$VHH$ production at the High-Luminosity LHC

We study the phenomenology of associated production of a vector boson with a pair of Higgs bosons ($VHH$) at the High-Luminosity LHC. Despite the low rate of this channel, the scaling of the cross section suggests a measurement could be a useful probe of modifications of the trilinear Higgs boson coupling and anomalous interactions in the gauge-Higgs sector. We focus on both $WHH$ and $ZHH$ production, using the leptonic ($W \to l \nu$, $Z \to ll$, $Z \to \nu \nu$) decay modes of the vector bosons and the $HH \to 4b$ di-Higgs decay mode. We show that top pair backgrounds are problematic for the $W \to l \nu$ and $Z \to \nu \nu$ channels, leaving $Z \to ll$ as the most promising decay mode. However, even for this channel, we find limited sensitivity due to a low signal rate. We discuss some potential avenues for improvement.