Physical Review Letters· 2018Q1
Elliptic Double-Box Integrals: Massless Scattering Amplitudes beyond Polylogarithms
- 129citations
- Q1SCImago
- 2018year
Short summary
Researchers derived an analytic representation of a ten-particle, two-loop double-box integral as an elliptic integral over weight-three polylogarithms, extending scattering amplitude calculations beyond standard polylogarithms.
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Key points
- Derived an analytic representation of the ten-particle, two-loop double-box integral.
- The representation is an elliptic integral over weight-three polylogarithms.
- A fourfold, rational parametric representation in terms of dual-conformally invariant cross ratios was developed.
- Proposes a normalization to make polylogarithmic degenerations pure.
AI-generated from the title and abstract; the full text is not read.
Abstract
We derive an analytic representation of the ten-particle, two-loop double-box integral as an elliptic integral over weight-three polylogarithms. To obtain this form, we first derive a fourfold, rational (Feynman-)parametric representation for the integral, expressed directly in terms of dual-conformally invariant cross ratios; from this, the desired form is easily obtained. The essential features of this integral are illustrated by means of a simplified toy model, and we attach the relevant expressions for both integrals in ancillary files. We propose a normalization for such integrals that renders all of their polylogarithmic degenerations pure, and we discuss the need for a new "symbology" of mixed iterated elliptic and polylogarithmic integrals in order to bring them to a more canonical form.
The authors' abstract, as published at the source. Physical Review Letters, 2018 · DOI ↗
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Field: Algebra and Number Theory
Algebra and Number TheoryMathematics