Study of the electromagnetic transitions $J/\psi \rightarrow P l^+l^-$ and probe dark photon

TL;DR

This paper investigates electromagnetic Dalitz decays of J/ψ to pseudoscalars and lepton pairs, exploring their potential to reveal transition form factors and to search for dark photons in BESIII data.

Contribution

It introduces a method to estimate decay rates using a pole approximation and assesses the potential to detect dark photons through these decays.

Findings

Decay rates estimated with pole approximation.

Potential to detect GeV-scale U bosons in J/ψ decays.

Guidelines for experimental searches at BESIII.

Abstract

We study the electromagnetic Dalitz decay modes of $J/\psi \rightarrow P l^+l^-$ ($P= \pi^0$, $\eta$ or $\eta^\prime$). In these decays, the lepton pairs are formed by internal conversion of an intermediate virtual photon with invariant mass $m_{l^+l^-}$. Study of the effective-mass spectrum of the $l^+l^-$ will shed light on the dynamic transition form factor $F_{J/\psi P}(q^2)$ ($q^2 = m^2_{l^+l^-}$), which characterizes the electromagnetic structure arising at the vertex of the transition $J/\psi$ to pseudoscalars. We also discuss the direct productions of a GeV scale vector $U$ boson in these processes $J/\psi \rightarrow PU$ ($U\rightarrow l^+l^-$). It is responsible for mediating a new $U(1)_d$ interaction, as recently exploited in the context of weakly interacting massive particle dark matter. In this paper, we firstly use the usual pole approximation for the form factor to estimate the decay rate of $J/\psi \rightarrow P l^+l^-$ in the standard model. Then the reach of searching for the dark photon is estimated. We suggest that these Dalitz decays can be used to search for the light $U$ boson in the BESIII experiment with a huge $J/\psi$ data set.