Lattice QCD study of the heavy-heavy-light quark potential

TL;DR

This study investigates the potential between two heavy quarks and a light quark in lattice QCD, revealing that the light quark reduces the confinement force between the heavy quarks.

Contribution

It provides the first lattice QCD analysis of the heavy-heavy-light quark potential, highlighting the finite-mass valence quark's role in modifying inter-quark forces.

Findings

The $QQq$ potential fits a Coulomb plus linear form.

The effective string tension between heavy quarks is reduced by the light quark.

Finite-mass valence quark weakens the inter-quark confinement force.

Abstract

We study the heavy-heavy-light quark ($QQq$) potential in SU(3) quenched lattice QCD, and discuss one of the roles of the finite-mass valence quark in the inter-quark potential. Monte Carlo simulations are performed with the standard gauge action on the $16^4$ lattice at $\beta =6.0$ and the $O(a)$-improved Wilson fermion action at four hopping parameters. For statistical improvement, the gauge configuration is fixed with the Coulomb gauge. We calculate the potential energy of $QQq$ systems as a function of the inter-heavy-quark distance $R$ in the range of $R \le$ 0.8 fm. The $QQq$ potential is well described with a Coulomb plus linear potential, and the effective string tension between the two heavy quarks is significantly smaller than the string tension $\sigma \simeq 0.89$ GeV/fm. It would generally hold that the effect of the finite-mass valence quark reduces the inter-two-quark confinement force in baryons.