An Improved Action for Heavy Quarks

TL;DR

This paper extends the Fermilab method for heavy quarks by including dimension six interactions, addressing subtle power counting issues, and providing tree-level matching to reduce discretization errors in lattice QCD simulations.

Contribution

It introduces an improved heavy quark action with dimension six interactions and discusses power counting subtleties, enhancing lattice QCD accuracy.

Findings

Removes discretization errors of order a^2 p^3/m_Q and a^3 p^3 at tree level.

Provides tree-level matching conditions from Compton scattering calculations.

Addresses power counting subtleties for dimension seven interactions.

Abstract

We extend the Fermilab method for heavy quarks to include all interactions of dimension six in the action. We discuss a subtlety in the power counting, which implies that, for heavy quarks, certain interactions of dimension seven are commensurate with some of those of dimension six. We then present tree-level matching conditions obtained from calculating the Compton scattering amplitude for (lattice) QCD. When the matching conditions have been applied, the improved action removes (tree-level) discretization errors of order $a^2\bm{p}^3/m_Q$ and $a^3\bm{p}^3$.