Modern Physics Letters A

This contribution attempts to determine the $b$-quark pole mass $M_b$ and $\overline{\mathrm{\text{MS}}}$ running mass ${\bar{m}}_b$ with two different approaches at the next-to-next-to-leading order (NNLO) corrections. At the first approach, we derive a relation between the $b$-quark pole mass $M_b$ and its $\overline{\mathrm{\text{MS}}}$ running mass ${\bar{m}}_b$ at the NNLO corrections based on the perturbative Quantum Chromo Dynamics (pQCD) predictions. At the second approach, we extract numerical values of the $b$-quark pole and $\overline{\mathrm{\text{MS}}}$ running masses based on the NNLO phenomenology of H1 and ZEUS Collaborations combined beauty vertex production experimental data. Then we discuss about the compatibility between the pQCD theory results and phenomenology approach in determination of the $b$-quark pole and $\overline{\mathrm{\text{MS}}}$ running masses at the NNLO corrections. Also, we investigate the role and influence of the $b$-quark mass as an extra degree of freedom added to the input parameters of the Standard Model Lagrangian, on the improvement of the uncertainty band of the proton parton distribution functions (PDFs) and particularly on the gluon distribution.

Gravity can play a role in critical phenomena. Topological singularities induce ground state degeneracy and break the continuum symmetry of the vacuum. They also generate momenta oscillations about an average momentum and a positive gravitational susceptibility. Gravitational analogues of the laws of Curie and Bloch have been found for a one-dimensional model. The critical temperature for a change in phase from bound to unbound vortices has also been calculated in a XY-model.

In this paper, we study the main cosmological properties of the classical Friedmann equations in the case of homogeneous and isotropic Friedmann–Robertson–Walker Universe and we also generalized the expression of the Friedmann equation in the case of Loop Quantum Cosmology (LQC). Considering the $M_{35}$-model, we found the solutions of the equations considered for two particular cases, i.e. $Q=0$ (i.e. the de Sitter solution) and $Q>0$. Moreover, we considered and studied two exact cosmological solutions of the $M_{35}$-model, in particular the power-law and the exponential ones. Moreover, we also considered a third more complicated case and we derived the solution for an arbitrary function of the time $f(t)$. A scalar field description of the model is presented by constructing its self-interacting potential.

We derive proper time Lyapunov exponent $({\lambda }_p)$ and coordinate time Lyapunov exponent $({\lambda }_c)$ for a regular Hayward class of black hole. The proper time corresponds to $\tau$ and the coordinate time corresponds to $t$, where $t$ is measured by the asymptotic observers both for Hayward black hole and for special case of Schwarzschild black hole. We compute their ratio as $\frac{{\lambda }_p}{{\lambda }_c}=\frac{(r_{\sigma }^3+2l^{2}m)}{\sqrt{{(r_{\sigma }^2+2l^{2}m)}^3-3m{r}_{\sigma }^5}}$ for time-like geodesics. In the limit of $l=0$ that means for Schwarzschild black hole this ratio reduces to $\frac{{\lambda }_p}{{\lambda }_c}=\sqrt{\frac{r_{\sigma }}{(r_{\sigma }-3m)}}$. Using Lyapunov exponent, we investigate the stability and instability of equatorial circular geodesics. By evaluating the Lyapunov exponent, which is the inverse of the instability time scale, we show that, in the eikonal limit, the real and imaginary parts of quasi-normal modes (QNMs) is specified by the frequency and instability time scale of the null circular geodesics. Furthermore, we discuss the unstable photon sphere and radius of shadow for this class of black hole.

In this work, we study the evolution of a fractal universe composed of Tsallis holographic dark energy (THDE) and a pressureless dark matter that interact with each other through a mutual interaction. We then reconstruct the interaction term of this model by considering the Hubble length as the IR cut-off scale. We also study the behavior of different cosmological parameters during the cosmic evolution from the early matter-dominated era until the late-time acceleration. The present study shows that the universe undergoes a smooth transition from a decelerated to an accelerated phase of expansion in the recent past. Moreover, we also shown the evolution of the normalized Hubble parameter for our model and compared that with the latest cosmic chronometer data. Finally, we test the viability of the model by exploring its stability against small perturbation by using the squared of the sound speed.

We extend the model of a 5D Brans–Dicke gravity theory reduced to 4D through the presence of a hypersurface-orthogonal space-like killing vector field in the underlying 5D spacetime by including a varying speed of light. The resulting model is characterized by the presence of two scalar fields. We focus on late-time power law solutions which emerge in general when scalar fields couple to spacetime curvature and do not contradict the SNIa astrophysical data. Analytic solutions in 4-dimensions are derived and late-time accelerated expansion was found. The universe is dominated by dark energy, free from phantom field and is characterized by a decaying energy matter density, decaying scalar fields, and a decreasing celerity of light. The model is confronted with astrophysical observations and is found to fit these data.

In the context of quantum mechanics reformulated in a modified Hilbert space, we can formulate the Feynman’s path integral approach for the quantum systems with position-dependent mass particle using the formulation of position-dependent infinitesimal translation operator. Which is similar a deformed quantum mechanics based on modified commutation relations. An illustration of calculation is given in the case of the harmonic oscillator, the infinite square well and the inverse square plus Coulomb potentials.

Arnold showed that the Euler equations of an ideal fluid describe geodesics in the Lie algebra of incompressible vector fields. We will show that helicity induces a splitting of the Lie algebra into two isotropic subspaces, forming a Manin triple. Viewed another way, this shows that there is an infinitesimal quantum group (a.k.a. Lie bi-algebra) underlying classical fluid mechanics.

For bipartite quantum states we obtain lower bounds on two important entanglement measures, concurrence and negativity, studying the inequalities for the expectation value of a projector on some subspace of the Hilbert space. Several applications, including analysis of stability of entanglement under various perturbations of a state, are discussed.