Further on up the road: $hhjj$ production at the LHC

A measurement of the $hh+2j$ channel at the LHC would be particularly thrilling for electroweak physics. It is not only the leading process which is sensitive to the $W^+W^- hh$ and $ZZhh$ interactions, but also provides a potentially clear window to study the electroweak symmetry-breaking sector by probing Higgs-Goldstone interactions through the weak boson fusion component of the scattering process. Until now, a phenomenologically complete analysis of this channel has been missing. This is mostly due to the high complexity of the involved one-loop gluon fusion contribution and the fact that a reliable estimate thereof cannot be obtained through simplified calculations in the $m_t\to \infty$ limit. In particular, the extraction of the Higgs trilinear coupling from this final state rests on a delicate $m_t$-dependent interference pattern which is not captured in an effective field theory approach. In this paper, we report on the LHC's potential to access di-Higgs production in association with two jets in a fully-showered hadron-level analysis. Our study includes the finite top and bottom mass dependencies for the gluon fusion contribution. On the basis of these results, we also comment on the potential sensitivity to the trilinear Higgs and $VV^\dagger hh$ ($V=W^\pm,Z$) couplings that can be expected from measurements of this final state.