Meson Mass Spectrum of Heavy-Light Quarks Combinations with Dirac Equation

TL;DR

This paper employs the Dirac equation with a funnel potential to accurately compute the mass spectrum and fine splittings of heavy-light mesons, improving parameter fitting over previous models.

Contribution

It introduces a numerical method to fit heavy-light meson spectra using the Dirac equation with a funnel potential, achieving high precision in mass and splitting predictions.

Findings

Parameters fit meson masses within 7 MeV error

Olsson's parameters fit average mass but not fine splitting

Successful application to D, D_s, B, B_s mesons

Abstract

We use the Dirac equation to study the mass spectrum of mesons with heavy-light quark combinations. First we study the Dirac equation with spherically symmetry and funnel potential, and apply them on the hydrogen-like atom problem to check the correctness of our numerical program. Then we test the parameters in Olsson's paper. We show that Olsson's parameters are good in fitting the averaged central mass, but fail to get correct energy fine splitting. Finally we fit the mass spectrum data of D, D_s, B and B_s mesons with our parameters by solve the Dirac equation and funnel potential, calculate the energy splitting of the S and P states. Our parameters can fit the mass and fine splitting with errors in less than 7 MeV.