Three-quark systems in MA and MC projected QCD

TL;DR

This study investigates three-quark potentials and hadron spectra in MA and MC projected QCD, revealing that confinement and mass splittings are primarily driven by monopole components and one-gluon exchange effects.

Contribution

It provides a detailed analysis of three-quark potentials and hadron mass splittings in projected QCD, highlighting the roles of monopole and center degrees of freedom in confinement.

Findings

Confinement potential obeys Y-Ansatz in projected QCD.

String tension in 3Q systems is similar to SU(3) QCD.

Mass splitting reduces significantly in monopole and projected QCD.

Abstract

We study three quark systems in Maximally Abelian (MA) and Maximal Center (MC) projected QCD on quenched SU(3) lattice, and also in the monopole/photon part, where only the color-electric/magnetic current exists, using the Hodge decomposition. First, we perform the quantitative study of the three-quark (3Q) potential V_{3Q} and the string tension \sigma_{3Q} in baryons. For MA projected QCD, the monopole part and MC projected QCD, we find that the confinement potential in V_{3Q} obeys the Y-Ansatz and the string tension \sigma_{3Q} is approximately equal to that in SU(3) QCD. The universality of the string tension, \sigma_{3Q} \simeq \sigma_{Q\bar Q}, is also found between the 3Q and the Q\bar Q potentials. We find a strong similarity of the inter-quark potential between the monopole part and MC projected QCD. In contrast, almost no confinement force is found in the inter-quark potential in the photon part. Next, we study the spectrum of light hadrons in MA projected QCD and the monopole/photon part, paying attention to the N-\Delta mass splitting. We find that the N-\Delta mass splitting is significantly reduced in MA projected QCD and the monopole part, where the one-gluon-exchange effect or the Coulomb-potential part is largely reduced due to the Abelianization or the Hodge decomposition. This fact seems to indicate that the main origin of the mass splitting is one-gluon exchange.