2,373 research outputs found

### On the Viability of Lattice Perturbation Theory

In this paper we show that the apparent failure of QCD lattice perturbation
theory to account for Monte Carlo measurements of perturbative quantities
results from choosing the bare lattice coupling constant as the expansion
parameter. Using instead ``renormalized'' coupling constants defined in terms
of physical quantities, like the heavy-quark potential, greatly enhances the
predictive power of lattice perturbation theory. The quality of these
predictions is further enhanced by a method for automatically determining the
coupling-constant scale most appropriate to a particular quantity. We present a
mean-field analysis that explains the large renormalizations relating lattice
quantities, like the coupling constant, to their continuum analogues. This
suggests a new prescription for designing lattice operators that are more
continuum-like than conventional operators. Finally, we provide evidence that
the scaling of physical quantities is asymptotic or perturbative already at
$\beta$'s as low as 5.7, provided the evolution from scale to scale is analyzed
using renormalized perturbation theory. This result indicates that reliable
simulations of (quenched) QCD are possible at these same low $\beta$'s.Comment: 3

### Pion Form Factor in the $k_T$ Factorization Formalism

Based on the light-cone (LC) framework and the $k_T$ factorization formalism,
the transverse momentum effects and the different helicity components'
contributions to the pion form factor $F_{\pi}(Q^2)$ are recalculated. In
particular, the contribution to the pion form factor from the higher helicity
components ($\lambda_1+\lambda_2=\pm 1$), which come from the spin-space Wigner
rotation, are analyzed in the soft and hard energy regions respectively. Our
results show that the right power behavior of the hard contribution from the
higher helicity components can only be obtained by fully keeping the $k_T$
dependence in the hard amplitude, and that the $k_T$ dependence in LC wave
function affects the hard and soft contributions substantially. As an example,
we employ a model LC wave function to calculate the pion form factor and then
compare the numerical predictions with the experimental data. It is shown that
the soft contribution is less important at the intermediate energy region.Comment: 21 pages, 4 figure

### Improving lattice perturbation theory

Lepage and Mackenzie have shown that tadpole renormalization and systematic
improvement of lattice perturbation theory can lead to much improved numerical
results in lattice gauge theory. It is shown that lattice perturbation theory
using the Cayley parametrization of unitary matrices gives a simple analytical
approach to tadpole renormalization, and that the Cayley parametrization gives
lattice gauge potentials gauge transformations close to the continuum form. For
example, at the lowest order in perturbation theory, for SU(3) lattice gauge
theory, at $\beta=6,$ the `tadpole renormalized' coupling $\tilde g^2 = {4\over
3} g^2,$ to be compared to the non-perturbative numerical value $\tilde g^2 =
1.7 g^2.$Comment: Plain TeX, 8 page

### Flavor-Symmetry Restoration and Symanzik Improvement for Staggered Quarks

We resolve contradictions in the literature concerning the origins and size
of unphysical flavor-changing strong interactions generated by the
staggered-quark discretization of QCD. We show that the leading contributions
are tree-level in \order(a^2) and that they can be removed by adding three
correction terms to the link operator in the standard action. These corrections
are part of the systematic Symanzik improvement of the staggered-quark action.
We present a new improved action for staggered quarks that is accurate up to
errors of \order(a^4,a^2\alpha_s) --- more accurate than most, if not all,
other discretizations of light-quark dynamics.Comment: 7 page

### Improved Nonrelativistic QCD for Heavy Quark Physics

We construct an improved version of nonrelativistic QCD for use in lattice
simulations of heavy quark physics, with the goal of reducing systematic errors
from all sources to below 10\%. We develop power counting rules to assess the
importance of the various operators in the action and compute all leading order
corrections required by relativity and finite lattice spacing. We discuss
radiative corrections to tree level coupling constants, presenting a procedure
that effectively resums the largest such corrections to all orders in
perturbation theory. Finally, we comment on the size of nonperturbative
contributions to the coupling constants.Comment: 40 pages, 2 figures (not included), in LaTe

### A quark action for very coarse lattices

We investigate a tree-level O(a^3)-accurate action, D234c, on coarse
lattices. For the improvement terms we use tadpole-improved coefficients, with
the tadpole contribution measured by the mean link in Landau gauge.
We measure the hadron spectrum for quark masses near that of the strange
quark. We find that D234c shows much better rotational invariance than the
Sheikholeslami-Wohlert action, and that mean-link tadpole improvement leads to
smaller finite-lattice-spacing errors than plaquette tadpole improvement. We
obtain accurate ratios of lattice spacings using a convenient ``Galilean
quarkonium'' method.
We explore the effects of possible O(alpha_s) changes to the improvement
coefficients, and find that the two leading coefficients can be independently
tuned: hadron masses are most sensitive to the clover coefficient, while hadron
dispersion relations are most sensitive to the third derivative coefficient
C_3. Preliminary non-perturbative tuning of these coefficients yields values
that are consistent with the expected size of perturbative corrections.Comment: 22 pages, LaTe

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