Excitation energy spectra of the $\Lambda_{c}$ and $\Lambda_{b}$ baryons in a finite-size diquark model

Abstract

The excitation energies of the $\Lambda_{c}$ and $\Lambda_{b}$ baryons are investigated in a finite-size diquark potential model, in which the heavy baryons are treated as bound states of a charm quark and a scalar-isoscalar diquark. The diquark is considered as a sizable object. The quark-diquark interaction is calculated as a sum of the quark-quark interaction which is assumed to be half of the quark-antiquark interaction for the color singlet. The potential parameters in the quark-antiquark interaction are fixed so as to reproduce the charmonium spectrum. We find the diquark size to be 1.1 fm for the diquark mass 0.5 GeV/c$^{2}$ to reproduce the $1p$ excitation energy of $\Lambda_{c}$. In this model, the $\Lambda_{c}$ and $\Lambda_{b}$ excitation spectra are reproduced well, while this model does not explain $\Lambda_{c}(2765)$, whose isospin nor spin-parity are unknown yet. Thus, the detailed properties of $\Lambda_{c}(2765)$ is very important to the presence of the diquark in heavy baryons as a effective constituent. We also discuss the $\Xi_{c}$ spectrum with the scalar strange diquark.