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SUMMARY:Feynman integral reduction using syzygy-constrained symbolic reduc
 tion rules - Sid Smith (U. Padua\, Dept. Phys. Astron.)
DTSTART:20251205T160000Z
DTEND:20251205T170000Z
UID:TALK240583@talks.cam.ac.uk
CONTACT:Terry Generet
DESCRIPTION:We present a new algorithm for integration-by-parts (IBP) redu
 ction of Feynman integrals with high powers of numerators or propagators\,
  a demanding computational step in evaluating multi-loop scattering amplit
 udes. The algorithm starts with solving syzygy equations in individual sec
 tors to produce IBP operators that turn seed integrals into IBP equations 
 without artificially raised propagator powers. The IBP operators are\nexpr
 essed in terms of index-shift operators and number operators. We perform r
 ow reduction to systematically reshuffle the IBP operators and expose redu
 ction rules with symbolic dependence on the powers of propagators and nume
 rators. When this is insufficient\, we produce more symbolic reduction rul
 es by directly solving the linear system of IBP equations in which some pr
 opagator/numerator powers are kept symbolic. This linear system is kept sm
 all\, as the equations are generated from a small set of seed integrals in
  the neighborhood of the target integral. We stress-test our algorithm aga
 inst two highly non-trivial examples\, namely rank-20 integrals for the do
 uble box with an external mass and the massless pentabox. As an applicatio
 n\, we revisit the IBP reduction in a calculation of scattering amplitudes
  for spinning black hole binary systems\, which involves two-loop Feynman 
 integrals with complexity greater than 20\, and achieve much faster IBP re
 duction than that of the original calculation.
LOCATION:MR19 (Potter Room\, Pavilion B)\, CMS
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