Hyperfine Structure of $B$ and $D$ Mesons in a QCD-Inspired Potential Model

Abstract

We investigate the hyperfine structure of $B$ and $D$ mesons within a QCD-inspired potential model based on the Cornell ansatz. The conventional contact spin--spin term is regularized with a Gaussian smearing to remove the short-distance singularity, and analytic wavefunctions are obtained using the Dalgarno--Lewis perturbative method with the Coulomb part as parent. The numerical study has been extended to include explicit 2S hyperfine predictions and results for the $B_c$ system; these additions probe the stability of the potential parameter space (effective ${\alpha }_s$, confinement strength and smearing width) for unequal-mass systems and radial excitations. We also present a short sensitivity study of the fixed effective coupling ${\alpha }_s$ and discuss the physical interpretation of the smearing parameter $\sigma$. The combined analytic and phenomenological framework provides compact, testable benchmarks for upcoming spectroscopy measurements.

arXiv comment8 pages, 2 Tables, 2 figures

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Cited by in corpus (1)

• Mass-Scaling of Quantum Tunnelling in Hydrogen Bonds: Analytical Model and Comparison with Multidimensional Potentials