Analysis of the 1S and 2S states of the $Λ_Q$ and $Ξ_Q$ 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 $Λ_Q$ and $Ξ_Q$ 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 $Λ_b(\rm 2S)$, $Λ_c(\rm 2S)$ and $Ξ_c(\rm 2S)$ respectively are in excellent agreement with the experimental data and support assigning the $Λ_b(6072)$, $Λ_c(2765)$ and $Ξ_c(2980/2970)$ to be the first radial excited states of the $Λ_b$, $Λ_c$ and $Ξ_c$, respectively, the predicted mass $6.24\pm0.07\,\rm{GeV}$ for the $Ξ_b(\rm 2S)$ can be confronted to the experimental data in the future.