1,307 research outputs found
Perturbation theory vs. simulation for tadpole improvement factors in pure gauge theories
We calculate the mean link in Landau gauge for Wilson and improved SU(3)
anisotropic gauge actions, using two loop perturbation theory and Monte Carlo
simulation employing an accelerated Langevin algorithm. Twisted boundary
conditions are employed, with a twist in all four lattice directions
considerably improving the (Fourier accelerated) convergence to an improved
lattice Landau gauge. Two loop perturbation theory is seen to predict the mean
link extremely well even into the region of commonly simulated gauge couplings
and so can be used remove the need for numerical tuning of self-consistent
tadpole improvement factors. A three loop perturbative coefficient is inferred
from the simulations and is found to be small. We show that finite size effects
are small and argue likewise for (lattice) Gribov copies and double Dirac
sheets.Comment: 13 pages of revtex
Irreducible Multiplets of Three-Quark Operators on the Lattice: Controlling Mixing under Renormalization
High luminosity accelerators have greatly increased the interest in
semi-exclusive and exclusive reactions involving nucleons. The relevant
theoretical information is contained in the nucleon wavefunction and can be
parametrized by moments of the nucleon distribution amplitudes, which in turn
are linked to matrix elements of three-quark operators. These can be calculated
from first principles in lattice QCD. However, on the lattice the problems of
operator mixing under renormalization are rather involved. In a systematic
approach we investigate this issue in depth. Using the spinorial symmetry group
of the hypercubic lattice we derive irreducibly transforming three-quark
operators, which allow us to control the mixing pattern.Comment: 13 page
Diffusive transport in networks built of containers and tubes
We developed analytical and numerical methods to study a transport of
non-interacting particles in large networks consisting of M d-dimensional
containers C_1,...,C_M with radii R_i linked together by tubes of length l_{ij}
and radii a_{ij} where i,j=1,2,...,M. Tubes may join directly with each other
forming junctions. It is possible that some links are absent. Instead of
solving the diffusion equation for the full problem we formulated an approach
that is computationally more efficient. We derived a set of rate equations that
govern the time dependence of the number of particles in each container
N_1(t),N_2(t),...,N_M(t). In such a way the complicated transport problem is
reduced to a set of M first order integro-differential equations in time, which
can be solved efficiently by the algorithm presented here. The workings of the
method have been demonstrated on a couple of examples: networks involving
three, four and seven containers, and one network with a three-point junction.
Already simple networks with relatively few containers exhibit interesting
transport behavior. For example, we showed that it is possible to adjust the
geometry of the networks so that the particle concentration varies in time in a
wave-like manner. Such behavior deviates from simple exponential growth and
decay occurring in the two container system.Comment: 21 pages, 18 figures, REVTEX4; new figure added, reduced emphasis on
graph theory, additional discussion added (computational cost, one
dimensional tubes
The B_s and D_s decay constants in 3 flavor lattice QCD
Capitalizing on recent advances in lattice QCD, we present a calculation of
the leptonic decay constants f_{B_s} and f_{D_s} that includes effects of one
strange sea quark and two light sea quarks. The discretization errors of
improved staggered fermion actions are small enough to simulate with 3
dynamical flavors on lattices with spacings around 0.1 fm using present
computer resources. By shedding the quenched approximation and the associated
lattice scale ambiguity, lattice QCD greatly increases its predictive power.
NRQCD is used to simulate heavy quarks with masses between 1.5 m_c and m_b. We
arrive at the following results: f_{B_s} = 260 \pm 7 \pm 26 \pm 8 \pm 5 MeV and
f_{D_s} = 290 \pm 20 \pm 29 \pm 29 \pm 6 MeV. The first quoted error is the
statistical uncertainty, and the rest estimate the sizes of higher order terms
neglected in this calculation. All of these uncertainties are systematically
improvable by including another order in the weak coupling expansion, the
nonrelativistic expansion, or the Symanzik improvement program.Comment: 4 page
One-loop matching coefficients for improved staggered bilinears
We calculate one-loop matching factors for bilinear operators composed of
improved staggered fermions. We compare the results for different improvement
schemes used in the recent literature, all of which involve the use of smeared
links. These schemes aim to reduce, though not completely eliminate, O(a^2)
discretization errors. We find that all these improvement schemes substantially
reduce the size of matching factors compared to unimproved staggered fermions.
The resulting corrections are comparable to, or smaller than, those found with
Wilson and domain-wall fermions. In the best case (``Fat-7'' and mean-field
improved HYP links) the corrections are 10 % or smaller at 1/a = 2 GeV.Comment: 13 pages, 1 figure (misleading sentence in sec. II removed; version
to appear in Physical Review D
Initial bound state studies in light-front QCD
We present the first numerical QCD bound state calculation based on a
renormalization group-improved light-front Hamiltonian formalism. The QCD
Hamiltonian is determined to second order in the coupling, and it includes
two-body confining interactions. We make a momentum expansion, obtaining an
equal-time-like Schrodinger equation. This is solved for quark-antiquark
constituent states, and we obtain a set of self-consistent parameters by
fitting B meson spectra.Comment: 38 pages, latex, 5 latex figures include
Improved lattice operators for non-relativistic fermions
In this work I apply a recently proposed improvement procedure, originally
conceived to reduce finite lattice spacing effects in transfer matrices for
dilute Fermi systems, to tuning operators for the calculation of observables. I
construct, in particular, highly improved representations for the energy and
the contact, as a first step in an improvement program for finite-temperature
calculations. I illustrate the effects of improvement on those quantities with
a ground-state lattice calculation at unitarity.Comment: 11 pages, 7 figures; replaced with published versio
Perturbative matching of staggered four-fermion operators with hypercubic fat links
We calculate the one-loop matching coefficients between continuum and lattice
four-fermion operators for lattice operators constructed using staggered
fermions and improved by the use of fattened links. In particular, we consider
hypercubic fat links and SU(3) projected Fat-7 links, and their mean-field
improved versions. We calculate only current-current diagrams, so that our
results apply for operators whose flavor structure does not allow
``eye-diagrams''. We present general formulae, based on two independent
approaches, and give numerical results for the cases in which the operators
have the taste (staggered flavor) of the pseudo-Goldstone pion. We find that
the one-loop corrections are reduced down to the 10-20% level, resolving the
problem of large perturbative corrections for staggered fermion calculations of
matrix elements.Comment: 37 pages, no figure, 20 table
Generalised Spin Projection for Fermion Actions
The majority of compute time doing lattice QCD is spent inverting the fermion
matrix. The time that this takes increases with the condition number of the
matrix. The FLIC(Fat Link Irrelevant Clover) action displays, among other
properties, an improved condition number compared to standard actions and hence
is of interest due to potential compute time savings. However, due to its two
different link sets there is a factor of two cost in floating point
multiplications compared to the Wilson action. An additional factor of two has
been attributed due to the loss of the so-called spin projection trick. We show
that any split-link action may be written in terms of spin projectors, reducing
the additional cost to at most a factor of two. Also, we review an efficient
means of evaluating the clover term, which is additional expense not present in
the Wilson action.Comment: 4 page
Progress on Perfect Lattice Actions for QCD
We describe a number of aspects in our attempt to construct an approximately
perfect lattice action for QCD. Free quarks are made optimally local on the
whole renormalized trajectory and their couplings are then truncated by
imposing 3-periodicity. The spectra of these short ranged fermions are
excellent approximations to continuum spectra. The same is true for free
gluons. We evaluate the corresponding perfect quark-gluon vertex function,
identifying in particular the ``perfect clover term''. First simulations for
heavy quarks show that the mass is strongly renormalized, but again the
renormalized theory agrees very well with continuum physics. Furthermore we
describe the multigrid formulation for the non-perturbative perfect action and
we present the concept of an exactly (quantum) perfect topological charge on
the lattice.Comment: 14 pages, 17 figures, Talk presented at LATTICE96(improvement
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