Indirect Signs of the Peccei-Quinn Mechanism

Abstract

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

27 pages, 3 figures. Comments welcome!