Indirect Signs of the Peccei-Quinn Mechanism

Abstract

In the Standard Model, the renormalization of the QCD vacuum angle $θ$ is extremely tiny, and small $θ$ is technically natural. In the general Standard Model effective field theory (SMEFT), however, $Δθ$ is quadratically divergent, reflecting the fact that new sources of hadronic CP-violation typically produce $\mathcal O(1)$ threshold corrections to $θ$. The observation of such CP-violating interactions would therefore be in tension with solutions to the strong CP problem in which $θ=0$ is an ultraviolet boundary condition, pointing to the Peccei-Quinn mechanism as the explanation for why $θ$ is small in the infrared. We study the quadratic divergences in $θ$ arising from dimension-6 SMEFT operators and discuss the discovery prospects for these operators at electric dipole moment experiments, the LHC, and future proton-proton colliders.