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

Four-dimensional integration by parts with differential renormalization as a method of evaluation of Feynman diagrams

It is shown how strictly four-dimensional integration by parts combined with differential renormalization and its infrared analogue can be applied for calculation of Feynman diagrams.Comment: 6 pages, late

Bimaximal Neutrino Mixing with Discrete Flavour Symmetries

In view of the fact that the data on neutrino mixing are still compatible with a situation where Bimaximal mixing is valid in first approximation and it is then corrected by terms of order of the Cabibbo angle, we present examples where these properties are naturally realized. The models are supersymmetric in 4-dimensions and based on the discrete non-Abelian flavour symmetry S4.Comment: 8 pages, 1 figure; contribution prepared for DISCRETE'10 - Symposium on Prospects in the Physics of Discrete Symmetrie

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

Enhancing the conductance of a two-electron nanomechanical oscillator

We consider electron transport through a mobile island (i.e., a nanomechanical oscillator) which can accommodate one or two excess electrons and show that, in contrast to immobile islands, the Coulomb blockade peaks, associated with the first and second electrons entering the island, have different functional dependences on the nano-oscillator parameters when the island coupling to its leads is asymmetric. In particular, the conductance for the second electron (i.e., when the island is already charged) is greatly enhanced in comparison to the conductance of the first electron in the presence of an external electric field. We also analyze the temperature dependence of the two conduction peaks and show that these exhibit different functional behaviors.Comment: 16 pages, 5 figure

Asymptotic Bound-state Model for Feshbach Resonances

We present an Asymptotic Bound-state Model which can be used to accurately describe all Feshbach resonance positions and widths in a two-body system. With this model we determine the coupled bound states of a particular two-body system. The model is based on analytic properties of the two-body Hamiltonian, and on asymptotic properties of uncoupled bound states in the interaction potentials. In its most simple version, the only necessary parameters are the least bound state energies and actual potentials are not used. The complexity of the model can be stepwise increased by introducing threshold effects, multiple vibrational levels and additional potential parameters. The model is extensively tested on the 6Li-40K system and additional calculations on the 40K-87Rb system are presented.Comment: 13 pages, 8 figure

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 $U(1)\times U(1)$ 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.

Two-Loop Iteration of Five-Point N=4 Super-Yang-Mills Amplitudes

We confirm by explicit computation the conjectured all-orders iteration of planar maximally supersymmetric N=4 Yang-Mills theory in the nontrivial case of five-point two-loop amplitudes. We compute the required unitarity cuts of the integrand and evaluate the resulting integrals numerically using a Mellin--Barnes representation and the automated package of ref.~[1]. This confirmation of the iteration relation provides further evidence suggesting that N=4 gauge theory is solvable.Comment: 4 pages, 3 figure

Scaling Limit and Critical Exponents for Two-Dimensional Bootstrap Percolation

Consider a cellular automaton with state space $\{0,1 \}^{{\mathbb Z}^2}$ where the initial configuration $\omega_0$ is chosen according to a Bernoulli product measure, 1's are stable, and 0's become 1's if they are surrounded by at least three neighboring 1's. In this paper we show that the configuration $\omega_n$ at time n converges exponentially fast to a final configuration $\bar\omega$, and that the limiting measure corresponding to $\bar\omega$ is in the universality class of Bernoulli (independent) percolation. More precisely, assuming the existence of the critical exponents $\beta$, $\eta$, $\nu$ and $\gamma$, and of the continuum scaling limit of crossing probabilities for independent site percolation on the close-packed version of ${\mathbb Z}^2$ (i.e., for independent $*$-percolation on ${\mathbb Z}^2$), we prove that the bootstrapped percolation model has the same scaling limit and critical exponents. This type of bootstrap percolation can be seen as a paradigm for a class of cellular automata whose evolution is given, at each time step, by a monotonic and nonessential enhancement.Comment: 15 page

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