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It is bought to the authors' attention from a recent study [1] that, one should consider the final state photon exchange symmetry in the process of two-photon decay widths for various charmonia. This renders the form factors in Eq. (23)-Eq. (26) of the original paper differ by a factor of two and the final decay width by a factor of four. Therefore, Eq. (23)-Eq. (26) now should read,
$ \begin{aligned}[b] F(0,0)_{B1} = & 2\times0.1283(1)(3)(77)\;, \\ = &0.2566(2)(6)(154)\; \end{aligned} $
(1) $ \begin{aligned}[b] F(0,0)_{C1} = & 2\times0.1240(4)(13)(68)\;, \\= &0.248(8)(26)(136)\; \end{aligned} $
(2) $ \begin{aligned}[b] G(0,0)_{B1} = & 2\times0.1017(7)(102)(126)\;, \\ = &0.2034(14)(204)(252)\; \end{aligned} $
(3) $ \begin{aligned}[b] G(0,0)_{C1} = & 2\times0.0907(8)(19)(90)\;,\\ = &0.1814(16)(38)(180)\;, \end{aligned} $
(4) and the decay widths shown in Eq.(27) of the original paper should be modified to the following:
$ \begin{aligned}[b] \Gamma(\eta_c\rightarrow \gamma\gamma)_{B1} = & 4\times1.62(19)\;{\rm{KeV}} , \\ = &6.48(76)\;{\rm{KeV}} , \end{aligned} $
(5) $ \begin{aligned}[b] \Gamma(\eta_c\rightarrow \gamma\gamma)_{C1} = & 4\times1.51(17)\;{\rm{KeV}} , \\ = &6.04(68)\;{\rm{KeV}} , \end{aligned} $
(6) $ \begin{aligned}[b] \Gamma(\chi_{c0}\rightarrow \gamma\gamma)_{B1} = & 4\times1.18(38)\;{\rm{KeV}} , \\ = &4.72(152)\;{\rm{KeV}} , \end{aligned} $
(7) $ \begin{aligned}[b] \Gamma(\chi_{c0}\rightarrow \gamma\gamma)_{C1} = & 4\times0.93(19)\;{\rm{KeV}} , \\ = &3.72(76)\;{\rm{KeV}} . \end{aligned} $
(8) The decay widths are now in better agreement with the experiment values.
Erratum: Lattice study of the two-photon decay widths for scalar and pseudo-scalar charmonium [Chin. Phys. C 44(8), 083108 (2020)]
- Received Date: 2022-01-10
- Available Online: 2022-05-15
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