$\Psi(2S)$ Decay to $J/\Psi(1S)$ + 2$\pi$ or $J/\Psi(1S)$ +$\sigma$ + 2$\pi$

TL;DR

This paper estimates the decay rates and angular distributions of $ ext{Ψ}(2S)$ decaying into $J/ ext{Ψ}(1S)$ plus two pions or a sigma and two pions, using the mixed hybrid theory and known coupling constants.

Contribution

It extends previous research by estimating decay rates for $ ext{Ψ}(2S)$ to $J/ ext{Ψ}(1S)$ plus $ ext{σ}$ and two pions, incorporating the $ ext{σ} ightarrow ext{π}^+ + ext{π}^-$ transition.

Findings

Estimated decay rates for $ ext{Ψ}(2S)$ to $J/ ext{Ψ}(1S)$ + 2$ ext{π}$ and $J/ ext{Ψ}(1S)$ + $ ext{σ}$ + 2$ ext{π}$.

Calculated angular distributions for the decay processes.

Extended previous models to include $ ext{σ}$ decay channels.

Abstract

The BES Collaboration has measured $\Psi(2S)$ decay to $J/\Psi \pi^+\pi^-$. Using the mixed hybrid theory for the $\Psi(2S)$ we estimate the decay to $J/\Psi(1S)$ + $\sigma$. Using the known $\sigma \rightarrow 2\pi$ coupling constant, we estimate the $\Psi(2S)$ to $J/\Psi(1S)$ + $2\pi$ decay rate and angular distribution. This is an extension of our previous research on $\Psi(2S)$ Decay to $J/\Psi(1S)$ +$\sigma$ + 2$\pi^o$, without the production of 2$\pi^o$, and with an estimate of the $\sigma \rightarrow \pi^+ + \pi^-$ transition.