Determines the unique two- and three-loop symbols for the four-point NMHV form factor from an 88-letter alphabet, providing first multi-loop non-MHV data and supporting alphabet universality.
Lectures on differential equations for Feynman integrals
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abstract
Over the last year significant progress was made in the understanding of the computation of Feynman integrals using differential equations. These lectures give a review of these developments, while not assuming any prior knowledge of the subject. After an introduction to differential equations for Feynman integrals, we point out how they can be simplified using algorithms available in the mathematical literature. We discuss how this is related to a recent conjecture for a canonical form of the equations. We also discuss a complementary approach that allows based on properties of the space-time loop integrands, and explain how the ideas of leading singularities and d-log representations can be used to find an optimal basis for the differential equations. Finally, as an application of the differential equations method we show how single-scale integrals can be bootstrapped using the Drinfeld associator of a differential equation.
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representative citing papers
Gravitational Compton amplitude computed to third post-Minkowskian order via worldline EFT with infrared and forward divergences regulated to connect to black hole perturbation theory.
Proves conjectural reformulation of motivic coaction and single-valued maps via zeta generators for multiple polylogarithms at genus zero on the Riemann sphere.
A basis of six uniform-transcendental five-point off-shell conformal integrals is constructed and mapped to known families, yielding symbol-level two-loop results for half-BPS correlators.
Analytic expressions for the planar master integrals in two-loop NLO EW light-fermion contributions to gg → ZH are derived via canonical differential equations and expressed using Goncharov polylogarithms or one-fold integrals over them.
Outlines a Schwinger-Keldysh path-integral framework that derives worldline equations of motion and computes weak-field gravitational waveforms independently for unspecified relativistic orbits.
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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Bootstrapping the Four-Point NMHV Stress-Tensor Form Factor
Determines the unique two- and three-loop symbols for the four-point NMHV form factor from an 88-letter alphabet, providing first multi-loop non-MHV data and supporting alphabet universality.
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The gravitational Compton amplitude at third post-Minkowskian order
Gravitational Compton amplitude computed to third post-Minkowskian order via worldline EFT with infrared and forward divergences regulated to connect to black hole perturbation theory.
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Deriving motivic coactions and single-valued maps at genus zero from zeta generators
Proves conjectural reformulation of motivic coaction and single-valued maps via zeta generators for multiple polylogarithms at genus zero on the Riemann sphere.
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Notes on off-shell conformal integrals and correlation functions at five points
A basis of six uniform-transcendental five-point off-shell conformal integrals is constructed and mapped to known families, yielding symbol-level two-loop results for half-BPS correlators.
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Planar master integrals for two-loop NLO electroweak light-fermion contributions to $g g \rightarrow Z H$
Analytic expressions for the planar master integrals in two-loop NLO EW light-fermion contributions to gg → ZH are derived via canonical differential equations and expressed using Goncharov polylogarithms or one-fold integrals over them.
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Weak-field waveforms for generic relativistic orbits
Outlines a Schwinger-Keldysh path-integral framework that derives worldline equations of motion and computes weak-field gravitational waveforms independently for unspecified relativistic orbits.
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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.
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