10,918 research outputs found
Problems with the Quenched Approximation in the Chiral Limit
In the quenched approximation, loops of the light singlet meson (the )
give rise to a type of chiral logarithm absent in full QCD. These logarithms
are singular in the chiral limit throwing doubt upon the utility of the
quenched approximation. In previous work, I summed a class of diagrams, leading
to non-analytic power dependencies such as \cond\propto
m_q^{-\delta/(1+\delta)}. I suggested, however, that these peculiar results
could be redefined away. Here I give an alternative derivation of the results,
based on the renormalization group, and argue that they cannot be redefined
away. I discuss the evidence (or lack thereof) for such effects in numerical
data.Comment: (talk given at Lattice '92), 4 pages latex, 3 postscript figures,
uses espcr2.sty and psfig.tex (all included) UW/PT-92-2
Using Staggered Fermions: An Update
Improved results for are discussed. Scaling corrections are argued to
be of , leading to a reduction in the systematic error. For a kaon
composed of degenerate quarks, the quenched result is .Comment: (poster presented at Lattice '93), 7 pages latex (it's in preprint
format!), 1 postscript figure, bundled with uufiles. Uses psfig.tex.
UW/PT-93-2
Staggered fermion matrix elements using smeared operators
We investigate the use of two kinds of staggered fermion operators, smeared
and unsmeared. The smeared operators extend over a hypercube, and tend to
have smaller perturbative corrections than the corresponding unsmeared
operators. We use these operators to calculate kaon weak matrix elements on
quenched ensembles at , 6.2 and 6.4. Extrapolating to the continuum
limit, we find . The
systematic error is dominated by the uncertainty in the matching between
lattice and continuum operators due to the truncation of perturbation theory at
one-loop. We do not include any estimate of the errors due to quenching or to
the use of degenerate and quarks. For the
electromagnetic penguin operators we find
and . We also use the ratio of unsmeared to
smeared operators to make a partially non-perturbative estimate of the
renormalization of the quark mass for staggered fermions. We find that tadpole
improved perturbation theory works well if the coupling is chosen to be
\alpha_\MSbar(q^*=1/a).Comment: 22 pages, 1 figure, uses eps
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