Finite-size scaling for the left-current correlator with non-degenerate quark masses

TL;DR

This paper analyzes how the left-current correlator in QCD depends on volume and quark mass regimes, providing theoretical results to connect lattice simulations with chiral effective theory.

Contribution

It extends finite-size scaling analysis of the left-current correlator to non-degenerate quark masses across different regimes, including mixed regimes, at next-to-leading order.

Findings

Derived volume dependence formulas for different quark mass regimes.

Provided matching conditions between lattice QCD and chiral effective theory.

Included results for both full and partially-quenched theories.

Abstract

We study the volume dependence of the left-current correlator with non-degenerate quark masses to next-to-leading order in the chiral expansion. We consider three possible regimes: all quark masses are in the $\epsilon$-regime, all are in the $p$-regime and a mixed-regime where the lighest quark masses satisfy $m_v \Sigma V \leq 1$ while the heavier $m_s \Sigma V \gg 1$. These results can be used to match lattice QCD and the Chiral Effective Theory in a large but finite box in which the Compton wavelength of the lightest pions is of the order of the box size. We consider both the full and partially-quenched results.