Lattice renormalization of the static quark derivative operator

TL;DR

This paper provides analytical and numerical results for radiative corrections to the static quark covariant derivative operator on the lattice, impacting the calculation of Isgur-Wise form factors with or without hypercubic blocking.

Contribution

It offers new analytical expressions and numerical values for radiative corrections relevant to lattice QCD calculations of heavy-light meson form factors.

Findings

Radiative corrections enhance renormalized quantities with hypercubic blocking.

Corrections reduce renormalized quantities without blocking.

Provides data useful for precise lattice QCD computations.

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.