Fine structure splittings of excited P and D states in charmonium

TL;DR

This paper analyzes the fine structure splittings of excited P and D states in charmonium, showing they are comparable across different states when using a consistent strong coupling constant, and predicts specific mass values with relativistic effects considered.

Contribution

It provides a detailed calculation of fine structure splittings in charmonium states using relativistic kinematics and compares mass predictions with previous models.

Findings

Fine structure splittings are similar across excited states with consistent alpha_s.

Predicted mass of 2^3P_0 state is 3.84 GeV, below the Dar D^* threshold.

Relativistic effects significantly influence the mass calculations.

Abstract

It is shown that the fine structure splittings of the $2 ^3P_J$ and $3 ^3P_J$ excited states in charmonium are as large as those of the $1^3P_J$ state if the same $\alpha_s(\mu)\approx 0.36$ is used. The predicted mass $M(2 ^3P_0)=3.84$ GeV appears to be 120 MeV lower that the center of gravity of the $2 ^3P_J$ multiplet and lies below the $D\bar D^*$ threshold. Our value of $M(2 ^3P_0)$ is approximately 80 MeV lower than that from the paper by Godfrey and Isgur while the differences in the other masses are $\la 20$ MeV. Relativistic kinematics plays an important role in our analysis.