Indirect signs of the Peccei-Quinn mechanism

In the standard model, the renormalization of the QCD vacuum angle theta is extremely tiny, and small theta is technically natural. In the general standard model effective field theory (SMEFT), however, Delta theta is quadratically divergent, reflecting the fact that new sources of hadronic CP-violation typically produce O(1) threshold corrections to theta. The observation of such CP-violating interactions would therefore be in tension with solutions to the strong CP problem in which theta = 0 is an ultraviolet boundary condition, pointing to the Peccei-Quinn mechanism as the explanation for why theta is small in the infrared. We study the quadratic divergences in theta 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.