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 ${\Lambda }_{\mathrm{SI}}$ exhibit enhanced sensitivity to external sources of $CP$ violation. In the presence of higher-dimensional $CP$-odd sources at a scale ${\Lambda }_{\mathrm{CP}}$, the same mechanisms that enhance the axion mass also modify the axion potential, shifting the potential minimum by a factor $\propto {\Lambda }_{\mathrm{SI}}^2/{\Lambda }_{\mathrm{CP}}^2$. 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 $\gtrsim 100$MeV, arising from new dynamics at ${\Lambda }_{\mathrm{SI}}\lesssim 10^{10}$GeV, $CP$ violation generated up to the Planck scale can be probed by future electric dipole moment experiments.

Comments: 21 pages, 4 figures; v2: version published in PRD