New lattice action for heavy quarks

TL;DR

This paper extends the Fermilab method for heavy quarks by including higher-dimension interactions, achieving improved accuracy in lattice QCD simulations with errors below 1% at current lattice spacings.

Contribution

The authors develop a new lattice action for heavy quarks that incorporates dimension 6 and 7 interactions, with tree-level matching and one-loop corrections to reduce discretization errors.

Findings

Six non-zero couplings identified in the extended action

Discretization errors can be reduced below 1% with current lattice spacings

Tree-level and one-loop matching effectively improve heavy-quark lattice simulations

Abstract

We extend the Fermilab method for heavy quarks to include interactions of dimensions 6 and 7 in the action. There are, in general, many new interactions, but we carry out the calculations needed to match the lattice action to continuum QCD at the tree level, finding six non-zero couplings. Using the heavy-quark theory of cutoff effects, we estimate how large the remaining discretization errors are. We find that our tree-level matching, augmented with one-loop matching of the dimension-five interactions, can bring these errors below 1%, at currently available lattice spacings.