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SUMMARY:A recursive structure for the \\eps-expansion of scalar one-loop i
 ntegrals
DTSTART:20260610T090000Z
DTEND:20260610T110000Z
DTSTAMP:20260609T054400Z
UID:indico-event-1518@indico.hiskp.uni-bonn.de
DESCRIPTION:Speakers: Paul Mork (Uni Bonn)\n\nScalar one-loop Feynman inte
 grals admit a geometric interpretation at \\eps=0 as volumes of simplices 
 in hyperbolic space\, which are known in terms of multiple polylogarithms 
 (MPLs). A natural question is how to compute the higher-order coefficients
  in the \\eps-expansion of dimensionally regularised scalar one-loop integ
 rals.\nIn this talk I discuss two complementary approaches to this problem
 . I briefly review a direct integration approach yielding MPL representati
 ons for triangle\, box and pentagon integrals with arbitrary masses and ki
 nematics. Afterwards\, I present a recursive relation connecting the Laure
 nt coefficients of an N-point integral to lower-order coefficients of inte
 grals with more external legs.\nSeeded by the corresponding integer-dimens
 ional contributions\, this recursion can then be iterated to arbitrary ord
 er in \\eps\, implying that every coefficient in the Laurent expansion of 
 a dimensionally regularised scalar one-loop integral can be expressed in t
 erms of MPLs.\n\nhttps://indico.hiskp.uni-bonn.de/event/1518/
URL:https://indico.hiskp.uni-bonn.de/event/1518/
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