Speaker
Description
FeynCalc is esteemed by many particle theorists as a very
useful tool for tackling symbolic Feynman diagram calculations
with a great amount of transparency and flexibility.
While the program enjoys an excellent reputation
when it comes to tree level and 1-loop calculations,
the usefulness of FeynCalc in multi-loop projects is
often doubted by the practitioners.
In this talk I will report on the upcoming version
of the package aiming to address
these shortcomings. In particular, FeynCalc 10
will introduce a number of new routines that facilitate
two very important steps of almost every multi-loop calculation.
The first one concerns the identification of the occurring
multi-loop topologies including the minimization of their
number by finding suitable mappings between integral families.
The second one deals with the handling (visualization,
expansions, analytic evaluation) of master integrals
obtained after a successful IBP reduction of multiple
integral families.
In FeynCalc 10 these nontrivial operations are implemented
in the form of versatile and easy-to-use functions such as
FCLoopFindTopologyMappings, FCLoopIntegralToGraph or
FCFeynmanParametrize etc. that will be introduced in my
presentation.
Significance
The task of identifying and minimizing the number of loop
integral topologies addressed in my talk is not something
sufficiently well covered by the publicly available software, although the relevant algorithms are available since long time
(cf. https://arxiv.org/abs/1111.0868 and in particular
and https://doi.org/10.5445/IR/1000047447). Here multi-loop practitioners tend to rely on their private codes (e.g. q2e/exp from KIT) or Reduze 2 which, however, often lacks the desired flexibility.
The ability to carry out this crucial step of virtually every
multi-loop calculation using FeynCalc is, therefore, a large
step forwards towards the goal of making such calculations
accessible to numerous HEP theorists instead of
a small number of specialized research groups.
This goes hand in hand with the second main aspect of my
talk that discusses useful manipulations of master integrals
using FeynCalc. This includes not only the derivation
of Feynman parametrizations suitable for analytic integration
and evaluation in terms of GPLs (e.g. using HyperInt or
PolyLogTools) but also the visualization of the integrals
by converting them from propagator into graph representation
(cf. https://github.com/FeynCalc/feyncalc/blob/master/FeynCalc/DocumentationFiles/Markdown/FCLoopGraphPlot.md for some examples of what is already possible) and of course mappings between masters from different integral families.
On the one hand, the new multi-loop capabilities of FeynCalc
make use of many ideas from FIRE, LiteRed, pySecDec, TopoID and of course Alexey Pak. On the other hand, having all these routines available at a fingertip in a unified framework
(including documentation and examples) significantly lowers
the bar for nonexperts to embark on multi-loop calculations.
In this sense the presented work has great potential
to challenge the status quo in the field of higher order
perturbative calculations, where only selected groups
possess the technical know how required for an efficient
evaluation of Feynman diagrams beyond 1-loop.
References
Previous publications on FeynCalc with my name in the list of authors.
https://arxiv.org/abs/1601.01167
https://arxiv.org/abs/1611.06793
https://arxiv.org/abs/2001.04407
https://arxiv.org/abs/2006.15451
| Speaker time zone | Compatible with Europe |
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