Hadronic decay properties of newly observed $\Omega_c$ baryons

TL;DR

This paper calculates the hadronic decay widths of newly observed $\\Omega_c$ baryons using a $^3P_0$ model, providing possible quantum state assignments consistent with experimental decay widths.

Contribution

It offers the first detailed decay width calculations for these states, suggesting specific quantum number assignments based on decay features and experimental data.

Findings

$\\Omega_c(3066)^0$ and $\Omega_c(3090)^0$ are likely $1P$-wave states.

$\\Omega_c(3000)^0$, $\\Omega_c(3050)^0$, and $\\Omega_c(3119)^0$ favor $1D$-wave state assignments.

Predicted decay widths align with experimental measurements for these assignments.

Abstract

Hadronic decay widths of the newly observed charmed strange baryons, $\Omega_c(3000)^0$, $\Omega_c(3050)^0$, $\Omega_c(3066)^0$, $\Omega_c(3090)^0$ and $\Omega_c(3119)^0$ have been calculated in a $^3P_0$ model. Our results indicate that $\Omega_c(3066)^0$ and $\Omega_c(3090)^0$ can be interpreted as the $1P-$wave $\Omega_{c2}(\frac{3}{2}^-)$ or $\Omega_{c2}(\frac{5}{2}^-)$. Though the measured masses of $\Omega_c(3000)^0$, $\Omega_c(3050)^0$ and $\Omega_c(3119)^0$ are lower than existed theoretical predictions of $1D-$wave $\Omega_c$, the hadronic decay features of these $\Omega_c$ favor assignments of the $1D-$wave states. $\Omega_c(3000)^0$ is possibly $\Omega_{c1}(\frac{1}{2}^+)$ or $\Omega_{c1}(\frac{3}{2}^+)$, $\Omega_c(3050)^0$ is possibly $\hat\Omega_{c3}(\frac{5}{2}^+)$ or $\hat\Omega_{c3}(\frac{7}{2}^+)$, and $\Omega_c(3119)^0$ is possibly $\hat\Omega_{c3}(\frac{5}{2}^+)$, $\hat\Omega_{c3}(\frac{7}{2}^+)$, $\Omega_{c3}(\frac{5}{2}^+)$ or $\Omega_{c3}(\frac{7}{2}^+)$. The predicted total decay widths in these assignments are consistent with experiment.

Tables

Table 1. Table 1: Quantum numbers of initial baryons

	Assignments	$J$	$J_l$	$L_{\rho }$	$L_{\lambda }$	$L$	$S_{\rho }$
	${\Omega }_{c0}\left({\frac{1}{2}}^{-}\right)$	$\frac{1}{2}$	0	0	1	1	1
	${\Omega }_{c1}({\frac{1}{2}}^{-},{\frac{3}{2}}^{-})$	$\frac{1}{2}$,$\frac{3}{2}$	1	0	1	1	1
	${\Omega }_{c2}({\frac{3}{2}}^{-},{\frac{5}{2}}^{-})$	$\frac{3}{2}$,$\frac{5}{2}$	2	0	1	1	1
	${\tilde{\Omega }}_{c1}({\frac{1}{2}}^{-},{\frac{3}{2}}^{-})$	$\frac{1}{2}$,$\frac{3}{2}$	1	1	0	1	0
	${\Omega }_{c1}({\frac{1}{2}}^{+},{\frac{3}{2}}^{+})$	$\frac{1}{2}$,$\frac{3}{2}$	1	0	2	2	1
	${\Omega }_{c2}({\frac{3}{2}}^{+},{\frac{5}{2}}^{+})$	$\frac{3}{2}$,$\frac{5}{2}$	2	0	2	2	1
	${\Omega }_{c3}({\frac{5}{2}}^{+},{\frac{7}{2}}^{+})$	$\frac{5}{2}$,$\frac{7}{2}$	3	0	2	2	1
	${\hat{\Omega }}_{c1}({\frac{1}{2}}^{+},{\frac{3}{2}}^{+})$	$\frac{1}{2}$,$\frac{3}{2}$	1	2	0	2	1
	${\hat{\Omega }}_{c2}({\frac{3}{2}}^{+},{\frac{5}{2}}^{+})$	$\frac{3}{2}$,$\frac{5}{2}$	2	2	0	2	1
	${\hat{\Omega }}_{c3}({\frac{5}{2}}^{+},{\frac{7}{2}}^{+})$	$\frac{5}{2}$,$\frac{7}{2}$	3	2	0	2	1
	${\check{\Omega }}_{c0}^0\left({\frac{1}{2}}^{+}\right)$	$\frac{1}{2}$	0	1	1	0	0
	${\check{\Omega }}_{c1}^1({\frac{1}{2}}^{+},{\frac{3}{2}}^{+})$	$\frac{1}{2}$,$\frac{3}{2}$	1	1	1	1	0
	${\check{\Omega }}_{c2}^1({\frac{3}{2}}^{+},{\frac{5}{2}}^{+})$	$\frac{3}{2}$,$\frac{5}{2}$	1	1	1	1	0

Table 2. Table 2: Decay widths (MeV) of Ω c ​ ( 3000 ) 0 subscript Ω 𝑐 superscript 3000 0 \Omega_{c}(3000)^{0} in different assignments.

	${\Omega }_c\left(J^P\right)$	${\Xi }_c^{+}{K}^{-}$	${\Xi }_c^0{K}^0$	$total$
	${\Omega }_{c0}\left({\frac{1}{2}}^{-}\right)$	$7.2\times {10}^2$	$6.6\times {10}^2$	$1.4\times {10}^2$
	${\Omega }_{c1}\left({\frac{1}{2}}^{-}\right)$	0.0	0.0	0.0
	${\Omega }_{c1}\left({\frac{3}{2}}^{-}\right)$	0.0	0.0	0.0
	${\Omega }_{c2}\left({\frac{3}{2}}^{-}\right)$	0.3	0.2	0.5
	${\Omega }_{c2}\left({\frac{5}{2}}^{-}\right)$	0.3	0.2	0.5
	${\tilde{\Omega }}_{c1}\left({\frac{1}{2}}^{-}\right)$	0.0	0.0	0.0
	${\tilde{\Omega }}_{c1}\left({\frac{3}{2}}^{-}\right)$	0.0	0.0	0.0
	${\Omega }_{c1}\left({\frac{1}{2}}^{+}\right)$	2.8	2.2	5.0
	${\Omega }_{c1}\left({\frac{3}{2}}^{+}\right)$	2.8	2.2	5.0
	${\Omega }_{c2}\left({\frac{3}{2}}^{+}\right)$	0.0	0.0	0.0
	${\Omega }_{c2}\left({\frac{5}{2}}^{+}\right)$	0.0	0.0	0.0
	${\Omega }_{c3}\left({\frac{5}{2}}^{+}\right)$	$6.9\times {10}^{-4}$	$6.9\times {10}^{-4}$	$1.0\times {10}^{-3}$
	${\Omega }_{c3}\left({\frac{7}{2}}^{+}\right)$	$6.9\times {10}^{-4}$	$6.9\times {10}^{-4}$	$1.0\times {10}^{-3}$
	${\hat{\Omega }}_{c1}\left({\frac{1}{2}}^{+}\right)$	25.7	19.4	45.1
	${\hat{\Omega }}_{c1}\left({\frac{3}{2}}^{+}\right)$	25.7	19.4	45.1
	${\hat{\Omega }}_{c2}\left({\frac{3}{2}}^{+}\right)$	0.0	0.0	0.0
	${\hat{\Omega }}_{c2}\left({\frac{5}{2}}^{+}\right)$	0.0	0.0	0.0
	${\hat{\Omega }}_{c3}\left({\frac{5}{2}}^{+}\right)$	$6.8\times {10}^{-3}$	$3.5\times {10}^{-3}$	$1.3\times {10}^{-2}$
	${\hat{\Omega }}_{c3}\left({\frac{7}{2}}^{+}\right)$	$6.8\times {10}^{-3}$	$3.5\times {10}^{-3}$	$1.3\times {10}^{-2}$
	${\check{\Omega }}_{c0}^0\left({\frac{1}{2}}^{+}\right)$	0.0	0.0	0.0
	${\check{\Omega }}_{c1}^1\left({\frac{1}{2}}^{+}\right)$	0.0	0.0	0.0
	${\check{\Omega }}_{c1}^1\left({\frac{3}{2}}^{+}\right)$	0.0	0.0	0.0
	${\check{\Omega }}_{c2}^1\left({\frac{3}{2}}^{+}\right)$	0.0	0.0	0.0
	${\check{\Omega }}_{c2}^1\left({\frac{5}{2}}^{+}\right)$	0.0	0.0	0.0

Table 3. Table 3: Decay widths (MeV) of Ω c ​ ( 3050 ) 0 subscript Ω 𝑐 superscript 3050 0 \Omega_{c}(3050)^{0} in different assignments.

	${\Omega }_c\left(J^P\right)$	${\Xi }_c^{+}{K}^{-}$	${\Xi }_c^0{K}^0$	$total$
	${\Omega }_{c0}\left({\frac{1}{2}}^{-}\right)$	$1.0\times {10}^3$	$1.0\times {10}^3$	$2.0\times {10}^3$
	${\Omega }_{c1}\left({\frac{1}{2}}^{-}\right)$	0.0	0.0	0.0
	${\Omega }_{c1}\left({\frac{3}{2}}^{-}\right)$	0.0	0.0	0.0
	${\Omega }_{c2}\left({\frac{3}{2}}^{-}\right)$	2.9	2.4	5.3
	${\Omega }_{c2}\left({\frac{5}{2}}^{-}\right)$	2.9	2.4	5.3
	${\tilde{\Omega }}_{c1}\left({\frac{1}{2}}^{-}\right)$	0.0	0.0	0.0
	${\tilde{\Omega }}_{c1}\left({\frac{3}{2}}^{-}\right)$	0.0	0.0	0.0
	${\Omega }_{c1}\left({\frac{1}{2}}^{+}\right)$	10.0	8.9	18.9
	${\Omega }_{c1}\left({\frac{3}{2}}^{+}\right)$	10.0	8.9	18.9
	${\Omega }_{c2}\left({\frac{3}{2}}^{+}\right)$	0.0	0.0	0.0
	${\Omega }_{c2}\left({\frac{5}{2}}^{+}\right)$	0.0	0.0	0.0
	${\Omega }_{c3}\left({\frac{5}{2}}^{+}\right)$	$1.4\times {10}^{-2}$	$1.1\times {10}^{-2}$	$2.5\times {10}^{-2}$
	${\Omega }_{c3}\left({\frac{7}{2}}^{+}\right)$	$1.4\times {10}^{-2}$	$1.1\times {10}^{-2}$	$2.5\times {10}^{-2}$
	${\hat{\Omega }}_{c1}\left({\frac{1}{2}}^{+}\right)$	89.4	80.4	168.8
	${\hat{\Omega }}_{c1}\left({\frac{3}{2}}^{+}\right)$	89.4	80.4	168.8
	${\hat{\Omega }}_{c2}\left({\frac{3}{2}}^{+}\right)$	0.0	0.0	0.0
	${\hat{\Omega }}_{c2}\left({\frac{5}{2}}^{+}\right)$	0.0	0.0	0.0
	${\hat{\Omega }}_{c3}\left({\frac{5}{2}}^{+}\right)$	0.1	0.1	0.2
	${\hat{\Omega }}_{c3}\left({\frac{7}{2}}^{+}\right)$	0.1	0.1	0.2
	${\check{\Omega }}_{c0}^0\left({\frac{1}{2}}^{+}\right)$	0.0	0.0	0.0
	${\check{\Omega }}_{c1}^1\left({\frac{1}{2}}^{+}\right)$	0.0	0.0	0.0
	${\check{\Omega }}_{c1}^1\left({\frac{3}{2}}^{+}\right)$	0.0	0.0	0.0
	${\check{\Omega }}_{c2}^1\left({\frac{3}{2}}^{+}\right)$	0.0	0.0	0.0
	${\check{\Omega }}_{c2}^1\left({\frac{5}{2}}^{+}\right)$	0.0	0.0	0.0

Table 4. Table 4: Decay widths (MeV) of Ω c ​ ( 3066 ) 0 subscript Ω 𝑐 superscript 3066 0 \Omega_{c}(3066)^{0} in different assignments.

	${\Omega }_c\left(J^P\right)$	${\Xi }_c^{+}{K}^{-}$	${\Xi }_c^0{K}^0$	$total$
	${\Omega }_{c0}\left({\frac{1}{2}}^{-}\right)$	$1.1\times {10}^3$	$1.1\times {10}^3$	$2.2\times {10}^3$
	${\Omega }_{c1}\left({\frac{1}{2}}^{-}\right)$	0.0	0.0	0.0
	${\Omega }_{c1}\left({\frac{3}{2}}^{-}\right)$	0.0	0.0	0.0
	${\Omega }_{c2}\left({\frac{3}{2}}^{-}\right)$	4.6	3.9	8.5
	${\Omega }_{c2}\left({\frac{5}{2}}^{-}\right)$	4.6	3.9	8.5
	${\tilde{\Omega }}_{c1}\left({\frac{1}{2}}^{-}\right)$	0.0	0.0	0.0
	${\tilde{\Omega }}_{c1}\left({\frac{3}{2}}^{-}\right)$	0.0	0.0	0.0
	${\Omega }_{c1}\left({\frac{1}{2}}^{+}\right)$	12.8	11.7	24.5
	${\Omega }_{c1}\left({\frac{3}{2}}^{+}\right)$	12.8	11.7	24.5
	${\Omega }_{c2}\left({\frac{3}{2}}^{+}\right)$	0.0	0.0	0.0
	${\Omega }_{c2}\left({\frac{5}{2}}^{+}\right)$	0.0	0.0	0.0
	${\Omega }_{c3}\left({\frac{5}{2}}^{+}\right)$	$2.6\times {10}^{-2}$	$2.1\times {10}^{-2}$	$4.7\times {10}^{-2}$
	${\Omega }_{c3}\left({\frac{7}{2}}^{+}\right)$	$2.6\times {10}^{-2}$	$2.1\times {10}^{-2}$	$4.7\times {10}^{-2}$
	${\hat{\Omega }}_{c1}\left({\frac{1}{2}}^{+}\right)$	$1.1\times {10}^2$	$1.0\times {10}^2$	$2.1\times {10}^2$
	${\hat{\Omega }}_{c1}\left({\frac{3}{2}}^{+}\right)$	$1.1\times {10}^2$	$1.0\times {10}^2$	$2.1\times {10}^2$
	${\hat{\Omega }}_{c2}\left({\frac{3}{2}}^{+}\right)$	0.0	0.0	0.0
	${\hat{\Omega }}_{c2}\left({\frac{5}{2}}^{+}\right)$	0.0	0.0	0.0
	${\hat{\Omega }}_{c3}\left({\frac{5}{2}}^{+}\right)$	0.3	0.2	0.5
	${\hat{\Omega }}_{c3}\left({\frac{7}{2}}^{+}\right)$	0.3	0.2	0.5
	${\check{\Omega }}_{c0}^0\left({\frac{1}{2}}^{+}\right)$	0.0	0.0	0.0
	${\check{\Omega }}_{c1}^1\left({\frac{1}{2}}^{+}\right)$	0.0	0.0	0.0
	${\check{\Omega }}_{c1}^1\left({\frac{3}{2}}^{+}\right)$	0.0	0.0	0.0
	${\check{\Omega }}_{c2}^1\left({\frac{3}{2}}^{+}\right)$	0.0	0.0	0.0
	${\check{\Omega }}_{c2}^1\left({\frac{5}{2}}^{+}\right)$	0.0	0.0	0.0

Table 5. Table 5: Decay widths (MeV) of Ω c ​ ( 3090 ) 0 subscript Ω 𝑐 superscript 3090 0 \Omega_{c}(3090)^{0} in different assignments.

	${\Omega }_c\left(J^P\right)$	${\Xi }_c^{+}{K}^{-}$	${\Xi }_c^0{K}^0$	${\Xi }_c^{{}_{}{}^{\prime }+}{K}^{-}$	${\Xi }_c^{{}_{}{}^{\prime }0}{K}^0$	$total$
	${\Omega }_{c0}\left({\frac{1}{2}}^{-}\right)$	$1.2\times {10}^3$	$1.1\times {10}^3$	0.0	0.0	$2.3\times {10}^3$
	${\Omega }_{c1}\left({\frac{1}{2}}^{-}\right)$	0.0	0.0	$3.6\times {10}^2$	$3.1\times {10}^2$	$6.7\times {10}^2$
	${\Omega }_{c1}\left({\frac{3}{2}}^{-}\right)$	0.0	0.0	$3.0\times {10}^{-2}$	$1.2\times {10}^{-2}$	$4.2\times {10}^{-2}$
	${\Omega }_{c2}\left({\frac{3}{2}}^{-}\right)$	8.0	7.0	$5.3\times {10}^{-2}$	$2.2\times {10}^{-2}$	15.1
	${\Omega }_{c2}\left({\frac{5}{2}}^{-}\right)$	8.0	7.0	$2.3\times {10}^{-2}$	$9.9\times {10}^{-3}$	15.1
	${\tilde{\Omega }}_{c1}\left({\frac{1}{2}}^{-}\right)$	0.0	0.0	$5.4\times {10}^2$	$4.6\times {10}^2$	$1.0\times {10}^3$
	${\tilde{\Omega }}_{c1}\left({\frac{3}{2}}^{-}\right)$	0.0	0.0	0.2	0.1	0.3
	${\Omega }_{c1}\left({\frac{1}{2}}^{+}\right)$	17.4	16.3	0.4	0.2	34.3
	${\Omega }_{c1}\left({\frac{3}{2}}^{+}\right)$	17.4	16.3	0.1	0.1	33.9
	${\Omega }_{c2}\left({\frac{3}{2}}^{+}\right)$	0.0	0.0	0.9	0.5	1.4
	${\Omega }_{c2}\left({\frac{5}{2}}^{+}\right)$	0.0	0.0	$4.0\times {10}^{-5}$	$1.1\times {10}^{-5}$	$5.1\times {10}^{-5}$
	${\Omega }_{c3}\left({\frac{5}{2}}^{+}\right)$	$5.7\times {10}^{-2}$	$4.8\times {10}^{-2}$	$4.5\times {10}^{-5}$	$1.3\times {10}^{-5}$	0.1
	${\Omega }_{c3}\left({\frac{7}{2}}^{+}\right)$	$5.7\times {10}^{-2}$	$4.8\times {10}^{-2}$	$2.5\times {10}^{-5}$	$7.6\times {10}^{-6}$	0.1
	${\hat{\Omega }}_{c1}\left({\frac{1}{2}}^{+}\right)$	$1.6\times {10}^2$	$1.5\times {10}^2$	3.4	2.0	$3.1\times {10}^2$
	${\hat{\Omega }}_{c1}\left({\frac{3}{2}}^{+}\right)$	$1.6\times {10}^2$	$1.5\times {10}^2$	0.8	0.5	$3.1\times {10}^2$
	${\hat{\Omega }}_{c2}\left({\frac{3}{2}}^{+}\right)$	0.0	0.0	7.6	4.6	12.6
	${\hat{\Omega }}_{c2}\left({\frac{5}{2}}^{+}\right)$	0.0	0.0	$3.9\times {10}^{-4}$	$1.2\times {10}^{-4}$	$5.1\times {10}^{-2}$
	${\hat{\Omega }}_{c3}\left({\frac{5}{2}}^{+}\right)$	0.6	0.5	$4.5\times {10}^{-4}$	$1.3\times {10}^{-4}$	1.0
	${\hat{\Omega }}_{c3}\left({\frac{7}{2}}^{+}\right)$	0.6	0.5	$2.5\times {10}^{-4}$	$7.5\times {10}^{-5}$	1.0
	${\check{\Omega }}_{c0}^0\left({\frac{1}{2}}^{+}\right)$	0.0	0.0	6.7	4.1	10.8
	${\check{\Omega }}_{c1}^1\left({\frac{1}{2}}^{+}\right)$	0.0	0.0	0.0	0.0	0.0
	${\check{\Omega }}_{c1}^1\left({\frac{3}{2}}^{+}\right)$	0.0	0.0	0.0	0.0	0.0
	${\check{\Omega }}_{c2}^1\left({\frac{3}{2}}^{+}\right)$	0.0	0.0	3.4	2.0	5.4
	${\check{\Omega }}_{c2}^1\left({\frac{5}{2}}^{+}\right)$	0.0	0.0	$3.9\times {10}^{-4}$	$1.2\times {10}^{-4}$	$5.1\times {10}^{-4}$

Table 6. Table 6: Decay widths (MeV) of Ω c ​ ( 3119 ) 0 subscript Ω 𝑐 superscript 3119 0 \Omega_{c}(3119)^{0} in different assignments.

	${\Omega }_c\left(J^P\right)$	${\Xi }_c^{+}{K}^{-}$	${\Xi }_c^0{K}^0$	${\Xi }_c^{{}_{}{}^{\prime }+}{K}^{-}$	${\Xi }_c^{{}_{}{}^{\prime }0}{K}^0$	$total$
	${\Omega }_{c0}\left({\frac{1}{2}}^{-}\right)$	$1.2\times {10}^3$	$1.2\times {10}^3$	0.0	0.0	$2.4\times {10}^3$
	${\Omega }_{c1}\left({\frac{1}{2}}^{-}\right)$	0.0	0.0	$5.4\times {10}^2$	$5.1\times {10}^2$	$10.5\times {10}^2$
	${\Omega }_{c1}\left({\frac{3}{2}}^{-}\right)$	0.0	0.0	0.2	0.2	0.5
	${\Omega }_{c2}\left({\frac{3}{2}}^{-}\right)$	13.9	12.5	0.4	0.4	27.3
	${\Omega }_{c2}\left({\frac{5}{2}}^{-}\right)$	13.9	12.5	0.2	0.2	26.8
	${\tilde{\Omega }}_{c1}\left({\frac{1}{2}}^{-}\right)$	0.0	0.0	$8.1\times {10}^2$	$7.7\times {10}^2$	$1.6\times {10}^3$
	${\tilde{\Omega }}_{c1}\left({\frac{3}{2}}^{-}\right)$	0.0	0.0	1.6	1.2	2.8
	${\Omega }_{c1}\left({\frac{1}{2}}^{+}\right)$	23.5	22.2	1.4	1.2	48.3
	${\Omega }_{c1}\left({\frac{3}{2}}^{+}\right)$	23.4	22.2	0.4	0.3	46.3
	${\Omega }_{c2}\left({\frac{3}{2}}^{+}\right)$	0.0	0.0	3.2	2.6	5.8
	${\Omega }_{c2}\left({\frac{5}{2}}^{+}\right)$	0.0	0.0	$9.0\times {10}^{-4}$	$5.8\times {10}^{-4}$	$1.5\times {10}^{-3}$
	${\Omega }_{c3}\left({\frac{5}{2}}^{+}\right)$	0.1	0.1	$1.0\times {10}^{-3}$	$6.6\times {10}^{-4}$	0.2
	${\Omega }_{c3}\left({\frac{7}{2}}^{+}\right)$	0.1	0.1	$5.8\times {10}^{-4}$	$3.7\times {10}^{-4}$	0.2
	${\hat{\Omega }}_{c1}\left({\frac{1}{2}}^{+}\right)$	$2.1\times {10}^2$	$2.0\times {10}^2$	12.6	10.6	$4.3\times {10}^2$
	${\hat{\Omega }}_{c1}\left({\frac{3}{2}}^{+}\right)$	$2.1\times {10}^2$	$2.0\times {10}^2$	3.2	2.6	$4.1\times {10}^2$
	${\hat{\Omega }}_{c2}\left({\frac{3}{2}}^{+}\right)$	0.0	0.0	28.5	23.7	52.3
	${\hat{\Omega }}_{c2}\left({\frac{5}{2}}^{+}\right)$	0.0	0.0	$8.9\times {10}^{-3}$	$5.7\times {10}^{-3}$	$1.4\times {10}^{-2}$
	${\hat{\Omega }}_{c3}\left({\frac{5}{2}}^{+}\right)$	1.2	1.1	$1.0\times {10}^{-2}$	$6.5\times {10}^{-3}$	2.3
	${\hat{\Omega }}_{c3}\left({\frac{7}{2}}^{+}\right)$	1.2	1.1	$5.8\times {10}^{-3}$	$3.7\times {10}^{-3}$	2.3
	${\check{\Omega }}_{c0}^0\left({\frac{1}{2}}^{+}\right)$	0.0	0.0	25.2	21.0	46.2
	${\check{\Omega }}_{c1}^1\left({\frac{1}{2}}^{+}\right)$	0.0	0.0	0.0	0.0	0.0
	${\check{\Omega }}_{c1}^1\left({\frac{3}{2}}^{+}\right)$	0.0	0.0	0.0	0.0	0.0
	${\check{\Omega }}_{c2}^1\left({\frac{3}{2}}^{+}\right)$	0.0	0.0	12.7	10.6	23.2
	${\check{\Omega }}_{c2}^1\left({\frac{5}{2}}^{+}\right)$	0.0	0.0	$9.0\times {10}^{-3}$	$5.7\times {10}^{-3}$	$1.5\times {10}^{-2}$

Equations

$${\Omega }_c(3000{)}^0:M$$

$$\Gamma$$

$${\Omega }_c(3050{)}^0:M$$

$$\Gamma$$

$${\Omega }_c(3066{)}^0:M$$

$$\Gamma$$

$${\Omega }_c(3090{)}^0:M$$

$$\Gamma$$

$${\Omega }_c(3119{)}^0:M$$

$$\Gamma$$

$$\Gamma ={\pi }^2\frac{|\vec{p}|}{m_A^2}\frac{1}{2J_A+1}\sum _{M_{J_A}{M}_{J_B}{M}_{J_C}}|{\mathcal{M}}^{M_{J_A}{M}_{J_B}{M}_{J_C}}{|}^2,$$

$${\mathcal{M}}^{M_{J_A}{M}_{J_B}{M}_{J_C}}$$

$$=-2\gamma \sqrt{8E_A{E}_B{E}_C}\sum _{M_{{\rho }_A}}\sum _{M_{L_A}}\sum _{M_{{\rho }_B}}\sum _{M_{L_B}}\sum _{M_{S_1},M_{S_3},M_{S_4},m}$$

$$⟨J_{l_A}{M}_{J_{l_A}}{S}_3{M}_{S_3}|J_A{M}_{J_A}⟩⟨L_{{\rho }_A}{M}_{L_{{\rho }_A}}{L}_{{\lambda }_A}{M}_{L_{{\lambda }_A}}|L_A{M}_{L_A}⟩$$

$$⟨L_A{M}_{L_A}{S}_{12}{M}_{S_{12}}|J_{L_A}{M}_{J_{L_A}}⟩⟨S_1{M}_{S_1}{S}_2{M}_{S_2}|S_{12}{M}_{S_{12}}⟩$$

$$⟨J_{l_B}{M}_{J_{l_B}}{S}_3{M}_{S_3}|J_B{M}_{J_B}⟩⟨L_{{\rho }_B}{M}_{L_{{\rho }_B}}{L}_{{\lambda }_B}{M}_{L_{{\lambda }_B}}|L_B{M}_{L_B}⟩$$

$$⟨L_B{M}_{L_B}{S}_{14}{M}_{S_{14}}|J_{14}{M}_{J_{14}}⟩⟨S_1{M}_{S_1}{S}_4{M}_{S_4}|S_{14}{M}_{S_{14}}⟩$$

$$⟨1m;1-m|00⟩⟨S_4{M}_{S_4}{S}_5{M}_{S_5}|1-m⟩$$

$$⟨L_C{M}_{L_C}{S}_C{M}_{S_C}|J_C{M}_{J_C}⟩⟨S_2{M}_{S_2}{S}_5{M}_{S_5}|S_C{M}_{S_C}⟩$$

$$\times ⟨{\phi }_B^{1,4,3}{\phi }_C^{2,5}|{\phi }_A^{1,2,3}{\phi }_0^{4,5}⟩\times I_{M_{L_B},M_{L_C}}^{M_{L_A},m}(\vec{p}).$$

$${\delta }^3(B+C)I_{M_{L_B},M_{L_C}}^{M_{L_A},m}(\vec{p})$$

$$=\int d{\vec{p}}_{1}d{\vec{p}}_{2}d{\vec{p}}_{3}d{\vec{p}}_{4}d{\vec{p}}_5$$

$$\times {\delta }^3({\vec{p}}_1+{\vec{p}}_2+{\vec{p}}_3-{\vec{p}}_A){\delta }^3({\vec{p}}_4+{\vec{p}}_5)$$

$$\times {\delta }^3({\vec{p}}_1+{\vec{p}}_4+{\vec{p}}_3-{\vec{p}}_B){\delta }^3({\vec{p}}_2+{\vec{p}}_5-{\vec{p}}_C)$$

$$\times {\Psi }_B^{\ast }({\vec{p}}_1,{\vec{p}}_4,{\vec{p}}_3){\Psi }_C^{\ast }({\vec{p}}_2,{\vec{p}}_5)$$

$$\times {\Psi }_A({\vec{p}}_1,{\vec{p}}_2,{\vec{p}}_3)y_{1m}\left(\frac{\overrightarrow{p_4}-{\vec{p}}_5}{2}\right).$$

Full text

I Introduction

Very recently, five narrow excited $\Omega_{c}^{0}$ baryons were reported by the LHCb collaboration LHCb1 . Their masses and decay widths were measured in $\Omega_{c}^{0}\to\Xi_{c}^{+}K^{-}$ as follows,

[TABLE]

[TABLE]

[TABLE]

[TABLE]

[TABLE]

The $J^{P}$ quantum numbers of these five $\Omega_{c}^{0}$ baryons have not been measured.

According to Particle Data Group pdg2016 , two $\Omega_{c}$ baryons have been observed: the ground state $\Omega_{c}^{0}$ and $\Omega_{c}(2770)^{0}$ (also known as $\Omega_{c}^{\ast}$) with $J^{P}=\frac{1}{2}^{+}$ and $\frac{3}{2}^{+}$, respectively. No other $\Omega_{c}$ baryon has been reported before the LHCb experiment.

Theoretical predictions of the spectra of orbitally excited $\Omega_{c}$ baryons have been conducted in many different models Capstick:2809 (1986) ; Ebert2011 ; Roberts2008 ; Gar2007 ; Yoshida ; Shah . Relevant references can be found in reviews Capstick:S241 (2000) ; klempt ; roberts and references therein. From the spectra, these newly observed baryons are most possibly the orbitally excited $1P$ or the radially excited $2S$ states. Theoretical predicted masses of the orbitally excited $1D$ $\Omega_{c}$ baryons are $100-200$ MeV higher than the observed ones.

Since the report of LHCb, the spectra of orbitally excited $\Omega^{0}_{c}$ baryons have been explored in Refs. Agaev2017 ; Marek2017 ; Padm ; wwang . The hadronic decays of these baryons have also been studied through QCD sum rules, chiral quark model or other models in Refs. CHX2017 ; Marek2017 ; Zhong2017 ; CHY2017 ; wwang . In these explorations, the observed $\Omega^{0}_{c}$ baryons were interpreted as the $1P$ or $2S$ $\Omega_{c}$, while the $1D$ possibility has not been explored for their lower masses. However, the mass prediction may be largely different in different models. As indicated in Ref. chen , the mass prediction of the excited $\Lambda_{c}$ and $\Xi_{c}$ baryons in Ref. Capstick:2809 (1986) were really largely different from the results in Ref. Ebert2011 . The study of $1D$ possibility of these $\Omega^{0}_{c}$ through their hadronic decays is necessary.

For the understanding of these excited baryons, it is useful to explore their hadronic decays in different model for a cross-check. ${}^{3}P_{0}$ model is a phenomenological method to study the OZI-allowed hadronic decays of hadrons. In addition to mesons, it is employed successfully to explain the hadronic decays of baryons yaouanc1 ; Capstick:2809 (1986) ; Roberts:171 (1992) ; Capstick:1994 (1993) ; Capstick:4507 (1994) ; Capstick:S241 (2000) ; Chong:094017 (2007) . In this paper, ${}^{3}P_{0}$ model will be employed to study the hadronic decays of $\Omega_{c}(3000)^{0}$, $\Omega_{c}(3050)^{0}$, $\Omega_{c}(3066)^{0}$, $\Omega_{c}(3090)^{0}$ and $\Omega_{c}(3119)^{0}$. In particular, the $1D$ possibility of these $\Omega_{c}^{0}$ will be examined in detail.

This work is organized as follows. In Sec.II, we give a brief review of the ${}^{3}P_{0}$ model. In Sec.III, we present our numerical results. We give our conclusions and discussions in Sec.IV.

II Baryon decay in the ${}^{3}P_{0}$ model

Proposed by Micumicu1969 and later developed by Yaouanc et al yaouanc1 ; yaouanc2 ; yaouanc3 , ${}^{3}P_{0}$ model is also known as a Quark Pair Creation (QPC) model. It assumes that a pair of quark $q\bar{q}$ is created from the vacuum with $J^{PC}=0^{++}(^{2S+1}L_{J}=$ ${}^{3}P_{0})$, and then the created quarks regroup with the quarks from the initial hadron A to form two daughter hadrons B and C. The process of a baryon decay is shown in Fig. I.

In the ${}^{3}P_{0}$ model, the hadronic decay width $\Gamma$ of a process $A\to B+C$ is as follows yaouanc3 ,

[TABLE]

where $m_{A}$ and $J_{A}$ are the mass and total angular momentum of the initial baryon A, respectively. $m_{B}$ and $m_{C}$ are the masses of the final hadrons. $\mathcal{M}^{M_{J_{A}}M_{J_{B}}M_{J_{C}}}$ is the helicity amplitude, which reads Chong:094017 (2007)

[TABLE]

The space integral $I_{M_{L_{B}},M_{L_{C}}}^{M_{L_{A}},m}(\vec{p})$ follows as 114020

[TABLE]

Simple harmonic oscillator (SHO) wave functions are employed as the baryon wave functionsCapstick:2809 (1986) ; Capstick:1994 (1993) ; Capstick:4507 (1994) . For practical calculations such as the flavor matrix $\langle\varphi_{B}^{1,4,3}\varphi_{C}^{2,5}|\varphi_{A}^{1,2,3}\varphi_{0}^{4,5}\rangle$ and the space integrals in the model, more details were presented in Refs.Capstick:1994 (1993) ; yaouanc3 ; Chong:094017 (2007) ; 114020 .

Two parameters, the $\beta$ in SHO and the quark pair creation strength $\gamma$, are adopted as those in Refs. Chong:094017 (2007) ; Blundell:3700 (1996) ; 114020 . $\gamma=13.4$, and $\beta=476$ MeV for meson $K$. For baryons, a universal value $\beta=600$ MeV is employed. The masses of $\Omega_{c}(3000)^{0}$, $\Omega_{c}(3050)^{0}$, $\Omega_{c}(3066)^{0}$, $\Omega_{c}(3090)^{0}$ and $\Omega_{c}(3119)^{0}$ are taken as $3000.4$ MeV, $3050.2$ MeV, $3065.6$ MeV, $3090.2$ MeV and $3119.1$ MeV, respectively. Masses of K mesons and $\Xi_{c}$ baryons are taken from PDG pdg2016 .

The quantum numbers of the P-wave and D-wave baryons are complicated CHX2015 ; CHX2016 , and we follow the notations in Ref. Chong:094017 (2007) . The quantum numbers involved in the calculations are listed in Table 1. In the table, $L_{\rho}$ denotes the orbital angular momentum between the two light quarks, $L_{\lambda}$ denotes the orbital angular momentum between the charm quark and the two light quark system, $L$ is the total orbital angular momentum of $L_{\rho}$ and $L_{\lambda}$. $S_{\rho}$ denotes the total spin of the two light quarks, $J_{l}$ is total angular momentum of $L$ and $S_{\rho}$. $J$ is the total angular momentum of the baryons. The hat and the check are also used to denote the assignments with $L_{\rho}=2$ and $L_{\rho}=1$, respectively. The superscript $L$ is adopted to denote the different total orbital angular momentum in $\check{\Omega}_{cJ_{l}}^{\ L}$.

III Numerical results

In the ${}^{3}P_{0}$ model, $u\bar{u}$, $d\bar{d}$ and $s\bar{s}$ could be created from the vacuum. However, there exists no experimental signal for the decay mode with a $s\bar{s}$ creation. Once the measured masses of $\Omega_{c}$ baryons and the mass threshold of the final particles, $\Xi_{c}^{+}K^{-}$ and $\Xi_{c}^{0}K^{0}$, have been taken into account, there are two decay channels for $\Omega_{c}(3000)^{0}$, $\Omega_{c}(3050)^{0}$ and $\Omega_{c}(3066)^{0}$. For $\Omega_{c}(3090)^{0}$ and $\Omega_{c}(3119)^{0}$, $\Xi_{c}^{{}^{\prime}+}K^{-}$ and $\Xi_{c}^{{}^{\prime}0}K^{0}$ are also allowed. Possible decay modes and corresponding hadronic decay widths of these $\Omega_{c}$ baryons in different $P-$wave and $D-$wave assignments have been computed and presented in from Table 2 to Table 6. The vanish modes in these five tables indicate forbidden channels.

All the five new $\Omega_{c}^{0}$ baryons were observed in the $\Xi_{c}^{+}K^{-}$ channel. The decay width of $\Omega_{c}(3000)^{0}$ is $\Gamma_{\Omega_{c}(3000)^{0}}=(4.5\pm 0.6\pm 0.3)$ MeV. From the results in Table 2, the most possible assignment of $\Omega_{c}(3000)^{0}$ is $\Omega_{c1}(\frac{1}{2}^{+})$ or $\Omega_{c1}(\frac{3}{2}^{+})$. In these two assignments, the total decay widths are the same $5.0$ MeV, which is very close to the experimental data.

The experimental measured decay width of $\Omega_{c}(3050)^{0}$ is extremely narrow, which is smaller than $1.0$ MeV. From Table 3, the possible assignment of $\Omega_{c}(3050)^{0}$ is $\hat{\Omega}_{c3}(\frac{5}{2}^{+})$ or $\hat{\Omega}_{c3}(\frac{7}{2}^{+})$. The theoretical prediction of the decay width is $0.2$ MeV.

For $\Omega_{c}(3066)^{0}$, the measured decay width is $(3.5\pm 0.4\pm 0.2)~{}{\rm MeV}$. From Table 4, the total decay widths of $\Omega_{c2}(\frac{3}{2}^{-})$ and $\Omega_{c2}(\frac{5}{2}^{-})$ are the same $8.5$ MeV, which is a little larger than the experimental result. Under the theoretical uncertainty, these assignments are possible for $\Omega_{c}(3066)^{0}$.

For $\Omega_{c}(3090)^{0}$ and $\Omega_{c}(3119)^{0}$, the channels $\Xi_{c}^{{}^{\prime}+}K^{-}$ and $\Xi_{c}^{{}^{\prime}0}K^{0}$ open. In Table 5 and Table 6, many channels decaying to $\Xi_{c}^{+}K^{-}$ and $\Xi_{c}^{0}K^{0}$ are forbidden while to $\Xi_{c}^{{}^{\prime}+}K^{-}$ and $\Xi_{c}^{{}^{\prime}0}K^{0}$ are not. In particular, the total decay widths of $\Omega_{c}(3090)^{0}$ and $\Omega_{c}(3119)^{0}$ in some assignments are extremely large. In comparison with experiment, the possible assignment for $\Omega_{c}(3090)^{0}$ is $\Omega_{c2}(\frac{3}{2}^{-})$ or $\Omega_{c2}(\frac{5}{2}^{-})$, and four $D-$wave assignments are possible for $\Omega_{c}(3119)^{0}$: $\Omega_{c3}(\frac{5}{2}^{+})$, $\Omega_{c3}(\frac{7}{2}^{+})$, $\hat{\Omega}_{c3}(\frac{5}{2}^{+})$ and $\hat{\Omega}_{c3}(\frac{7}{2}^{+})$. In these assignments, the decay widths to $\Xi_{c}^{{}^{\prime}+}K^{-}$ and $\Xi_{c}^{{}^{\prime}0}K^{0}$ channels are very tiny and could be neglected.

IV Conclusions and discussions

In this work, we study the hadronic decays of five newly observed baryons $\Omega_{c}(3000)^{0}$, $\Omega_{c}(3050)^{0}$, $\Omega_{c}(3066)^{0}$, $\Omega_{c}(3090)^{0}$ and $\Omega_{c}(3119)^{0}$ in the ${}^{3}P_{0}$ model. In different assignments of $1P-$wave and $1D-$wave $\Omega_{c}$, hadronic decay widths of these baryons have been calculated. In comparison with experiment, possible assignments of these $\Omega_{c}^{0}$ have been made.

All the five $\Omega_{c}^{0}$ baryons were observed in the $\Xi_{c}^{+}K^{-}$ channel with very narrow decay widths. Our results indicates that these $\Omega_{c}^{0}$ could be $P-$wave or $D-$wave $\Omega_{c}^{0}$ baryons. $\Omega_{c}(3000)^{0}$ is possibly $1D-$wave $\Omega_{c1}(\frac{1}{2}^{+})$ or $\Omega_{c1}(\frac{3}{2}^{+})$. $\Omega_{c}(3050)^{0}$ is possibly $1D-$wave $\hat{\Omega}_{c3}(\frac{5}{2}^{+})$ or $\hat{\Omega}_{c3}(\frac{7}{2}^{+})$. $\Omega_{c}(3066)^{0}$ is possibly $1P-$wave $\Omega_{c2}(\frac{3}{2}^{-})$ or $\Omega_{c2}(\frac{5}{2}^{-})$. The possible assignment for $\Omega_{c}(3090)^{0}$ is $1P-$wave $\Omega_{c2}(\frac{3}{2}^{-})$ or $\Omega_{c2}(\frac{5}{2}^{-})$, and four $D-$wave assignments $\Omega_{c3}(\frac{5}{2}^{+})$, $\Omega_{c3}(\frac{7}{2}^{+})$, $\hat{\Omega}_{c3}(\frac{5}{2}^{+})$ and $\hat{\Omega}_{c3}(\frac{7}{2}^{+})$ are possible for $\Omega_{c}(3119)^{0}$. The predicted decay widths are consistent with experimental data.

In experiment, only $\Omega_{c}^{0}\to\Xi_{c}^{+}K^{-}$ were observed, which may not provide enough information on their identification. Furthermore, resonance with the same $J^{P}$ numbers and similar masses may mix with each other, which may make it difficult to distinguish them. As for $1D-$wave $\Omega_{c}$, the channels $\Xi_{c}^{{}^{\prime}+}K^{-}$ and $\Xi_{c}^{{}^{\prime}0}K^{0}$ is hardly to be observed for the tiny decay widths. More information on these $\Omega_{c}$ baryons are expected to be given in forthcoming experiment.

Acknowledgements.

This work is supported by National Natural Science Foundation of China under the grants: 11475111 and 11075102.