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

Abstract

We analyze the low lying spin-$\frac{3}{2}$ $\Xi$ spectrum by means of the two point QCD sum rule approach. The analysis is motivated by the BESIII observation of the $\Xi (1720)$ resonance, reported with mass $1721.0\pm 5.2_{stat.}\pm 3.4_{syst.}\mathrm{MeV}$ 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 $1527.53\pm 111.38\mathrm{MeV}$, $1615.30\pm 50.98\mathrm{MeV}$, $1727.52\pm 42.39\mathrm{MeV}$ and $1803.71\pm 64.50\mathrm{MeV}$ 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 $\Xi (1720)$ as the first radial spin-$\frac{3}{2}$ excitation of the $\Xi$ baryon.

Comments: 10 Pages, 8 Figures and 3 Tables