Semi-numerical resummation of event shapes

For many event-shape observables, the most difficult part of a resummation in the Born limit is the analytical treatment of the observable's dependence on multiple emissions, which is required at single logarithmic accuracy. We present a general numerical method, suitable for a large class of event shapes, which allows the resummation specifically of these single logarithms. It is applied to the case of the thrust major and the oblateness, which have so far defied analytical resummation and to the two-jet rate in the Durham algorithm, for which only a subset of the single logs had up to now been calculated.Comment: 29 pages, 7 figures. Version 2 adds some clarifications, a reference, as well as corrections to the subleading fixed-order coefficients and to figures 4 and

Implementation of the Combined--Nonlinear Condensation Transformation

We discuss several applications of the recently proposed combined nonlinear-condensation transformation (CNCT) for the evaluation of slowly convergent, nonalternating series. These include certain statistical distributions which are of importance in linguistics, statistical-mechanics theory, and biophysics (statistical analysis of DNA sequences). We also discuss applications of the transformation in experimental mathematics, and we briefly expand on further applications in theoretical physics. Finally, we discuss a related Mathematica program for the computation of Lerch's transcendent.Comment: 23 pages, 1 table, 1 figure (Comput. Phys. Commun., in press

An algorithm for the rapid numerical evaluation of Bessel functions of real orders and arguments

We describe a method for the rapid numerical evaluation of the Bessel functions of the first and second kinds of nonnegative real orders and positive arguments. Our algorithm makes use of the well-known observation that although the Bessel functions themselves are expensive to represent via piecewise polynomial expansions, the logarithms of certain solutions of Bessel's equation are not. We exploit this observation by numerically precomputing the logarithms of carefully chosen Bessel functions and representing them with piecewise bivariate Chebyshev expansions. Our scheme is able to evaluate Bessel functions of orders between $0$ and 1\sep,000\sep,000\sep,000 at essentially any positive real argument. In that regime, it is competitive with existing methods for the rapid evaluation of Bessel functions and has several advantages over them. First, our approach is quite general and can be readily applied to many other special functions which satisfy second order ordinary differential equations. Second, by calculating the logarithms of the Bessel functions rather than the Bessel functions themselves, we avoid many issues which arise from numerical overflow and underflow. Third, in the oscillatory regime, our algorithm calculates the values of a nonoscillatory phase function for Bessel's differential equation and its derivative. These quantities are useful for computing the zeros of Bessel functions, as well as for rapidly applying the Fourier-Bessel transform. The results of extensive numerical experiments demonstrating the efficacy of our algorithm are presented. A Fortran package which includes our code for evaluating the Bessel functions as well as our code for all of the numerical experiments described here is publically available

Automation of the Dipole Subtraction Method in MadGraph/MadEvent

We present the implementation of the dipole subtraction formalism for the real radiation contributions to any next-to-leading order QCD process in the MadGraph/MadEvent framework. Both massless and massive dipoles are considered. Starting from a specific (n+1)-particle process the package provides a Fortran code for all possible dipoles to all Born processes that constitute the subtraction term to the (n+1)-particle process. The output files are given in the usual "MadGraph StandAlone" style using helicity amplitudes.Comment: 14 pages, 4 figure