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arXiv 1601.01047hep-phhep-ex
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$^3D_2(2^{--})$和$^3D_3(3^{--})$重夸克偶素的湮灭率

Annihilation Rates of $^3D_2(2^{--})$ and $^3D_3(3^{--})$ Heavy Quarkonia

Tianhong Wang, Hui-Feng Fu, Yue Jiang, Qiang Li, Guo-Li Wang

摘要:

用瞬时Bethe-Salpeter方法计算了$^3D_2(2^{--})$和$^3D_3(3^{--})$ charmonia和bottomonia的湮没衰变率。构造了量子数为$J^{PC}=2^{--}$和$3^{--}$的态的波函数。通过求解相应的瞬时Bethe-Salpeter方程,我们得到了夸克偶素的质量谱和波函数。湮灭振幅写在曼德尔维形式主义和相对论修正适当考虑。这是很重要的,特别是对于高激发态,因为它们的相对论修正很大。$3g$通道的结果如下:$Γ_{^3D_2(c\bar c)\rightarrow ggg} = 9.24$ keV、$Γ_{^3D_3(c\bar c)\rightarrow ggg}=25.0$ keV、$Γ_{^3D_2(b\bar b)\rightarrow ggg}= 1.87$ keV和$Γ_{^3D_3(b\bar b)\rightarrow ggg}= 0.815$ keV。

英文摘要:

We calculate the annihilation decay rates of the $^3D_2(2^{--})$ and $^3D_3(3^{--})$ 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: $Γ_{^3D_2(c\bar c)\rightarrow ggg} = 9.24$ keV, $Γ_{^3D_3(c\bar c)\rightarrow ggg}=25.0$ keV, $Γ_{^3D_2(b\bar b)\rightarrow ggg}= 1.87$ keV, and $Γ_{^3D_3(b\bar b)\rightarrow ggg}= 0.815$ keV.

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