Determining F_pi from spectral sum rules

TL;DR

This paper derives spectral sum rules for a two-quark system with an imaginary isospin chemical potential, linking the eigenvalue spectrum of the Dirac operator to the pion decay constant, enabling its measurement.

Contribution

It introduces a novel set of spectral sum rules that depend explicitly on F_pi, facilitating its extraction from spectral data in the epsilon regime.

Findings

Sum rules depend explicitly on F_pi

Eigenvalue spectrum can be used to measure F_pi

Provides a new method for F_pi determination

Abstract

We derive spectral sum rules for a system with two quarks coupled to an imaginary isospin chemical potential in the \epsilon regime. The sum rules show an explicit dependence on the pion decay constant which should make it possible to measure F_pi from the eigenvalue spectrum of this particular Dirac operator.