Analysis of the 1S and 2S states of the $\Lambda_Q$ and $\Xi_Q$ with the QCD sum rules

Abstract

In this article, we study the ground states and the first radial excited states of the flavor antitriplet heavy baryon states $\Lambda_Q$ and $\Xi_Q$ with the spin-parity $J^P={1\over 2}^{+}$ by carrying out the operator product expansion up to the vacuum condensates of dimension $10$ in a consistent way. We observe that the higher dimensional vacuum condensates play an important role, and obtain very stable QCD sum rules with variations of the Borel parameters for the heavy baryon states for the first time. The predicted masses $6.08\pm0.09\,\rm{GeV}$, $2.78\pm0.08\,\rm{GeV}$ and $2.96\pm0.09\,\rm{GeV}$ for the first radial excited states $\Lambda_b(\rm 2S)$, $\Lambda_c(\rm 2S)$ and $\Xi_c(\rm 2S)$ respectively are in excellent agreement with the experimental data and support assigning the $\Lambda_b(6072)$, $\Lambda_c(2765)$ and $\Xi_c(2980/2970)$ to be the first radial excited states of the $\Lambda_b$, $\Lambda_c$ and $\Xi_c$, respectively, the predicted mass $6.24\pm0.07\,\rm{GeV}$ for the $\Xi_b(\rm 2S)$ can be confronted to the experimental data in the future.