A New Method for Determining $F_\pi$ on the Lattice

TL;DR

This paper introduces a novel lattice QCD method to determine the pion decay constant $F_$ by analyzing the spectral correlation function of the Dirac operator, validated through quenched simulations.

Contribution

The paper presents a new approach to extract $F_$ from lattice QCD using spectral correlation functions sensitive to $F_$, tested in quenched simulations.

Findings

Spectral correlation function strongly depends on $F_$

Method successfully applied in quenched lattice simulations

Provides a new tool for precise $F_$ determination

Abstract

We derive the two-point spectral correlation function of the Dirac operator with a specific external source in the $\epsilon$-regime of QCD. This correlation function has a unique and strong dependence on $F_\pi$, and thus provides an novel way to extract $F_\pi$ from lattice simulations. We test the method in a quenched lattice simulation with staggered fermions.