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

Abstract

Strong decays of $Ξ_c$ baryons with radial or orbital excitations with positive parity have been studied in a $^3P_0$ model. As candidates of these $Xi_c$, possible configurations and $J^P$ of $Ξ_c(2930)$, $Ξ_c(2980)$, $Ξ_c(3055)$, $Ξ_c(3080)$ and $Ξ_c(3123)$ have been assigned. There are $40$ kinds of configurations to describe these excited $Ξ_c$. In these assignments, $Ξ_c(2930)$ may be a $2S$-wave excited $\tildeΞ_{c1}(\frac{1}{2}^+)$ or $\tildeΞ_{c1}(\frac{3}{2}^+)$, or a $D$-wave excited $\hatΞ_{c1}^{' }(\frac{1}{2}^+)$, $\checkΞ_{c1}^{\ 0}(\frac{1}{2}^+)$, $\checkΞ_{c1}^{\ 2}(\frac{1}{2}^+)$, $\hatΞ_{c1}^{' }(\frac{3}{2}^+)$, $\checkΞ_{c1}^{\ 0}(\frac{3}{2}^+)$ or $\checkΞ_{c1}^{\ 2}(\frac{3}{2}^+)$. $Ξ_c(2980)^+$ may be a $2S$-wave excited $\tildeΞ_{c1}(\frac{1}{2}^+)$ or $\tildeΞ_{c0}^{'}(\frac{1}{2}^+)$ with $J^P={1\over 2}^+$, or a $D$-wave excited $\checkΞ_{c0}^{'0}(\frac{1}{2}^+)$ or $\checkΞ_{c1}^{\ 0}(\frac{1}{2}^+)$ with $J^P={1\over 2}^+$. $Ξ_c(3055)^+$ may be a $2S$-wave excited $\acuteΞ_{c1}^{'}(\frac{3}{2}^+)$ or $\acuteΞ_{c0}(\frac{1}{2}^+)$. It may be a $D$-wave excited $Ξ_{c1}^{' }(\frac{3}{2}^+)$, $Ξ_{c2}^{' }(\frac{5}{2}^+)$, $Ξ_{c2}^{ }(\frac{3}{2}^+)$ or $Ξ_{c2}^{ }(\frac{5}{2}^+)$. $Ξ_c(3080)^+$ is very possibly a $2S$-wave excited $\acuteΞ_{c0}(\frac{1}{2}^+)$, and seems not a $D$-wave excitation of $Ξ_c$. For the poor experimental information of $Ξ_c(3123)$, it is impossible to identify this state at present. It is found that the channel $ΛD$ vanishes in the strong decay of $P$-wave, $D$-wave and $2S$-wave excited $Ξ_c$ without $ρ$- mode excitation between the two light quarks ($n_ρ=L_ρ=0$). Some branching fraction ratios have been computed and can be employed to distinguish different configurations in forthcoming experiments.