6 research outputs found
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 decays almost
exclusively to pairs of and bosons. We calculate the dominant two-loop
corrections of to the partial widths of these decays. In
the on-mass-shell renormalization scheme, the correction factor is found to be
, 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