Finite Volume Scaling of Pseudo Nambu-Goldstone Bosons in QCD

TL;DR

This paper develops a finite-volume chiral perturbation theory framework for mixed quark mass regimes in QCD, enabling more accurate lattice simulations of light meson physics.

Contribution

It introduces a new mixed regime approach combining epsilon- and p-regimes, with finite-size scaling formulas for various meson correlators, extendable to partially quenched theories.

Findings

Finite-size scaling formulas for scalar, pseudoscalar, vector, axial vector channels.

Extension of results to partially quenched theories using the replica method.

Guidance for lattice QCD simulations with 2+1 flavors and very light quarks.

Abstract

We consider chiral perturbation theory in a finite volume and in a mixed regime of quark masses. We take N_l light quarks near the chiral limit, in the so-called epsilon-regime, while the remaining N_h quarks are heavier and in the standard p-regime. We compute in this new mixed regime the finite-size scaling of the light meson correlators in the scalar, pseudoscalar, vector and axial vector channels.Using the replica method, we easily extend our results to the partially quenched theory. With the help of our results, lattice QCD simulations with 2+1 flavors can safely investigate pion physics with very light up and down quark masses even in the region where the pion's correlation length overcomes the size of the space-time lattice.