Two-loop mixed QCD-EW corrections to qq¯ → Hg, qg → Hq, and q¯ g → Hq¯

We compute the two-loop mixed QCD-Electroweak corrections to qq¯ → Hg and its crossed channels qg → Hq, q¯ g→Hq¯ , limiting ourselves to the contribution of light virtual quarks. We compute the independent helicity amplitudes as well as the form factors for this process, expressing them in terms of hyperlogarithms with algebraic arguments. The Feynman integrals are computed by direct integration over Feynman parameters and the results are expressed in terms of a basis of rational prefactors.