Decays of $J/\psi$ and ${\psi }^{\prime }$ into vector and pseudoscalar meson and the pseudoscalar glueball-$q\bar{q}$ mixing

Abstract

We introduce a parametrization scheme for $J/\psi ({\psi }^{\prime })\to VP$ where the effects of SU(3) flavor symmetry breaking and doubly OZI-rule violation (DOZI) can be parametrized by certain parameters with explicit physical interpretations. This scheme can be used to clarify the glueball-$q\bar{q}$ mixing within the pseudoscalar mesons. We also include the contributions from the electromagnetic (EM) decays of $J/\psi$ and ${\psi }^{\prime }$ via $J/\psi ({\psi }^{\prime })\to {\gamma }^{\ast }\to VP$. Via study of the isospin violated channels, such as $J/\psi ({\psi }^{\prime })\to \rho \eta$, $\rho {\eta }^{\prime }$, $\omega {\pi }^0$ and $\varphi {\pi }^0$, reasonable constraints on the EM decay contributions are obtained. With the up-to-date experimental data for $J/\psi ({\psi }^{\prime })\to VP$, $J/\psi ({\psi }^{\prime })\to \gamma P$ and $P\to \gamma \gamma$, etc, we arrive at a consistent description of the mentioned processes with a minimal set of parameters. As a consequence, we find that there exists an overall suppression of the ${\psi }^{\prime }\to 3g$ form factors, which sheds some light on the long-standing "$\rho \pi$ puzzle". By determining the glueball components inside the pseudoscalar $\eta$ and ${\eta }^{\prime }$ in three different glueball-$q\bar{q}$ mixing schemes, we deduce that the lowest pseudoscalar glueball, if exists, has rather small $q\bar{q}$ component, and it makes the $\eta (1405)$ a preferable candidate for $0^{-+}$ glueball.

Revised version to appear on J. Phys. G; An error in the code was corrected. There's slight change to the numerical results, while the conclusion is intact

References in corpus (2)

• Study on contributions of hadronic loops to decays of $J/\psi \to$ vector $+$ pseudoscalar mesons
• Study of electromagnetic decay of $J/\psi$ and ${\psi }^{\prime }$ to vector and pseudoscalar

Cited by in corpus (18)

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