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Multiple Mellin-Barnes integrals and triangulations of point configurations | | Sumit Banik
; Samuel Friot
; | | Date: |
1 Sep 2023 | | Abstract: | We present a novel technique for the analytic evaluation of multifold
Mellin-Barnes (MB) integrals, which commonly appear in physics, as for instance
in the calculations of multi-loop multi-scale Feynman integrals. Our approach
is based on triangulating a set of points which can be assigned to a given MB
integral, and yields the final analytic results in terms of linear combinations
of multiple series, each triangulation allowing the derivation of one of these
combinations. When this technique is applied to the computation of Feynman
integrals, the involved series are of the (multivariable) hypergeometric type.
We implement our method in the Mathematica package MBConicHulls.wl, an already
existing software dedicated to the analytic evaluation of multiple MB
integrals, based on a recently developed computational approach using
intersections of conic hulls. The triangulation method is remarkably faster
than the conic hulls approach and can thus be used for the calculation of
higher-fold MB integrals as we show here by computing triangulations for highly
complicated objects such as the off-shell massless scalar one-loop 15-point
Feynman integral whose MB representation has 104 folds. As other applications
we show how this technique can provide new results for the off-shell massless
conformal hexagon and double box Feynman integrals, as well as for the hard
diagram of the two loop hexagon Wilson loop. | | Source: | arXiv, 2309.00409 | | Services: | Forum | Review | PDF | Favorites | |
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