Mass dependence of the hairpin vertex in quenched QCD

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 the quark mass. I show that this mass dependence can be used to determine the quenched Gasser-Leutwyler constant L-5. This complements the calculation of L-5 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.