Pseuduscalar Heavy Quarkonium Decays With Both Relativistic and QCD Radiative Corrections

Abstract

We estimate the decay rates of ${\eta }_c\to 2\gamma$, ${\eta }_c^{\prime }\to 2\gamma$, and $J/\psi \to e^{+}{e}^{-}$, ${\psi }^{\prime }\to e^{+}{e}^{-}$, by taking into account both relativistic and QCD radiative corrections. The decay amplitudes are derived in the Bethe-Salpeter formalism. The Bethe-Salpeter equation with a QCD-inspired interquark potential are used to calculate the wave functions and decay widths for these $c\bar{c}$ states. We find that the relativistic correction to the ratio $R\equiv \Gamma ({\eta }_c\to 2\gamma )/\Gamma (J/\psi \to e^{+}{e}^{-})$ is negative and tends to compensate the positive contribution from the QCD radiative correction. Our estimate gives $\Gamma ({\eta }_c\to 2\gamma )=(6-7)keV$ and $\Gamma ({\eta }_c^{\prime }\to 2\gamma )=2keV$, which are smaller than their nonrelativistic values. The hadronic widths $\Gamma ({\eta }_c\to 2g)=(17-23)MeV$ and $\Gamma ({\eta }_c^{\prime }\to 2g)=(5-7)MeV$ are then indicated accordingly to the first order QCD radiative correction, if ${\alpha }_s(m_c)=0.26-0.29$. The decay widths for $b\bar{b}$ states are also estimated. We show that when making the assmption that the quarks are on their mass shells our expressions for the decay widths will become identical with that in the NRQCD theory to the next to leading order of $v^2$ and ${\alpha }_s$.

14 pages LaTex (2 figures included)

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• Spectroscopy of ground and excited states of pseudoscalar and vector charmonium and bottomonium
• Tests of Two-Body Dirac Equation Wave Functions in the Decays of Quarkonium and Positronium into Two Photons
• Two-photon width of eta_c and eta'_c from Heavy-Quark Spin Symmetry
• Large corrections to asymptotic $F_{{\eta }_c\gamma }$ and $F_{{\eta }_b\gamma }$ in the light-cone perturbative QCD
• Decay rates of charmonia within a quark-antiquark confining potentials
• Relativistic Correction to Color Octet J/psi Production at Hadron Colliders
• η_b and η_c radiative decays in the Salpeter model with the AdS/QCD inspired potential
• Heavy quarkonium 2S states in light-front quark model
• Revisiting the $P$-wave charmonium radiative decays $h_c\to \gamma {\eta }^{(\prime )}$ with relativistic corrections
• How vacuum fluctuations determine the properties of the vacuum
• Radiative and leptonic decays of the pseudoscalar charmonium state ${\eta }_c$
• Measurement of eta_c(1S), eta_c(2S) and non-resonant eta' pi+ pi- production via two-photon collisions