Triangulation of 2-loop MHV Amplituhedron from Sign Flips
Ryota Kojima
TL;DR
This paper presents a new triangulation method for the 2-loop MHV amplituhedron based on sign flips, offering a different structure from BCFW and providing a formula similar to the 1-loop Kermit representation.
Contribution
It introduces a direct triangulation of the 2-loop MHV amplituhedron from sign flips and derives a canonical form formula analogous to the 1-loop Kermit representation.
Findings
New triangulation method from sign flips
Consistent results up to 22-point amplitudes
A formula for the 2-loop MHV amplituhedron's canonical form
Abstract
In this paper, we consider the triangulation of 2-loop MHV amplituhedron from "sign flip" definition. Using the isomorphism between tree amplituhedron and 1-loop MHV physical amplituhedron, we found the direct triangulation of 2-loop MHV amplituhedron from sign flip. This triangulation is different from the BCFW triangulation because of the structure of the cells. And we also found a formula of the canonical form of -point 2-loop MHV amplituhedron. This formula looks like a 2-loop version of the Kermit representation of 1-loop MHV amplitude. We checked that the sum of these cells of direct triangulation and BCFW or double pentagon diagram, these are consistent up to at least 22-pt amplitude numerically.
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