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

TL;DR

This work addresses the question of the mass splitting between the spin-orbit partners of the $P$-wave $\\text{Ω}$ baryon, treating $\\Omega(2012)$ as a $J^P=3/2^-$ excitation. It develops a dedicated QCD sum-rule for the mass splitting by expanding the correlation functions in the small splitting parameters $\\delta M$ and $\\delta f$ and matching hadron-level and OPE expressions after a Borel transform. The main result is a small splitting, $\\delta M = -18.0^{+33.6}_{-17.1}$ MeV, robust to alternative treatments, with the individual masses consistent with prior estimates $M_{3/2^-} \\approx 2.05$ GeV and $M_{1/2^-} \\approx 2.07$ GeV. This refined splitting sharpens the Ω spectrum predictions and suggests that the Ω(2109) state is unlikely to be the spin–orbit partner of Ω(2012), guiding future experimental analyses.

Abstract

Using the QCD sum rule method, we investigate the mass splitting for the spin-orbit partner states of the $Ω(2012)$ 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, $δM = M_{3/2^-} - M_{1/2^-} = -18.0^{+ 33.6}_{-17.1}$ MeV. This result provides a more quantitative insight into the spectrum of $P$-wave $Ω$ baryons and serves as a useful reference for future experiments.