Strong and radiative decays of the doubly charmed baryons

We have systematically studied the strong and radiative decays of the low-lying $1P$-wave doubly charmed baryons. Some interesting observations are: (i) The states ${\mathrm{\Xi }}_{cc}^{*}$ and ${\mathrm{\Omega }}_{cc}^{*}$ with $J^P=3/2^{+}$ have a fairly large decay rate into the ${\mathrm{\Xi }}_{cc}\gamma$ and ${\mathrm{\Omega }}_{cc}\gamma$ channels with a width $\sim 15$ and $\sim 7\mathrm{keV}$, respectively. (ii) The lowest lying excited doubly charmed baryons are dominated by the $1P$ $\rho$ mode excitations, which should be quite narrow states. They decay into the ground state with $J^P=1/2^{+}$ through the radiative transitions with a significant ratio. (iii) The total decay widths of the first orbital excitations of $\lambda$ mode ($1P_{\lambda }$ states with $J^P=1/2^{-}$, $3/2^{-}$, $5/2^{-}$) are about $\mathrm{\Gamma }\sim 100\mathrm{MeV}$, and the ratio between the radiative and hadronic decay widths is about $\mathcal{O}({10}^{-3})$.

Figure 1

The $\rho -$ and $\lambda -$ mode excitations of the $ccq$ system where $\rho$ and $\lambda$ are the Jacobi coordinates defined as $\rho =\frac{1}{\sqrt{2}}({\mathbf{r}}_1-{\mathbf{r}}_2)$ and $\lambda =\frac{1}{\sqrt{6}}({\mathbf{r}}_1+{\mathbf{r}}_2-2{\mathbf{r}}_3)$, respectively. $Q_1$ and $Q_2$ stand for the charm quark, and $q_3$ stands for the light ($u,d,s$) quark.

Figure 2

Light-quark mass dependence of the excitation energy of the $\lambda$ mode (blue solid line) and the $\rho$ mode (red solid line) in Eq. (13).

Figure 3

The radiative decay widths of the low-lying $S$- and $P$-wave ${\mathrm{\Xi }}_{ccu}$ states as a function of the mass. In the figure, ${\mathrm{\Xi }}_{cc}$ and ${\mathrm{\Xi }}_{cc}^{*}$ stand for the $|{\mathrm{\Xi }}_{ccu}{}^{2}S{\frac{1}{2}}^{+}⟩$ and $|{\mathrm{\Xi }}_{ccu}{}^{4}S{\frac{3}{2}}^{+}⟩$ states. Their masses are 3621 MeV and 3727 MeV, respectively.

Figure 4

The radiative decay widths of the low-lying $S$- and $P$-wave ${\mathrm{\Xi }}_{ccd}$ states as a function of the mass.

Figure 5

The radiative decay widths of the low-lying $S$- and $P$-wave ${\mathrm{\Omega }}_{cc}$ states as a function of the mass. In the figure, ${\mathrm{\Omega }}_{cc}$ and ${\mathrm{\Omega }}_{cc}^{*}$ stand for the $|{\mathrm{\Omega }}_{cc}{}^{2}S{\frac{1}{2}}^{+}⟩$ and $|{\mathrm{\Omega }}_{cc}{}^{4}S{\frac{3}{2}}^{+}⟩$ states. Their masses are 3778 MeV and 3872 MeV, respectively.

Figure 6

The strong decay partial widths of the $1P_{\lambda }$-wave ${\mathrm{\Xi }}_{cc}$ states as a function of the mass.

Figure 7

The strong decay partial widths of the $1P_{\lambda }$-wave ${\mathrm{\Omega }}_{cc}$ states as a function of the mass.