NNLO QCD corrections to Higgs pair production via vector boson fusion at hadron colliders

The measurement of the Higgs pair production via vector boson fusion can be used to test the trilinear Higgs self-coupling and the $VVHH$ $(V=Z,W)$ quartic gauge interactions. In this paper we present the calculations of the next-to-next-to-leading-order QCD corrections to the SM Higgs boson pair production via vector boson fusion at hadron colliders with the center-of-mass energy of $14$, $33$, and $100 {\rm TeV}$ by using the structure function approach, and study the residual uncertainties from the factorization/renormalization scale, parton distribution functions and $\alpha_s$ on the total cross section. We also provide the distributions of transverse momenta, rapidities, invariant mass and azimuthal angle separations of final Higgs bosons. We observe a considerable quantitative reduction in the scale uncertainty due to the next-to-next-to-leading-order QCD corrections, and find that the total cross section is sensitive to the trilinear Higgs self-coupling.