FCLoopScalelessQ[int, {p1, p2, ...}]
checks whether the loop integral int
depending on the loop momenta p1, p2, ...
is scaleless. Only integrals that admit a Feynman parametrization with proper and polynomials are supported.
The function uses the algorithm of Alexey Pak arXiv:1111.0868. Cf. also the PhD thesis of Jens Hoff 10.5445/IR/1000047447 for the detailed description of a possible implementation.
Overview, FCTopology, GLI, FCLoopToPakForm, FCLoopPakOrder, FCLoopScalelessQ.
A scaleless 2-loop tadpole
[FAD[p1, p2, p1 - p2], {p1, p2}] FCLoopScalelessQ
A 1-loop massless eikonal integral.
[SFAD[{{0, 2 p . q}, 0}, p], {p}] FCLoopScalelessQ
A 1-loop massive eikonal integral.
[SFAD[{{0, 2 p . q}, 0}, p], {p}] FCLoopScalelessQ
A scaleless topology
[topo, {SFAD[{{I p3, 0}, {0, 1}, 1}], SFAD[{{I p1, 0}, {0, 1}, 1}],
FCTopology[{{0, -2 p1 . q}, {0, 1}, 1}], SFAD[{{I p3 + I q, 0}, {-mb^2, 1}, 1}],
SFAD[{{0, p1 . p3}, {0, 1}, 1}]}, {p1, p3}, {q}, {}, {}]
SFAD
[%] FCLoopScalelessQ