  Theoretical predictions with next-to-next-to-leading order (NNLO) QCD
accuracy combined with the next-to-leading order (NLO) electroweak (EW)
corrections are presented for differential observables of the double-Higgs
production process via vector-boson fusion. While the QCD corrections were
previously known, the EW ones are computed here for the first time. The
numerical results are obtained for a realistic experimental set-up at the LHC
and are presented in the form of fiducial cross sections and differential
distributions. Within this setup we find that the VBF approximation employed in
the NNLO QCD correction is accurate at the sub-percent level. We find that the
NLO EW corrections within the fiducial volume are $-6.1\%$, making them of
almost the same order as the NLO QCD corrections. In some kinematic regions
they can grow as large as $-30\%$ making them the dominant radiative
corrections. When the EW corrections are combined with the NNLO QCD corrections
we find a total correction of $-14.8\%$. The results presented here thus
comprise the state-of-the-art theoretical predicition for the double-Higgs
production via vector-boson fusion, which will be of value to the
high-luminosity programme at the LHC.
