Improved Indirect Limits on Muon Electric Dipole Moment
Yohei Ema, Ting Gao, Maxim Pospelov
Abstract
Given current discrepancy in muon $g\ensuremath{-}2$ and future dedicated efforts to measure muon electric dipole moment (EDM) ${d}_{\ensuremath{\mu}}$, we assess the indirect constraints imposed on ${d}_{\ensuremath{\mu}}$ by the EDM measurements performed with heavy atoms and molecules. We notice that the dominant muon EDM effect arises via the muon-loop induced ``light-by-light'' $CP$-odd amplitude $\ensuremath{\propto}\mathbf{B}{\mathbf{E}}^{3}$, and in the vicinity of a large nucleus the corresponding parameter of expansion can be significant, $e{E}_{\mathrm{nucl}}/{m}_{\ensuremath{\mu}}^{2}\ensuremath{\sim}0.04$. We compute the ${d}_{\ensuremath{\mu}}$-induced Schiff moment of the $^{199}\mathrm{Hg}$ nucleus, and the linear combination of ${d}_{e}$ and semileptonic ${C}_{S}$ operator (dominant in this case) that determine the $CP$-odd effects in the ThO molecule. The results, ${d}_{\ensuremath{\mu}}(^{199}\mathrm{Hg})<6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}20}\text{ }\text{ }e\text{ }\mathrm{cm}$ and ${d}_{\ensuremath{\mu}}(\mathrm{ThO})<2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}20}\text{ }\text{ }e\text{ }\mathrm{cm}$, constitute approximately threefold and ninefold improvements over the limits on ${d}_{\ensuremath{\mu}}$ extracted from the Brookhaven National Laboratory muon beam experiment.