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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A geometric order relation in IBP reduction yields a master-integral basis with Laurent-polynomial differential equations on the maximal cut that are then ε-factorized.
Proposes motivic coaction formulae for genus-one iterated integrals over holomorphic Eisenstein series using zeta generators, verifies expected coaction properties, and deduces f-alphabet decompositions of multiple modular values.
Feynman integrals with mixed geometries (K3 surfaces, curves, points) can be computed more efficiently by extracting and using their algebraic geometric properties.
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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New algorithms for Feynman integral reduction and $\varepsilon$-factorised differential equations
A geometric order relation in IBP reduction yields a master-integral basis with Laurent-polynomial differential equations on the maximal cut that are then ε-factorized.
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Towards Motivic Coactions at Genus One from Zeta Generators
Proposes motivic coaction formulae for genus-one iterated integrals over holomorphic Eisenstein series using zeta generators, verifies expected coaction properties, and deduces f-alphabet decompositions of multiple modular values.
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From geometry to phenomenology
Feynman integrals with mixed geometries (K3 surfaces, curves, points) can be computed more efficiently by extracting and using their algebraic geometric properties.
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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.