The mass of the lightest gluelump

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 $\Lambda_{B}^{\rm PV}=2.44(7)r_0^{-1}$.