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We compute the two-loop result for the null pentagonal Wilson loop with aLagrangian insertion (normalized by the Wilson loop without insertion) inplanar, maximally supersymmetric Yang-Mills theory. This finite observable isclosely related to the Amplituhedron, and it is reminiscent of finite parts ofplanar two-loop five-particle scattering amplitudes. We verify that, up to thisloop order, the leading singularities are given by the same conformallyinvariant expressions that appear in all-plus pure Yang-Mills amplitudes. Theaccompanying weight-four transcendental functions are expressed in terms of thepentagon functions space known from planar two-loop five-particle amplitudes,but interestingly only a subset of the functions appears. Being a function offour dimensionless variables, the observable has interesting asymptotic limits.We verify that our analytic result is consistent with soft and collinearlimits, and find an intriguingly simple pattern in the multi-Regge limit.Thanks to the new result we can also conjecturally predict, for generalkinematics, the maximal weight piece of the planar three-loop five-particleall-plus amplitude in pure Yang-Mills theory. Motivated by the Amplituhedrongeometry, we investigate positivity properties of the integrated answer.Generalizing previous results at four particles, we find numerical evidencethat the two-loop five-particle result has uniform sign in a kinematic regionsuggested by the loop Amplituhedron.

Pentagon Wilson loop with Lagrangian insertion at two loops in ${\mathcal N}=4$ super Yang-Mills theory