Hidden Analytic Relations for Two-Loop Higgs Amplitudes in QCD

Abstract

We compute the Higgs plus two-quark and one-gluon amplitudes ($H\to q\bar{q}g$) and Higgs plus three-gluon amplitudes ($H\to 3g$) 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 $H\to q\bar{q}g$ amplitudes turn out to be equivalent to that of the $H\to 3g$ 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 to 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 $H\to q\bar{q}g$ amplitudes and the minimal density form factors in $\mathcal{N}=4$ SYM.

v4: 8 pages + supplemental material; with small extension and clarifications; published version