Finite size scaling of meson propagators with isospin chemical potential

TL;DR

This paper analytically studies how meson propagators depend on volume, mass, and isospin chemical potential in QCD, providing formulas that can improve lattice QCD determinations of fundamental constants.

Contribution

It derives new analytical results for meson two-point functions at finite volume and chemical potential, including corrections and group integrals, enhancing the understanding of QCD in these conditions.

Findings

Derived volume and mass dependence of meson propagators

Provided analytical expressions for zero-mode group integrals

Rectified previous finite-volume correction calculations

Abstract

We determine the volume and mass dependence of scalar and pseudoscalar two-point functions in N_f-flavour QCD, in the presence of an isospin chemical potential and at fixed gauge-field topology. We obtain these results at second order in the \epsilon-expansion of Chiral Perturbation Theory and evaluate all relevant zero-mode group integrals analytically. The virtue of working with a non-vanishing chemical potential is that it provides the correlation functions with a dependence on both the chiral condensate, \Sigma, and the pion decay constant, F, already at leading order. Our results may therefore be useful for improving the determination of these constants from lattice QCD calculations. As a side product, we rectify an earlier calculation of the O(\epsilon^2) finite-volume correction to the decay constant appearing in the partition function. We also compute a generalised partition function which is useful for evaluating U(N_f) group integrals.