Integrating the full four-loop negative geometries and all-loop ladder-type negative geometries in ABJM theory

Li, Zhenjie

doi:10.1007/jhep10(2024)124

Integrating the full four-loop negative geometries and all-loop ladder-type negative geometries in ABJM theory

Journal Article · Thu Oct 17 00:00:00 EDT 2024 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/jhep10(2024)124· OSTI ID:2575036

^[1]

Stanford Univ., CA (United States); SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States)

The decomposition of the four-point ABJM amplituhedron into negative geometries produces compact integrands of logarithmic of amplitudes such that the infrared divergence only comes from the last loop integration, from which we can compute the cusp anomalous dimension of the ABJM theory. In this note, we integrate L – 1 loop momenta of the L-loop negative geometries for all four-loop negative geometries and a special class of all-loop ladder-type negative geometries by a method based on Mellin transformation, and from these finite quantities we extract the corresponding contribution to the cusp anomalous dimension. We find that the infrared divergence of a box-type negative geometry at L = 4 is weaker than other negative geometries, then only tree-type negative geometries contribute to the cusp anomalous dimension at L = 4. For the all-loop ladder-type negative geometries, we prove and conjecture some recursive structures as integral equations in Mellin space and find that they cannot contribute zeta values like ζ₃, ζ₅ to the cusp anomalous dimension.

View Accepted Manuscript (DOE)

Research Organization:: SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: AC02-76SF00515

OSTI ID:: 2575036

Journal Information:: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 10 Vol. 2024; ISSN 1029-8479

Publisher:: Springer NatureCopyright Statement

Country of Publication:: United States

Language:: English

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