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 b-quark mass, m_b( m_b) at the NNLO. We find m_b( m_b) = (4.26 ± 0.03 ± 0.05) GeV. The inclusion of the two-loop is one of the steps necessary to extract m_b( m_b) with a precision better than O( Λ_QCD), 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 24 ³ × 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 T _ζL Collaboration.