Lattice QCD Study for Confinement and Hadrons

TL;DR

This study uses lattice QCD to analyze three-quark and multi-quark potentials, confirming the Y-Ansatz for flux-tube formation and revealing large gluonic excitations, supporting the flux-tube picture in multi-quark systems.

Contribution

It provides detailed lattice QCD calculations of 3Q, tetra-quark, and penta-quark potentials, confirming the Y-Ansatz and flux-tube formation, and introduces the inverse Mercedes Ansatz for gluonic excitations.

Findings

3Q potential well described by Coulomb plus Y-type linear potential

Y-type flux-tube formation observed on the lattice

Gluonic excitation energy around 1 GeV supports quark model success

Abstract

Using SU(3) lattice QCD, we perform the detailed studies of the three-quark and the multi-quark potentials. From the accurate calculation for more than 300 different patterns of 3Q systems, the static ground-state 3Q potential $V_{\rm 3Q}^{\rm g.s.}$ is found to be well described by the Coulomb plus Y-type linear potential (Y-Ansatz) within 1%-level deviation. As a clear evidence for Y-Ansatz, Y-type flux-tube formation is actually observed on the lattice in maximally-Abelian projected QCD. For about 100 patterns of 3Q systems, we perform the accurate calculation for the 1st excited-state 3Q potential $V_{\rm 3Q}^{\rm e.s.}$ by diagonalizing the QCD Hamiltonian in the presence of three quarks, and find a large gluonic-excitation energy $\Delta E_{\rm 3Q} \equiv V_{\rm 3Q}^{\rm e.s.}-V_{\rm 3Q}^{\rm g.s.}$ of about 1 GeV, which gives a physical reason of the success of the quark model. $\Delta E_{\rm 3Q}$ is found to be reproduced by the ``inverse Mercedes Ansatz'', which indicates a complicated bulk excitation for the gluonic-excitation mode. We study also the tetra-quark and the penta-quark potentials in lattice QCD, and find that they are well described by the OGE Coulomb plus multi-Y type linear potential, which supports the flux-tube picture even for the multi-quarks.