Resonant top pair searches at the LHC: a window to electroweak phase transition

The dynamics of electroweak phase transition could have profound consequences for particle physics and cosmology. We study the prospects for the HL-LHC to probe the strong first-order electroweak phase transition (SFOEWPT) regime in the type-I 2HDM. We focus on the Higgstrahlung channel $pp\to ZH\mathrm{/}A$ with a resonant top-quark pair final state $H\mathrm{/}A\to t\bar{t}$. We find that the top-quark pair final state renders the largest sensitivity to the SFOEWPT regime, in comparison to the other Higgstrahlung searches already performed by ATLAS and CMS, that focus on the $H\mathrm{/}A\to bb$ and $H\to WW$ final states. We also derive the complementarity of the Higgstrahlung searches with other relevant classes of searches at the HL-LHC and compare them with the gravitational wave sensitivity at LISA.