Two-loop Feynman integrals involve Riemann spheres, elliptic curves, hyperelliptic curves of genus 2 and 3, K3 surfaces, and a rationalizable Del Pezzo surface of degree 2.
Algorithms for minimal Picard–Fuchs operators of Feynman integrals,
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The paper develops reduction operators from resonance in GKZ systems to contract edges in Feynman graphs for one-loop, sunrise, and banana graphs, closing differential equation systems to master integrals.
An extension of the Griffiths-Dwork algorithm produces twisted Picard-Fuchs operators for hypergeometric, elliptic, and Calabi-Yau motives from families of Feynman integrals.
The extra-involution mechanism for genus drop is a special case of unramified double covering between curves, which explains genus drops with non-hyperelliptic to hyperelliptic transitions in certain three-loop Feynman integrals.
The report reviews progress since 2021 in fixed-order computations for LHC applications and identifies processes requiring missing higher-order corrections to match anticipated experimental precision.
citing papers explorer
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The spectrum of Feynman-integral geometries at two loops
Two-loop Feynman integrals involve Riemann spheres, elliptic curves, hyperelliptic curves of genus 2 and 3, K3 surfaces, and a rationalizable Del Pezzo surface of degree 2.
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Resonance and Differential Reduction of Feynman Integrals
The paper develops reduction operators from resonance in GKZ systems to contract edges in Feynman graphs for one-loop, sunrise, and banana graphs, closing differential equation systems to master integrals.
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Picard-Fuchs Equations of Twisted Differential forms associated to Feynman Integrals
An extension of the Griffiths-Dwork algorithm produces twisted Picard-Fuchs operators for hypergeometric, elliptic, and Calabi-Yau motives from families of Feynman integrals.
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Genus drop involving non-hyperelliptic curves in Feynman integrals
The extra-involution mechanism for genus drop is a special case of unramified double covering between curves, which explains genus drops with non-hyperelliptic to hyperelliptic transitions in certain three-loop Feynman integrals.
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Les Houches 2023 -- Physics at TeV Colliders: Report on the Standard Model Precision Wishlist
The report reviews progress since 2021 in fixed-order computations for LHC applications and identifies processes requiring missing higher-order corrections to match anticipated experimental precision.