Renormalization of the Classical Velocity in the Lattice Heavy Quark Effective Theory

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 of the effect.

Contribution

It presents the first detailed analysis of velocity renormalization in lattice HQET, including explicit calculations and comparisons between perturbative and non-perturbative methods.

Findings

Renormalization depends on discretization form.

Perturbative and non-perturbative estimates agree reasonably well.

Classical velocity is reduced by approximately 20-25%.

Abstract

In the lattice formulation of the Heavy Quark Effective Theory (LHQET), the classical velocity becomes renormalized. The origin of this renormalization is the reduction of Lorentz (or O(4)) invariance to (hyper)cubic invariance. The renormalization is finite, depends on the form of the discretization of the reduced heavy quark Dirac equation, and can persist down to zero lattice spacing. 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 ACP-MAPS collaboration. The estimates of the leading multiplicative shift agree reasonably well, and indicate that to first order, the classical velocity is reduced by about 20-25%.