Modern Physics Letters A

In this paper, I review one of the most important and interesting parts of my new book “Fuzzy Systems to Quantum Mechanics” (see Ref. 1). Several conclusions in this part are worth introducing here. First of all, the motion of a mass point in classic mechanics has also waviness and the wave function of the motion of a mass point is composed of wave functions of countably infinite microscopic particles. Secondly, based on the waviness of the motion of a mass point we surely know the new conclusion described as the wave-mass-point dualism in classic mechanics. And thirdly, by using the closed relation between the wave-mass-point dualism in classic mechanics and the wave-particle dualism in quantum mechanics, unified theory of classic mechanics and quantum mechanics is naturally formed.

We study analytically the Branching Ratio (BR) and Charge-Parity (CP) asymmetries of the $\overline{B_s^0}\to \omega \varphi$ decay mode within QCDF approach. We find the $BR(\overline{B_s^0}\to \omega \varphi )=(0.51\pm 0.12)\times 10^{-6}$. We also find the values of CP asymmetries are ${{𝒜}}_{CP}^{\text{dir}}(\overline{B_s^0}\to \omega \varphi )=0.080\pm 0.008$, ${{𝒜}}_{CP}^{\text{mix}}(\overline{B_s^0}\to \omega \varphi )=0.184\pm 0.035$ and ${{𝒜}}_{CP}^{\mathrm{\Delta }\mathrm{\Gamma }}(\overline{B_s^0}\to \omega \varphi )=0.980\pm 0.006$. The reported results are consistent with the recent theoretical predictions and can be used as a reference values in the forthcoming experiments.

We show that Gribov diffusion of the partons in the impact parameter plane, which leads to the square-root-of-logarithmic growth of the transverse size of the hadrons, can occur only simultaneously with a similar diffusion in the transverse-momentum space. At the same time, a restriction of the partons in the transverse momenta entails an increase in their propagation in the impact parameter plane. Ultimately this leads to a logarithmic growth of the transverse size of hadrons at asymptotically high energies.

We propose a renormalizable $\mathrm{\text{U}}{(1)}_{B-L}$ extension of the Standard model with $A_4$ symmetry that leads to the successful cobimaximal lepton mixing ansatz, thus providing a predictive explanation for leptonic mixing observables. The smallness of the active neutrino masses and neutrino masses ordering are produced by the type-I seesaw mechanism at the tree-level. The obtained physical parameters are well consistent with the global fit of neutrino oscillation.¹ The model is predictive in the sense that it reproduces the experimental values of neutrino parameters in which the reactor neutrino mixing angle ${𝜃}_{13}$ get the best-fit value and the solar and atmospheric neutrino mixing angles have little deviations from the best-fit values given in Ref. 1, however, they are consistent with the other experimental results.${}^{3,4}$ The effective neutrino masses governing the neutrinoless double beta decay is predicted to be $〈m_{ee}〉=8.25\times 10^{-3}\mathrm{\text{eV}}$ for normal hierarchy and $〈m_{ee}〉=4.92\times 10^{-2}\mathrm{\text{eV}}$ for inverted hierarchy which are well consistent with the recent experimental limits on neutrinoless double beta decay.

In a recent paper [Eur. Phys. J. C 80, 68 (2020)], a definition of oscillating neutrino states in quantum field theory was proposed. We show that such definition can be derived as a particular case of the Blasone–Vitiello approach, when mass vacuum is chosen as the physical vacuum. We discuss some problems of such an approach, which appears to be mathematically inconsistent and physically not acceptable.

In this paper, based on the thin-shell formalism, we introduce a classical model for particles in the framework of $(n+1)$-dimensional $\left[\frac{n}{2}\right]$-order pure Lovelock gravity. In particular, we construct a spherically symmetric particle of radius $a$ whose inside is a flat Minkowski spacetime while its outside is charged pLG solution. Knowing that in $(n+1)$-dimensional spherically symmetric Einstein gravity ($R$-gravity) such a particle model cannot be constructed, as we have discussed first, provides the main motivation for this study. In fact, it is the richness of Lovelock parameters that provides such a particle construction possible. On the thin-shell, the energy-momentum components are chosen to vanish, yet their normal derivatives are nonzero.

In this work, we have considered the recently proposed new Tsallis agegraphic dark energy (NTADE) model [Mod. Phys. Lett. A 34, 1950086 (2019)] within the framework of a flat Friedmann–Robertson–Walker (FRW) Universe by taking various values of the parameter $\delta$. The NTADE model shows the current phase transition of the Universe from decelerated to accelerated phase. The NTADE equation of state (EoS) parameter shows a rich behavior as it can be quintessence-like or phantom-like depending on the value of $\delta$. For discriminating the NTADE model from $\mathrm{\Lambda }$CDM, we have plotted the statefinder parameters $r(z)$, $s(z)$ and $(r,s)$, $(r,q)$ pair. The NTADE model shows distinct evolutionary trajectories of their evolution in ($r,s$) and ($r,q$) plane. An analysis using the snap parameter and the ${\omega }_D-{\omega }_D^{\prime }$ pair dynamical analysis have also been performed.

In this work, we have studied LRS Bianchi type I cosmological models in $f(R,T)$ gravity with tilted observers, where $R$ is the Ricci scalar and $T$ is the trace of the stress energy tensor. We have explored a tilted model and determined the solutions of the field equations by assuming special law of variation of Hubble’s parameter, proposed by Berman (1983) that yields constant deceleration parameter. In this scenario, we have used the equation of state $p=(\gamma -1)\rho$ and power law of velocity to describe the different anisotropic physical models such as Dust Universe, Radiation Universe, Hard Universe and Zedovich Universe. We have discussed graphical presentation of all parameters of the derived models with the help of MATLAB. Some physical and geometrical aspects of the models are also discussed.

Excitation-energy dependent parity ratios in the level densities of ${}^{159\text{–}166}\mathrm{\text{Dy}}$ isotopes are calculated within a microscopic approach. Introducing a parity equilibration parameter, energy dependence of the transition from where a single parity dominates to a parity equilibrated state is compared among ${}^{159\text{–}166}\mathrm{\text{Dy}}$ isotopes and its relation to the pairing effect is investigated. A correlation between the pair-breaking and the equilibration of parity distributions is observed for the considered isotopes.