Local subtraction reduces pseudo-evanescent Feynman integrals to products of one-loop integrals or one-fold integrals, with the finite part of the two-loop all-plus five-point amplitude arising solely from ultraviolet regions after infrared cancellations.
Borinsky,Tropical Monte Carlo quadrature for Feynman integrals, Ann
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Tropicalized massive scalar QFT is exactly solvable via a non-linear recursion for effective action coefficients that computes graph moduli space volumes, enabling a polynomial-time sampling algorithm for high-order perturbative contributions.
Chebyshev polynomial approximations with adaptive sampling solve canonical differential equations for Feynman integrals, demonstrated to be stable and competitive for two-loop five-point cases in double precision.
Quasi-finite Feynman integrals produce sparse Fano and reflexive polytopes that encode degenerate Calabi-Yau varieties and link to del Pezzo surfaces, K3 surfaces, and Calabi-Yau threefolds.
SubTropica is a software package that automates symbolic integration of linearly-reducible Euler integrals via tropical subtraction, supported by HyperIntica and an AI-driven Feynman integral database.
The paper describes in detail a reduction-to-free-QED method for evaluating vacuum polarization potential corrections up to α²(Zα)⁷ in the Coulomb field of a pointlike nucleus.
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.
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