Enhanced EDMs from small instantons

Abstract

We show that models in which the strong $CP$ problem is solved by introducing an axion field with a mass enhanced by non-QCD UV dynamics at a scale ${\mathrm{\ensuremath{\Lambda}}}_{\mathrm{SI}}$ exhibit enhanced sensitivity to external sources of $CP$ violation. In the presence of higher-dimensional $CP$-odd sources at a scale ${\mathrm{\ensuremath{\Lambda}}}_{\mathrm{CP}}$, the same mechanisms that enhance the axion mass also modify the axion potential, shifting the potential minimum by a factor $\ensuremath{\propto}{\mathrm{\ensuremath{\Lambda}}}_{\mathrm{SI}}^{2}/{\mathrm{\ensuremath{\Lambda}}}_{\mathrm{CP}}^{2}$. This phenomenon of $CP$-violation enhancement, which puts stringent constraints on the scale of new physics, is explicitly demonstrated within a broad class of ``small instanton'' models with $CP$-odd sources arising from the dimension-six Weinberg gluonic and four-fermion operators. We find that for heavy axion masses $\ensuremath{\gtrsim}100\text{ }\text{ }\mathrm{MeV}$, arising from new dynamics at ${\mathrm{\ensuremath{\Lambda}}}_{\mathrm{SI}}\ensuremath{\lesssim}{10}^{10}\text{ }\text{ }\mathrm{GeV}$, $CP$ violation generated up to the Planck scale can be probed by future electric dipole moment experiments.