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High Energy Physics - Theory, hep-th
Abstract:
This article provides a direct calculation of the 4-particle amplituhedron at
3-loop level, by introducing a set of practical tricks. After delicately
rearranging each piece by this calculation, we find a suggestive connection
between positivity conditions and Mondrian diagrams, which will be
quantitatively defined. Such a pattern can be generalized for all Mondrian
diagrams among all those contribute to the 4-particle integrand of planar N=4
SYM to all loop orders, as a subsequent work will show.