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Rare decay $π^{0}\to e^+ e^-$ constraints on the light CP-odd Higgs in NMSSM

We constrain the light CP-odd Higgs $A_{1}^{0}$ in NMSSM via the rare decay $π^{0}\to e^{+}e^{-}$. It is shown that the possible $3σ$ discrepancy between theoretical predictions and the recent KTeV measurement of ${\cal B}(π^{0}\to e^+ e^-)$ cannot be resolved when the constraints from $Υ\toγA_1^0$, $a_μ$ and $π^{0}\to γγ$ are combined. Furthermore, the combined constraints also exclude the scenario involving $m_{A_1^0}=214.3$ MeV, which is invoked to explain the anomaly in the $Σ^{+}\to p μ^{+}μ^{-}$ decay found by the HyperCP Collaboration.