---
res:
bibo_abstract:
- Loop integrals are essential for the computation of predictions in quantum field
theories like the Standard Model of elementary particle physics. For instance,
in the case of anomalous dimensions of QCD or the pressure in thermal QCD we face
so-called tadpole loop integrals. In this thesis we study an important subset
of these integrals, the fully massive vacuum (bubble) integrals. For the first
time, we consider fully massive tadpoles at the 5-loop level pioneering the way
for future high-precision calculations. We have implemented a Laporta algorithm
in the algebraic manipulator \texttt{FORM} using generalized recurrence relations,
a combination of integration-by-parts and space-time dimensional identities. This
enabled us to perform the reduction of fully massive tadpoles up to the 5-loop
level to a basis of master integrals. We modified the implementation in such a
way that difference equations are obtained for a large number of the yet unknown
master integrals. We started to solve the system of difference equations by means
of factorial series expansions.@eng
bibo_authorlist:
- foaf_Person:
foaf_givenName: Jan
foaf_name: Möller, Jan
foaf_surname: Möller
foaf_workInfoHomepage: http://www.librecat.org/personId=7916960
dct_date: 2012^xs_gYear
dct_language: eng
dct_publisher: Universität Bielefeld@
dct_title: 'Fully massive tadpoles at 5-loop : reduction and difference equations@'
...