Hadrophobic axion from a GUT

We propose a new kind of axion model derived from the grand unified theory (GUT) based on $\mathrm{SU}\left(5\right)\times U(1{)}_{\mathrm{PQ}}$. We demonstrate that, given a certain charge assignment and potential flavor models, the axion is naturally hadrophobic and provides a novel explanation for the required condition using isospin symmetry. This axion can be the QCD axion that solves the strong $CP$ problem. Furthermore, to satisfy the limit on the axion-electron coupling from the tip of the red giant branch, we impose the condition of electrophobia to determine a possible Peccei-Quinn charge assignment consistent with GUT. We then discuss the possibility that the hadrophobic and electrophobic axion serves as an inflaton and dark matter, as in the axionlike particle miracle scenario. Interestingly, in the viable parameter region, the strong $CP$ phase must be suppressed, providing another solution to the strong $CP$ problem. This scenario is intimately linked to flavor physics, dark matter searches, and stellar cooling. Detecting such an axion with peculiar couplings in various experiments would serve as a probe for GUT and the origin of flavor.