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We compute the two-loop mixed QCD-Electroweak corrections to $q \overline{q}\to H g$ and its crossed channels $q g \to H q$, $\overline{q} g \to H\overline{q}$, limiting ourselves to the contribution of light virtual quarks.We compute the independent helicity amplitudes as well as the form factors forthis process, expressing them in terms of hyperlogarithms with algebraicarguments. The Feynman integrals are computed by direct integration overFeynman parameters and the results are expressed in terms of a basis ofrational prefactors.

Two-loop mixed QCD-EW corrections to $q \overline{q} \to H g$, $qg \to Hq$, and $\overline{q}g \to H\overline{q}$