Short distance singularities and automatic O($a$) improvement: the cases of the chiral condensate and the topological susceptibility

TL;DR

This paper investigates how short-distance singularities affect lattice correlators and demonstrates that automatic O(a) improvement remains valid for Wilson twisted mass fermions at maximal twist, using the chiral condensate and topological susceptibility as examples.

Contribution

It provides a detailed analysis of short-distance singularities' impact on lattice correlators and confirms the preservation of automatic O(a) improvement in specific fermion formulations.

Findings

Short-distance singularities can introduce additional O(a) artifacts.

Automatic O(a) improvement is preserved at maximal twist.

The analysis applies to the chiral condensate and topological susceptibility.

Abstract

Short-distance singularities in lattice correlators can modify their Symanzik expansion by leading to additional O($a$) lattice artifacts. At the example of the chiral condensate and the topological susceptibility, we show how to account for these lattice artifacts for Wilson twisted mass fermions and show that the property of automatic O($a$) improvement is preserved at maximal twist.