Erratum: Lattice study of the two-photon decay widths for scalar and pseudo-scalar charmonium [Chin. Phys. C 44(8), 083108 (2020)]

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Ying Chen, Ming Gong, Ning Li, Chuan Liu, Yu-Bin Liu, Zhaofeng Liu, Jian-Ping Ma, Yu Meng, Chao Xiong and Ke-Long Zhang. Erratum: Lattice study of the two-photon decay widths for scalar and pseudo-scalar charmonium [Chin. Phys. C 44(8), 083108 (2020)][J]. Chinese Physics C. doi: 10.1088/1674-1137/ac4bcd
Ying Chen, Ming Gong, Ning Li, Chuan Liu, Yu-Bin Liu, Zhaofeng Liu, Jian-Ping Ma, Yu Meng, Chao Xiong and Ke-Long Zhang. Erratum: Lattice study of the two-photon decay widths for scalar and pseudo-scalar charmonium [Chin. Phys. C 44(8), 083108 (2020)][J]. Chinese Physics C.  doi: 10.1088/1674-1137/ac4bcd shu
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Received: 2022-01-10
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Erratum: Lattice study of the two-photon decay widths for scalar and pseudo-scalar charmonium [Chin. Phys. C 44(8), 083108 (2020)]

    Corresponding author: Ning Li, lining@xatu.edu.cn
  • 1. Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China
  • 2. School of Physics, University of Chinese Academy of Sciences, Beijing 100049, China
  • 3. School of Science, Xi’an Technological University, Xi’an 710032, China
  • 4. School of Physics and Center for High Energy Physics, Peking University, Beijing 100871, China
  • 5. Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
  • 6. School of Physics, Nankai University, Tianjin 300071, China
  • 7. Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China
  • 8. School of Physics, Peking University, Beijing 100871, China

Abstract: 

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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.

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