Three-quark systems in MA and MC 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 colorelectric/magnetic current exists, using the Hodge decomposition. First, we perform the quantitative study of the three-quark (3Q) potential V3Q and the string tension σ3Q in baryons. For MA projected QCD, the monopole part and MC projected QCD, we find that the confinement potential in V3Q obeys the Y-Ansatz and the string tension σ3Q is approximately equal to that in SU(3) QCD. The universality of the string tension, σ3Q ’ σ Q ¯ Q , is also found between the 3Q and the Q ¯ 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-Δ mass splitting. We find that the N- Δ 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.