Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2006-01-20
Nucl.Phys.B742:208-229,2006
Physics
High Energy Physics
High Energy Physics - Phenomenology
27 pages, 3 figures, a citation is added, final version
Scientific paper
10.1016/j.nuclphysb.2006.02.030
It is shown that for every problem within dimensional regularization, using the Integration-By-Parts method, one is able to construct a set of master integrals such that each corresponding coefficient function is finite in the limit of dimension equal to four. We argue that the use of such a basis simplifies and stabilizes the numerical evaluation of the master integrals. As an example we explicitly construct the ep-finite basis for the set of all QED-like four-loop massive tadpoles. Using a semi-numerical approach based on Pade approximations we evaluate analytically the divergent and numerically the finite part of this set of master integrals. The calculations confirm the recent results of Schr\"oder and Vuorinen. All the contributions found there by fitting the high precision numerical results have been confirmed by direct analytical calculation without using any numerical input.
Chetyrkin K. G.
Faisst M.
Sturm Chris
Tentyukov Mikhail
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