The mass of the lightest gluelump

TL;DR

This paper provides updated determinations of renormalon normalizations and the mass of the lightest gluelump, a bound state in quantum chromodynamics, using renormalization group techniques and principal value summation.

Contribution

It introduces new precise calculations of renormalon normalizations and the mass of the lightest gluelump, improving understanding of nonperturbative QCD effects.

Findings

Renormalon normalizations for various potentials are precisely determined.

Two independent methods yield consistent gluelump mass estimates.

The combined gluelump mass is 2.44(7) in units of r_0^{-1}.

Abstract

We give the most up-to-date determinations of the normalization of the leading renormalons of the pole mass, the singlet static potential, the octet static potential, and the gluelump energy. They read $Z^{\rm MS}_m=-Z^{\rm MS}_{V_s}/2=\{0.604(17),0.551(20)\}$, $Z^{\rm MS}_{V_o}=\{0.136(8),0.121(13)\}$, and $Z^{\rm MS}_A=\{-1.343(36),-1.224(43)\}$, for $n_f=0$ and $n_f=3$ respectively. We obtain two independent renormalization group invariant and renormalization scale independent determinations of the energy of the ground state gluelump in the principal value summation scheme: $\Lambda_{B}^{\rm PV}=2.47(9)r_0^{-1}$ and $\Lambda_{B}^{\rm PV}=2.38(11)r_0^{-1}$. They combine in $\Lambda_{B}^{\rm PV}=2.44(7)r_0^{-1}$.