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Improved indirect limits on charm and bottom quark EDMs

We derive indirect limits on the charm and bottom quark electric dipole moments (EDMs) from paramagnetic AMO and neutron EDM experiments. The charm and bottom quark EDMs generate $CP$-odd photon-gluon operators and light quark EDMs at the $c$- and $b$-quark mass thresholds. These $CP$-odd operators induce the $CP$-odd semi-leptonic operator $C_S$ and the neutron EDM below the QCD scale that are probed by the paramagnetic and neutron EDM experiments, respectively. The bound from $C_S$ is $\vert d_c \vert < 1.3\times 10^{-20}\,e\,\mathrm{cm}$ for the charm quark and $\vert d_b \vert < 7.6\times 10^{-19}\,e\,\mathrm{cm}$ for the bottom quark, with its uncertainty estimated as 10%. The neutron EDM provides a stronger bound, $\vert d_c \vert < 6\times 10^{-22}\,e\,\mathrm{cm}$ and $\vert d_b \vert < 2\times 10^{-20}\,e\,\mathrm{cm}$, though with a larger hadronic uncertainty.