Speaker
Prof.
Kiyoshi Kato
(Kogakuin Univ.)
Description
For the investigation of physics beyond and within the Standard Model, the precise
evaluation of higher order corrections in perturbative quantum field theory is required.
We have been developing a computational method for Feynman loop integrals with a
fully numerical approach. It is based on a numerical integration techniques and an
extrapolation. In this presentation, we describe the status and new
developments in our approaches for the numerical computation of Feynman loop
integrals up to four loops.
Founded on underlying asymptotic error expansions, extrapolation and transformation
methods allow for accurate automatic evaluation of Feynman loop integrals in
the presence of integration difficulties such as boundary singularities. These
techniques include linear and non-linear extrapolations, and double exponential and
other transformations. Iterated one-dimensional integration with extrapolation
has provided good accuracy for low-dimensional problems, such as for an ultra-violet
2-loop vertex diagram that gives rise to a 3-dimensional integral.
We are further focusing on improving the efficiency of these computations with respect
to speed as well as precision. For accelerating the performance we have used the
transparent and portable approach for multivariate integration offered by the
parallel/distributed package ParInt, layered over MPI message passing for execution
on a cluster, which implements a variety of methods and also comes with a quadruple
(C long double) precision version. Alternatively, excellent speedups and precision
have been obtained using dedicated hardware acceleration on double exponential/
trapezoidal rule sum approximations. Multivariate integration results will be included
for 3- and 4-loop self-energy diagrams.
Author
Prof.
Kiyoshi Kato
(Kogakuin Univ.)
Co-authors
Prof.
Elise de Doncker
(Western Michigan University)
Prof.
Fukuko Yuasa
(KEK)
Prof.
John Kapenga
(Western Michigan University)
Ms
O. Olagbemi
(Western Michigan University)
Prof.
Tadashi Ishikawa
(KEK)
