Symmetries of the Three Heavy-Quark System and the Color-Singlet Static Energy at NNLL

TL;DR

This paper investigates the symmetries of a three heavy-quark system in QCD, determines the leading ultrasoft contributions to the static potential, and performs resummation of ultrasoft logarithms for specific geometric configurations.

Contribution

It introduces a detailed symmetry analysis within pNRQCD, calculates the leading ultrasoft corrections to the static energy, and provides resummed results for equilateral geometries.

Findings

Derived symmetry constraints on effective theory coefficients

Calculated the leading ultrasoft contribution to the static potential

Resummed ultrasoft logarithms for equilateral three-quark configurations

Abstract

We study the symmetries of the three heavy-quark system under exchange of the quark fields within the effective field theory framework of potential non-relativistic QCD. The symmetries constrain the form of the matching coefficients in the effective theory. We then focus on the color-singlet sector and determine the so far unknown leading ultrasoft contribution to the static potential, which is of order alpha_s^4 ln(\mu), and consequently to the static energy, which is of order alpha_s^4 ln(alpha_s). Finally, in the case of an equilateral geometry, we solve the renormalization group equations and resum the leading ultrasoft logarithms for the static potential of three quarks in a color singlet, octet and decuplet representation.