Modern Physics Letters A

The branching fractions of the decays ${\eta }^{\prime }\to \pi \rho$ and $\rho \to \pi \eta$ are calculated in the chiral quark NJL model. The decays exist due to the mass difference between $u$- and $d$-quarks leading to ${\pi }^0-{\eta }^{\prime }$ and ${\pi }^0-\eta$ mixing. Two different approaches are applied: the approximate calculation of this process, taking into account the transitions ${\pi }^0-{\eta }^{\prime }$ and ${\pi }^0-\eta$ explicitly without diagonalization and a more precise approach consisting in the diagonalization of the singlet and octet states leading to the physical fields ${\pi }^0$, $\eta$ and ${\eta }^{\prime }$. The obtained results are in satisfactory agreement with current experimental data.

By implementing the inverse seesaw mechanism into the well-known 3-3-1 model in order to explain the experimental data of neutrino oscillation, the 3-3-1 model can predict promoting signals of the lepton flavor violating decays $e_a\to e_b\gamma$ and $e_i\to e_j{e}_k\overline{e_l}$. In this work, we introduce analytic formulas of one-loop contributions to decays $e_i\to e_j{e}_k\overline{e_l}$ predicted by this model. Numerical results show that there exist regions of the parameter space that allow these decay branching ratios to reach the planned experimental sensitivities and satisfy all upper experimental constraints of the branching ratios $\mathrm{\text{Br}}(e_b\to e_a\gamma )$. The analytic formulas introduced in this work will be very useful for studying these decays in new extended versions of the 3-3-1 model explaining successfully the experimental data of anomalous magnetic moments of charged leptons ${(g-2)}_{e,\mu }$.

We obtain the statistical entropy of a scalar field on the Schwarzschild black hole in holographic massive gravity by considering corrections on the density of quantum states to all orders in the Planck length from a generalized uncertainty principle (GUP). As a result, we find not only the generalized Bekenstein–Hawking entropy depending on holographically massive gravitons without any artificial cutoff, but also new additional correction terms, which are proportional to surface gravity. Moreover, we also observe that all order GUP corrected entropy is improved to have smaller GUP parameter $\lambda$ than the previous results.

In this paper, our focus is to discuss galaxy clustering in an accelerated universe through different approaches, viz., the extended structure of galaxies, the halo approximation, in which we evaluate the configurational integral between two finite limits and the most recent technique known as mean-field theory or approximation. Through these approximations, we were able to eliminate the divergence of the involved configurational integral. These approximations have been employed to develop a gravitational partition function, which has been used to evaluate the thermodynamics of galaxy clustering and the distribution function that goes with it. Throughout this paper, we will use the concept of Maxwell–Boltzmann’s statistics to study the galaxy clustering under the modified Yukawa potential. These thermodynamical quantities, such as Helmholtz free energy, entropy internal energy, and so on, were later plotted.

At finite temperatures, the field along a linear stretch of correlation length size is supposed to trace the shortest path in the field space given the two end point values, known as the geodesic rule. In this study, we compute the probability that, the field variations over distances of correlation length follow this rule in theories with $O(2)$ global symmetry. We consider a simple ferromagnetic $O(2)$-spin model and a complex ${\varphi }^4$ theory. The computations are carried out on an ensemble of equilibrium configurations, generated using Monte Carlo simulations. The numerical results suggest a significant deviation to the geodesic rule, relevant for the formation of topological defects during quench in second-order phase transition. Also for the case of $O(2)$-spins in two dimensions, the distribution and density of vortices, have been studied. It is found that, for quench temperatures close to the transition point, the Kibble–Zurek mechanism underestimates the equilibrium density of defects. The exponents corresponding to the width of the distributions are found to be smaller than Kibble mechanism estimates and match only when there is no deviation from the geodesic rule.

We construct a quantum Hamiltonian for the isotonic Mathews–Lakshmanan oscillator system within the Dunkl formalism. It is shown that the Dunkl Hamiltonian does not admit bound states if the isotonic term is present. If the isotonic term is not present, then the Dunkl Hamiltonian admits bound states of even parity only. These results are in contrast to the findings for the conventional Mathews–Lakshmanan oscillator system.

Holonomic quantum computation makes use of non-abelian geometric phases, associated to the evolution of a subspace of quantum states, to encode logical gates. We identify a special class of subspaces, for which a sequence of rotations results in a non-abelian holonomy of a topological nature, so that it is invariant under any SO(3)-perturbation. Making use of a Majorana-like stellar representation for subspaces, we give explicit examples of topological-holonomic (or toponomic) NOT and CNOT gates.