Next-to-next-to-leading order QCD corrections to light Higgs pair production via vector boson fusion in type-II two-Higgs-doublet model

We present the precision predictions on the pair production of light, $CP$-even Higgs in weak vector boson fusion (VBF) up to the QCD next-to-next-to-leading-order (NNLO) at hadron colliders within the $CP$-conserving type-II two-Higgs-doublet model (2HDM(II)) by adopting the structure function approach. We investigate the model parameter dependence, residual uncertainties from the factorization/renormalization scale, PDFs and $\alpha_s$ on the integrated cross section at the QCD NNLO, and find that the NNLO QCD corrections can reduce the scale uncertainty significantly. By analyzing the kinematic distributions of final Higgs bosons, we can extract the $CP$-even Higgs resonance via $H^0 \to h^0 h^0$ channel as a means of probing the extension of the Standard Model (SM) Higgs sector.