Heavy quarkonium potential model and theP11state of charmonium

Abstract

A theoretical explanation of the observed splittings among the P states of charmonium is given with the use of a nonsingular potential model for heavy quarkonia. We also show that the recently observed mass difference between the center of gravity of the 3 P J states and the 1 P 1 state of cc does not provide a direct test of the color hyperfine interaction in heavy quarkonia. Our theoretical value for the mass of the 1 P 1 state is in agreement with the experimental result, and its E1 transition width is 341.8 keV. The mass of the η ′ c state is predicted to be 3622.3 MeV.

Potential model calculations and predictions for heavy quarkonium

“…(5a) and (5d), we 'soften' their singularity by adopting the quasistatic approximation of Ref. [10], which leads to the replacement δ( r) → m where m is the quark mass. This softening helps the stability of the eigenvalue calculation, particularly in the non-perturbative approach.…”

Quantum-chromodynamic potential model for light-heavy quarkonia and the heavy quark effective theory

“…We shall here investigate the spectra of light-heavy quarkonia with the use of a quantum chromodynamic model similar to the highly successful model used earlier for the heavy quarkonia cc and bb [3]. The complexity of the model is necessarily enhanced for a light-heavy system because the potential has a complicated dependence on the light and heavy quark masses m and M, and it contains a spin-orbit mixing term.…”

Variational estimation of the wave function at the origin for heavy quarkonium

“…It is noteworthy that in Gupta's papers [6,7] , the non-relativistic reduction was performed with respect to the power of p 2 /E 2 so that the singular r −3 potential term can be avoided. Our recent study indicates that the variational method can give some interesting sight to the singular 1 r 3 problem.…”