Nonperturbative ``Lattice Perturbation Theory''

We discuss a program for replacing standard perturbative methods with Monte Carlo simulations in short distance lattice gauge theory calculations.Comment: 3 pages, uuencoded Latex file, two embedded figures and .sty file include

Moving NRQCD for B Form Factors at High Recoil

We derive the continuum and lattice tree-level moving NRQCD (mNRQCD) through order 1/m^2. mNRQCD is a generalization of NRQCD for dealing with hadrons with nonzero velocity u_mu. The quark's total momentum is written as P^mu=Mu^mu+k^mu where k^mu << Mu^mu is discretized and Mu^mu is treated exactly. Radiative corrections to couplings on the lattice are discussed. mNRQCD is particularly useful for calculating B->pi and B->D form factors since errors are similar at low and high recoil.Comment: 3 pages, 1 figure, Lattice2002(heavyquark

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

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 kTk_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

DEPENDENCE OF THE CURRENT RENORMALISATION CONSTANTS ON THE QUARK MASS

We study the behaviour of the vector and axial current renormalisation constants $Z_V$ and $Z_A$ as a function of the quark mass, $m_q$. We show that sizeable $O(am_q)$ and $O(g_0^2 a m_q)$ systematic effects are present in the Wilson and Clover cases respectively. We find that the prescription of Kronfeld, Lepage and Mackenzie for correcting these artefacts is not always successful.Comment: Contribution to Lattice'94, 3 pages PostScript, uuencoded compressed