Decay properties of $P$-wave charmed baryons from light-cone QCD sum rules

We study decay properties of the $P$-wave charmed baryons using the method of light-cone QCD sum rules, including the $S$-wave decays of the flavor ${\overline{\mathbf{3}}}_F$ $P$-wave charmed baryons into ground-state charmed baryons accompanied by a pseudoscalar meson ($\pi$ or $K$) or a vector meson ($\rho$ or $K^{*}$), and the $S$-wave decays of the flavor ${\mathbf{6}}_F$ $P$-wave charmed baryons into ground-state charmed baryons accompanied by a pseudoscalar meson ($\pi$ or $K$). We study both two-body and three-body decays which are kinematically allowed. We find two mixing solutions from internal $\rho$- and $\lambda$-mode excitations, which can well describe both masses and decay properties of the ${\mathrm{\Lambda }}_c(2595)$, ${\mathrm{\Lambda }}_c(2625)$, ${\mathrm{\Xi }}_c(2790)$ and ${\mathrm{\Xi }}_c(2815)$. We also discuss the possible interpretations of $P$-wave charmed baryons for the ${\mathrm{\Sigma }}_c(2800)$, ${\mathrm{\Xi }}_c(2930)$, ${\mathrm{\Xi }}_c(2980)$, and the recently observed ${\mathrm{\Omega }}_c(3000)$, ${\mathrm{\Omega }}_c(3050)$, ${\mathrm{\Omega }}_c(3066)$, ${\mathrm{\Omega }}_c(3090)$, and ${\mathrm{\Omega }}_c(3119)$.

Figure 1

The coupling constant $g_{{\mathrm{\Xi }}_c^0[{\frac{1}{2}}^{-}]\to {\mathrm{\Xi }}_c^{\prime +}{\pi }^{-}}$ as a function of the Borel mass $T$. The current $J_{1/2,-,{\mathrm{\Xi }}_c^0,1,1,\rho }$ belonging to the baryon doublet $[{\overline{\mathbf{3}}}_F,1,1,\rho ]$ is used here.

Figure 2

The coupling constants $g_{{\mathrm{\Xi }}_c^0[{\frac{1}{2}}^{-}]\to {\mathrm{\Xi }}_c^{+}{\pi }^{-}}$ and $g_{{\mathrm{\Xi }}_c^0[{\frac{1}{2}}^{-}]\to {\mathrm{\Lambda }}_c^{+}{K}^{-}}$ as functions of the Borel mass $T$. The currents belonging to the baryon singlet $[{\overline{\mathbf{3}}}_F,0,1,\rho ]$ are used here.

Figure 3

The coupling constants $g_{{\mathrm{\Lambda }}_c^{+}[{\frac{1}{2}}^{-}]\to {\mathrm{\Sigma }}_c^{++}{\pi }^{-}}$ (top-left), $g_{{\mathrm{\Xi }}_c^0[{\frac{1}{2}}^{-}]\to {\mathrm{\Xi }}_c^{\prime +}{\pi }^{-}}$ (top-right), $g_{{\mathrm{\Lambda }}_c^{+}[{\frac{3}{2}}^{-}]\to {\mathrm{\Sigma }}_c^{*++}{\pi }^{-}}$ (middle-left), $g_{{\mathrm{\Xi }}_c^0[{\frac{3}{2}}^{-}]\to {\mathrm{\Xi }}_c^{*+}{\pi }^{-}}$ (middle-right), $g_{{\mathrm{\Xi }}_c^0[{\frac{1}{2}}^{-}]\to {\mathrm{\Xi }}_c^{+}{\rho }^{-}}$ (bottom-left) and $g_{{\mathrm{\Xi }}_c^0[{\frac{3}{2}}^{-}]\to {\mathrm{\Xi }}_c^{+}{\rho }^{-}}$ (bottom-right) as functions of the Borel mass $T$. The currents belonging to the baryon doublet $[{\overline{\mathbf{3}}}_F,1,1,\rho ]$ are used here.

Figure 4

The coupling constants $g_{{\mathrm{\Lambda }}_c^{+}[{\frac{3}{2}}^{-}]\to {\mathrm{\Sigma }}_c^{*++}{\pi }^{-}}$ (top-left), $g_{{\mathrm{\Xi }}_c^0[{\frac{3}{2}}^{-}]\to {\mathrm{\Xi }}_c^{*+}{\pi }^{-}}$ (top-right), $g_{{\mathrm{\Lambda }}_c^{+}[{\frac{5}{2}}^{-}]\to {\mathrm{\Sigma }}_c^{*++}{\rho }^{-}}$ (bottom-left) and $g_{{\mathrm{\Xi }}_c^0[{\frac{5}{2}}^{-}]\to {\mathrm{\Xi }}_c^{*+}{\rho }^{-}}$ (bottom-right) as functions of the Borel mass $T$. The currents belonging to the baryon doublet $[{\overline{\mathbf{3}}}_F,2,1,\rho ]$ are used here.

Figure 5

The coupling constants $g_{{\mathrm{\Lambda }}_c^{+}[{\frac{1}{2}}^{-}]\to {\mathrm{\Sigma }}_c^{++}{\pi }^{-}}$ (top-left), $g_{{\mathrm{\Xi }}_c^0[{\frac{1}{2}}^{-}]\to {\mathrm{\Xi }}_c^{\prime +}{\pi }^{-}}$ (top-right), $g_{{\mathrm{\Lambda }}_c^{+}[{\frac{3}{2}}^{-}]\to {\mathrm{\Sigma }}_c^{*++}{\pi }^{-}}$ (middle-left), $g_{{\mathrm{\Xi }}_c^0[{\frac{3}{2}}^{-}]\to {\mathrm{\Xi }}_c^{*+}{\pi }^{-}}$ (middle-right), $g_{{\mathrm{\Xi }}_c^0[{\frac{1}{2}}^{-}]\to {\mathrm{\Xi }}_c^{+}{\rho }^{-}}$ (bottom-left) and $g_{{\mathrm{\Xi }}_c^0[{\frac{3}{2}}^{-}]\to {\mathrm{\Xi }}_c^{+}{\rho }^{-}}$ (bottom-right) as functions of the Borel mass $T$. The currents belonging to the baryon doublet $[{\overline{\mathbf{3}}}_F,1,0,\lambda ]$ are used here.

Figure 6

The coupling constants $g_{{\mathrm{\Sigma }}_c^0[{\frac{1}{2}}^{-}]\to {\mathrm{\Sigma }}_c^{+}{\pi }^{-}}$ (top-left), $g_{{\mathrm{\Xi }}_c^{\prime 0}[{\frac{1}{2}}^{-}]\to {\mathrm{\Xi }}_c^{\prime +}{\pi }^{-}}$ (top-right), $g_{{\mathrm{\Xi }}_c^{\prime 0}[{\frac{1}{2}}^{-}]\to {\mathrm{\Sigma }}_c^{+}{K}^{-}}$ (middle-left), $g_{{\mathrm{\Omega }}_c^0[{\frac{1}{2}}^{-}]\to {\mathrm{\Xi }}_c^{\prime +}{K}^{-}}$ (middle-right), $g_{{\mathrm{\Sigma }}_c^0[{\frac{3}{2}}^{-}]\to {\mathrm{\Sigma }}_c^{*+}{\pi }^{-}}$ (middle-left), $g_{{\mathrm{\Xi }}_c^{\prime 0}[{\frac{3}{2}}^{-}]\to {\mathrm{\Xi }}_c^{*+}{\pi }^{-}}$ (middle-right), $g_{{\mathrm{\Xi }}_c^{\prime 0}[{\frac{3}{2}}^{-}]\to {\mathrm{\Sigma }}_c^{*+}{K}^{-}}$ (bottom-left) and $g_{{\mathrm{\Omega }}_c^0[{\frac{3}{2}}^{-}]\to {\mathrm{\Xi }}_c^{*+}{K}^{-}}$ (bottom-right) as functions of the Borel mass $T$. The currents belonging to the baryon doublet $[{\mathbf{6}}_F,1,0,\rho ]$ are used here.

Figure 7

The coupling constants $g_{{\mathrm{\Sigma }}_c^0[{\frac{1}{2}}^{-}]\to {\mathrm{\Lambda }}_c^{+}{\pi }^{-}}$ (top-left), $g_{{\mathrm{\Xi }}_c^{\prime 0}[{\frac{1}{2}}^{-}]\to {\mathrm{\Xi }}_c^{+}{\pi }^{-}}$ (top-right), $g_{{\mathrm{\Xi }}_c^{\prime 0}[{\frac{1}{2}}^{-}]\to {\mathrm{\Lambda }}_c^{+}{K}^{-}}$ (bottom-left) and $g_{{\mathrm{\Omega }}_c^0[{\frac{1}{2}}^{-}]\to {\mathrm{\Xi }}_c^{+}{K}^{-}}$ (bottom-right) as functions of the Borel mass $T$. The currents belonging to the baryon doublet $[{\mathbf{6}}_F,0,1,\lambda ]$ are used here.

Figure 8

The coupling constants $g_{{\mathrm{\Sigma }}_c^0[{\frac{1}{2}}^{-}]\to {\mathrm{\Sigma }}_c^{+}{\pi }^{-}}$ (top-left), $g_{{\mathrm{\Xi }}_c^{\prime 0}[{\frac{1}{2}}^{-}]\to {\mathrm{\Xi }}_c^{\prime +}{\pi }^{-}}$ (top-right), $g_{{\mathrm{\Xi }}_c^{\prime 0}[{\frac{1}{2}}^{-}]\to {\mathrm{\Sigma }}_c^{+}{K}^{-}}$ (middle-left), $g_{{\mathrm{\Omega }}_c^0[{\frac{1}{2}}^{-}]\to {\mathrm{\Xi }}_c^{\prime +}{K}^{-}}$ (middle-right), $g_{{\mathrm{\Sigma }}_c^0[{\frac{3}{2}}^{-}]\to {\mathrm{\Sigma }}_c^{*+}{\pi }^{-}}$ (middle-left), $g_{{\mathrm{\Xi }}_c^{\prime 0}[{\frac{3}{2}}^{-}]\to {\mathrm{\Xi }}_c^{*+}{\pi }^{-}}$ (middle-right), $g_{{\mathrm{\Xi }}_c^{\prime 0}[{\frac{3}{2}}^{-}]\to {\mathrm{\Sigma }}_c^{*+}{K}^{-}}$ (bottom-left) and $g_{{\mathrm{\Omega }}_c^0[{\frac{3}{2}}^{-}]\to {\mathrm{\Xi }}_c^{*+}{K}^{-}}$ (bottom-right) as functions of the Borel mass $T$. The currents belonging to the baryon doublet $[{\mathbf{6}}_F,1,1,\lambda ]$ are used here.

Figure 9

The coupling constants $g_{{\mathrm{\Sigma }}_c^0[{\frac{3}{2}}^{-}]\to {\mathrm{\Sigma }}_c^{*+}{\pi }^{-}}$ (top-left), $g_{{\mathrm{\Xi }}_c^{\prime 0}[{\frac{3}{2}}^{-}]\to {\mathrm{\Xi }}_c^{*+}{\pi }^{-}}$ (top-right), $g_{{\mathrm{\Xi }}_c^{\prime 0}[{\frac{3}{2}}^{-}]\to {\mathrm{\Sigma }}_c^{*+}{K}^{-}}$ (bottom-left) and $g_{{\mathrm{\Omega }}_c^0[{\frac{3}{2}}^{-}]\to {\mathrm{\Xi }}_c^{*+}{K}^{-}}$ (bottom-right) as functions of the Borel mass $T$. The currents belonging to the baryon doublet $[{\mathbf{6}}_F,2,1,\lambda ]$ are used here.