Study of $2S$- and $1D$- excitations of observed charmed strange baryons

Strong decays of ${\mathrm{\Xi }}_c$ baryons with radial or orbital excitations with positive parity have been studied in a ${}^3{P}_0$ model. As candidates of these $X{i}_c$, possible configurations and $J^P$ of ${\mathrm{\Xi }}_c(2930)$, ${\mathrm{\Xi }}_c(2980)$, ${\mathrm{\Xi }}_c(3055)$, ${\mathrm{\Xi }}_c(3080)$ and ${\mathrm{\Xi }}_c(3123)$ have been assigned. There are $40$ kinds of configurations to describe these excited ${\mathrm{\Xi }}_c$. In these assignments, ${\mathrm{\Xi }}_c(2930)$ may be a $2S$-wave excited ${\tilde{\mathrm{\Xi }}}_{c1}({\frac{1}{2}}^{+})$ or ${\tilde{\mathrm{\Xi }}}_{c1}({\frac{3}{2}}^{+})$, or a $D$-wave excited ${\widehat{\mathrm{\Xi }}}_{c1}^{{}^{\mathrm{\prime }}}({\frac{1}{2}}^{+})$, $\check\Xi_{c1}^{
0}(\frac{1}{2}^+)$,$\check\Xi_{c1}^{\ 2}(\frac{1}{2}^+)$,$\hat\Xi_{c1}^{’ }(\frac{3}{2}^+)$,$\check\Xi_{c1}^{\ 0}(\frac{3}{2}^+)$or$\check\Xi_{c1}^{
2}(\frac{3}{2}^+)$\mathrm{.}$\Xi_c(2980)^+$maybea$2S$-waveexcited$\tilde{\Xi}{c1}(\frac{1}{2}^+)$or$\tilde{\Xi}{c0}^{'}(\frac{1}{2}^+)$with$J^P={1\over 2}^+$,ora$D$-waveexcited$\check\Xi_{c0}^{‘0}(\frac{1}{2}^+)$or$\check\Xi_{c1}^{\ 0}(\frac{1}{2}^+)$with$J^P={1\over 2}^+$\mathrm{.}$\Xi_c(3055)^+$maybea$2S$-waveexcited$\acute{\Xi}{c1}^{'}(\frac{3}{2}^+)$or$\acute{\Xi}{c0}(\frac{1}{2}^+)$. It may be a $D$-wave excited ${\mathrm{\Xi }}_{c1}^{{}^{\mathrm{\prime }}}({\frac{3}{2}}^{+})$, $\Xi_{c2}^{’ }(\frac{5}{2}^+)$,$\Xi_{c2}^{ }(\frac{3}{2}^+)$or$\Xi_{c2}^{ }(\frac{5}{2}^+)$\mathrm{.}$\Xi_c(3080)^+$isverypossiblya$2S$-waveexcited$\acute{\Xi}_{c0}(\frac{1}{2}^+)$,andseemsnota$D$-waveexcitationof$\Xi_c$\mathrm{.}Forthepoorexperimentalinformationof$\Xi_c(3123)$, it is impossible to identify this state at present. It is found that the channel $\mathrm{\Lambda }D$ vanishes in the strong decay of $P$-wave, $D$-wave and $2S$-wave excited ${\mathrm{\Xi }}_c$ without $\rho$- mode excitation between the two light quarks ($n_{\rho }=L_{\rho }=0$). Some branching fraction ratios have been computed and can be employed to distinguish different configurations in forthcoming experiments.