Improved indirect limits on muon EDM

Abstract

Given current discrepancy in muon $g-2$ and future dedicated efforts to measure muon electric dipole moment (EDM) $d_{\mu }$, we assess the indirect constraints imposed on $d_{\mu }$ 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 $\propto \mathbf{B}{\mathbf{E}}^3$, and in the vicinity of a large nucleus the corresponding parameter of expansion can be significant, $e{E}_{\mathrm{nucl}}/m_{\mu }^2\sim 0.04$. We compute the $d_{\mu }$-induced Schiff moment of the ${}^{199}$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 ThO molecule. The results, $d_{\mu }{(}^{199}\mathrm{Hg})<6\times 10^{-20}e$cm and $d_{\mu }(\mathrm{ThO})<2\times 10^{-20}e$cm, constitute approximately three- and nine-fold improvements over the limits on $d_{\mu }$ extracted from the BNL muon beam experiment.

Comments: 5 pages, 2 figures; v2: references added; v3: supplemental material added, version accepted in PRL