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.

Comments: 17 pages, 8 figures