Quark confinement potential examined by excitation energy of the Lambda_c and Lambda_b baryons in a quark-diquark model

TL;DR

This paper investigates the quark confinement potential in heavy baryons Lambda_c and Lambda_b using a quark-diquark model, revealing discrepancies with traditional potentials and suggesting finite diquark size effects are important.

Contribution

It introduces a nonrelativistic potential model with a scalar diquark to analyze heavy baryon spectra, highlighting the need for modified confinement parameters and diquark size considerations.

Findings

Standard quarkonium potentials fail to reproduce baryon excitation spectra.

A reduced string tension better fits the Lambda_c and Lambda_b spectra.

Finite diquark size effects can resolve spectrum reproduction issues.

Abstract

The possibility to have diquark configuration in heavy baryons, such as Lambda_c and Lambda_b, is examined by a nonrelativistic potential model with a heavy quark and a light scalar diquark. Assuming that the Lambda_c and Lambda_b baryons are composed of the heavy quark and the point-like scalar-isoscalar ud diquark, we solve the two-body Schrodinger equation with the Coulomb plus linear potential and obtain the energy spectra for the heavy baryons. Contrary to our expectation, it is found that the potential determined by the quarkonium spectra fails to reproduce the excitation spectra of the Lambda_c and Lambda_b in the quark-diquark picture, while the Lambda_c and Lambda_b spectra is reproduced with a half strength of the confinement string tension than for the quarkonium. The finite size effect of the diquark is also examined and it is found that introduction of a finite size diquark would resolve the failure of the spectrum reproduction. The Xi_c excitation energy is also calculated and is found to be smaller than Lambda_c in the quark-diquark model. This is not consistent with the experimental observation.