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

Abstract

We derive the two-point spectral correlation function of the Dirac operator with a specific external source in the $ϵ$-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.

Comments: 5 pages, 3 figures