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SUMMARY:Numerical Evaluation of Feynman Integrals Using Positivity Propert
 ies
DTSTART:20260428T120000Z
DTEND:20260428T130000Z
DTSTAMP:20260426T073600Z
UID:indico-event-102@indico.zdv.uni-mainz.de
DESCRIPTION:Speakers: Prashanth Raman (MPI for Physics)\n\nPositivity prop
 erties in quantum field theory provide powerful constraints on observables
 \, often reflecting underlying principles such as unitarity and analyticit
 y. In this talk\, we explore two related notions of positivity: complete m
 onotonicity (CM)\, where an observable and all its signed derivatives rema
 in positive\, and its refinement\, the Stieltjes property. These positivit
 y properties impose infinitely many constraints on functions and have rece
 ntly been shown to arise in a wide range of quantum field theory observabl
 es\, including scalar Feynman integrals in the Euclidean region\, tree-lev
 el string amplitudes\, and 2–2 scattering amplitudes satisfying dispersi
 on relations.After introducing these positivity properties\, we will focus
  on scalar Feynman integrals\, discussing in detail how these properties f
 ollow from parametric representations and under what conditions they hold.
  We will then present two novel approaches to leveraging these properties 
 for the numerical evaluation of multi-loop Feynman integrals. The first ap
 proach combines the differential equations satisfied by Feynman integrals 
 with CM constraints to formulate a convex optimization problem. Implemente
 d as a linear program\, this allows us to numerically bootstrap integral v
 alues with high precision in the Euclidean region. The second approach use
 s the Stieltjes property to construct efficient rational approximations vi
 a Padé approximants\, which converge across the cut complex plane and ena
 ble high-precision evaluation in physical kinematics. Finally\, we will pr
 esent examples and\, time permitting\, discuss how this framework leads to
  rational approximations of certain transcendental functions.\n\nhttps://i
 ndico.zdv.uni-mainz.de/event/102/
LOCATION:R. 05-127 (Lorentz-Room)
URL:https://indico.zdv.uni-mainz.de/event/102/
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