Annihilation Rate of $2^{++}$ Charmonium and Bottomonium

Abstract

Two-photon annihilation rates of $2^{+}$ tensor charmonium and bottomonium up to third radial excited states are estimated in the relativistic Salpeter method. Full Salpeter equation for $2^{+}$ tensor state is solved with a well defined relativistic wave function and we calculated the annihilation amplitude using the Mandelstam formalism. Our estimates of the decay widths are: $\Gamma ({\chi }_{c2}\to 2\gamma )=501$ eV, $\Gamma ({\chi }_{c2}^{\prime }\to 2\gamma )=534$ eV, $\Gamma ({\chi }_{b2}\to 2\gamma )=7.4$ eV and $\Gamma ({\chi }_{b2}^{\prime }\to 2\gamma )=7.7$ eV. We also give total decay widths of the lowest states estimated by the two-gluon decay rates, and the results are: ${\Gamma }_{tot}({\chi }_{c2})=2.64$ MeV, ${\Gamma }_{tot}({\chi }_{b2})=0.220$ MeV and ${\Gamma }_{tot}({\chi }_{b2}^{\prime })=0.248$ MeV.

9 pages,1 figure, 3 tables

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• $D$-Wave Charmonia ${\eta }_{c2}$($1{}^1{D}_2$), ${\psi }_2$($1{}^3{D}_2$), and ${\psi }_3$($1{}^3{D}_3$) in $B_c$ Decays
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• Mixing angle and decay constants of $J^P=1^{+}$ heavy-light mesons
• Average speed and its powers $v^n$ of a heavy quark in quarkonia
• The rare semi-leptonic $B_c$ decays involving orbitally excited final mesons
• The electromagnetic decays of $X(3823)$ as the ${\psi }_2(1^3{D}_2)$ state and its radial excited states
• Strong decays of $D_J(3000)$ and $D_{sJ}(3040)$
• Strong decays of $2^{+}$ charm and charm-strange mesons
• The study of light invisible particles in $B_c$ decays
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• Strong Decays of the Orbitally Excited Scalar $D_0^{\ast }$ Mesons
• Hadronic Production of $ch{i}_c$-mesons at LHC
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• Strong decays of excited $2^{+}$ charmed mesons
• Rare radiative decays of the $B_c$ meson