Taste Non-Goldstone Pion Decay Constants and Beyond the Standard Model B-parameters in Lattice QCD with Staggered Fermions

Abstract

In part I, we calculate the next-to-leading order corrections to pion decay constants for the taste non-Goldstone pions using staggered chiral perturbation theory. This is a generalization of the calculation for the taste Goldstone case. New low-energy couplings are limited to analytic corrections that vanish in the continuum limit

the chiral logarithms contain no new couplings. We report results for quenched, fully dynamical, and partially quenched cases of interest in the chiral SU(3) and SU(2) theories. The results can be used to refine existing determinations of decay constants and low energy constants. In part II, we calculate the beyond the standard model B-parameters using HYP-smeared improved staggered fermions on the MILC asqtad lattices with Nf = 2 + 1 flavors. We use three different lattice spacings (a ? 0.045, 0.06 and 0.09 fm) to obtain the continuum results. Operator matching is done using one-loop perturbative matching, and results are run to 2 and 3 GeV in the MS scheme. For the chiral and continuum extrapolations, we use SU(2) staggered chiral perturbation theory. We present preliminary results with only statistical errors. In part III, we give a detailed introduction to the data anlysis including basic probability theory, error anlalysis techniques and least chi-square fitting method. We also explain how to analyse highly correlated data by applying a number of prescriptions such as diagonal approximation, singular value decomposition (SVD) method and Bayesian method. We propose a brand new method, the eigenmode shift method which allows a full covariance fitting without modifying the covariance matrix.