Explicit results for all orders of the epsilon-expansion of certain massive and massless diagrams

An arbitrary term of the epsilon-expansion of dimensionally regulated off-shell massless one-loop three-point Feynman diagram is expressed in terms of log-sine integrals related to the polylogarithms. Using magic connection between these diagrams and two-loop massive vacuum diagrams, the epsilon-expansion of the latter is also obtained, for arbitrary values of the masses. The problem of analytic continuation is also discussed.Comment: 8 pages, late

A magic connection between massive and massless diagrams

A useful connection between two-loop massive vacuum integrals and one-loop off-shell triangle diagrams with massless internal particles is established for arbitrary values of the space-time dimension n.Comment: 11 pages, plain latex, 1 figure (in latex); ps file available by anonymous ftp at ftp://vsfys1.fi.uib.no/anonymous/pub/bergen95-07.p

Numerical evaluation of loop integrals

We present a new method for the numerical evaluation of arbitrary loop integrals in dimensional regularization. We first derive Mellin-Barnes integral representations and apply an algorithmic technique, based on the Cauchy theorem, to extract the divergent parts in the epsilon->0 limit. We then perform an epsilon-expansion and evaluate the integral coefficients of the expansion numerically. The method yields stable results in physical kinematic regions avoiding intricate analytic continuations. It can also be applied to evaluate both scalar and tensor integrals without employing reduction methods. We demonstrate our method with specific examples of infrared divergent integrals with many kinematic scales, such as two-loop and three-loop box integrals and tensor integrals of rank six for the one-loop hexagon topology

Heavy-Higgs Lifetime at Two Loops

The Standard-Model Higgs boson with mass $M_H >> 2M_Z$ decays almost exclusively to pairs of $W$ and $Z$ bosons. We calculate the dominant two-loop corrections of $O( G_F^2 M_H^4 )$ to the partial widths of these decays. In the on-mass-shell renormalization scheme, the correction factor is found to be $1 + 14.6$, where the second term is the one-loop correction. We give full analytic results for all divergent two-loop Feynman diagrams. A subset of finite two-loop vertex diagrams is computed to high precision using numerical techniques. We find agreement with a previous numerical analysis. The above correction factor is also in line with a recent lattice calculation.Comment: 26 pages, 6 postscript figures. The complete paper including figures is also available via WWW at http://www.physik.tu-muenchen.de/tumphy/d/T30d/PAPERS/TUM-HEP-247-96.ps.g

Calculation of Feynman Diagrams from their Small Momentum Expansion

A new powerful method to calculate Feynman diagrams is proposed. It consists in setting up a Taylor series expansion in the external momenta squared (in general multivariable). The Taylor coefficients are obtained from the original diagram by differentiation and putting the external momenta equal to zero, which means a great simplification. It is demonstrated that it is possible to obtain by analytic continuation of the original series high precision numerical values of the Feynman integrals in the whole cut plane. For this purpose conformal mapping and subsequent resummation by means of Pad\'{e} approximants or Levin transformation are applied.Comment: 21 pages, Bielefeld Unviersity preprint BI-TP %%93-7