The mass of the lightest gluelump

Abstract 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 MS ¯ $$ {Z}_m^{\overline{\textrm{MS}}} $$ = − Z V s MS ¯ / 2 $$ -{Z}_{V_s}^{\overline{\textrm{MS}}}/2 $$ = {0.604(17), 0.551(20)}, Z V o MS ¯ $$ {Z}_{V_o}^{\overline{\textrm{MS}}} $$ = {0.136(8), 0.121(13)}, and Z A MS ¯ $$ {Z}_A^{\overline{\textrm{MS}}} $$ = {–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: Λ B PV = 2.47 9 r 0 − 1 $$ {\Lambda}_B^{\textrm{PV}}=2.47(9){r}_0^{-1} $$ and Λ B PV = 2.38 11 r 0 − 1 $$ {\Lambda}_B^{\textrm{PV}}=2.38(11){r}_0^{-1} $$ where r 0 − 1 $$ {r}_0^{-1} $$ ≈ 400 MeV. Averaging these results, we obtain Λ B PV = 2.44 7 r 0 − 1 $$ {\Lambda}_B^{\textrm{PV}}=2.44(7){r}_0^{-1} $$ .