arXiv2019
The production of a Higgs boson in association with at least two jets receives contributions both from the fusion of weak vector bosons (VBF) and from QCD processes, especially gluon fusion (GF). The former process is important for measuring the coupling of the Higgs boson to weak bosons, whereas the latter process plays an important role in determining any $CP$-admixtures in the Higgs sector. In this paper we go beyond the current state-of-the-art for fixed order calculations of the GF process (i.e. one loop $H+2j$ including full quark mass effects) by including the all-order effects in leading $\log(\hat s/p_t^2)$, together with full quark mass and loop-propagator kinematic effects. We calculate the mass-dependent components and implement the resummation within the framework of High Energy Jets. The high energy effects suppress the prediction compared to fixed order at large $Δy_{12}$ and $m_{jj}$ (and therefore within the usual VBF cuts of widely separated jets), just as found in the limit of $m_t\to \infty$. The mass dependence is more significant than at fixed order, because the systematic inclusion of the leading logarithms in $\hat s/p_t^2$ results in a hardening of the transverse momentum of the Higgs boson, which in turn probes in more detail the loop-structure of the coupling. In particular, the full mass dependence reduces the cross section within VBF cuts by 11\% compared to a calculation based just on the infinite top mass limit, but the impact of the bottom quark remains small. This all implies that the gluon-fusion contribution within VBF-cuts is less severe than current estimates suggest.