High Scale Validity of the DFSZ Axion Model with Precision

With the assumption of classical scale invariance at the Planck scale, the DFSZ axion model can generate the Higgs mass terms of the appropriate size through technically natural parameters and may be valid up to the Planck scale. We discuss the high scale validity of the Higgs sector, namely the absence of Landau poles and the vacuum stability. The Higgs sector is identical to that of the type-II two Higgs doublet model with a limited number of the Higgs quartic couplings. We utilize the state-of-the-art method to calculate vacuum decay rates and find that they are enhanced at most by 10^10 compared with the tree level evaluation. We also discuss the constraints from flavor observables, perturbative unitarity, oblique parameters and collider searches. We find that the high scale validity tightly constrains the parameter region, but there is still a chance to observe at most about 10% deviation of the $125~{\rm GeV}$ Higgs couplings to the fermions.