Constraining a Lighter Exotic Scalar via Same-sign Top

It was shown recently that, in two Higgs doublet models without $Z_2$ symmetry, extra Yukawa couplings such as ${\rho }_{tc}$, ${\rho }_{tt}$ can fuel enough $CP$ violation for electroweak baryogenesis (EWBG). We revisit an old proposal where a pseudoscalar $A^0$ has mass between $t\bar{c}$ and $t\bar{t}$ thresholds. With ${\rho }_{tt}$ small, it evades $gg\to A^0\to h^0(125)Z$ constraints, where approximate alignment also helps. We find this scenario with relatively light $A^0$ is not yet ruled out, and $cg\to t{A}^0\to tt\bar{c}$ can probe sizable ${\rho }_{tc}$ at the LHC, giving access to the second mechanism of EWBG provided by such models.