WKB approximation under Killingbeck potential and its application to double heavy meson mass spectrum

TL;DR

This paper applies the WKB approximation to the Killingbeck potential within a constituent quark model to predict the mass spectra of double heavy mesons, including high excited states, enhancing understanding of meson properties.

Contribution

It introduces a novel application of WKB approximation to Killingbeck potential for calculating double heavy meson spectra and predicts masses of high excited states.

Findings

Predicted masses of high excited states in $c\bar{c}$, $b\bar{b}$, and $b\bar{c}$ meson families.

Demonstrated the applicability of Killingbeck potential in heavy meson spectroscopy.

Provided insights into the scope of double heavy mesons in this potential model.

Abstract

As we all known that non-relativistic or semi-relativistic constituent quark models can describe a large number of the meson sand baryon properties with surprising accuracy. In this work, we studied Killingbeck potential by using WKB approximation in the constituent quark model. The implicit approximate solution of the energy eigenvalue of the Schr\"{o}dinger equation is obtained by using appropriate quantization conditions. Under the Killingbeck potential with the WKB approximation, we studied the spectra of double heavy mesons and predict the masses of high excited states in $c\bar{c}$, $b\bar{b}$ and $b\bar{c}$ families. Finally, we discuss the application scope of double heavy mesons in Killingbeck potential.