Lattice QCD Study for Confinement in Hadrons

TL;DR

This study uses lattice QCD to analyze quark confinement, demonstrating that the static three-quark potential follows a Y-Ansatz, multi-quark potentials align with string theory, and low-momentum gluons are key to confinement.

Contribution

It provides detailed lattice QCD calculations confirming the Y-Ansatz for 3Q systems, supports the string picture for multi-quark potentials, and identifies low-momentum gluons as essential for confinement.

Findings

3Q potential well described by Y-Ansatz

Multi-quark potentials fit string-theory models

Confinement mainly due to low-momentum gluons below 1.5GeV

Abstract

We study three subjects on quark confinement in hadrons 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 is well described by Y-Ansatz, i.e., the Coulomb plus Y-type linear potential. We also study the multi-quark (4Q, 5Q) potentials in lattice QCD, and find that they are well described by the one-gluon-exchange (OGE) Coulomb plus string-theoretical linear potential, which supports the {\it infrared string picture} even for the multi-quarks. The second subject is a lattice-QCD determination of the relevant gluonic momentum component for confinement. The string tension (confining force) is found to be almost unchanged even after cutting off the high-momentum gluon component above 1.5GeV in the Landau gauge. In fact, {\it quark confinement originates from the low-momentum gluon below about 1.5GeV.} Finally, we consider a possible gauge of QCD for the quark potential model, by investigating "instantaneous inter-quark potential" in generalized Landau gauge, which describes a continuous change from the Landau gauge to the Coulomb gauge.