximation in the spatially separated two electric fields. We found that the analytical approximation could almost estimate the DHW results.

THE ROLE OF HIGHER MOMENTS ON THE DISTRIBUTION OF PARTICLES IN THE SPACE OF IMPULSES AT CYCLOTRON RESONANCES

The results of the analysis of the dynamics of charged particles under conditions of cyclotron resonances in the field of an intense electromagnetic wave are presented. Particular attention is paid to regimes with dynamic chaos. It is shown that there are two qualitatively different regimes. The appearance of the first one is due to the overlap of nonlinear cyclotron resonances. The second mode is related to intermittency. The moments and spectra of each of these regimes are determined. It is shown that with an increase in the intensity of an external electromagnetic wave, the first regime appears at the beginning and only then the second regime appears. A characteristic feature of the second regime is intermittency. Steps appear on the time dynamics of pulses in the second mode. It is shown that the spectra in the second mode are narrower than in the first mode. A characteristic feature of the second regime (the regime with intermittency) is the fact that the higher moments turn out to be larger than the lower moments. In the first regime, the highest moments decrease rapidly. To find the particle momentum distribution function, the generalized Fokker-Planck equation was used. Solutions of this equation are written out for some important cases.

Transverse Momentum Distribution of Secondary Particles in High-Energy Collisions of Protons and Nuclei and the Possibility of Detecting Dark Matter Particles in the Spectra of Soft Photons

Transverse Momentum Distribution of Secondary Particles in High-Energy Collisions of Protons and Nuclei and the Possibility of Detecting Dark Matter Particles in the Spectra of Soft Photons

Pseudorapidity, transverse momentum and multiplicity distributions of charged particles in pp collisions at 13 TeV

Pseudorapidity, transverse momentum and multiplicity distributions of charged particles in pp collisions at 13 TeV

Langevin simulation of dark matter kinetic equilibration

Recently it has been questioned, notably in the context of the scalar singlet dark matter model with mφ ≃ 60 GeV, how efficiently kinetic equilibrium is maintained if freeze-out dynamics is pushed down to low temperatures by resonant effects. We outline how Langevin simulations can be employed for addressing the non-equilibrium momentum distribution of non-relativistic particles in a cosmological background. For a scalar singlet mass mφ ≃ 60 GeV, these simulations suggest that kinetic equilibrium is a good approximation down to T ∼ 1 GeV, with the deviation first manifesting itself as a red-tilted spectrum. This reduces the annihilation cross section, confirming findings from other methods that a somewhat larger (< 20%) coupling than in equilibrium is needed for obtaining the correct abundance.

The wave energy density and growth rate for the resonant instability in relativistic plasmas

ABSTRACT The wave instability acts in astrophysical plasmas to redistribute energy and momentum in the absence of frequent collisions. There are many different types of waves, and it is important to quantify the wave energy density and growth rate for understanding what types of wave instabilities are possible in different plasma regimes. There are many situations throughout our Universe where plasmas contain a significant fraction of relativistic particles. Theoretical estimates for the wave energy density and growth rate are constrained to either field-aligned propagation angles or non-relativistic considerations. Based on linear theory, we derive the analytic expressions for the energy density and growth rate of an arbitrary resonant wave with an arbitrary propagation angle in relativistic plasmas. For this derivation, we calculate the Hermitian and anti-Hermitian parts of the relativistic-plasma dielectric tensor. We demonstrate that our analytic expression for the wave energy density presents an explicit energy increase in resonant waves in the wavenumber range where the analytic expression for the growth rate is positive (i.e. where a wave instability is driven). For this demonstration, we numerically analyse the loss-cone driven instability, as a specific example, in which the whistler-mode waves scatter relativistic electrons into the loss cone in the radiation belt. Our analytic results further develop the basis for linear theory to better understand the wave instability, and have the potential to combine with quasi-linear theory, which allows to study the time evolution of not only the particle momentum distribution function but also resonant wave properties through an instability.

Nonlinear transport in the presence of a local dissipation

We characterize the particle transport, particle loss, and nonequilibrium steady states in a dissipative one-dimensional lattice connected to reservoirs at both ends. The free-fermion reservoirs are fixed at different chemical potentials, giving rise to particle transport. The dissipation is due to a local particle loss acting on the center site. We compute the conserved current and loss current as functions of voltage in the nonlinear regime using a Keldysh description. The currents show step-like features which are affected differently by the local loss: The steps are either smoothened, nearly unaffected, or even enhanced, depending on the spatial symmetry of the single-particle eigenstate giving rise to the step. Additionally, we compute the particle density and momentum distributions in the chain. At a finite voltage, two Fermi momenta can occur, connected to different wavelengths of Friedel oscillations on either side of the lossy site. We find that the wavelengths are determined by the chemical potentials in the reservoirs rather than the average density in the lattice.

Multicomponent Current Sheet of the Magnetopause with an Arbitrary Energy Distribution of Particles

An exact solution to the Maxwell–Vlasov equations has been found for a large class of multicomponent current sheets in collisionless plasma, which describe the spatial structure of the current in the magnetopause and consistent inhomogeneous anisotropic momentum distributions of particles with different effective temperatures. Devised sheets allow a nonmonotonic variation of the magnetic field and can have asymmetric, multihump, and sign-alternating profiles of the current density. Profiles of the current of different particle populations can have different scales, contain countercurrents, and be spatially shifted with respect to each other. The model under consideration is applicable to qualitatively describe a magnetopause separating a magnetosphere of a planet from a solar wind or separating regions of the solar wind with different parameters of the plasma and magnetic field.

Resonance production and interaction from low to high energy

Measurements of short-lived hadronic resonances are used to probe the properties of the hadronic phase in ultra-relativistic heavy-ion collisions. Since these resonances have lifetimes comparable to that of the produced fireball, they are sensitive to the competitive re-scattering and regeneration effects in the hadronic gas, which modifies the observed particle momentum distributions and yields after hadronization. With different masses, quantum numbers, and quark content, hadronic resonances can provide insight into processes that determine the shapes of particle momentum spectra, strangeness production, and the possible onset of collective effects. The system size and collision-energy dependence of resonance production will be presented.

The lowest excited states of 14C and 14O nuclei within a five-cluster model

We study the ground and the first excited 0+ states of two mirror nuclei 14C and 14O within a five cluster model (three alpha-particles and two extra nucleons) with the use of high accuracy variational approach with Gaussian bases. The first excited 0+ state of these nuclei is shown to be connected with a change of the structure of the two nucleon subsystem moving in the field of the 12C cluster. The density distributions, electric form factors (both the elastic and transition ones), pair correlation functions, and the momentum distributions of the constituent particles are found. The most probable shapes of five-cluster systems are revealed.

Particle Production in Strong Electromagnetic Fields and Local Approximations

We investigate the phenomenon of electron–positron pair production in intense external backgrounds within the strong-field regime. We perform nonperturbative calculations by solving the quantum kinetic equations, and obtain the momentum distributions of particles created and the total number of pairs. In particular, we analyze the validity of the locally constant field approximation (LCFA), which represents a powerful method for treating inhomogeneous external backgrounds. We consider a combination of two consecutive time-dependent Sauter pulses and thoroughly examine the effects of quantum interference and the role of the Pauli exclusion principle. It is shown that the latter can be approximately incorporated within the LCFA when computing the momentum distributions, while the closed-form LCFA expression for the total particle yield completely disregards Pauli blocking. It is demonstrated that in the presence of multiple turning points of classical electron trajectories, one observes interference patterns in the particle spectra, and the LCFA may significantly overestimate the number of pairs. To further elaborate this issue, we perform the analogous calculations in the case of scalar QED. It is shown that the quantum statistics effects enhance the number of bosons produced.

Inclusive Charged-Particle Kinematic Distributions at LHC Energies: Data versus Theory

The transverse momentum distributions of inclusive charged particles in pseudorapidity bins with a width of 0.2 are reported for a simulation study of PYTHIA8, Sibyll, and EPOS. The models’ predictions are compared with the experimental measurements reported by the CMS experiment in symmetric pp collisions, allowing the maximum energy for new particle production at s = 0.9, 2.36, and 7 TeV. While comparing the models’ predictions with the data, we found that the default module of the PYTHIA model reproduced a good prediction of the data because it tuned the lower cut-off phase space parameter of the transverse momentum. In the second place, the EPOS model reproduced predictions that were close to the data, while the Sibyll model reproduced the data in a narrow region of the pT distributions. In addition to that, the fit of the pT distribution of the data by the standard distribution function was used to obtain the effective temperature of the hadronic medium. The effective temperature increased with an increase in the pseudorapidity and had a more significant value at higher center-of-mass energies, which may indicate a change in the reaction mechanism or possible formation of a different phase of hadronic matter.

Extensive/Nonextensive Statistics for pT Distributions of Various Charged Particles Produced in p + p and A + A Collisions in a Wide Range of Energies

A comprehensive review on various experimental parametrizations proposed to fit the transverse momentum distributions of charged pions, kaons, and protons produced at energies ranging between 7.7 GeV and 2.76 TeV is introduced. We present a systematic study for their statistical fits to the extensive Maxwell–Boltzmann (MB) and nonextensive statistics (generic axiomatic statistics and the Tsallis one as a special case). The inconsistency that the MB approach is to be utilized in characterizing the chemical freezeout, while the Tsallis approach determining the kinetic freezeout is discussed. The resulting energy dependence of the different fit parameters largely varies with the particle species and the degree of (non)extensivity. This manifests itself in that the Tsallis nonextensive approach seems to work well for p + p, rather than for A + A collisions. Nevertheless, discussing the deeper physical insights of nonextensive statistical approaches is not targeted, drawing a complete picture of the utilization of the Tsallis statistics in modeling the transverse momentum distributions of several charged particles produced at a wide range of energies and, accordingly, presenting a criticism or a support of the relevant works. This may be considered as the main advantage of this review.

Tomographic reconstruction techniques optimized for velocity-map imaging applications.

Examples of extracting meaningful information from image projection data using tomographic reconstruction techniques can be found in many areas of science. Within the photochemical dynamics community, tomography allows for complete three-dimensional (3D) charged particle momentum distributions to be reconstructed following a photodissociation or photoionization event. This permits highly differential velocity- and angle-resolved measurements to be made simultaneously. However, the generalized tomographic reconstruction strategies typically adopted for use with photochemical imaging-based around the Fourier-slice theorem and filtered back-projection algorithms-are not optimized for these specific types of problems. Here, we discuss pre-existing alternative strategies-namely, the simultaneous iterative reconstruction technique and Hankel Transform Reconstruction (HTR)-and introduce them in the context of velocity-map imaging applications. We demonstrate the clear advantages they afford, and how they can perform considerably better than approaches commonly adopted at present. Most notably, with HTR we can set a bound on the minimum number of projections required to reliably reconstruct 3D photoproduct distributions. This bound is significantly lower than what is currently accepted and will help make tomographic imaging far more accessible and efficient for many experimentalists working in the field of photochemical dynamics.

Pseudorapidity dependence of the transverse momentum distribution of charged particles in [formula omitted] collisions at 0.9, 2.36, and 7 TeV

We study the transverse momentum spectra of charged particles from 0.1−2 GeV/c in bins of pseudorapidity η of width 0.2 ranging from 0 to 2.4 produced in pp collisions, at three different center of mass energies, namely s=0.9, 2.36, 7TeV. We used PYTHIA8.307 and QGSJETII-04 and compared the simulation results with experimental data under the same conditions. The PYTHIA8 model has an excellent description of the experimental data, particularly at the high pT region of the distribution, and the prediction is independent of the η ranges. Furthermore, the predictions are more or less the same at lower values of pT, but a more prominent bump is observed for 0.4≤pT≤0.8GeV/c with increasing the center-of-mass energy. The QGSJET model reproduces the data only in the intermediate region of the pT over all the η slices and underpredicts for low and high pT regions. With the increase in the center of mass energy, the model’s predictions got closer to the data, particularly at a high part of the pT distributions. Furthermore, the Blast wave model with Tsallis statistics is applied to the pT spectra of CMS data and PYTHIA8 and QGSJET models, and the kinetic freeze-out temperature, transverse flow velocity, and the entropy parameter q are extracted. The kinetic freeze-out temperature increases from lower pseudorapidity regions to higher pseudo-rapidity regions. Transverse flow velocity and the entropy parameter q have the opposite trend to kinetic freeze-out temperature. All these parameters are also more significant at 7TeV and have the lowest values at 0.9TeV, which shows the dependence of these parameters on the collision energy.

Momentum distribution of dark matter produced in inflaton decay: Effect of inflaton mediated scatterings

Postinflationary reheating is a widely discussed mechanism for nonthermal production of dark matter (DM). In this scenario the momentum distribution of the produced DM particles is usually taken to be the one obtained at reheating, redshifted at later times due to the expansion of the Universe. However, since in such a scenario both the DM and the standard model (SM) fields couple to the inflaton, the DM particles necessarily undergo self-scatterings, as well as elastic and inelastic scattering reactions with the SM bath, all of which proceed through $s$-channel or $t$-channel inflaton exchange. We compute the momentum distribution of the DM particles including the effect of these scatterings, and find that the distributions can be significantly altered, even though DM remains nonthermal throughout the cosmological evolution. We observe that if the inflaton dominantly couples to the SM Higgs boson through a renormalizable interaction, then reheating temperatures and inflaton masses at the TeV scale lead to a large effect from the scattering processes, with the DM-inflaton coupling constrained by the DM density. The scattering effects are found to be sensitive to the duration of the reheating process---larger the duration, more momentum modes are filled at reheating, leading to an enhanced scattering probability. We also obtain the free-streaming length of such DM using the resulting nonthermal momentum distribution, which can be used to estimate the implications of the Lyman-$\ensuremath{\alpha}$ constraints on the DM mass. It is observed that in the scenarios considered, including the scattering effects can reduce the DM average velocity at matter-radiation equality, and its free-streaming length, by up to a factor of 40, thereby making the constraints on light DM produced in inflaton decay significantly weaker.

Measurement of angular and momentum distributions of charged particles within and around jets with the ATLAS detector

Studies of jet fragmentation in heavy-ion collisions can provide information about the mechanism of jet quenching inside the hot and dense QCD matter created in these collisions. These proceedings present results from measurements of charged particle yields within and around the jets in dijet, gamma+jet and Z+jet systems measured in $5.02$~TeV Pb+Pb and $pp$ collisions using the ATLAS detector at the LHC.

Anomalous periodicity in superpositions of localized periodic patterns

Interference between overlapping periodic patterns gives rise to important phenomena, such as Moiré fringes, appearing when the patterns have different periods or orientations. Here we present a novel phenomenon, applicable to both the classical and quantum regimes, where two one-dimensional localized periodic patterns with the same period interfere to create fringes with anomalous periodicity. We analyze the effect theoretically and demonstrate it with atomic matter waves. When a central parameter of the system is scanned continuously, we observe a discontinuous but piecewise-rigid periodicity of the resulting fringes. We show that this is a universal phenomenon that emerges from a superposition of two spatially shifted localized periodic patterns of any source or nature when they interfere with a global phase difference. The rigidity of the spectrum becomes even more robust for a coherent superposition of non-overlapping wavepackets, although the conventional interferometric visibility drops to zero. The effect is expected to appear in space and time, as well as in the momentum distribution of quantum particles.

Measurements of the groomed and ungroomed jet angularities in pp collisions at sqrt{s} = 5.02 TeV

The jet angularities are a class of jet substructure observables which characterize the angular and momentum distribution of particles within jets. These observables are sensitive to momentum scales ranging from perturbative hard scatterings to nonperturbative fragmentation into final-state hadrons. We report measurements of several groomed and ungroomed jet angularities in pp collisions at sqrt{s} = 5.02 TeV with the ALICE detector. Jets are reconstructed using charged particle tracks at midrapidity (|η| < 0.9). The anti-kT algorithm is used with jet resolution parameters R = 0.2 and R = 0.4 for several transverse momentum {p}_{mathrm{T}}^{mathrm{ch}} jet intervals in the 20–100 GeV/c range. Using the jet grooming algorithm Soft Drop, the sensitivity to softer, wide-angle processes, as well as the underlying event, can be reduced in a way which is well-controlled in theoretical calculations. We report the ungroomed jet angularities, λα, and groomed jet angularities, λα,g, to investigate the interplay between perturbative and nonperturbative effects at low jet momenta. Various angular exponent parameters α = 1, 1.5, 2, and 3 are used to systematically vary the sensitivity of the observable to collinear and soft radiation. Results are compared to analytical predictions at next-to-leading-logarithmic accuracy, which provide a generally good description of the data in the perturbative regime but exhibit discrepancies in the nonperturbative regime. Moreover, these measurements serve as a baseline for future ones in heavy-ion collisions by providing new insight into the interplay between perturbative and nonperturbative effects in the angular and momentum substructure of jets. They supply crucial guidance on the selection of jet resolution parameter, jet transverse momentum, and angular scaling variable for jet quenching studies.