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The Elliptic Double-Box Integral: Massless Amplitudes Beyond Polylogarithms

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arxiv 1712.02785 v2 pith:LFVLLPDW submitted 2017-12-07 hep-th hep-ph

The Elliptic Double-Box Integral: Massless Amplitudes Beyond Polylogarithms

Jacob L. Bourjaily , Andrew J. McLeod , Marcus Spradlin , Matt von Hippel , Matthias Wilhelm This is my paper
classification hep-th hep-ph
keywords integralellipticformintegralsderivedouble-boxpolylogarithmicpolylogarithms
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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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 four-fold, 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 iterated elliptic/polylogarithmic integrals in order to bring them to a more canonical form.

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Cited by 2 Pith papers

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    Cluster algebras for planar conformal kinematics are identified as G(4,n) subalgebras and used to bootstrap the symbol of an 8-point three-loop wheel integral via D3 and new algebraic letters.