Renormalization of the effective theory for heavy quarks at small velocity

The slope of the Isgur-Wise function at the normalization point, xi(1) (1), is one of the basic parameters for the extraction of the CKM matrix element V(cb) from exclusive semileptonic decay data. A method for measuring this parameter on the lattice is the effective theory for heavy quarks at small velocity nu. This theory is a variant of the heavy quark effective theory in which the motion of the quark is treated as a perturbation. In this work we study the lattice renormalization of the slow heavy quark effective theory. We show that the renormalization of xi(1) (1) is not affected by ultraviolet power divergences, implying no need of difficult non-perturbative subtractions. A lattice computation of xi(1) (1) with this method is therefore feasible in principle. The one-loop renormalization constants of the effective theory for slow heavy quarks are computed to order nu2 together with the lattice-continuum renormalization constant of xi(1) (1). We demonstrate that the expansion in heavy-quark velocity reproduces correctly the infrared structure of the original (non-expanded) theory to every order. We compute also the one-loop renormalization constants of the slow heavy quark effective theory to higher orders in nu2 and the lattice-continuum renormalization constants of the higher derivatives of the xi function. Unfortunately, the renormalization constants of the higher derivatives are affected by ultraviolet power divergences, implying the necessity of numerical non-perturbative subtractions. The lattice computation of higher derivatives of the Isgur-Wise function seems therefore problematic