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Register a new userTesting the fixed-point QCD action and the construction of chiral currents
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We present the first set of quenched QCD measurements using the recently parametrized fixed-point Dirac operator D^FP. We also give a general and practical construction of covariant densities and conserved currents for chiral lattice actions. The measurements include (a) hadron spectroscopy, (b) corrections of small chiral deviations, (c) the renormalized quark condensate from finite-size scaling and, independently, spectroscopy, (d) the topological susceptibility, (e) small eigenvalue distributions and random matrix theory, and (f) local chirality of near-zero modes and instanton-dominance.
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In this preliminary study, we examine the chiral properties of the parametrized Fixed-Point Dirac operator D^FP, see how to improve its chirality via the Overlap construction, measure the renormalized quark condensate Sigma and the topological susceptibility chi_t, and investigate local chirality of near zero modes of the Dirac operator. We also give a general construction of chiral currents and densities for chiral lattice actions.
We have constructed a new fermion action which is an approximation to the (chirally symmetric) Fixed-Point action, containing the full Clifford algebra with couplings inside a hypercube and paths built from renormalization group inspired fat links. We present an exploratory study of the light hadron spectrum and the energy-momentum dispersion relation.
We report on the pion-pion scattering length in the I=2 channel using the parametrized fixed point action. Pion masses of 320 MeV were reached in this quenched calculation of the scattering length.
The topological charge distribution P(Q) is calculated for lattice ${rm CP}^{N-1}$ models. In order to suppress lattice cut-off effects we employ a fixed point (FP) action. Through transformation of P(Q) we calculate the free energy $F(theta)$ as a function of the $theta$ parameter. For N=4, scaling behavior is observed for P(Q), $F(theta)$ as well as the correlation lengths $xi(Q)$. For N=2, however, scaling behavior is not observed as expected. For comparison, we also make a calculation for the ${rm CP}^{3}$ model with standard action. We furthermore pay special attention to the behavior of P(Q) in order to investigate the dynamics of instantons. For that purpose, we carefully look at behavior of $gamma_{it eff}$, which is an effective power of P(Q)($sim exp(-CQ^{gamma_{it eff}})$), and reflects the local behavior of P(Q) as a function of Q. We study $gamma_{it eff}$ for two cases, one of which is the dilute gas approximation based on the Poisson distribution of instantons and the other is the Debye-Huckel approximation of instanton quarks. In both cases we find similar behavior to the one observed in numerical simulations.
We study lattice QCD with a gauge action, which suppresses small plaquette values. Thus the MC history is confined to a single topological sector over a significant time, while other observables are decorrelated. This enables the cumulation of statistics with a specific topological charge, which is needed for simulations of QCD in the $epsilon$-regime. The same action may also be useful for simulations with dynamical quarks. The update is performed with a local HMC algorithm.
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