Improved indirect limits on muon EDM

TL;DR

This paper refines the indirect experimental limits on the muon electric dipole moment by analyzing heavy atom and molecule measurements, resulting in significantly tighter constraints than previous direct experiments.

Contribution

The authors provide new calculations linking muon EDM effects to atomic and molecular observables, improving existing bounds by factors of three to nine.

Findings

New upper limit on muon EDM from Hg atom measurements: < 6×10^{-20} e·cm

New upper limit on muon EDM from ThO molecule: < 2×10^{-20} e·cm

Significant improvement over previous direct muon EDM bounds.

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 $\propto{\bf B}{\bf E}^3$, and in the vicinity of a large nucleus the corresponding parameter of expansion can be significant, $eE_{\rm nucl}/m_\mu^2 \sim 0.04$. 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, $d_\mu(^{199}{\rm Hg}) < 6\times 10^{-20}e$cm and $d_\mu({\rm ThO}) < 2\times 10^{-20}e$cm, constitute approximately three- and nine-fold improvements over the limits on $d_\mu$ extracted from the BNL muon beam experiment.