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

Abstract

We introduce a parametrization scheme for $J/\ddot{I}ˆ(\ddot{I}{ˆ}^{\prime })\to VP$ 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 $J/\ddot{I}ˆ$ and $\ddot{I}{ˆ}^{\prime }$ via $J/ψ(ψ^\prime)\to γ^*\to VP$. Via study of the isospin violated channels, such as $J/\ddot{I}ˆ(\ddot{I}{ˆ}^{\prime })\to \ddot{I}\hat{I}\cdot$, $\ddot{I}\hat{I}{\cdot }^{\prime }$, $\ddot{I}‰\ddot{I}{€}^0$ and $\ddot{I}•\ddot{I}{€}^0$, reasonable constraints on the EM decay contributions are obtained. With the up-to-date experimental data for $J/\ddot{I}ˆ(\ddot{I}{ˆ}^{\prime })\to VP$, $J/\ddot{I}ˆ(\ddot{I}{ˆ}^{\prime })\to {\hat{I}}^{3}P$ and $P\to {\hat{I}}^3{\hat{I}}^3$, 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 $\ddot{I}{ˆ}^{\prime }\to 3g$ form factors, which sheds some light on the long-standing "$\ddot{I}\ddot{I}€$ puzzle". By determining the glueball components inside the pseudoscalar $\hat{I}\cdot$ and $\hat{I}{\cdot }^{\prime }$ 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 $\hat{I}\cdot (1405)$ 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