Heavy mesons mass spectroscopy under a spin-dependent Cornell potential within the framework of the spinless Salpeter equation

Abstract

Abstract The energy bound-state solutions of the spinless Salpeter equation (SSE) have been obtained under a spin-dependent Cornell potential function via the Wentzel–Kramers–Brillouin approximation. The energy levels were applied to predict the mass spectra for the charmonium, bottomonium, and bottom-charmed mesons. The relativistic corrections for the angular momentum quantum number <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>l</m:mi> <m:mo>&gt;</m:mo> <m:mn>0</m:mn> </m:math> l\gt 0 , total angular momentum quantum numbers <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>j</m:mi> <m:mo>=</m:mo> <m:mi>l</m:mi> <m:mo>,</m:mo> <m:mspace width=".3em"/> <m:mi>j</m:mi> <m:mo>=</m:mo> <m:mi>l</m:mi> <m:mo>±</m:mo> <m:mn>1</m:mn> </m:math> j=l,\hspace{.3em}j=l\pm 1 , and the radial quantum numbers n = 1–4 improve the mass spectra. The results agree fairly with experimental data and theoretic results reported in existing works, where the authors utilized different forms of the inter-quark potentials and methods. The deviation of the obtained masses for the charmonium and bottomonium from the observed data yields a total percentage error of 3.32 and 1.11%, respectively. The results indicate that the accuracy of the masses is correlated with the magnitude of masses for the charm and bottom quarks. The SSE together with the phenomenological spin-dependent Cornell potential provides an adequate account of the mass spectroscopy for the heavy mesons and may be used to predict other spectroscopic parameters.