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 $Z_m^{\mathrm{MS}}=-Z_{V_s}^{\mathrm{MS}}/2=\{0.604(17),0.551(20)\}$, $Z_{V_o}^{\mathrm{MS}}=\{0.136(8),0.121(13)\}$, and $Z_A^{\mathrm{MS}}=\{-1.343(36),-1.224(43)\}$, 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: ${\Lambda }_B^{\mathrm{PV}}=2.47(9)r_0^{-1}$ and ${\Lambda }_B^{\mathrm{PV}}=2.38(11)r_0^{-1}$. They combine in ${\Lambda }_B^{\mathrm{PV}}=2.44(7)r_0^{-1}$.

Comments: 33 pages, 13 figures; 2nd version: 35 pages, three extra references. Minor changes to meet journal version