Updated $Σ_{c}$ excitation spectrum including the $2P$- and $1F$-wave fine structures

Abstract

In order to study the new $Σ_{c}$ baryons observed by the LHCb collaboration recently, we update the previously predicted $Σ_{c}$ excitation spectrum by extending the excited states up to the highly excited $2P$- and $1F$-wave states. The calculation is performed in the framework of the relativized quark model and Gaussian expansion method by considering the mixing effect. The radially and orbitally excited states in the calculation are determined by the truncation convention proposed in this work and the mechanism of the heavy-quark dominance. The contribution of each Hamiltonian term to the energy levels is precisely calculated by using the two-step Gaussian expansion method. Then, the concerned $Σ_{c}$ states are obtained and the $Σ_{c}$ excitation spectrum including the $2P$- and $1F$-wave fine structures is established. Based on these, several important topics are discussed and analyzed, including the root-mean-square radii, off-diagonal matrix elements, mixing effect, fine structures and assignments of the newly observed $Σ_{c}(2800)^{0}$, $Σ_{c}(2900)^{0}$ and $Σ_{c}(3200)^{0}$ states. Meanwhile, it is found that the approximate decoupling phenomenon emerges in different $nL$-wave groups. This implies the reasonability of the truncation convention and is of great significance for further improving the calculation scheme for all the baryon spectra. Moreover, it is demonstrated that in the very high-lying $nL$-wave groups such as the $1F$-wave group, the energy level gaps become small even degenerate, and each of the baryon states has a big radius and therefore a loosely bound structure. In addition, by examining the experimental and calculated data, we suggest more precise experiments to search for more $Σ_{c}$ baryon states in the predicted $1P$- and $2P$-wave fine structures whose central energies are around 2822 and 3210 MeV, respectively.