Search for a $CP$-odd light Higgs boson in $J/\psi \to \gamma {A}^{0}$

Using $J/\psi $ radiative decays from 9.0 billion $J/\psi $ events collected by the BESIII detector, we search for di-muon decays of a $CP$-odd light Higgs boson (${A}^{0}$), predicted by many new physics models beyond the Standard Model, including the next-to-minimal supersymmetric Standard Model. No evidence for the $CP$-odd light Higgs production is found, and we set 90% confidence level upper limits on the product branching fraction $B\left(J/\psi \to \gamma {A}^{0}\right)×B\left({A}^{0}\to {\mu }^{+}{\mu }^{-}\right)$ in the range of $\left(1.2-778.0\right)×{10}^{-9}$ for $0.212\le {m}_{{A}^{0}}\le 3.0\text{}\text{}\mathrm{GeV}/{c}^{2}$. The new measurement is a 6–7 times improvement over our previous measurement, and is also slightly better than the BABAR measurement in the low-mass region for $\mathrm{tan}\beta =1$.