Probing the Electroweak Phase Transition in the Flipped Two-Higgs-Doublet Model at the LHC

We study the CP-conserving flipped (Type-Y) Two-Higgs-Doublet Model (2HDM) in the large-$\tan\beta$ regime ($\tan\beta>30$), focusing on its implications for electroweak phase transitions (EWPTs) and LHC phenomenology. Viable parameter regions supporting a strong first-order EWPT fall into two heavy-Higgs hierarchies: (A) $m_{H^\pm}\simeq m_H<m_A$ and (B) $m_H<m_{H^\pm} \simeq m_A$, both featuring a heaviest CP-odd Higgs $A$. Scenario~A typically proceeds via one-step transitions with lower nucleation temperatures, while Scenario~B allows one-step or two-step transitions, opening the decay $A\to H^\pm W^\mp$ and yielding richer collider signatures. In all cases, nucleation conditions are satisfied, avoiding false-vacuum trapping. We assess LHC prospects through bottom-associated production with multi-$b$ final states: $pp\to bbH\to 4b$ and $pp\to bbA\to bb W^\pm H^\mp\to 4b\ell\ell\nu\nu$. The $4b$ channel offers high-statistics discovery potential, reaching signal significances $z\gtrsim 25$ at the 13 TeV LHC with 300 fb$^{-1}$ and up to $z\gtrsim 100$ at the 14 TeV HL-LHC with 3 ab$^{-1}$. The cascade channel, while experimentally more challenging, directly probes the heavy Higgs spectrum and can discriminate between EWPT scenarios. Using optimized selections with a BDT-based multivariate analysis, significances of $z \simeq 6.8$ can be achieved in favorable regions of Scenario~B at the HL-LHC. These results indicate that the HL-LHC can realistically probe the BSM Higgs sector responsible for a strong first-order EWPT and provide insight into the underlying phase transition dynamics in the flipped 2HDM.