Triple Higgs boson production to six $b$-jets at a 100 TeV proton collider

We investigate the production of three Higgs bosons at a proton-proton collider running at a centre-of-mass energy of 100 TeV, all of which decay into $b$-jets. This final state encapsulates by far the largest fraction of the total cross section of triple Higgs boson production, approximately $20\%$. We examine, by constructing detailed phenomenological analyses, two scenarios: (i) one in which the triple and quartic Higgs boson self-couplings are modified independently by new phenomena with respect to their Standard Model (SM) values and (ii) an extension of the SM by a gauge-singlet scalar that could drive first-order electroweak phase transition, within the context of the so-called xSM. In the former, we find that competitive constraints of $\mathcal{O}(1)$ can be placed on the quartic coupling and in the latter we demonstrate that it will be possible to obtain important information on the structure of the extended scalar sector.