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

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

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

Chiral Lagrangian Parameters for Scalar and Pseudoscalar Mesons

The results of a high-statistics study of scalar and pseudoscalar meson propagators in quenched lattice QCD are presented. For two values of lattice spacing, $\beta=5.7$ ($a \approx .18$ fm) and 5.9 ($a \approx .12$ fm), we probe the light quark mass region using clover improved Wilson fermions with the MQA pole-shifting ansatz to treat the exceptional configuration problem. The quenched chiral loop parameters $m_0$ and $\alpha_{\Phi}$ are determined from a study of the pseudoscalar hairpin correlator. From a global fit to the meson correlators, estimates are obtained for the relevant chiral Lagrangian parameters, including the Leutwyler parameters $L_5$ and $L_8$. Using the parameters obtained from the singlet and nonsinglet pseudoscalar correlators, the quenched chiral loop effect in the nonsinglet scalar meson correlator is studied. By removing this QCL effect from the lattice correlator, we obtain the mass and decay constant of the ground state scalar, isovector meson $a_0$.Comment: 36 pages, 12 figures, LaTe

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

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

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