Accidental Peccei-Quinn Symmetry from Chiral Gauge Symmetry and Mirror QCD

We present a solution to the strong CP problem in which a simple chiral U(1) gauge symmetry gives rise to an accidental Peccei-Quinn symmetry that is both explicitly and spontaneously broken by mirror QCD dynamics, yielding a framework without massless fermions or a light QCD axion. The model contains no stable domain walls or colored relics, and it accommodates a sufficiently high reheating temperature to account for the baryon asymmetry of the Universe via leptogenesis. Metastable domain walls and first-order mirror QCD phase transition generate a stochastic background of primordial gravitational waves. Additionally, one of the pseudo-Nambu-Goldstone bosons serves as a viable WIMP dark matter candidate. The gauge boson associated with the chiral U(1) gauge symmetry, which kinetically mixes with the Standard Model hypercharge gauge boson, provides a vector portal connecting dark matter to the Standard Model and plays a central role in the dark-matter phenomenology. Colored pseudo-Nambu-Goldstone bosons can be probed at the LHC through searches for dijet resonances, jets plus missing energy, multijet events with leptons, and displaced vertices.