Heavy-Light Mesons in the Non-Relativistic Quark Model Using Laplace Transformation Method

TL;DR

This paper analytically solves the N-dimensional Schrödinger equation with a complex potential to study heavy-light mesons, calculating their masses, decay constants, and decay widths, and examining the effects of dimensionality.

Contribution

It introduces an analytic Laplace transformation method to solve for meson properties in N-dimensional space with extended potentials including spin interactions.

Findings

Meson masses increase with higher dimensional space.

Calculated decay constants and decay widths agree well with experimental data.

Method improves upon previous theoretical approaches.

Abstract

An analytic solution of the N-dimensional radial Schr\"odinger equation with the mixture of vector and scalar potentials via the Laplace transformation method (LTM) is studied. The present potential is extended to include the spin hyperfine, spin-orbit and tensor interactions. The energy eigenvalues and the corresponding eigenfunctions have been determined in the N-dimensional space. The present results are employed to study the different properties of the heavy-light mesons. The masses of the scalar, vector, pseudoscalar and pseudovector of B, Bs, D and Ds mesons have been calculated in the three dimensional space. The effect of the dimensional number space is studied on the masses of the heavy-light mesons. We find that the meson mass increases with increasing dimensional space. The decay constants of the pseudoscalar and vector mesons have been computed. In addition, the leptonic decay widths and branching ratio for the B+, D+ and Ds+ mesons have been studied. Therefore, the present method with the present potential gives good results which are in good agreement with experimental data and are improved in comparison with recently theoretical works.