Hidden analytic relations for two-loop Higgs amplitudes in QCD

We compute the Higgs plus two-quark and one-gluon amplitudes ($Hto qbar{q}g$) and Higgs plus three-gluon amplitudes ($Hto 3g$) in the Higgs effective theory with a general class of operators. By changing the quadratic Casimir C_F to C_A, the maximally transcendental parts of the $Hto qbar{q}g$ amplitudes turn out to be equivalent to that of the $Hto 3g$ amplitudes, which also coincide with the counterparts in ${ mathcal N }=4$ SYM. This generalizes the so-called maximal transcendentality principle to the Higgs amplitudes with external quark states, thus the full QCD theory. We further verify that the correspondence applies also to two-loop form factors of more general operators, in both QCD and scalar-YM theory. Another interesting relation is also observed between the planar $Hto qbar{q}g$ amplitudes and the minimal density form factors in ${ mathcal N }=4$ SYM.