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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Weinzierl,Feynman Integrals, arXiv e-prints (Jan., 2022) arXiv:2201.03593 [2201.03593]
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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.
Tree-level open bosonic string amplitudes satisfy a complete system of linear difference equations in kinematic variables whose number matches the independent parameters, recovering algebraic QFT structure as alpha approaches zero.
An extension of the Griffiths-Dwork algorithm produces twisted Picard-Fuchs operators for hypergeometric, elliptic, and Calabi-Yau motives from families of Feynman integrals.
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.
Computes 1PN conservative dynamics for gravitational/EM/Proca fields and 2PN for scalar, plus radiation effects from axion-photon coupling at high PN orders in binary black hole systems with dark matter.
Soft contributions stabilize NNLO QCD corrections for S-wave color-singlet quarkonium processes, yielding better perturbative convergence and experimental agreement.
Characterizes numerators yielding finite or evanescent massless pentabox integrals, gives compact generators via momentum basis and Gram determinants, and evaluates lowest-rank cases in polylogarithms and pentagon functions.
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.
Relates free scalar in Minkowski space to codimension-two sphere field via Radon transform to dS/EAdS slice and bulk reconstruction, with Mellin modes as generalized hypergeometric functions via Lee-Pomeransky method.
A new open FORM package implements parametric hyperlogarithm integration, demonstrated on zigzag Feynman integrals up to six loops.
A general numerical framework is described for high-precision evaluation and analytic continuation of multivariate hypergeometric functions via Pfaffian systems and the Frobenius method.
Extends H3+-WZNW celestial CFT to holographically generate MHV amplitudes in Klein space, deriving dictionary, stress tensor, correlators, OPE and PDEs from KZ equations.
Reversing the direction of tubing evolution yields splitting rules that reproduce the kinematic flow differential equations at tree level and suggest time emerges from kinematic space in conformally coupled scalar models and tr phi^3 theory.
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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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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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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Towards Equations for String Amplitudes
Tree-level open bosonic string amplitudes satisfy a complete system of linear difference equations in kinematic variables whose number matches the independent parameters, recovering algebraic QFT structure as alpha approaches zero.
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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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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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Worldline effective field theory of inspiralling black hole binaries in presence of dark photon and axionic dark matter
Computes 1PN conservative dynamics for gravitational/EM/Proca fields and 2PN for scalar, plus radiation effects from axion-photon coupling at high PN orders in binary black hole systems with dark matter.
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Soft Contributions Stabilize NNLO QCD Corrections to Quarkonium Production and Decay
Soft contributions stabilize NNLO QCD corrections for S-wave color-singlet quarkonium processes, yielding better perturbative convergence and experimental agreement.
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Finite Massless Pentaboxes
Characterizes numerators yielding finite or evanescent massless pentabox integrals, gives compact generators via momentum basis and Gram determinants, and evaluates lowest-rank cases in polylogarithms and pentagon functions.
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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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Minkowski Space holography and Radon transform
Relates free scalar in Minkowski space to codimension-two sphere field via Radon transform to dS/EAdS slice and bulk reconstruction, with Mellin modes as generalized hypergeometric functions via Lee-Pomeransky method.
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HyperFORM -- a FORM package for parametric integration with hyperlogarithms
A new open FORM package implements parametric hyperlogarithm integration, demonstrated on zigzag Feynman integrals up to six loops.
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Numerical analytical continuation of multivariate hypergeometric functions
A general numerical framework is described for high-precision evaluation and analytic continuation of multivariate hypergeometric functions via Pfaffian systems and the Frobenius method.
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Comments on Celestial CFT and $AdS_{3}$ String Theory
Extends H3+-WZNW celestial CFT to holographically generate MHV amplitudes in Klein space, deriving dictionary, stress tensor, correlators, OPE and PDEs from KZ equations.
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An Alternative Viewpoint on Kinematic Flow from Tubing Splitting
Reversing the direction of tubing evolution yields splitting rules that reproduce the kinematic flow differential equations at tree level and suggest time emerges from kinematic space in conformally coupled scalar models and tr phi^3 theory.
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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.