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We analyze CP-violating effects in both Electric Dipole Moment (EDM)measurements and future analyses at the Large Hadron Collider (LHC) assuming aTwo-Higgs-Doublet Model (2HDM) with "soft" CP-violation. Our analysis of EDMsand current LHC constraints shows that, in the case of a 2HDM Type II and TypeIII, 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. Forthese 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 byfuture neutron EDM tests, with LHC data providing a complementary cross-check.

Two-Higgs-Doublet Model with Soft CP-violation Confronting Electric Dipole Moments and Colliders