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

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

Higgs Mass in the Standard Model from Coupling Constant Reduction

Plausible interrelations between parameters of the standard model are studied. The empirical value of the top quark mass, when used in the renormalization group equations, suggests that the ratio of the colour SU(3) gauge coupling $g_3$, and the top coupling $g_t$ is independent of the renormalization scale. On the other hand, variety of top-condensate models suggest that the Higgs self-coupling $\lambda$ is proportional to $g_t^2$. Invoking the requirement that the ratio $\lambda(t)/g_t^2(t)$ is independent of the renormalization scale $t$, fixes the Higgs mass. The pole mass of the Higgs [which differs from the renormalization group mass by a few percent] is found to be $\sim 154$ GeV for the one-loop equations and $\sim 148$ GeV for the two-loop equations.Comment: 17 pages RevTeX including 7 figure

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

Dirac's Observables for the SU(3)XSU(2)XU(1) Standard Model

The complete, missing, Hamiltonian treatment of the standard SU(3)xSU(2)xU(1) model with Grassmann-valued fermion fields in the Higgs phase is given. We bypass the complications of the Hamiltonian theory in the Higgs phase, resulting from the spontaneous symmetry breaking with the Higgs mechanism, by studying the Hamiltonian formulation of the Higgs phase for the gauge equivalent Lagrangian in the unitary gauge. A canonical basis of Dirac's observables is found and the reduced physical Hamiltonian is evaluated. Its self-energy part is nonlocal for the electromagnetic and strong interactions, but local for the weak ones. Therefore, the Fermi 4-fermion interaction reappears at the nonperturbative level.Comment: 90 pages, RevTeX, no figure

Resolving Exceptional Configurations

In lattice QCD with Wilson fermions, exceptional configurations arise in the quenched approximation at small quark mass. The origin of these large previously uncontrolled lattice artifacts is identified. A simple well-defined procedure (MQA) is presented which removes the artifacts while preserving the correct continuum limit.Comment: Talk presented by E. Eichten at Lattice 97, Edinburgh(UK), July97. 6 pages, LaTeX, 1 table, 5 figure

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