Determination of F_pi from Distributions of Dirac Operator Eigenvalues with Imaginary Density

TL;DR

This paper presents a method to determine the pion decay constant F_pi in lattice QCD by analyzing Dirac operator eigenvalue distributions under imaginary chemical potentials, using chiral Random Two-Matrix Theory.

Contribution

It derives explicit eigenvalue distribution formulas in the epsilon-regime and shows how to compute them from the chiral Lagrangian, advancing lattice QCD analysis techniques.

Findings

Derived eigenvalue distributions using chiral Random Two-Matrix Theory.

Showed how to compute eigenvalue distributions directly from the chiral Lagrangian.

Provided a new approach to measure F_pi in lattice QCD.

Abstract

In the epsilon-regime of lattice QCD one can get an accurate measurement of the pion decay constant F_pi by monitoring how just one single Dirac operator eigenvalue splits into two when subjected to two different external vector sources. Because we choose imaginary chemical potentials our Dirac eigenvalues remain real. Based on the relevant chiral Random Two-Matrix Theory we derive individual eigenvalue distributions in terms of density correlations functions to leading order in the finite-volume epsilon-expansion. As a simple byproduct we also show how the associated individual Dirac eigenvalue distributions and their correlations can be computed directly from the effective chiral Lagrangian.