Decades of precision measurements have firmly established the Kobayashi-Maskawa phase as the dominant source of the CP violation observed in weak quark decays. However, it is still unclear whether CP violation is explicitly encoded in complex Yukawa matrices or instead stems from spontaneous symmetry breaking with underlying CP-conserving Yukawa and Higgs sectors. Here we study the latter possibility for the case of a generic two-Higgs-doublet model. We find that theoretical constraints limit the ratio $t_beta$ of the vacuum expectation values to the range $0.22 leq t_beta leq 4.5$ and imply the upper bounds $M_{H^pm}leq 435$ GeV, $M_{H_{2}^0} leq 485$ GeV and $M_{H_{3}^0} leq 545$ GeV for the charged and extra neutral Higgs masses. We derive lower bounds on charged-Higgs couplings to bottom quarks which provide a strong motivation to study the non-standard production and decay signatures $p p to qb H^pm(to q^prime b)$ with all flavors $q,q^prime=u,c,t$ in the search for the charged Higgs boson. We further present a few benchmark scenarios with interesting discovery potential in collider analyses.
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