The decay : Spin dependence of amplitude and angular distributions of photons with linear polarizations

A. A. Kozhevnikov

doi:10.1140/epja/i2019-12845-8

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Hadrons and Nuclei

Eur. Phys. J. A (2019) 55: 155
https://doi.org/10.1140/epja/i2019-12845-8

Regular Article - Theoretical Physics

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

A. A. Kozhevnikov¹^,2^*

¹ Laboratory of Theoretical Physics, S. L. Sobolev Institute for Mathematics, Novosibirsk, Russia
² Novosibirsk State University, Novosibirsk, Russia

^* e-mail: kozhev@math.nsc.ru

Received: 12 April 2019
Accepted: 3 August 2019
Published online: 20 September 2019

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.