${\eta }_c$ mixing effects on charmonium and $B$ meson decays

Abstract

We include the ${\eta }_c$ meson into the $\eta$-${\eta }^{\prime }$-$G$ mixing formalism constructed in our previous work, where $G$ represents the pseudoscalar gluball. The mixing angles in this tetramixing matrix are constrained by theoretical and experimental implications from relevant hadronic processes. Especially, the angle between ${\eta }_c$ and $G$ is found to be about $11^{\circ }$ from the measured decay widths of the ${\eta }_c$ meson. The pseudoscalar glueball mass $m_G$, the pseudoscalar densities $m_{qq,ss,cc}$ and the U(1) anomaly matrix elements associated with the mixed states are solved from the anomalous Ward identities. The solution $m_G\approx 1.4$ GeV obtained from the $\eta$-${\eta }^{\prime }$-$G$ mixing is confirmed, while $m_{qq}$ grows to above the pion mass, and thus increases perturbative QCD predictions for the branching ratios $Br(B\to {\eta }^{\prime }K)$. We then analyze the ${\eta }_c$-mixing effects on charmonium magnetic dipole transitions, and on the $B\to {\eta }^{(\prime )}{K}_S$ branching ratios and CP asymmetries, which further improve the consistency between theoretical predictions and data. A predominant observation is that the ${\eta }_c$ mixing enhances the perturbative QCD predictions for $Br(B\to {\eta }^{\prime }K)$ by 18%, but does not alter those for $Br(B\to \eta K)$. The puzzle due to the large $Br(B\to {\eta }^{\prime }K)$ data is then resolved.

12 pages, version to appear in PRD

References in corpus (12)

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• Measurement of the pseudoscalar mixing angle and ${\eta }^{\prime }$ gluonium content with KLOE detector
• Pseudoscalar glueball mass from $\eta$-${\eta }^{\prime }$-$G$ mixing
• Branching ratios and CP asymmetries of $B\to K{\eta }^{(\prime )}$ decays in the pQCD approach
• Gluonic contribution to $B\to {\eta }^{(\prime )}$ form factors
• Decays of $J/\psi$ and ${\psi }^{\prime }$ into vector and pseudoscalar meson and the pseudoscalar glueball-$q\bar{q}$ mixing
• Hadronic loop contributions to $J/\psi$ and ${\psi }^{\prime }$ radiative decays into $\gamma {\eta }_c$ or $\gamma {\eta }_c^{\prime }$
• $O({\alpha }_s{v}^2)$ Corrections to Hadronic and Electromagnetic Decays of ${}^1{S}_0$ Heavy Quarkonium
• $B\to {\eta }^{(\prime )}({\ell }^{-}{\bar{\nu }}_{\ell },{\ell }^{+}{\ell }^{-},K,K^{\ast })$ decays in the quark-flavor mixing scheme
• Okubo-Zweig-Iizuka-rule violation and B\to η^{(\prime)}K branching ratios
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Cited by in corpus (20)

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• Implications on $\eta$-${\eta }^{\prime }$-glueball mixing from $B_{d/s}\to J/\Psi {\eta }^{{(}^{\prime })}$ Decays
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• Updated study of the ${\eta }_c$ and ${\eta }_c^{\prime }$ decays into light vector mesons
• Revisiting the pseudoscalar meson and glueball mixing and key issues in the search for pseudscalar glueball state
• The Glueball content of ${\eta }_c$
• New puzzle in charmonium decays
• Insight into $f_0(980)$ through the $B_{(s)}$ charmed decays
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• Dispersive analysis of excited glueball states
• Gluon-pair-Creation Production Model of Strong Interaction Vertices
• Mixing effects of $\eta -{\eta }^{\prime }$ in ${\Lambda }_b\to \Lambda {\eta }^{{(}^{\prime })}$ decays
• An analysis of B meson decays to two light pseudoscalar nonets with deltaS=1 in QCD factorization approach