Structural Properties of the Lattice Heavy Quark Effective Theory

TL;DR

This paper analyzes the lattice heavy quark effective theory, focusing on the effects of high-momentum modes and the unique renormalization features, demonstrating their suppression or finiteness in the continuum limit.

Contribution

It provides insights into the suppression of high-momentum mode effects and introduces the finite renormalization of classical velocity in lattice HQET.

Findings

High-momentum modes are dynamically suppressed in lattice HQET.

Contributions to bound states and loop integrals vanish in the continuum limit.

Classical velocity undergoes finite renormalization on the lattice.

Abstract

We discuss two related aspects of the lattice version of the heavy quark effective theory (HQET). They are the effects of heavy quark modes with large momenta, near the boundary of the Brillouin zone, and the renormalization of the lattice HQET. We argue that even though large momentum modes are present, their contributions to heavy-light bound states and perturbative loop integrals are dynamically suppressed and vanish in the continuum limit. We also discuss a new feature of the renormalization of the lattice HQET not present in the continuum theory, namely that the classical velocity is finitely renormalized.