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_{\pi}^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 \alpha_{\Phi} and the Leutwyler parameter L_5. Since \alpha_{\Phi} 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.Comment: 4 pages, 1 figure, LaTe

QED2 as a testbed for interpolations between quenched and full QCD

Lattice QED2 with the Wilson formulation of fermions is used as a convenient model system to study artifacts of the quenched approximation on a finite lattice. The quenched functional integral is shown to be ill-defined in this system as a consequence of the appearance of exactly real modes for physical values of the fermion mass. The location and frequency of such modes is studied as a function of lattice spacing, lattice volume, topological charge and improved action parameters. The efficacy of the recently proposed modified quenched approximation is examined, as well as a new approach to the interpolation from the quenched to full dynamical theory employing a truncated form of the fermion determinant.Comment: Talk presented by A. Duncan at LATTICE97 (theoretical developments

Low Dirac Eigenmodes and the Topological and Chiral Structure of the QCD Vacuum

Several lattice calculations which probe the chiral and topological structure of QCD are discussed. The results focus attention on the low-lying eigenmodes of the Dirac operator in typical gauge field configurations.Comment: Talk presented at the DPF2000 Conferenc

Evidence for quenched chiral logs

Using the pole shifting procedure of the modified quenched approximation (MQA) to cure the exceptional configuration problem, accurate hadron hadron spectrum calculations can be obtained at very light quark mass. Here we use the MQA to extend and improve our previous investigation of chiral logs in the pion mass. At beta=5.7 for Wilson fermion, we see clear evidence for quenched chiral logarithms in the pion mass as a function of quark mass. The size of the observed chiral log exponent delta is in good agreement with the value obtained from a direct calculation of the eta' hairpin diagram.Comment: 3 pages, 4 figures, Lattice 98 tal

The eta-prime propagator in quenched QCD

The calculation of the eta-prime hairpin diagram is carried out in the modified quenched approximation (MQA) in which the lattice artifact which causes exceptional configurations is removed by shifting observed poles at kappa<kappa_c in the quark propagators to the critical value of hop ping parameter. By this method, the eta-prime propagator can be accurately calculated even for very light quark mass. A determination of the topological susceptibility for quenched QCD is also obtained, using the fermionic method of Smit and Vink to calculate winding numbers.Comment: 3 pages, 3 postscript figure

Chiral Loops and Ghost States in the Quenched Scalar Propagator

The scalar, isovector meson propagator is analyzed in quenched QCD, using the MQA pole-shifting ansatz to study the chiral limit. In addition to the expected short-range exponential falloff characteristic of a heavy scalar meson, the propagator also exhibits a longer-range, negative metric contribution which becomes pronounced for smaller quark masses. We show that this is a quenched chiral loop effect associated with the anomalous structure of the $\eta '$ propagator in quenched QCD. Both the time dependence and the quark mass dependence of this effect are well-described by a chiral loop diagram corresponding to an $\eta '- \pi$ intermediate state, which is light and effectively of negative norm in the quenched approximation. The relevant parameters of the effective Lagrangian describing the scalar sector of the quenched theory are determined.Comment: 29 pages, 10 figures, Late