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Manuscript Title: MATAD: a program package for the computation of MAssive TADpoles.
Authors: M. Steinhauser
Program title: MATAD
Catalogue identifier: ADNG_v1_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 134(2001)335
Programming language: FORM.
Operating system: UNIX, FORM 2.3.
Keywords: Elementary particle physics, QCD, Three-loop computations, Vacuum integrals, Computer algebra, Automation of computations.
Classification: 11.5.

Nature of problem:
Multi-loop integrals are needed for the evaluation of quantum corrections. An important class of loop diagrams is covered by so-called vacuum integrals which have no external momentum. MATAD can analytically compute those one-, two- and three-loop vacuum integrals where one mass scale is present.

Solution method:
The method of integration-by-parts is used in order to obtain recurrence relations which reduce complicated integrals to a small set of so-called master integrals. They have to be evaluated once and for all. In addition a user interface is provided which makes it easy to put in complicated diagrams in a rather compact way.

Restrictions:
The restrictions on the complexity are given by the hardware limitations of the computer and the limits on the size of the storage files inside FORM [1].

Running time:
The runtime strongly depends on the complexity of the diagram under consideration. It may vary from a few seconds to the order of a few weeks.

References:
[1] J.A.M. Vermaseren, Symbolic Manipulation with FORM, (Computer Algebra Netherlands, Amsterdam, 1991).