CP violation from charged Higgs bosons in the three Higgs doublet model

We demonstrate a new type of cancellation of contributions to the electron and neutron electric dipole moments (EDMs) that occurs in three Higgs doublet models (3HDMs) when CP violation appears in the charged Higgs sector. The cancellation becomes exact when the two physical charged Higgs bosons in the model are degenerate in mass. Depending on the model parameters, degeneracies at the 10% level are however sufficient to evade current bounds on the electron and neutron EDMs. We demonstrate that viable parameter space remains with both charged Higgs bosons lighter than 500 GeV and large CP-violating phases while also satisfying theoretical constraints from perturbativity and experimental ones from $\bar{B}\to X_s\gamma$ and direct searches.