abstract

A previously introduced reduction of the Dirac equation is used to study the charmonium spectrum. A regularized vector potential that only depends on the coupling constant and the regularization radius is adopted, considering the interacting quark as an extended source of the chromo-electric field. A scalar interaction is also introduced with some constraints for its parameters. A good description of the structure of the charmonium spectrum is obtained with only three free parameters.

abstract

Calculation of hadronization, decay or scattering processes at nonzero temperatures and densities within the Nambu–Jona-Lasinio-like models requires some techniques for computation of Feynmann diagrams. Decomposition of Feynmann diagrams at the one-loop level leads to the appearance of elementary integrals with one, two, three, and four fermion lines. For example, evaluation of the \(\pi \pi \) scattering amplitude requires calculating of a box diagram with four fermion lines. In this work, the real and imaginary parts of the box integral at the one-loop level are provided in the form suitable for numerical evaluation. The obtained expressions are applicable to any value of temperature, particle mass, and chemical potential. We pay special attention to the conditions for the existence of the appearing improper integrals. As a result, we have obtained constraints on possible values of particle momenta. Among the expressions for the box integral, the general formulas for the integral with an arbitrary number of lines are derived for the case with zero or collinear fermion momenta.

abstract

It has been argued that the bosonic large-\(N\) master field of the IIB matrix model can give rise to an emergent classical spacetime. In a recent paper, we have obtained solutions of a simplified bosonic master-field equation from a related matrix model. In this simplified equation, the effects of dynamic fermions were removed. We now consider the full bosonic master-field equation from a related supersymmetric matrix model for dimensionality \(D=3\) and matrix size \(N=3\). In this last equation, the effects of dynamic fermions are included. With an explicit realization of the random constants entering this algebraic equation, we establish the existence of nontrivial solutions. The small matrix size, however, does not allow us to make a definitive statement as to the appearance of a diagonal/band-diagonal structure in the obtained matrices.

abstract

The calculations of the \(\alpha \)-decay half-lives of some polonium isotopes in the mass range of 186–218 have been carried out using the Wentzel–Kramers–Brillouin (WKB) semiclassical approximation. The \(\alpha \)-nucleus effective potential used contains the Coulomb potential, centrifugal potential, and nuclear potential. The nuclear potential is obtained via the double folding model, with the microscopic \(NN\) effective interactions derived from the relativistic mean field theory Lagrangian (termed R3Y). Different parametrizations of the R3Y interactions have been employed in the computation of nuclear potentials. The results obtained using the R3Y \(NN\) interactions are compared with the ones obtained using the famous Michigan-3-Yukawa (M3Y) interactions. The use of density-dependent \(NN\) interaction is also considered. When compared to available experimental data, there are improvements in the results when density-dependent interaction potentials are used compared to when density-independent interactions are employed.