Toward establishing the low-lying $P$-wave excited $\Sigma_c$ baryon states

In this study, by combining the equal spacing rule with recent observations of $\Omega_c(X)$ and $\Xi_c(X)$ baryons, we predict the spectrum of the low-lying $\lambda$-mode $1P$-wave excited $\Sigma_c$ states. Furthermore, their strong decay properties are predicted using the chiral quark model and the nature of $\Sigma_c(2800)$ is investigated by analyzing the $\Lambda_c\pi$ invariant mass spectrum. The $\Sigma_c(2800)$ structure observed in the $\Lambda_c \pi$ mass spectrum was found to potentially arise from two overlapping $P$-wave $\Sigma_c$ resonances, $\Sigma_c(2813)3/2^-$ and $\Sigma_c(2840)5/2^-$. These resonances have similar decay widths of $\Gamma\sim 40$ MeV and predominantly decay into the $\Lambda_c \pi$ channel. The $\Sigma_c(2755)1/2^-$ state is likely to be a very narrow state with a width of $\Gamma\sim 15$ MeV, with its decays almost saturated by the $\Lambda_c \pi$ channel. Additionally, evidence of the $\Sigma_c(2755)\frac{1}{2}^-$ resonance as a very narrow peak may be seen in the $\Lambda_c\pi$ invariant mass spectrum. The other two $P$-wave states, $\Sigma_c(2746)\frac{1}{2}^-$ and $\Sigma_c(2796)\frac{3}{2}^-$, are relatively narrow states with similar widths of $\Gamma\sim 30$ MeV and predominantly decay into $\Sigma_c\pi$ and $\Sigma^{*}_c\pi$, respectively. We hope our study can provide useful references for discovering these low-lying $P$-wave states in forthcoming experiments.