We introduce the Mathematica package MT which can be used to compute, both analytically and numerically, convolutions involving harmonic polylogarithms, polynomials or generalized functions. As applications contributions to next-to-next-to-next-to leading order Higgs boson production and the Drell-Yan process are discussed.
Program summary
Title of program: MT
Available from: http://www-ttp.physik.uni-karlsruhe.de/Progdata/ttp13/ttp13-27/
Computer for which the program is designed and others on which it is operable: Any computer where Mathematica version 6 or higher is running.
Operating system or monitor under which the program has been tested: Linux
No. of bytes in distributed program including test data etc.: approximately 50 000 bytes, and tables of approximately 60 megabytes
Distribution format: source code
Keywords: Convolution of partonic cross sections and splitting functions, Mellin transformation, harmonic sums, harmonic polylogarithms, Higgs boson production, Drell-Yan process
Nature of physical problem:
For the treatment of collinear divergences connected to initial-state radiation it is necessary to consider convolutions of partonic cross sections with splitting functions. MT can be used to compute such convolutions.
Method of solution:
MT is implemented in Mathematica and we provide several functions in order to perform transformations to Mellin space, manipulation's of the expressions, and inverse Mellin transformations.
Restrictions on the complexity of the problem:
In case the weight of the input quantities is too high the tables for the (inverse) Mellin transforms have to be extended. In the current implementation the tables contain expressions up to weight eight, code for the generation of tables of even higher weight is provided, too.
MT can only handle convolutions of expressions involving harmonic polylogarithms, plus distributions and polynomials in the partonic variable x.
Typical running time:
In general the run time for the individual operations is at most of the order of a few minutes (depending on the speed and memory of the computer). (C) 2013 Elsevier B.V. All rights reserved.