Theoretical interpretation of $\Xi_c(2970)$

The open charm strong decay widths and certain ratio of branching fractions of a charmed strange baryon $\Xi_c(2970)$ are calculated in a $^3P_0$ model. The results are compatible with the latest experimental data. The theoretical ratio of decay branching fractions $R = \mathcal{B} [ \Xi_{c}(2970)^+ \rightarrow \Xi_c(2645)^{0}\pi^{+} ] / \mathcal{B} [ \Xi_{c}(2970)^+ \rightarrow \Xi_c^{\prime0}\pi^{+}] \approx 1.0$. The spin-parity $J^P = 1/2^+$ and $3/2^+$ for different assignments are analyzed. From the results of our calculation, $\Xi_{c}(2970)$ can be interpreted as a $2S$-wave state with $J^P(s_l) = 1/2^+(0)$. The distinguishing between the 2S-wave $n_\rho$- and $n_\lambda$-excitation states and between states with $s_l = 0$ and $s_l = 1$ and between states with total spin $1/2$ and $3/2$($s_l = 1$) are also discussed.