The authors present explicit two-loop results for all planar four-point master integrals in massive Bhabha scattering in the fixed-angle, high-energy limit.
- XSummer - Transcendental Functions and Symbolic Summation in Form
8 Pith papers cite this work. Polarity classification is still indexing.
8
Pith papers citing it
abstract
Harmonic sums and their generalizations are extremely useful in the evaluation of higher-order perturbative corrections in quantum field theory. Of particular interest have been the so-called nested sums,where the harmonic sums and their generalizations appear as building blocks, originating for example from the expansion of generalized hypergeometric functions around integer values of the parameters. In this Letter we discuss the implementation of several algorithms to solve these sums by algebraic means, using the computer algebra system Form.
representative citing papers
A Mathematica package computes high-precision epsilon-expansions of Lauricella functions using one-dimensional Frobenius series and interpolation.
A general numerical framework is described for high-precision evaluation and analytic continuation of multivariate hypergeometric functions via Pfaffian systems and the Frobenius method.
PrecisionLauricella is a Mathematica package that computes epsilon-expansions of Lauricella F_A, F_B, and F_D functions for n up to 3 using Frobenius-series analytic continuation.
All planar two-loop five-point master integrals with one off-shell leg are expressed analytically in terms of Goncharov polylogarithms using simplified differential equations, and validated numerically.
This is a self-contained review of loop integral computation methods, focusing on algebraic structures such as Hopf algebras of nested sums and multiple polylogarithms.
citing papers explorer
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The planar four-point master integrals for massive two-loop Bhabha scattering
The authors present explicit two-loop results for all planar four-point master integrals in massive Bhabha scattering in the fixed-angle, high-energy limit.
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High-precision numerical evaluation of Lauricella functions
A Mathematica package computes high-precision epsilon-expansions of Lauricella functions using one-dimensional Frobenius series and interpolation.
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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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$\texttt{PrecisionLauricella}$: package for numerical computation of Lauricella functions depending on a parameter
PrecisionLauricella is a Mathematica package that computes epsilon-expansions of Lauricella F_A, F_B, and F_D functions for n up to 3 using Frobenius-series analytic continuation.
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Analytic representation of all planar two-loop five-point Master Integrals with one off-shell leg
All planar two-loop five-point master integrals with one off-shell leg are expressed analytically in terms of Goncharov polylogarithms using simplified differential equations, and validated numerically.
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The Art of Computing Loop Integrals
This is a self-contained review of loop integral computation methods, focusing on algebraic structures such as Hopf algebras of nested sums and multiple polylogarithms.
- HyperPrecision: A Mathematica package for High-Precision Numerical Evaluation of Multivariate Hypergeometric Functions
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