The mass of the lightest gluelump

We consider QCD with n_f = 0 and n_f = 3 light quarks. We present the most up-to-date determinations for the normalizations of the leading renormalons of the pole mass, the singlet static potential, the octet static potential, and the gluelump energy. These read \( {Z}_m^{\overline{\textrm{MS}}} \) = \( -{Z}_{V_s}^{\overline{\textrm{MS}}}/2 \) = {0.604(17), 0.551(20)}, \( {Z}_{V_o}^{\overline{\textrm{MS}}} \) = {0.136(8), 0.121(13)}, and \( {Z}_A^{\overline{\textrm{MS}}} \) = {–1.343(36), –1.224(43)}, for n_f = 0 and n_f = 3, respectively. For n_f = 0, 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: \( {\Lambda}_B^{\textrm{PV}}=2.47(9){r}_0^{-1} \) and \( {\Lambda}_B^{\textrm{PV}}=2.38(11){r}_0^{-1} \) where \( {r}_0^{-1} \) ≈ 400 MeV. Averaging these results, we obtain \( {\Lambda}_B^{\textrm{PV}}=2.44(7){r}_0^{-1} \).