of the ${\ensuremath{\Pg \Pg \to \PH}\xspace}$ process at NNLO accuracy in perturbative QCD and next-to-next-to-leading-logarithmic (NNLL) accuracy in the resummation of soft-gluon effects at small transverse momenta [@deFlorian:2012mx; @Grazzini:2013mca]. Since the resummation is inclusive over the QCD radiation recoiling against the Higgs boson, <span style="font-variant:small-caps;">HRes</span> is considered for the estimation of fiducial cross sections that are inclusive in the associated jet activity. The <span style="font-variant:small-caps;">HRes</span> estimations are obtained by choosing the central values for the renormalization and factorization scales to be $m_{\PH}=125.0\GeV$. The <span style="font-variant:small-caps;">Powheg</span> generator is a partonic level matrix-element generator that implements NLO perturbative QCD calculations and additionally provides an interface with parton shower programs. It provides a description of the ${\ensuremath{\Pg \Pg \to \PH}\xspace}$ production in association with zero jets at NLO accuracy. For the purpose of this analysis, it has been tuned using the damping factor $hdump$ of $104.16\GeV$, to closely match the Higgs boson $\pt$ spectrum in the full phase space, as estimated by the <span style="font-variant:small-caps;">HRes</span> generator. This factor minimises emission of the additional jets in the limit of large $\pt$, and enhances the contribution from the Sudakov form factor as $\pt$ approaches zero [@powheg; @powhegvv]. The <span style="font-variant:small-caps;">Powheg MiNLO HJ</span> generator is an 