Study on the effects of the light CP-odd Higgs via the leptonic decays of pseudoscalar mesons

Abstract

To explain the anomalously large decay rate of $Σ^+\to p+μ^+μ^-$, it was proposed that a new mechanism where a light CP-odd pseudoscalar boson of $m_{A_1^0}=214.3$ MeV makes a crucial contribution. Later, some authors have studied the transition $π^0\to e^+e^-$ and $Υ\to γA_1^0$ in terms of the same mechanism and their result indicates that with the suggested mass one cannot fit the data. This discrepancy might be caused by experimental error of $Σ^+\to p+μ^+μ^-$ because there were only a few events. Whether the mechanism is a reasonable one motivates us to investigate the transitions $π^0\to e^+e^-; η(η^\prime)\to μ^+μ^-; η_c\to μ^+μ^-; η_b\toτ^+τ^-$ within the same framework. It is noted that for $π^0\to e^+e^-$, the standard model (SM) prediction is smaller than the data, whereas the experimental central value of $η\to μ^+μ^-$ is also above the SM prediction. It means that there should be extra contributions from other mechanisms and the contribution of $A_1^0$ may be a possible one. Theoretically calculating the branching ratios of the concerned modes, we would check if we can obtain a universal mass for $A_1^0$ which reconcile the theoretical predictions and data for all the modes. Unfortunately, we find that it is impossible to have such a mass with the same coupling $|g_\ell|$. Therefore we conclude that the phenomenology does not favor such a light $A_1^0$, even though a small window is still open.