Heavy quark effective theory on the lattice. The b-quark mass including 1/m_b

by Della Morte, Michele (CERN-PH/TH)

Thursday 19 Apr 2007, 14:00 → 15:00 Europe/Zurich

TH Auditorium (CERN)

The b-quark is too heavy to be treated dynamically on the lattice. Indeed, in units of nowadays affordable resolutions am_b >>1, a theoretically attractive option is to use effective theories like Heavy Quark Effective Theory (HQET), which provides the correct asymptotic description of QCD correlation functions in the limit m_b -> infinity. Subleading effects are described by higher dimensional operators whose coupling constants are formally O(1/ m_b) to the appropriate power. The degrees of freedom in the effective theory are strongly coupled and therefore a non-perturbative approach is needed. In addition HQET has to be matched to the full theory, a step which must also be performed non-perturbatively beyond leading order in 1/m_b. A framework for non-perturbative HQET on the lattice has been developed by the ALPHA collaboration. We present here a specific application of that approach to the computation of the b-quark mass in the quenched approximation. We include the subleading, 1/m_b, terms in each step. Our final result is m_b (m_b) = 4.347(48) GeV in the MSbar scheme. The extension to the computation of the decay constant F_B is also briefly discussed.