NNLO unquenched calculation of the b quark mass

By combining the first unquenched lattice computation of the B-meson binding energy with the recently calculated two-loop contribution to the lattice HQET mass, we determine the MS-bar b-quark mass, m-barb(m-barb) at the NNLO. We find m-barb(m-barb) = (4.26 ± 0.03 ± 0.04 ± 0.05) GeV. The inclusion of the two-loop effects is one of the steps necessary to extract m-barb(m-barb) with a precision better than CHARACTER OMITTED(ΛQCD), which is the uncertainty due to the presence of an IR renormalon singularity in the perturbative series of the residual mass. Our results have been obtained on a sample of 60 lattices of size 243 x 40 at β = 5.6, using the unquenched Wilson action with two degenerate sea quarks. The quark propagators have been computed using the unquenched links generated by the TχL Collaboration