Extracting $F_\pi$ from small lattices: unquenched results

TL;DR

This paper introduces a new lattice QCD method to measure the pion decay constant $F_pi$ using the microscopic Dirac spectrum response to an imaginary isospin chemical potential, extending previous quenched results to unquenched theory.

Contribution

It extends the spectral correlation method for measuring $F_pi$ from quenched to unquenched lattice QCD with two dynamical flavors.

Findings

Successful application of the method in a hybrid Monte Carlo simulation.

Validation of the spectral correlation approach for unquenched $F_pi$ measurement.

Demonstration of the method's efficiency and potential for lattice QCD studies.

Abstract

We calculate the response of the microscopic Dirac spectrum to an imaginary isospin chemical potential for QCD with two dynamical flavors in the chiral limit. This extends our previous calculation from the quenched to the unquenched theory. The resulting spectral correlation function in the $\epsilon$-regime provides here, too, a new and efficient way to measure $F_\pi$ on the lattice. We test the method in a hybrid Monte Carlo simulation of the theory with two staggered quarks.