International Journal of Modern Physics A

In order to have a new perspective on the long-standing problem of the mass gap in Yang–Mills theory, we study in this paper the quantum Yang–Mills theory in the presence of topologically nontrivial backgrounds. The topologically stable gauge fields are constrained by the form invariance condition and the topological properties. Obeying these constraints, the known classical solutions to the Yang–Mills equation in the three- and four-dimensional Euclidean spaces are recovered, and the other allowed configurations form the nontrivial topological fluctuations at quantum level. Together, they constitute the background configurations, upon which the quantum Yang–Mills theory can be constructed. We demonstrate that the theory mimics the Higgs mechanism in a certain limit and develops a mass gap at semiclassical level on a flat space with finite size or on a sphere.

Experimental measurements of decay branching fractions of semitaunic and semimuonic $B_c$ into $J/\psi$ have challenged the lepton flavor universality in standard models with about two standard deviations. In this paper, we first investigate the unitary constraint on form factors of $B_c$ meson into $S$-wave and $P$-wave charmonium. Such constraint leads to the exploration of the $R_{J/\psi }$ and other ratios $R_{{\eta }_c}$, $R_{h_c}$, and $R_{{\chi }_{cJ}}$ in a model-independent way. These results together with future experimental measurements can be used to explore the lepton flavor universality in a more systematic way. In addition, we point out that the helicity-dependent ratios $R_{J/\psi }^L$ and $R_{J/\psi }^{\perp }$ can also provide complementary information.

In this paper, we consider Klein–Gordon particle near Reissner–Nordström black hole. The symmetry of such a background led us to compare the corresponding Laplace equation with the generalized Heun functions. Such relations help us achieve the generalized $sl(2)$ algebra and some suitable results for describing the above-mentioned symmetry. On the other hand, in case of $r\to r_{+}$, which is near the proximity black hole, we obtain the energy spectrum. When we compare the equation of RN background with Laguerre differential equation, we show that the obtained energy spectrum is same as the three-dimensional harmonic oscillator. So, finally we take advantage of harmonic oscillator energy and make suitable partition function. Such function help us to obtain all thermodynamical properties of black hole. Also, the structure of obtained entropy lead us to have some bit and information theory in the RN black hole.

$XXX$ spin chain with spin $s=-1$ appears as an effective theory of Quantum Chromodynamics. It is equivalent to lattice nonlinear Schroediger’s equation: interacting chain of harmonic oscillators [bosonic]. In thermodynamic limit each energy level is a scattering state of several elementary excitations [lipatons]. Lipaton is a fermion: it can be represented as a topological excitation [soliton] of original [bosonic] degrees of freedom, described by the group $Z_2$. We also provide the CFT description (including local quenches) and Yang–Yang thermodynamics of the model.

The SU(3) Polyakov linear-sigma model (PLSM) in mean-field approximation is utilized in analyzing the chiral condensates ${\sigma }_u$, ${\sigma }_d$, ${\sigma }_s$ and the deconfinement order parameters $\varphi$, $\bar{\varphi }$, at finite isospin asymmetry. The bulk thermodynamics including pressure density, interaction measure, susceptibility and second-order correlations with baryon, strange and electric charge quantum numbers are studied in thermal and dense medium. The PLSM results are confronted to the available lattice quantum chromodynamics (QCD) calculations. The excellent agreement obtained strengthens the reliability of fixing the PLSM parameters and therefore supports further predictions even beyond the scope of the lattice QCD numerical applicability. From the QCD phase structure at finite isospin chemical potential $({\mu }_I)$, we find that the pseudocritical temperatures decrease with the increase in ${\mu }_I$. We conclude that the QCD phase structure in $(T_{\chi }\text{–}{\mu }_I)$ plane seems to extend the one in $(T_{\chi }\text{–}{\mu }_B)$ plane.

In this work, we study kink–antikink and antikink–kink collisions in hyperbolic models of fourth and sixth orders. We compared the patterns of scattering with known results from polynomial models of the same order. The hyperbolic models considered here tend to the polynomial ${\varphi }^4$ and ${\varphi }^6$ models in the limit of small values of the scalar field. We show that kinks and antikinks that interact hyperbolically with the fourth order differ sensibly from those governed by the polynomial ${\varphi }^4$ model. The increasing of the order of interaction to the sixth order shows that the hyperbolic and polynomial models give intricate structures of scattering that differ only slightly. The dependence on the order of interaction is related to some characteristics of the models such as the potential of perturbations and the number of vibrational modes.

By using the conformable fractional of the Nikiforov–Uvarov (CF–NU) method, the radial Schrödinger equation is analytically solved. The energy eigenvalues and corresponding functions are obtained, in which the dependent temperature potential is employed. The effect of fraction-order parameter is studied on the heavy-quarkonium masses such as charmonium and bottomonium in a hot QCD medium in the 3D and the higher-dimensional space. This paper discusses the flavor dependence of their binding energies and explores the nature of dissociation by employing the perturbative, nonperturbative, and the lattice-parametrized form of the Debye masses in the medium-modified potential. A comparison is studied with recent works. We conclude that the fractional-order plays an important role in a hot QCD medium in the 3D with consideration of a form of the Debye mass.

By applying the Hamilton’s quaternion algebra, we propose the generalized electromagnetic-fluid dynamics of dyons governed by the combination of the Dirac–Maxwell, Bernoulli and Navier–Stokes equations. The generalized quaternionic hydro-electromagnetic field of dyonic cold plasma consists of electrons and magnetic monopoles in which there exist dual-mass and dual-charge species in the presence of dyons. We construct the conservation of energy and conservation of momentum equations by equating the quaternionic scalar and vector parts for generalized hydro-electromagnetic field of dyonic cold plasma. We propose the quaternionic form of conservation of energy is related to the Bernoulli-like equation while the conservation of momentum is related to Navier–Stokes-like equation for dynamics of dyonic plasma fluid. Further, the continuity equation, i.e. the conservation of electric and magnetic charges with the dynamics of hydro-electric and hydro-magnetic flow of conducting cold plasma fluid is also analyzed. The quaternionic formalism for dyonic plasma wave emphasizes that there are two types of waves propagation, namely the Langmuir-like wave propagation due to electrons, and the ’t Hooft–Polyakov-like wave propagation due to magnetic monopoles.

Using the Monte Carlo data at 7 TeV collected by the ATLAS collaboration (PYTHIA 6), we examine the necessity of applying the three-negative binomial distribution (T-NBD). By making use of the T-NBD formulation, we analyze the multiplicity distribution (MD) and the Bose–Einstein correlation (BEC) at the Large Hadron Collider (LHC). In the T-NBD framework, the BEC is expressed by two degrees of coherence ${\lambda }_1$ and ${\lambda }_2$ and two kinds of exchange functions $E_1^2$ and $E_2^2$ that act over interaction ranges $R_1$ and $R_2$, respectively. Using the calculated ${\lambda }_1$ and ${\lambda }_2$ based on the T-NBD, along with free ${\lambda }_1$ and ${\lambda }_2$, we analyze the BEC data at 0.9 and 7 TeV. The estimated parameters $R_1$ and $R_2$ are almost coincident and seem to be consistent with $pp$ collisions. We also present an enlarged Koba–Nielsen–Olesen (KNO) scaling function based on the T-NBD, and apply it to KNO scaling at LHC energies. The enlarged scaling function describes the observed violation of the KNO scaling.

We consider string meson and string baryon models in the framework of the modified measure theory, the theory that does not use the determinant of the metric to construct the invariant volume element. As the outcome of this theory, the string tension is not placed ad hoc but is derived. When the charges are presented, the tension undergoes alterations. In the string meson model there are one string and two opposite charges at the endpoints. In the string baryon model, there are two strings, two pairs of opposite charges at the endpoints and one additional charge at the intersection point, the point where these two strings are connected. The application of the modified measure theory is justified because the Neumann boundary conditions are obtained dynamically at every point where the charge is located and Dirichlet boundary conditions arise naturally at the intersection point. In particular, the Neumann boundary conditions that are obtained at the intersection point differ from that considered before by ’t Hooft in arXiv:hep-th/0408148 and are stronger, which appears to solve the nonlocality problem that was encountered in the standard measure approach. The solutions of the equations of motion are presented. Assuming that each endpoint is the dynamical massless particle, the Regge trajectory with the slope parameter that depends on three different tensions is obtained.

We propose a novel theory of gravity that by construction is renormalizable, evades Ostrogradsky’s no-go theorem, is locally scale-invariant in the high-energy limit, and equivalent to general relativity in the low-energy limit. The theory is defined by a pure $f(R)=R^n$ action in the Palatini formalism, where the dimensionless exponent $n$ runs from a value of two in the high-energy limit to one in the low-energy limit. We show that the proposed model contains no obvious cosmological curvature singularities. The viability of the proposed model is qualitatively assessed using several key criteria.

In this paper, we consider homogeneous and isotropic noncommutative cosmological models induced by a symplectic formalism coupled to phantom perfect fluids and a cosmological constant. After computing the field equations, we solve them to find the scalar factor dynamics. We restrict our attention to expansive solutions that may represent the present expansion of our Universe. These solutions generate big rip singularities. We study how the parameters, of these models, modify the time it takes for the scalar factor to expand from zero till infinity, at the big rip.

In this article, the Dirac electron scattering problem on circular barrier of radius $R$ is studied under the generalized uncertainty principle (GUP). The expressions of scattering coefficients, scattering cross-section and scattering efficiency of massless Dirac particle are obtained by solving the massless Dirac equation under GUP and discussed by numerical methods. It shows that the scattering coefficient, the scattering cross-section, and the scattering efficiency depend explicitly on the GUP parameter $\alpha$. For the scattering coefficient $R_l$, GUP may cause slight shift in the oscillation position of $|R_l{|}^2$ and make some peaks value of $|R_l{|}^2$ smaller. For scattering cross-section and scattering efficiency, GUP may also lead to slight shift in their oscillation position and increase of amplitude when the GUP parameter increases.