20,246 research outputs found

### Renormalization-group analysis of the validity of staggered-fermion QCD with the fourth-root recipe

I develop a renormalization-group blocking framework for lattice QCD with
staggered fermions. Under plausible, and testable, assumptions, I then argue
that the fourth-root recipe used in numerical simulations is valid in the
continuum limit. The taste-symmetry violating terms, which give rise to
non-local effects in the fourth-root theory when the lattice spacing is
non-zero, vanish in the continuum limit. A key role is played by reweighted
theories that are local and renormalizable on the one hand, and that
approximate the fourth-root theory better and better as the continuum limit is
approached on the other hand.Comment: Minor corrections. Revtex, 58 page

### Renormalization of Bilinear Quark Operators for Overlap Fermions

We present non-perturbative renormalization constants of fermionic bilinears
on the lattice in the quenched approximation at beta=6.1 using an overlap
fermion action with hypercubic(HYP)-blocked links. We consider the effects of
the exact zero modes of the Dirac operator and find they are important in
calculating the renormalization constants of the scalar and pseudoscalar
density. The results are given in the RI' and MS bar schemes and compared to
the perturbative calculations.Comment: 14 pages, 13 figure

### Finite-volume two-pion energies and scattering in the quenched approximation

We investigate how L\"uscher's relation between the finite-volume energy of
two pions at rest and pion scattering lengths has to be modified in quenched
QCD. We find that this relation changes drastically, and in particular, that
``enhanced finite-volume corrections" of order $L^0=1$ and $L^{-2}$ occur at
one loop ($L$ is the linear size of the box), due to the special properties of
the $\eta'$ in the quenched approximation. We define quenched pion scattering
lengths, and show that they are linearly divergent in the chiral limit. We
estimate the size of these various effects in some numerical examples, and find
that they can be substantial.Comment: 22 pages, uuencoded, compressed postscript fil

### Applications of Partially Quenched Chiral Perturbation Theory

Partially quenched theories are theories in which the valence- and sea-quark
masses are different. In this paper we calculate the nonanalytic one-loop
corrections of some physical quantities: the chiral condensate, weak decay
constants, Goldstone boson masses, B_K and the K+ to pi+ pi0 decay amplitude,
using partially quenched chiral perturbation theory. Our results for weak decay
constants and masses agree with, and generalize, results of previous work by
Sharpe. We compare B_K and the K+ decay amplitude with their real-world values
in some examples. For the latter quantity, two other systematic effects that
plague lattice computations, namely, finite-volume effects and unphysical
values of the quark masses and pion external momenta are also considered. We
find that typical one-loop corrections can be substantial.Comment: 22 pages, TeX, refs. added, minor other changes, version to appear in
Phys. Rev.

### Lattice QCD at the end of 2003

I review recent developments in lattice QCD. I first give an overview of its
formalism, and then discuss lattice discretizations of fermions. We then turn
to a description of the quenched approximation and why it is disappearing as a
vehicle for QCD phenomenology. I describe recent claims for progress in
simulations which include dynamical fermions and the interesting theoretical
problems they raise. I conclude with brief descriptions of the calculations of
matrix elements in heavy flavor systems and for kaons.Comment: Review for Int J Mod Phys A. 58 pages, latex, WSPC macros,, 22
postscript figure

### On the fourth root prescription for dynamical staggered fermions

With the aim of resolving theoretical issues associated with the fourth root
prescription for dynamical staggered fermions in Lattice QCD simulations, we
consider the problem of finding a viable lattice Dirac operator D such that
(det D_{staggered})^{1/4} = det D. Working in the flavour field representation
we show that in the free field case there is a simple and natural candidate D
satisfying this relation, and we show that it has acceptable locality behavior:
exponentially local with localisation range vanishing ~ (a/m)^{1/2} for lattice
spacing a -> 0. Prospects for the interacting case are also discussed, although
we do not solve this case here.Comment: 29 pages, 2 figures; some revision and streamlining of the
discussions; results unchanged; to appear in PR

### Chiral perturbation theory for K+ to pi+ pi0 decay in the continuum and on the lattice

In this paper we use one-loop chiral perturbation theory in order to compare
lattice computations of the K+ to pi+ pi0 decay amplitude with the experimental
value. This makes it possible to investigate three systematic effects that
plague lattice computations: quenching, finite-volume effects, and the fact
that lattice computations have been done at unphysical values of the quark
masses and pion external momenta (only this latter effect shows up at tree
level). We apply our results to the most recent lattice computation, and find
that all three effects are substantial. We conclude that one-loop corrections
in chiral perturbation theory help in explaining the discrepancy between
lattice results and the real-world value. We also revisit B_K, which is closely
related to the K+ to pi+ pi0 decay amplitude by chiral symmetry.Comment: 50 pages, TeX, two eps figures included, minor changes, no changes in
results or conclusions, version to appear in Phys.Rev.

### Chiral properties of two-flavor QCD in small volume and at large lattice spacing

We present results from simulations of two flavors of dynamical overlap
fermions on 8^4 lattices at three values of the sea quark mass and a lattice
spacing of about 0.16 fm. We measure the topological susceptibility and the
chiral condensate. A comparison of the low-lying spectrum of the overlap
operator with predictions from random matrix theory is made. To demonstrate the
effect of the dynamical fermions, we compare meson two-point functions with
quenched results. Algorithmic improvements over a previous publication and the
performance of the algorithm are discussed.Comment: 16 pages, 12 figure

### Enhanced chiral logarithms in partially quenched QCD

I discuss the properties of pions in ``partially quenched'' theories, i.e.
those in which the valence and sea quark masses, $m_V$ and $m_S$, are
different. I point out that for lattice fermions which retain some chiral
symmetry on the lattice, e.g. staggered fermions, the leading order prediction
of the chiral expansion is that the mass of the pion depends only on $m_V$, and
is independent of $m_S$. This surprising result is shown to receive corrections
from loop effects which are of relative size $m_S \ln m_V$, and which thus
diverge when the valence quark mass vanishes. Using partially quenched chiral
perturbation theory, I calculate the full one-loop correction to the mass and
decay constant of pions composed of two non-degenerate quarks, and suggest
various combinations for which the prediction is independent of the unknown
coefficients of the analytic terms in the chiral Lagrangian. These results can
also be tested with Wilson fermions if one uses a non-perturbative definition
of the quark mass.Comment: 14 pages, 3 figures, uses psfig. Typos in eqs (18)-(20) corrected
(alpha_4 is replaced by alpha_4/2

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