Fine structure splittings of excited P and D states in charmonium

Abstract

It is shown that the fine structure splittings of the $2^3{P}_J$ and $3^3{P}_J$ excited states in charmonium are as large as those of the $1^3{P}_J$ state if the same ${\alpha }_s(\mu )\approx 0.36$ is used. The predicted mass $M(2^3{P}_0)=3.84$ GeV appears to be 120 MeV lower that the center of gravity of the $2^3{P}_J$ multiplet and lies below the $D{\bar{D}}^{\ast }$ threshold. Our value of $M(2^3{P}_0)$ is approximately 80 MeV lower than that from the paper by Godfrey and Isgur while the differences in the other masses are $\text{la}20$ MeV. Relativistic kinematics plays an important role in our analysis.

Comments: 12 pages