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.
Connection between Feynman integrals having different values of the space-time dimension
7 Pith papers cite this work. Polarity classification is still indexing.
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abstract
A systematic algorithm for obtaining recurrence relations for dimensionally regularized Feynman integrals w.r.t. the space-time dimension $d$ is proposed. The relation between $d$ and $d-2$ dimensional integrals is given in terms of a differential operator for which an explicit formula can be obtained for each Feynman diagram. We show how the method works for one-, two- and three-loop integrals. The new recurrence relations w.r.t. $d$ are complementary to the recurrence relations which derive from the method of integration by parts. We find that the problem of the irreducible numerators in Feynman integrals can be naturally solved in the framework of the proposed generalized recurrence relations.
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representative citing papers
The all-loop bare perturbative part of the four-quark Bethe-Salpeter kernel is computed analytically in the large-Nf limit of massless QCD.
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.
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.
Contour equivalence in Feynman parameterization yields universal reduction formulas for one-loop integrals without integration-by-parts.
Connects recurrence techniques and dispersive methods with dimension shifts to reduce multi-point functions to two-point basis, minimizing dispersive integrals for one- and two-loop calculations.
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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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All-loop four-quark Bethe-Salpeter kernel
The all-loop bare perturbative part of the four-quark Bethe-Salpeter kernel is computed analytically in the large-Nf limit of massless QCD.
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Pseudo-Evanescent Feynman Integrals from Local Subtraction
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.
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Fano and Reflexive Polytopes from Feynman Integrals
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.
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Feynman Integral Reduction without Integration-By-Parts
Contour equivalence in Feynman parameterization yields universal reduction formulas for one-loop integrals without integration-by-parts.
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Recurrence Relations and Dispersive Techniques for Precision Multi-Loop Calculations
Connects recurrence techniques and dispersive methods with dimension shifts to reduce multi-point functions to two-point basis, minimizing dispersive integrals for one- and two-loop calculations.
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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.