Renormalization of the Lattice Heavy Quark Classical Velocity

TL;DR

This paper investigates how the classical velocity in lattice Heavy Quark Effective Theory is renormalized due to symmetry reduction, providing both perturbative and non-perturbative estimates showing significant velocity reduction.

Contribution

It presents a detailed analysis of the renormalization of classical velocity in LHQET, including perturbative and non-perturbative calculations for the first time.

Findings

Renormalization depends on discretization scheme.

Perturbative and non-perturbative estimates agree.

Velocity is reduced by about 25-30% for small velocities.

Abstract

In the lattice formulation of the Heavy Quark Effective Theory (LHQET), the classical velocity is renormalized. The origin of this renormalization is the reduction of Lorentz (or O(4)) invariance to (hyper)cubic invariance. The renormalization is finite and depends on the form of the decretization of the reduced heavy quark Dirac equation. For the Forward Time - Centered Space discretization, the renormalization is computed both perturbatively, to one loop, and non-perturbatively using an ensemble of lattices provided by the Fermilab lattice collaboration. The estimates of the leading (linear) shift agree, and indicate that for small classical velocities, the renormalized velocity is reduced by about 25-30% relative to its bare (input) value.