Improved Indirect Limits on Muon Electric Dipole Moment

Given current discrepancy in muon g-2 and future dedicated efforts to measure muon electric dipole moment (EDM) d_{μ}, we assess the indirect constraints imposed on d_{μ} 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 ∝BE^{3}, and in the vicinity of a large nucleus the corresponding parameter of expansion can be significant, eE_{nucl}/m_{μ}^{2}∼0.04. We compute the d_{μ}-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 the ThO molecule. The results, d_{μ}(^{199}Hg)<6×10^{-20}  e cm and d_{μ}(ThO)<2×10^{-20}  e cm, constitute approximately threefold and ninefold improvements over the limits on d_{μ} extracted from the Brookhaven National Laboratory muon beam experiment.