Lessons from the LHC Run 2 on the Nature of the Electroweak Phase Transition and Future Prospects

The unprecedented energy of the Large Hadron Collider (LHC) offers us a
once-in-a-generation opportunity to explore the nature of the electroweak
phase transition (EWPT) in the early universe. While the Standard Model (SM)
predicts a smooth crossover, models with extended Higgs sectors can realize
a strong first-order EWPT, a key ingredient for generating the baryon
asymmetry of the universe (BAU) through electroweak baryogenesis. Such a
phase transition would also produce a stochastic primordial gravitational
wave (GW) background that could be detected by future space-based GW
observatories like LISA. In this talk, I will explore how the LHC Run 2 data
constrains the parameter space for an EWPT, highlighting the implications
for electroweak baryogenesis and the potential for GW detection. I will
discuss in detail a compelling smoking-gun signature of a strong EWPT in the
Two-Higgs-Doublet Model (2HDM): the decay of a heavy pseudoscalar A into a
lighter scalar H and a Z boson, observable in l+l- tt
final states. Current analysis techniques by ATLAS and CMS do not
differentiate between the possible signatures A -> ZH and H -> ZA if
both predict the same total cross sections. I will demonstrate how angular
variables sensitive to spin correlations of the final-state top quarks canenhance experimental sensitivity, and, more importantly, these techniques
allow for a clear distinction between $A \to ZH$ and $H \to ZA$, offering a
new way to test electroweak baryogensis using top-quark polarimetry.