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 ∝ BE³, and in the vicinity of a large nucleus the corresponding parameter of expansion can be significant, eE_nucl/m_μ² ∼ 0.04. We compute the dμ-induced Schiff moment of the ¹⁹⁹Hg nucleus, and the linear combination of de and semileptonic CS operator (dominant in this case) that determine the CP-odd effects in the ThO molecule. The results, d_μ(¹⁹⁹Hg) < 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.