Improved prediction of the mass splitting for $P$-wave $\Omega$ baryons

Abstract

Using the QCD sum rule method, we investigate the mass splitting for the spin-orbit partner states of the $\Omega (2012)$ baryon assuming that it is a $P$-wave excitation with $J^P=3/2^{-}$. This study is an extension of the previous work [1] in which the masses of these states were estimated with uncertainties too large to extract the reliable mass splitting. In the present study, by directly formulating a sum rule for the mass splitting, we obtain an improved prediction, $\delta M=M_{3/2^{-}}-M_{1/2^{-}}=-18.0_{-17.1}^{+33.6}$ MeV. This result provides a more quantitative insight into the spectrum of $P$-wave $\Omega$ baryons and serves as a useful reference for future experiments.

6 pages,1 table,suggestions and comments welcome