Non-perturbative renormalization of the static axial current in two-flavour QCD

We perform the non-perturbative renormalization of matrix elements of the static-light axial current by a computation of its scale dependence in lattice QCD with two flavours of massless O(a) improved Wilson quarks. The regularization independent factor that relates any running renormalized matrix element of the axial current in the static e r ective theory to the renormalization group invariant one is evaluated in the Schr " odinger functional scheme, where in this case we find a significant deviation of the non- perturbative running from the perturbative prediction. An important technical ingredient to improve the precision of the results consists in the use of modified discretizations of the static quark action introduced earlier by our collaboration. As an illustration how to apply the renormalization of the static axial current presented here, we connect the bare matrix element of the current to the B-s-meson decay constant in the static approximation for one value of the lattice spacing, a approximate to 0.08 fm, employing large-volume N-f=2 data at ss=5.3.