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

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

2007-01-03

arxiv.org/abs/hep-ph/0701020v3

J.Phys.G35:055002,2008

Physics

High Energy Physics

High Energy Physics - Phenomenology

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

Scientific paper

10.1088/0954-3899/35/5/055002

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 $J/\psi(\psi^\prime)\to \gamma^*\to VP$. Via study of the isospin violated channels, such as $J/\psi(\psi^\prime)\to \rho\eta$, $\rho\eta^\prime$, $\omega\pi^0$ and $\phi\pi^0$, 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.

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