Electroweak baryogenesis via bottom transport: complementarity between LHC and future lepton collider probes

We study the complementarity between the Large Hadron Collider (LHC) and future lepton colliders in probing electroweak baryogenesis induced by an additional bottom Yukawa coupling $\rho_{bb}$. The context is general two Higgs doublet model (g2HDM) where such additional bottom Yukawa coupling can account for the observed baryon asymmetry of the Universe if $\mbox{Im}(\rho_{bb}) \gtrsim 0.058$. We find that LHC would probe the nominal $\mbox{Im}(\rho_{bb})$ required for baryogenesis to some extent via $bg \to bA \to bZh$ process if $300~\mbox{GeV}\lesssim m_A \lesssim 450$ GeV, where $A$ is the CP-odd scalar in g2HDM. We show that future electron positron collider such as International Linear Collider with $500$ GeV and 1 TeV collision energies may offer unique probe for the nominal $\mbox{Im}(\rho_{bb})$ via $e^+ e^- \to Z^*\to A H$ process followed by $A,H \to b \bar b$ decays in four $b$-jets signature. For complementarity we also study the resonant diHiggs productions, which may give an insight into strong first-order electroweak phase transition, via $e^+ e^- \to Z^*\to A H \to A h h$ process in six $b$-jets signature. We find that 1 TeV collision energy with $\mathcal{O}(1)~\text{ab}^{-1}$ integrated luminosity could offer an ideal environment for the discovery.