Higgs amplitudes from $\mathcal{N}=4$ super Yang-Mills theory

Higgs plus multigluon amplitudes in QCD can be computed in an effective Lagrangian description. In the infinite top-mass limit, an amplitude with a Higgs boson and n gluons is computed by the form factor of the operator TrF2. Up to two loops and for three gluons, its maximally transcendental part is captured entirely by the form factor of the protected stress tensor multiplet operator T2 in N=4 supersymmetric Yang-Mills theory. The next order correction involves the calculation of the form factor of the higher-dimensional, trilinear operator TrF3. We present explicit results at two loops for three gluons, including the subleading transcendental terms derived from a particular descendant of the Konishi operator that contains TrF3. These are expressed in terms of a few universal building blocks already identified in earlier calculations. We show that the maximally transcendental part of this quantity, computed in nonsupersymmetric Yang-Mills theory, is identical to the form factor of another protected operator, T3, in the maximally supersymmetric theory. Our results suggest that the maximally transcendental part of Higgs amplitudes in QCD can be entirely computed through N=4 super Yang-Mills theory.