Lattice QCD at maximal twist

TL;DR

This review discusses maximally twisted lattice QCD, highlighting automatic O(a) improvement, avoiding wrong chirality mixing, and reducing cutoff effects through clover term addition or parity restoration.

Contribution

It explains how to achieve automatic O(a) improvement and avoid chirality mixing issues in maximally twisted lattice QCD, with strategies to suppress lattice artifacts.

Findings

Automatic O(a) improvement is achievable in maximally twisted lattice QCD.

Adding a clover term or restoring parity reduces cutoff effects.

The scheme ensures positive determinant even for non-degenerate quark pairs.

Abstract

In this review we discuss the general features of maximally twisted lattice QCD. In particular, we illustrate how automatic O(a) improvement can be achieved and how it is possible to set up a lattice regularization scheme where the problem of wrong chirality mixing (be it finite or infinite) affecting the computation of the matrix elements of the CP-conserving effective weak Hamiltonian is neatly avoided, while having at the same time a positive determinant even for non-degenerate quark pairs. The question of reducing the large cutoff effects that appear when the quark mass tends to zero as a consequence of parity and iso-spin breaking in the action is also addressed. It is shown that such dangerous lattice artifacts are strongly suppressed if the clover term is added to the action or, alternatively, the critical mass is chosen so as to enforce the restoration of parity.