$γ, J/ψ$ production through ISR process in electron-positron annihilation at B-factories

We study the Initial state radiation (ISR) process, $e^- e^+ \rightarrow^*γ\rightarrow γ+J/ψ$ observed at high luminosity $e^- e^+$ colliders such as B-factories, with the ISR photon being emitted through the initial electron or positron, prior to their annihilation. The emitted $J/Ψ$ is produced through the photon fragmentation process, with the produced $J/ψ$ in turn decaying into a pair of leptons, $μ^-+μ^+$ through the leptonic decay process, $J/Ψ\rightarrow γ^*\rightarrow γμ^- μ^+$. The cross section for the $J/Ψ$ production, and the branching ratio for the leptonic decay of $J/Ψ\rightarrow μ^- μ^+$, both calculated in the framework of Bethe-Salpeter equation are used to work out the cross section for the complete process, $e^- e^+ \rightarrow γ+J/ψ\rightarrow γ+μ^- +μ^+$. Our results are compared with the BaBar data, and other models. This study is then extended to production and decays of $Υ(1S)$ through the ISR process.