We investigate the implications of spontaneous $CP$ violation in the general two Higgs doublet model, which leads to a nondecoupling structure of the Higgs sector. All the masses of the Higgs bosons are purely determined by the vacuum expectation value of the Higgs fields, and are thus constrained to be smaller than $\mathcal{O}(500)\mathrm{GeV}$ by the perturbative unitarity bound. Such a nondecoupling nature predicts sizable deviations from the Standard Model expectations in the observables of the discovered Higgs boson ($h$). We find that the magnitude of deviations in ${\mathcal{B}}_{h\to \gamma \gamma }$ (${\mathcal{B}}_{h\to Z\gamma }$) are larger than $\sim 10\%(4\%)$ in the Higgs alignment limit. Moreover, we show that a robust correlation emerges between the deviations in the one-loop corrected $hhh$ coupling and ${\mathcal{B}}_{h\to \gamma \gamma }$ to be, e.g., 200% (50%) and $-10.3\%$ ($-10.8\%$), respectively, under the constraints from theoretical bounds and current experimental data. Using a few benchmark points, we highlight that flavor-violating decays of the additional Higgs bosons can be sizable due to the constrained structure of the Yukawa interactions.

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• Electroweak interaction
• Electroweak symmetry breaking
• Extensions of Higgs sector