One-loop QCD amplitudes for vector-boson-fusion Higgs-boson production to higher orders in $\epsilon$

We consider one-loop QCD corrections to Higgs-boson production via vector-boson fusion at hadron colliders. As an input for future exact NNLO computations, we derive the one-loop helicity amplitudes to higher orders in the dimensional regulator. We present a direct calculation of the amplitudes with spinor-helicity techniques and different ${\gamma }_5$ schemes. In addition, we compare this approach to a projector-based calculation. In order to derive analytical results to higher orders in $\epsilon$, we calculate the pentagon master integrals by the method of $\epsilon$-factorised differential equations and express them in terms of an algebraically independent set of basis functions.