The decay J/ ψ→ γϕϕ: Spin dependence of amplitude and angular distributions of photons with linear polarizations

Based on the effective invariant amplitudes of the transitions J/ ψ→ γX(J^P) and X(J^P) → ϕϕ, the spin dependence of the J/ ψ→ γX(J^P) → γϕϕ decay amplitude is obtained in the case of the intermediate resonances X with J^P= 0 ^±, 1 ^±, 2 ^±. 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 ϕϕ pair in the reaction e⁺e^-→ J/ ψ→ γX(J^P) → γϕϕ 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 PX(-1)JX of the X resonance with given spin-parity JXPX 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) → ϕϕ amplitude.