Spectroscopic and Structural Properties of B, Bs, and Bc 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, Bs, and Bc 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 Schrödinger 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.
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BibTeX
@misc{nath2026spectroscopic,
title = {{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}},
author = {Pritom Kumar Nath and Rishan Dev Choudhury and Jugal Lahkar},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.08515},
eprint = {2608.08515},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.08515},
}
RIS
TY - UNPB
TI - 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
AU - Pritom Kumar Nath
AU - Rishan Dev Choudhury
AU - Jugal Lahkar
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2608.08515
UR - https://arxiv.org/abs/2608.08515
AB - 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 Schrödinger 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.
ER -