# Towards a lattice calculation of the coefficients of the QCD chiral Lagrangian

## TL;DR

This paper proposes a method to calculate the coefficients of the QCD chiral Lagrangian using lattice QCD with Wilson fermions, involving an effective Lagrangian and renormalization, with analytical insights in strong coupling and large N limits.

## Contribution

It introduces a strategy to determine QCD chiral Lagrangian coefficients via lattice regularization and analytical computation of the effective Lagrangian, addressing chiral symmetry breaking effects.

## Key findings

- Analytical computation of the lattice effective Lagrangian in strong coupling and large N limits.
- A proposed renormalization procedure to handle chiral symmetry breaking.
- Framework for extracting continuum QCD chiral Lagrangian coefficients from lattice data.

## Abstract

We discuss a general strategy to compute the coefficients of QCD chiral Lagrangian by using the lattice regularization of QCD with Wilson fermions. This procedure requires the introduction of an effective Lagrangian for lattice QCD as an intermediate step in the calculation. The continuum QCD chiral Lagrangian can be then obtained by expanding the lattice effective Lagrangian in increasing powers of the external momenta. A suitable renormalization procedure is required to account for the chiral symmetry breaking introduced by the Wilson term in the lattice action. In anticipation of a numerical simulation, the lattice effective Lagrangian is computed analytically and investigated in the strong coupling and large $N$ limit