# QCD chiral Lagrangian on the lattice, strong coupling expansion and Ward identities with Wilson fermions

## TL;DR

This paper presents a method to compute the QCD chiral Lagrangian coefficients using lattice QCD with Wilson fermions, analyzing chiral symmetry breaking and renormalization effects at strong coupling and large N.

## Contribution

It introduces a systematic approach to derive the lattice QCD chiral Lagrangian and demonstrates how to account for Wilson term effects through renormalization at leading order.

## Key findings

- Wilson term effects can be absorbed by renormalization.
- Chiral symmetry is restored at leading order with proper renormalization.
- The method applies at strong coupling and large N expansions.

## Abstract

We discuss a general strategy to compute the coefficients of the QCD chiral Lagrangian using lattice QCD with Wilson fermions. This procedure requires the introduction of a lattice chiral Lagrangian as an intermediate step in the calculation. The QCD chiral Lagrangian is then obtained by expanding the lattice effective theory in increasing powers of the lattice spacing and the external momenta. In order to investigate the consequences of the chiral symmetry breaking induced by the Wilson term, we study the lattice chiral Lagrangian at the leading order of the strong coupling and large $N$ expansion. We show that the effects of the Wilson term can be conveniently taken into account, in the lattice effective theory, by a suitable renormalization procedure. In particular, we show that, at the leading order of the strong coupling and large N expansion, the chiral symmetry is exactly recovered on the lattice provided that the bare quark mass and the lattice operators are properly renormalized.