Abstract
We derive an algorithm for computing the total differentials of multiloop integrals expressed as onefold integrals of multiple polylogarithms, which can involve square roots of polynomials up to degree 4 and may evaluate to (elliptic) multiple polylogarithms [(e)MPLs]. This gives simple algebraic rules for computing the (, 1) coproduct of the resulting weight- functions up to period terms, and iterating it gives the symbol without actually performing any integration. In particular, our algorithm generalizes existing MPL integration rules and sidesteps the complicated rationalization procedure in the presence of square roots. We apply our algorithm to conformal double--gon integrals in dimensions with generic kinematics and possibly massive circumferential propagators. We directly compute, for the first time, the total differential and symbol (up to period terms) of the double triangle and the double box, which in the special case with massless propagators represent the first appearance of eMPL functions in (two-loop) scattering amplitudes of Aharony-Bergman-Jafferis-Maldacena theory and super-Yang-Mills theory, respectively.
- Received 19 June 2023
- Accepted 4 July 2023
- Corrected 26 January 2024
DOI:https://doi.org/10.1103/PhysRevD.108.L041702
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.
Published by the American Physical Society
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Corrections
26 January 2024
Correction: The last sentence of the Acknowledgments section contained errors and has been fixed (the grant numbers have been reordered, two were deleted, and a new one was added). In addition, a new funding statement has been added.