Mass dependence of the hairpin vertex in quenched QCD

TL;DR

This paper investigates how the hairpin vertex in quenched QCD varies with quark mass and demonstrates how this dependence can be used to determine a key low-energy constant in quenched chiral perturbation theory.

Contribution

It introduces a method to extract the quenched Gasser-Leutwyler constant L5 from the mass dependence of the hairpin vertex in lattice QCD simulations.

Findings

Mass dependence of the hairpin vertex is significant.

Method to determine L5 from lattice data.

Complementary to existing L5 calculations.

Abstract

The pseudoscalar ``hairpin'' vertex (i.e. quark-disconnected vertex) plays a key role in quenched chiral perturbation theory. Direct calculations using lattice simulations find that it has a significant dependence on quark mass. I show that this mass dependence can be used to determine the quenched Gasser-Leutwyler constant L5. This complements the calculation of L5 using the mass dependence of the axial decay constant of the pion. In an appendix, I discuss power counting for quenched chiral perturbation theory and describe the particular scheme used in this paper.