First shot of the smoking gun: probing the electroweak phase transition in the 2HDM with novel searches for A → ZH in${\ell}^{+}{\ell}^{-}t\overline{t}$ and $ \nu \nu b\overline{b}$ final states

Recently the ATLAS collaboration has reported the first results of searches for
heavy scalar resonances decaying into a Z boson and a lighter new scalar resonance, where
the Z boson decays leptonically and the lighter scalar decays into a top-quark pair, giving rise
to ${\ell}^{+}{\ell}^{-}t\overline{t}$ final states. This had previously been identified as a smoking-gun signature at the
LHC for a first-order electroweak phase transition (FOEWPT) within the framework of two
Higgs doublet models (2HDMs). In addition, ATLAS also presented new limits where the Z
boson decays into pairs of neutrinos and the lighter scalar resonance into bottom-quark pairs,
giving rise to the $ \nu \nu b\overline{b}$ final state. We analyze the impact of these new searches on the 2HDM
parameter space, with emphasis on their capability to probe currently allowed 2HDM regions
featuring a strong FOEWPT. We also study the complementarity of these new searches
with other LHC probes that could target the FOEWPT region of the 2HDM. Remarkably,
the ATLAS search in the ${\ell}^{+}{\ell}^{-}t\overline{t}$ final state shows a local 2.85 σ excess (for masses of about
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650 GeV and 450 GeV for the heavy and light resonance) in the 2HDM parameter region that
would yield a FOEWPT in the early universe, which could constitute the first experimental hint of baryogenesis at the electroweak scale. We analyze the implications of this excess,
and discuss the detectability prospects for the associated gravitational wave signal from
the FOEWPT. Furthermore, we project the sensitivity reach of the ${\ell}^{+}{\ell}^{-}t\overline{t}$ signature for
the upcoming runs of the LHC. Finally, we introduce the python package thdmTools, a
state-of-art tool for the exploration of the 2HDM.