The 2-Higgs-Doublet Model with Soft CP-violation Confronting Electric Dipole Moments and Colliders.

We analyze CP-violating effects in both Electric Dipole Moment (EDM) measurements and future analyses at the Large Hadron Collider (LHC) assuming a 2-Higgs-Doublet Model (2HDM) with "soft" CP-violation. Our analysis of EDMs and current LHC constraints shows that, in the case of a 2HDM Type II and Type III, an $\mathcal{O}(0.1)$ CP-violating phase in the Yukawa interaction between $H_1$ (the $125~\textrm{GeV}$ Higgs boson) and fermions is still allowed. For these scenarios, we study CP-violating effects in the neutron EDM and $t\bar{t}H_1$ production at the LHC. Our analysis shows that such an $\mathcal{O}(0.1)$ CP-violating phase can be easily confirmed or excluded by future neutron EDM tests with LHC data providing a complementary cross-check.