Speaker
Prof.
Toshiaki Kaneko
(KEK)
Description
Numerically stable analytic expression of a one-loop integration
is one of the most important elements of the accurate
calculations of one-loop corrections to the physical processes.
It is known that these integrations are expressed by some
generalized classes of Gauss hypergeometric functions. Power
series expansions, differential equations, contiguous and many
other identities are known for them. For Lauricella $F_D$
functions, analytic properties are studied in detail, which
provide useful information for the numerical stabilities.
We show that two- and three-point functions are exactly expressed
in terms of $F_D$ for arbitrary combinations of mass parameters
in any space-time dimensions. We also show the relation between
four-point functions and Aomoto-Gelfand hypergeometric functions.
Primary author
Prof.
Toshiaki Kaneko
(KEK)
