29,685 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
Scalar Meson Spectroscopy with Lattice Staggered Fermions
With sufficiently light up and down quarks the isovector () and
isosinglet () scalar meson propagators are dominated at large distance by
two-meson states. In the staggered fermion formulation of lattice quantum
chromodynamics, taste-symmetry breaking causes a proliferation of two-meson
states that further complicates the analysis of these channels. Many of them
are unphysical artifacts of the lattice approximation. They are expected to
disappear in the continuum limit. The staggered-fermion fourth-root procedure
has its purported counterpart in rooted staggered chiral perturbation theory
(rSXPT). Fortunately, the rooted theory provides a strict framework that
permits the analysis of scalar meson correlators in terms of only a small
number of low energy couplings. Thus the analysis of the point-to-point scalar
meson correlators in this context gives a useful consistency check of the
fourth-root procedure and its proposed chiral realization. Through numerical
simulation we have measured correlators for both the and channels
in the ``Asqtad'' improved staggered fermion formulation in a lattice ensemble
with lattice spacing fm. We analyze those correlators in the context
of rSXPT and obtain values of the low energy chiral couplings that are
reasonably consistent with previous determinations.Comment: 23 pp., 3 figs., submitted to Phys. Rev.
Heavy-Light Semileptonic Decays in Staggered Chiral Perturbation Theory
We calculate the form factors for the semileptonic decays of heavy-light
pseudoscalar mesons in partially quenched staggered chiral perturbation theory
(\schpt), working to leading order in , where is the heavy quark
mass. We take the light meson in the final state to be a pseudoscalar
corresponding to the exact chiral symmetry of staggered quarks. The treatment
assumes the validity of the standard prescription for representing the
staggered ``fourth root trick'' within \schpt by insertions of factors of 1/4
for each sea quark loop. Our calculation is based on an existing partially
quenched continuum chiral perturbation theory calculation with degenerate sea
quarks by Becirevic, Prelovsek and Zupan, which we generalize to the staggered
(and non-degenerate) case. As a by-product, we obtain the continuum partially
quenched results with non-degenerate sea quarks. We analyze the effects of
non-leading chiral terms, and find a relation among the coefficients governing
the analytic valence mass dependence at this order. Our results are useful in
analyzing lattice computations of form factors and when the
light quarks are simulated with the staggered action.Comment: 53 pages, 8 figures, v2: Minor correction to the section on finite
volume effects, and typos fixed. Version to be published 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
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 and occur at
one loop ( is the linear size of the box), due to the special properties of
the 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
The isentropic equation of state of 2-flavor QCD
Using Taylor expansions of the pressure obtained previously in studies of
2-flavor QCD at non-zero chemical potential we calculate expansion coefficients
for the energy and entropy densities up to in the quark
chemical potential. We use these series in to determine lines of
constant entropy per baryon number () that characterize the expansion of
dense matter created in heavy ion collisions. In the high temperature regime
these lines are found to be well approximated by lines of constant .
In the low temperature phase, however, the quark chemical potential is found to
increase with decreasing temperature. This is in accordance with resonance gas
model calculations. Along the lines of constant we calculate the energy
density and pressure. Within the accuracy of our present analysis we find that
the ratio for as well as the softest point of the equation
of state, , show no significant dependence on
.Comment: 7 pages, 10 figure
Lattice Calculation of Heavy-Light Decay Constants with Two Flavors of Dynamical Quarks
We present results for , , , and their ratios in
the presence of two flavors of light sea quarks (). We use Wilson light
valence quarks and Wilson and static heavy valence quarks; the sea quarks are
simulated with staggered fermions. Additional quenched simulations with
nonperturbatively improved clover fermions allow us to improve our control of
the continuum extrapolation. For our central values the masses of the sea
quarks are not extrapolated to the physical , masses; that is, the
central values are "partially quenched." A calculation using "fat-link clover"
valence fermions is also discussed but is not included in our final results. We
find, for example,
MeV, , MeV, and , where in each case the first error is
statistical and the remaining three are systematic: the error within the
partially quenched approximation, the error due to the missing strange
sea quark and to partial quenching, and an estimate of the effects of chiral
logarithms at small quark mass. The last error, though quite significant in
decay constant ratios, appears to be smaller than has been recently suggested
by Kronfeld and Ryan, and Yamada. We emphasize, however, that as in other
lattice computations to date, the lattice quark masses are not very light
and chiral log effects may not be fully under control.Comment: Revised version includes an attempt to estimate the effects of chiral
logarithms at small quark mass; central values are unchanged but one more
systematic error has been added. Sections III E and V D are completely new;
some changes for clarity have also been made elsewhere. 82 pages; 32 figure
A precise determination of T_c in QCD from scaling
Existing lattice data on the QCD phase transition are analyzed in
renormalized perturbation theory. In quenched QCD it is found that T_c scales
for lattices with only 3 time slices, and that T_c/Lambda_msbar=1.15 \pm 0.05.
A preliminary estimate in QCD with two flavours of dynamical quarks shows that
this ratio depends on the quark mass. For realistic quark masses we estimate
T_c/Lambda_msbar=0.49 \pm 0.02. We also investigate the equation of state in
quenched QCD at 1-loop order in renormalised perturbation theory.Comment: 7 pages, 5 eps figures; improved error analysis yields smaller errors
on T_
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