Heavy Quarkonium Potential Model and the ${}^1{P}_1$ State 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 $c\bar{c}$ 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 $\hat{I}{\cdot }_c^{\prime }$ state is predicted to be 3622.3~MeV.

15 page REVTEX document