Hadrophobic Axion from GUT

We propose a new kind of axion model from the Grand Unified Theory (GUT) based on $SU(5)\times U(1)_{\rm PQ}$. We show that for a certain charge assignment and possible flavor models the axion is naturally hadrophobic, and provide a novel explanation for the required condition using the isospin symmetry. If this axion is the QCD axion that solves the strong CP problem, its photon coupling is larger than the conventional GUT QCD axion by a factor of $\sim 3.6$. Furthermore, in order to satisfy the limit on the axion-electron coupling from the tip of red giant branch, we impose the condition of electrophobia to determine a possible PQ charge assignment consistent with GUT. Then we discuss the possibility that the hadrophobic and electrophobic axion is an inflaton and dark matter as in the ALP 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 together in various experiments would be a probe for GUT as well as the origin of flavor.