Interpreting the Newly Observed $Ξ(1720)$ State in the Spin-$\frac{3}{2}$ $Ξ$ Spectrum

Abstract

We analyze the low lying spin-$\frac{3}{2}$ $Ξ$ spectrum by means of the two point QCD sum rule approach. The analysis is motivated by the BESIII observation of the $Ξ(1720)$ resonance, reported with mass $1721.0\pm5.2_{\mathrm{stat.}}\pm3.4_{\mathrm{syst.}}~\mathrm{MeV}$ and favored quantum numbers $J^P=\frac{3}{2}^{+}$. In this framework, we include the $1S$, $1P$, $2S$ and $2P$ configurations as possible low lying spin-$\frac{3}{2}$ cascade states. The extracted masses are $1527.53\pm111.38~\mathrm{MeV}$, $1615.30\pm50.98~\mathrm{MeV}$, $1727.52\pm42.39~\mathrm{MeV}$ and $1803.71\pm64.50~\mathrm{MeV}$ for the $1S$, $1P$, $2S$ and $2P$ states, respectively. The mass obtained for the $2S$ configuration agrees with the BESIII value within uncertainties and favors the assignment of $Ξ(1720)$ as the first radial spin-$\frac{3}{2}$ excitation of the $Ξ$ baryon.