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Diphotons, New Vacuum Angles, and Strong CP

The Standard Model contains a well-understood, natural, spin-0 diphoton resonance: the $π^0$. Numerous studies have pointed out that the hint of a new diphoton resonance at 750 GeV could be a pion analog, identified with the pseudo-Nambu-Goldstone boson of a chiral symmetry spontaneously broken by new strong dynamics at the TeV scale. These "hypercolor" models are generically expected to violate parity through a topological angle $\tildeθ$. We discuss the physics of $\tildeθ$ and its impact on the phenomenology of the new sector. We also describe some of the theoretical implications of a nonzero $\tildeθ$. In particular, $\tildeθ$ can generate an ${\cal O}(1)$ threshold correction to the QCD vacuum angle $θ$ near the TeV scale, sharply constraining ultraviolet solutions to the strong CP problem. Alternatively, finding that $\tildeθ$ is small may be interpreted as evidence in favor of UV solutions to strong CP, particularly those based on spontaneously broken P or CP symmetries.