Anomaly-free axion dark matter in three Higgs doublet model and its phenomenological implications

Abstract: We study phenomenological implications of an axion that arises as a pseudo Nambu-Goldstone boson due to the spontaneous breaking of anomaly-free global flavor symmetry. One interesting possibility for such anomaly-free axion to explain dark matter (DM) is when it has a mass of order keV and an intermediate scale decay constant, since it can be explored through direct search experiments, X-ray observations, various stellar cooling processes, and the misalignment mechanism naturally explains the DM abundance. As a concrete renormalizable model of such axion, we consider an extended Higgs sector with global flavor symmetry, which consists of three Higgs doublet fields and three singlet Higgs fields with $U(1)_{\rm B-L}$ charges. We identify viable parameter regions that satisfy theoretical bounds on the Higgs potential and various experimental limits on this model, and evaluate the mass spectra of the axion and extra Higgs bosons. We find that even an anomaly-free axion can generally couple to photons through mixing with CP-odd Higgs, and that its strength depends on the vacuum expectation values of the Higgs doublets as well as the axion mass. As a result, the ratios of the vacuum expectation values of the Higgs doublets are tightly constrained to satisfy the X-ray constraints. We show the favored parameter region where axion DM explains the XENON1T excess. We also demonstrate that the axion-electron coupling is correlated with the extra Higgs boson masses and mixing angles for CP-even Higgs bosons. Thus, if the axion is detected in future observations, the extra Higgs boson masses and the coupling of the standard model-like Higgs boson with the weak gauge bosons are restricted. This is a good example of the synergy between searches for the axion DM and the BSM around the electroweak scale.