254,338 research outputs found
Improved correlation dimension calculation
For many chaotic systems, accurate calculation of the correlation dimension from measured data is difficult because of very slow convergence as the scale size is reduced. This problem is often caused by the highly nonuniform measure on the attractor. This paper proposes a method for collecting data at large scales and extrapolating to the limit of zero scale. The result is a vastly reduced required number of data points for a given accuracy in the measured dimension. The method is illustrated in detail for one-dimensional maps and then applied to more complicated maps and flows. Values are given for the correlation dimension of many standard chaotic systems
Light Hadron Weak Matrix Elements
I review this year's developments in the study of weak matrix elements of
light hadrons on the lattice, with emphasis on K^0-\bar K^0 mixing and K -> pi
pi decays.Comment: Lattice 2000 (Plenary), 17 pages (LaTeX), 6 postscript figures;
plenary talk at 18th International Symposium on Lattice Field Theory (Lattice
2000), Bangalore, India, 17-22 Aug 200
Improved Renormalization of Lattice Operators: A Critical Reappraisal
We systematically examine various proposals which aim at increasing the
accuracy in the determination of the renormalization of two-fermion lattice
operators. We concentrate on three finite quantities which are particularly
suitable for our study: the renormalization constants of the vector and axial
currents and the ratio of the renormalization constants of the scalar and
pseudoscalar densities. We calculate these quantities in boosted perturbation
theory, with several running boosted couplings, at the "optimal" scale q*. We
find that the results of boosted perturbation theory are usually (but not
always) in better agreement with non-perturbative determinations of the
renormalization constants than those obtained with standard perturbation
theory. The finite renormalization constants of two-fermion lattice operators
are also obtained non-perturbatively, using Ward Identities, both with the
Wilson and the tree-level Clover improved actions, at fixed cutoff (=6.4
and 6.0 respectively). In order to amplify finite cutoff effects, the quark
masses (in lattice units) are varied in a large interval 0<am<1. We find that
discretization effects are always large with the Wilson action, despite our
relatively small value of the lattice spacing ( GeV). With
the Clover action discretization errors are significantly reduced at small
quark mass, even though our lattice spacing is larger ( GeV).
However, these errors remain substantial in the heavy quark region. We have
implemented a proposal for reducing O(am) effects, which consists in matching
the lattice quantities to their continuum counterparts in the free theory. We
find that this approach still leaves appreciable, mass dependent,
discretization effects.Comment: 54 pages, Latex, 5 figures. Minor changes in text between eqs.(86)
and (88
Lattice calculation of SU(3) flavor breaking ratios in B - anti-B mixing
We present an unquenched lattice calculation for the SU(3) flavor breaking
ratios of the heavy-light decay constants and the matrix
elements. The calculation was performed on lattices with two
dynamical flavors of domain-wall quarks and inverse lattice spacing GeV. Heavy quarks were implemented using an improved lattice
formulation of the static approximation. In the infinite heavy-quark mass limit
we obtain , , where the first error is statistical and the second systematic.Comment: 23 pages, 8 figures, RevTeX4; mentioned existence of 1/m_b
corrections, minor changes improving readabilit
Kaon Distribution Amplitude from QCD Sum Rules
We present a new calculation of the first Gegenbauer moment of the
kaon light-cone distribution amplitude. This moment is determined by the
difference between the average momenta of strange and nonstrange valence quarks
in the kaon. To calculate , QCD sum rule for the diagonal correlation
function of local and nonlocal axial-vector currents is used. Contributions of
condensates up to dimension six are taken into account, including
-corrections to the quark-condensate term. We obtain
, differing by the sign and magnitude from the recent
sum-rule estimate from the nondiagonal correlation function of pseudoscalar and
axial-vector currents. We argue that the nondiagonal sum rule is numerically
not reliable. Furthermore, an independent indication for a positive is
given, based on the matching of two different light-cone sum rules for the
form factor. With the new interval of we update our previous
numerical predictions for SU(3)-violating effects in form
factors and charmless (B) decays.Comment: a comment and a reference added, version to appear in Phys.Rev.D, 17
pages, 7 figure
Infinite disorder scaling of random quantum magnets in three and higher dimensions
Using a very efficient numerical algorithm of the strong disorder
renormalization group method we have extended the investigations about the
critical behavior of the random transverse-field Ising model in three and four
dimensions, as well as for Erd\H os-R\'enyi random graphs, which represent
infinite dimensional lattices. In all studied cases an infinite disorder
quantum critical point is identified, which ensures that the applied method is
asymptotically correct and the calculated critical exponents tend to the exact
values for large scales. We have found that the critical exponents are
independent of the form of (ferromagnetic) disorder and they vary smoothly with
the dimensionality.Comment: 6 pages, 5 figure
Renormalization Constants of Quark Operators for the Non-Perturbatively Improved Wilson Action
We present the results of an extensive lattice calculation of the
renormalization constants of bilinear and four-quark operators for the
non-perturbatively O(a)-improved Wilson action. The results are obtained in the
quenched approximation at four values of the lattice coupling by using the
non-perturbative RI/MOM renormalization method. Several sources of systematic
uncertainties, including discretization errors and final volume effects, are
examined. The contribution of the Goldstone pole, which in some cases may
affect the extrapolation of the renormalization constants to the chiral limit,
is non-perturbatively subtracted. The scale independent renormalization
constants of bilinear quark operators have been also computed by using the
lattice chiral Ward identities approach and compared with those obtained with
the RI-MOM method. For those renormalization constants the non-perturbative
estimates of which have been already presented in the literature we find an
agreement which is typically at the level of 1%.Comment: 36 pages, 13 figures. Minor changes in the text and in one figure.
Accepted for publication on JHE
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