XLOOPS
XLOOPS is a package for automated calculation of
1- and 2-loop radiative corrections in Particle Physics.
Visit its own homepage
here.
Its recently completed manual is
available (html).
Its functionality under Maple was rather restricted, and so it
is currently reconstructed to run under
GiNaC, which can help you also
with many other problems.
Xloops focuses around the idea of doing Feynman integrals
in terms of parallel- and orthogonal space variables.
Any Green function is a function of several
external momenta. Thus, measures for integration
of internal loop momoneta can be split into separate
integrations in two disjoint vector spaces.
We define a parallel space as the linear span of all
external momenta. It is a finite dimensional vector space.
Internal loop momenta decompose into components in the parallel space
and its orthogonal complement in a Lorentz covariant manner.
Every scalar product between a an internal loop
momentum k and an external momentum q remains unchanged when we
replace the internal momentum by its parallel space component,
while the scalar product between an external momentum q and the
orthogonal part of k
vanishes.
This decomposition of internal loop momenta into two orthogonal
subspaces carries through to the associated Clifford algebra.
The two corresponding algebras anticommute,
and thus any string of gamma-matrices can be written
as a series of terms, with a natural expansion in terms
of invariants provided by the basis in the Clifford algebra.
Traces on such expressions are trivial, and this enables Xloops
to discard the use of sophisticated "High Energy Packages"
altogether. Also, the usual form-factor decompositions are obtained
in this setup naurally.
Further, any Green-function now becomes a polynomial
in orthogonal and parallel space variables (P-O variables).
There is no need to apply a Passarino-Veltman type tensor decomposition,
as the obtained polynomial in P-O variables is directly used
as the integral representation.
This is the big advantage coming from what could be called the
naturality of P-O variables.
For one-loop integrals, we then use the fact that after a few
appropriate residue integrations, one-loop 2-,3- and 4-point
functions provide integral representations of Rfunctions.
We then utilize recursion relations on these functions
to generate the Xloops library. Finally, Xloops knows how
to translate these functions into the more familiar hypergeometrics,
and offers the user a variety of ways to express the final result.
At the two-loop level massive Green functions exceed the
standard special functions of mathematical physics considerably.
Xloops provides two-fold integral representations in terms of P-O
variables in such cases, covering all relevant two- and three-point functions.
Xloops also enables the user to start a numerical routine
to evaluate these functions. It uses a parallelized version of
VEGAS, developped here in Mainz by
Richard Kreckel.
Add to this the generation of Feynman graphs at the one- and two-loop level
for a given process, and you see that XLOOPS provides a fully automated calculation
of radiative corrections up to the two-loop level.
XLOOPS supports the Standard Model and related theories, and enables the user to provide
his own Feynman rules.
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