Annihilation Rates of ${}^3{D}_2(2^{--})$ and ${}^3{D}_3(3^{--})$ Heavy Quarkonia

Abstract

We calculate the annihilation decay rates of the ${}^3{D}_2(2^{--})$ and ${}^3{D}_3(3^{--})$ charmonia and bottomonia by using the instantaneous Bethe-Salpeter method. The wave functions of states with quantum numbers $J^{PC}=2^{--}$ and $3^{--}$ are constructed. By solving the corresponding instantaneous Bethe-Salpeter equations, we obtain the mass spectra and wave functions of the quarkonia. The annihilation amplitude is written within Mandelstam formalism and the relativistic corrections are taken into account properly. This is important, especially for high excited states, since their relativistic corrections are large. The results for the $3g$ channel are as follows: ${\Gamma }_{{}^3{D}_2(c\bar{c})\to ggg}=9.24$ keV, ${\Gamma }_{{}^3{D}_3(c\bar{c})\to ggg}=25.0$ keV, ${\Gamma }_{{}^3{D}_2(b\bar{b})\to ggg}=1.87$ keV, and ${\Gamma }_{{}^3{D}_3(b\bar{b})\to ggg}=0.815$ keV.

12 pages, 4 figures, 2 tables

References in corpus (4)

• Evidence of a new narrow resonance decaying to ${\chi }_{c1}\gamma$ in $B\to {\chi }_{c1}\gamma K$
• Observation of the $\psi (1^3{D}_2)$ state in $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}\gamma {\chi }_{c1}$ at BESIII
• Annihilation rate of $2^{-+}$ charmonium and bottomonium
• The process $e^{+}{e}^{-}\to \pi \pi X(3823)$ in the soft pion limit

Cited by in corpus (7)

• The mass spectrum and wave functions of the $B_c$ system
• Phenomenology of $J^{PC}=3^{--}$ tensor mesons
• Search for new decay modes of the ${\psi }_2(3823)$ and the process $e^{+}{e}^{-}\to {\pi }^0{\pi }^0{\psi }_2(3823)$
• Mixing angle and decay constants of $J^P=1^{+}$ heavy-light mesons
• Study of the excited $1^{-}$ charm and charm-strange mesons
• The electromagnetic decays of $X(3823)$ as the ${\psi }_2(1^3{D}_2)$ state and its radial excited states
• Mass spectra, wave functions and mixing effects of the $(bcq)$ baryon