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

Abstract.

Based on the effective invariant amplitudes of the transitions $J/\psi\rightarrow\gamma X(J^{P})$ and $X(J^{P}) \rightarrow\phi\phi$, the spin dependence of the $J/\psi \rightarrow\gamma X(J^{P})\rightarrow\gamma\phi\phi$ 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 $e^{+}e^{-}\rightarrow J/\psi\rightarrow\gamma X(J^{P})\rightarrow \gamma\phi\phi$ 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 $X(J^{P}) \rightarrow\phi\phi$ amplitude.