Lattice renormalization of the static quark derivative operator

Abstract

We give the analytical expressions and numerical values of radiative corrections to the covariant derivative operator on the static quark line, used for the lattice calculation of the Isgur-Wise form factors ${\tau }_{1/2}(1)$ and ${\tau }_{3/2}(1)$. Those corrections induce an enhancement of renormalized quantities if an hypercubic blocking is applied to the Wilson line, whereas there is a reduction without such a blocking.