The Symmetries of the Three Heavy Quark Bound State and the Singlet Static Energy

TL;DR

This paper investigates the symmetries and ultrasoft contributions in three heavy-quark systems within potential non-relativistic QCD, providing high-precision calculations of the singlet static potential and energy.

Contribution

It introduces a detailed analysis of heavy-quark symmetries and resums ultrasoft logarithms to NNLL accuracy in the singlet static potential.

Findings

Determined symmetries under heavy-quark exchange.

Calculated ultrasoft contributions to static energy.

Resummed ultrasoft logarithms to NNLL accuracy.

Abstract

Potential non-relativistic QCD provides a convenient framework to study the three heavy-quark system. We have studied its symmetries under exchange of the heavy quarks and determined the leading ultrasoft contributions to the singlet static potential and to the singlet static energy. Specializing to an equilateral geometry, we have solved the renormalization group equations in order to resum the leading ultrasoft logarithms for the singlet static potential, which is thus known at NNLL accuracy.