TY - JOUR
T1 - Elliptic Double-Box Integrals
T2 - Massless Scattering Amplitudes beyond Polylogarithms
AU - Bourjaily, Jacob L.
AU - McLeod, Andrew J.
AU - Spradlin, Marcus
AU - Von Hippel, Matt
AU - Wilhelm, Matthias
N1 - Publisher Copyright:
© 2018 authors. Published by the American Physical Society.
PY - 2018/3/23
Y1 - 2018/3/23
N2 - 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.
AB - 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.
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U2 - 10.1103/PhysRevLett.120.121603
DO - 10.1103/PhysRevLett.120.121603
M3 - Article
C2 - 29694086
AN - SCOPUS:85044428598
SN - 0031-9007
VL - 120
JO - Physical review letters
JF - Physical review letters
IS - 12
M1 - 121603
ER -