First beyond-NLO tensor decomposition and higher-order analytic one-loop amplitudes for e+e- to pi+pi-gamma, paired with a fast numerical five-point integral evaluator.
Petit Rosàs and W
8 Pith papers cite this work. Polarity classification is still indexing.
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abstract
Building on the idea of numerically integrating differential equations satisfied by Feynman integrals, we propose a novel strategy for handling branch cuts within a numerical framework. We develop an integrator capable of evaluating a basis of integrals in both double and quadruple precision, achieving significantly reduced computational times compared to existing tools. We demonstrate the performance of our integrator by evaluating one- and two-loop five-point Feynman integrals with up to nine complex kinematic scales. In particular, we apply our method to the radiative return process of massive electron-positron annihilation into pions plus an energetic photon within scalar QED, for which we also build the differential equation, and extend it to the case where virtual photons acquire an auxiliary complex mass under the Generalised Vector-Meson Dominance model. Furthermore, we validate our approach on two integral families relevant for the two-loop production of $t\bar{t}+\text{jet}$. The integrator achieves, in double precision, execution times of the order of milliseconds for one-loop topologies and hundreds of milliseconds for the two-loop families, enabling for on-the-fly computation of Feynman integrals in Monte Carlo generators and a more efficient generation of grids for the topologies with prohibitive computational costs.
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representative citing papers
Leading-colour two-loop virtual amplitudes for ttbar+jet are extracted analytically via finite-field evaluations and differential equations, then packaged in a C++ library with new numerical integration techniques.
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.
A strategy is introduced to solve canonical differential equations for Feynman master integrals on arbitrary geometries by reducing numerical evaluation to an enlarged system of rational differential equations.
Disperon QED is a new technique that feeds experimental data into higher-order QED loop calculations in Monte Carlo generators via dispersion relations and threshold subtraction.
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.
AMFlow 2.0 cuts symbolic and numerical cost of multi-loop Feynman integral evaluation via an FT recursion mode, a C++ DE solver, and modern IBP reducers, demonstrated on a three-loop five-point family.
Describes a geometric-ordering approach to the Laporta algorithm plus transformation matrices that produce ε-factorised differential equations for arbitrary Feynman integral families.
citing papers explorer
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Tensor decomposition of $e^+e^-\to\pi^+\pi^-\gamma$ to higher orders in the dimensional regulator
First beyond-NLO tensor decomposition and higher-order analytic one-loop amplitudes for e+e- to pi+pi-gamma, paired with a fast numerical five-point integral evaluator.
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A strategy is introduced to solve canonical differential equations for Feynman master integrals on arbitrary geometries by reducing numerical evaluation to an enlarged system of rational differential equations.
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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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AMFlow 2.0: significant algorithmic and software improvements for Feynman integral evaluation
AMFlow 2.0 cuts symbolic and numerical cost of multi-loop Feynman integral evaluation via an FT recursion mode, a C++ DE solver, and modern IBP reducers, demonstrated on a three-loop five-point family.
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The geometric bookkeeping guide for $\varepsilon$-factorised differential equations
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