Quark mass dependence of the pseudoscalar hairpin vertex
In a recent investigation of chiral behavior in quenched lattice QCD, the flavor-singlet pseudoscalar ``hairpin'' vertex associated with the eta prime mass was studied for pion masses ranging from approximately 275 to 675 MeV. Throughout this mass range, the quark-disconnected pseudoscalar correlator is well-described by a pure double-pion-pole diagram with a p^2 independent mass insertion. The residue of the double pole was found to exhibit a significant quark mass dependence, evidenced by a negative slope of the effective mass insertion (m_0^{eff})^2 as a function of m_π^2. It has been observed by Sharpe that, with a consistent NLO calculation in quenched chiral perturbation theory, this mass dependence is uniquely predicted in terms of the single-pole coefficient α_Φ and the Leutwyler parameter L_5. Since α_Φ is found to be approximately zero, the chiral slope of the double-pole residue determines a value for L_5. This provides a consistency check between the chiral slope of the hairpin mass insertion and that of the pion decay constant. We investigate the consistency of these mass dependences in our Monte Carlo results at two values of lattice spacing. Within statistics, the slopes are found to be consistent with the Q\chiPT prediction, confirming that the observed negative slope of m_0^{eff} arises as an effect of the L_5 Leutwyler term.