Some Aspects of Three-Quark Potentials (Part II)

TL;DR

This paper advances the understanding of three-quark potentials in pure gauge theories by deriving asymptotic expressions, exploring symmetry breaking, and connecting theoretical models with lattice QCD results.

Contribution

It provides analytical and numerical analysis of three-quark potentials, revealing universality, symmetry breaking, and implications for heavy quark states in gauge theories.

Findings

Asymptotic potential expressions in the infrared limit

Identification of permutational symmetry breaking at specific angles

Discussion of Y- and Δ-law relations and lattice QCD connections

Abstract

We continue our investigation of the effective string model for the triply heavy quark system, mimicking that in pure $SU(3)$ gauge theory. We present analytical and numerical studies of the three-quark potential for isosceles and collinear geometries. In the general case, we derive the asymptotic expression of the potential in the infrared limit. Here we also demonstrate the universality of the string tension and interpret the transition between two distinct regimes, occurring when one of the triangle's angles formed by the quarks is equal to $\frac{2}{3}\pi$, as a breaking of permutational symmetry. This symmetry breaking implies the emergence of a heavy quark dressed by gluons, transforming in the two-index antisymmetric representation. Additionally, we discuss various aspects of the $Y$- and $\Delta$-laws, diquarks, and connections to lattice QCD.