Multi-Higgs production from a theory of varying Higgs quartic and top Yukawa couplings

We study the collider phenomenology of a theory in which the Higgs quartic self-coupling and the top Yukawa coupling are $\mathit{\text{varying}}\mathit{\text{couplings}}$, which arise dynamically from two scalar fields, ${\phi }_1$ and ${\phi }_2$. Depending on the scalar masses relative to twice the top-quark mass, the heavy scalars decay mainly to Higgs boson pairs ($hh$) or to top-quark pairs ($t\bar{t}$), giving two distinct signatures. We find sizeable cross sections for resonant $hh$ production, and also for the background-suppressed process with three Higgs bosons ($hhh$) from associated production, $pp\to h{\phi }_i\to hhh$. By recasting ATLAS resonance searches, we set bounds on the effective new-physics scales ${\mathrm{\Lambda }}_1$ and ${\mathrm{\Lambda }}_2$ at the TeV scale. We also show that the High-Luminosity LHC (HL-LHC) will probe this parameter space further, through combined measurements of the $hh$, $t\bar{t}$ and multi-Higgs channels. This gives a strong, multi-channel test of whether the electroweak sector has a dynamical origin.