The decay $J/\psi\to\gamma\phi\phi$: spin dependence of amplitude and angular distributions of photons with linear polarizations

TL;DR

This paper derives the spin-dependent decay amplitudes and angular distributions of photons with linear polarization in the decay process of $J/\psi$ to $\phi\phi$, providing a model-independent way to determine the resonance's quantum numbers.

Contribution

It presents a comprehensive analysis of the spin dependence and polarization effects in $J/\psi$ decay, enabling quantum number determination without relying on specific decay models.

Findings

Angular distributions correlate with the resonance's parity and spin.

Photon polarization asymmetries can identify quantum numbers.

Method is model-independent for $X(J^P) \to \phi\phi$ amplitude analysis.

Abstract

Based on the effective invariant amplitudes of the transitions $J/\psi\to\gamma X(J^P)$ and $X(J^P)\to\phi\phi$, the spin dependence of the $J/\psi\to\gamma X(J^P)\to\gamma\phi\phi$ decay amplitude is obtained in the case of the intermediate resonances $X$ with $J^P=0^\pm,1^\pm,2^\pm$. Angular distributions of photons with the definite linear polarizations relative to the plane spanned by the momentum of initial electron and the total momentum of the $\phi\phi$ pair in the reaction $e^+e^-\to J/\psi\to\gamma X(J^P)\to\gamma\phi\phi$ are calculated. It is shown that the sign of the asymmetry of the distributions of the photons polarized in the above plane and orthogonal to it correlates with the signature $P_X(-1)^{J_X}$ of the $X$ resonance with given spin-parity $J_X^{P_X}$ so it may help to establish this quantum number in a way which does not depend on the specific model of the $X(J^P)\to\phi\phi$ amplitude.