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We consider two-loop renormalization of high-dimensional Lorentz scalaroperators in the gluonic sector of QCD. These operators appear also in theHiggs effective theory obtained by integrating out the top quark loop in thegluon fusion process. We first discuss the classification of operators and howto construct a good set of basis using both off-shell field theory method andon-shell form factor formalism. To study loop corrections, we apply efficientunitarity-IBP strategy and compute the two-loop minimal form factors oflength-3 operators up to dimension sixteen. From the UV divergences of formfactor results, we extract the renormalization matrices and analyze theoperator mixing behavior in detail. The form factors we compute are alsoequivalent to Higgs plus three-gluon amplitudes that capture high-order topmass corrections in Higgs EFT. We obtain the analytic finite remainderfunctions which exhibit several universal transcendentality structures.

Two-Loop anomalous dimensions of QCD operators up to dimension-sixteen and Higgs EFT amplitudes