On the impact of non-factorisable corrections in VBF single and double Higgs production

We study the non-factorisable QCD corrections, computed in the eikonal approximation, to Vector-Boson Fusion single and double Higgs production and show the combined factorisable and non-factorisable corrections for both processes at $$ \mathcal{O}\left({\alpha}_s^2\right) $$ . We investigate the validity of the eikonal approximation with and without selection cuts, and carry out an in-depth study of the relative size of the non-factorisable next-to-next-to-leading order corrections compared to the factorisable ones. In the case of single Higgs production, after selection cuts are applied, the non-factorisable corrections are found to be mostly contained within the factorisable scale uncertainty bands. When no cuts are applied, instead, the non-factorisable corrections are slightly outside the scale uncertainty band. Interestingly, for double Higgs production, we find that both before and after applying cuts, non-factorisable corrections are enhanced compared to the single Higgs case. We trace this enhancement to the existence of delicate cancellations between the various leading-order Feynman diagrams, which are partly spoiled by radiative corrections. All contributions studied here have been implemented in proVBFH v1.2.0 and proVBFHH v1.1.0.