Triangle singularities in $J/\psi \to \eta {\pi }^0\varphi$ and ${\pi }^0{\pi }^0\varphi$

Abstract

The BESIII Collaboration recently reported the observation of the $a_0(980{)}^0-f_0(980)$ mixing in the isospin breaking decay $J/\psi \to \eta {\pi }^0\varphi$. In the Dalitz plot for that decay with the $\eta$ reconstructed from two photons, there is a band around $1.4$~GeV on the ${\pi }^0\varphi$ distribution. In general, this peak can be due to a resonance or a kinematic effect. In this paper, we study the effects of a set of $K^{\ast }K\bar{K}$ triangle diagrams, and show that due to triangle singularities such diagrams can lead to a peak around 1.4~GeV in the ${\pi }^0\varphi$ invariant mass distribution. The Dalitz plot induced by such a mechanism has a feature consistent with the BESIII observation, namely events along the band accumulate at both ends close to the Dalitz plot boundary. The effect of the same mechanism on the $J/\psi \to {\pi }^0{\pi }^0\varphi$ and $J/\psi \to \eta {\pi }^0{K}^{+}{K}^{-}$ decays are also investigated. We suggest to take more data for the $J/\psi \to \eta {\pi }^0\varphi \to \eta {\pi }^0{K}^{+}{K}^{-}$ and check whether the structure around $1.4$~GeV persists for the $K^{+}{K}^{-}$ invariant mass away from the $\varphi$ mass region. This is crucial for understanding whether the band is due to triangle singularities or due to a resonance. Were it the latter, the band should remain while it would not if it is due to the former.

26 pages,9 figures