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

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 $ϵ$-regime, all are in the $p$-regime and a mixed-regime where the lighest quark masses satisfy $m_v\Sigma V\le 1$ 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.

Comments: 27 pages, 4 figures