Inter-Quark Potentials in Baryons and Multi-Quark Systems in QCD

TL;DR

This paper investigates inter-quark potentials in baryons and multi-quark systems using lattice QCD, confirming the Y-Ansatz for three-quark potentials and flux-tube models for multi-quark systems, including heavy-heavy-light quarks.

Contribution

It provides the first comprehensive lattice QCD analysis of multi-quark potentials, validating the Y-Ansatz and flux-tube models for complex quark configurations.

Findings

Three-quark potential fits Y-Ansatz with Coulomb plus linear terms.

Multi-quark potentials are described by multi-Y type linear potentials.

Flux-tube picture is supported for multi-quark systems.

Abstract

We perform the first studies of various inter-quark potentials in SU(3)$_{\rm c}$ lattice QCD. From the accurate lattice calculation for more than 300 different patterns of three-quark (3Q) systems, we find that the static 3Q potential $V_{\rm 3Q}$ is well described by Y-Ansatz, i.e., the Coulomb plus Y-type linear potential. Quark confinement mechanism in baryons is also investigated in maximally-Abelian projected QCD. We next study the multi-quark potentials $V_{n{\rm Q}}$ ($n$=4,5) in SU(3)$_{\rm c}$ lattice QCD, and find that they are well described by the one-gluon-exchange Coulomb plus multi-Y type linear potential, which supports the flux-tube picture even for the multi-quarks. Finally, we study the heavy-heavy-light quark (QQq) potential both in lattice QCD and in a lattice-QCD-based quark model.