16,614 research outputs found
Analytic Results for Massless Three-Loop Form Factors
We evaluate, exactly in d, the master integrals contributing to massless
three-loop QCD form factors. The calculation is based on a combination of a
method recently suggested by one of the authors (R.L.) with other techniques:
sector decomposition implemented in FIESTA, the method of Mellin--Barnes
representation, and the PSLQ algorithm. Using our results for the master
integrals we obtain analytical expressions for two missing constants in the
ep-expansion of the two most complicated master integrals and present the form
factors in a completely analytic form.Comment: minor revisions, to appear in JHE
Q2237+0305 source structure and dimensions from light curves simulation
Assuming a two-component quasar structure model consisting of a central
compact source and an extended outer feature, we produce microlensing
simulations for a population of star-like objects in the lens galaxy. Such a
model is a simplified version of that adopted to explain the brightness
variations observed in Q0957 (Schild & Vakulik 2003). The microlensing light
curves generated for a range of source parameters were compared to the light
curves obtained in the framework of the OGLE program. With a large number of
trials we built, in the domain of the source structure parameters, probability
distributions to find "good" realizations of light curves. The values of the
source parameters which provide the maximum of the joint probability
distribution calculated for all the image components, have been accepted as
estimates for the source structure parameters. The results favour the
two-component model of the quasar brightness structure over a single compact
central source model, and in general the simulations confirm the Schild-Vakulik
model that previously described successfully the microlensing and other
properties of Q0957. Adopting 3300 km/s for the transverse velocity of the
source, the effective size of the central source was determined to be about
2x10^15 cm, and Epsilon =2 was obtained for the ratio of the integral
luminosity of the outer feature to that of the central source.Comment: 7 pages, 4 figures, LaTe
Monte Carlo Tests of SLE Predictions for the 2D Self-Avoiding Walk
The conjecture that the scaling limit of the two-dimensional self-avoiding
walk (SAW) in a half plane is given by the stochastic Loewner evolution (SLE)
with leads to explicit predictions about the SAW. A remarkable
feature of these predictions is that they yield not just critical exponents,
but probability distributions for certain random variables associated with the
self-avoiding walk. We test two of these predictions with Monte Carlo
simulations and find excellent agreement, thus providing numerical support to
the conjecture that the scaling limit of the SAW is SLE.Comment: TeX file using APS REVTeX 4.0. 10 pages, 5 figures (encapsulated
postscript
Two-Loop Sudakov Form Factor in a Theory with Mass Gap
The two-loop Sudakov form factor is computed in a U(1) model with a massive
gauge boson and a model with mass gap. We analyze the result
in the context of hard and infrared evolution equations and establish a
matching procedure which relates the theories with and without mass gap setting
the stage for the complete calculation of the dominant two-loop corrections to
electroweak processes at high energy.Comment: Latex, 5 pages, 2 figures. Bernd Feucht is Bernd Jantzen in later
publications. (The contents of the paper is unchanged.
Raising and lowering operators, factorization and differential/difference operators of hypergeometric type
Starting from Rodrigues formula we present a general construction of raising
and lowering operators for orthogonal polynomials of continuous and discrete
variable on uniform lattice. In order to have these operators mutually adjoint
we introduce orthonormal functions with respect to the scalar product of unit
weight. Using the Infeld-Hull factorization method, we generate from the
raising and lowering operators the second order self-adjoint
differential/difference operator of hypergeometric type.Comment: LaTeX, 24 pages, iopart style (late submission
Computing the Loewner driving process of random curves in the half plane
We simulate several models of random curves in the half plane and numerically
compute their stochastic driving process (as given by the Loewner equation).
Our models include models whose scaling limit is the Schramm-Loewner evolution
(SLE) and models for which it is not. We study several tests of whether the
driving process is Brownian motion. We find that just testing the normality of
the process at a fixed time is not effective at determining if the process is
Brownian motion. Tests that involve the independence of the increments of
Brownian motion are much more effective. We also study the zipper algorithm for
numerically computing the driving function of a simple curve. We give an
implementation of this algorithm which runs in a time O(N^1.35) rather than the
usual O(N^2), where N is the number of points on the curve.Comment: 20 pages, 4 figures. Changes to second version: added new paragraph
to conclusion section; improved figures cosmeticall
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