Spectroscopic and Structural Properties of $B$, $B_s$, and $B_c$ Mesons within a Non-Relativistic Potential Model: A Comparative Analysis via Matrix Numerov and Variational Methods

Abstract

In this work, we studied the spectroscopic masses, decay constants, oscillation frequencies, and Isgur-Wise function parameters of $B$, $B_s$, and $B_c$ mesons within the framework of a non-relativistic potential model. The interaction is modelled using the Killingbeck potential, with calculations performed using two complementary approaches: the matrix Numerov method for solving the Schr\"odinger equation and the quantum mechanical variational method employing the Gaussian wave function. We determined the unknown parameters of the Killingbeck potential by fitting it to the Cornell potential using the ordinary least squares (OLS) method. These calibrated parameters are then used to compute the aforementioned physical observables.We obtained the masses of the heavy mesons with deviations of less than 0.5\% from the highly precise experimental data. We also discussed the drawbacks and limitations of the non-relativistic model and highlighted its domain of applicability. At the end, we compare our results obtained from both methods with those from other theoretical frameworks, including QCD sum rules, lattice QCD, and alternative potential model studies.