Feynman integrals are completely monotonic (and often Stieltjes) functions, enabling a CM bootstrap for bounds from differential equations and Padé approximants with provable convergence.
LINE: Loop Integrals Numerical Evaluation
9 Pith papers cite this work. Polarity classification is still indexing.
9
Pith papers citing it
abstract
We present methods for the numerical evaluation of the master integrals that appear in the calculation of scattering amplitudes at higher order in perturbative quantum field theory. We follow the general strategy of solving first-order ordinary differential equations through series expansion. We have collected these procedures in an open source computer program that we dub \Line{}. Boundary conditions can be provided by the user or computed internally using the method of expansion by regions. Illustrative examples are also given.
representative citing papers
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.
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.
CHESS package implements Chebyshev-Lobatto spectral collocation for transporting epsilon-factorized differential equations of Feynman master integrals with benchmarks showing rapid convergence and shorter wall times than local series methods.
Describes a geometric-ordering approach to the Laporta algorithm plus transformation matrices that produce ε-factorised differential equations for arbitrary Feynman integral families.
Analytic expressions for one-loop helicity amplitudes in ttj and ttγ production are derived to O(ε²) as linear combinations of pentagon functions with rational coefficients in momentum-twistor variables, obtained via differential equations solved numerically by generalized power series expansion.
citing papers explorer
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Approximating Feynman integrals using complete monotonicity and Stieltjes properties
Feynman integrals are completely monotonic (and often Stieltjes) functions, enabling a CM bootstrap for bounds from differential equations and Padé approximants with provable convergence.
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Chebyshev Approximations of Feynman Integrals for Collider Physics
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.
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Solution of Canonical Differential Equations for Integrals on Arbitrary Geometries
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.
-
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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CHESS: CHEbyshev pSeudo-Spectral transport for Feynman integral differential equations
CHESS package implements Chebyshev-Lobatto spectral collocation for transporting epsilon-factorized differential equations of Feynman master integrals with benchmarks showing rapid convergence and shorter wall times than local series methods.
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The geometric bookkeeping guide for $\varepsilon$-factorised differential equations
Describes a geometric-ordering approach to the Laporta algorithm plus transformation matrices that produce ε-factorised differential equations for arbitrary Feynman integral families.
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One-loop amplitudes for $t\bar{t}j$ and $t\bar{t}\gamma$ productions at the LHC through $\mathcal{O}(\epsilon^2)$
Analytic expressions for one-loop helicity amplitudes in ttj and ttγ production are derived to O(ε²) as linear combinations of pentagon functions with rational coefficients in momentum-twistor variables, obtained via differential equations solved numerically by generalized power series expansion.
- HyperPrecision: A Mathematica package for High-Precision Numerical Evaluation of Multivariate Hypergeometric Functions