Two-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 two-Higgs-doublet model (2HDM) with ``soft'' $CP$ violation. Our analysis of EDMs and current LHC constraints shows that, in the case of Type II and Type III 2HDMs, an O(0.1) $CP$-violating phase in the Yukawa interaction between H₁ (the 125 GeV Higgs boson) and fermions is still allowed. For these scenarios, we study $CP$-violating effects in the neutron EDM and tt̄H₁ production at the LHC. Our analysis shows that such an 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.