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Lattice study of form factors for charmonium

  • Regular Article – Theoretical Physics
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Abstract

Form factors for \(\eta _c\) and \(\chi _{c0}\) have been simulated based on \(N_f=2\) Twisted Mass Lattice Quantum Chromodynamics (Lattice QCD) gauge configurations. We construct particle interpolation operators by variational method that can significantly improve signal-to-noise ratio of correlation functions. We apply twisted boundary conditions to compute corresponding correlation functions which make us obtain form factors with more small four-momentum transfer. Furthermore, we fit charge radius for \(\eta _c\) and \(\chi _{c0}\), respectively. The results obtained in this simulation could be considered as a ground test to calculate branch ratio decay width of \(\chi _{c0,1,2}\rightarrow {\gamma {J/\psi }}\) on lattice in future.

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Data Availability Statement

This manuscript has no associated data or the data will not be deposited. [Authors’ comment: Since all data in the study have been presented in figures and tables of the manuscript, we could extract the numerical data readily in the paper.]

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Acknowledgements

The authors would like to thank the European Twisted Mass Collaboration (ETMC) to allow us to use their gauge field configurations. The authors also would like to thank Li-Chen Zhao for helpful discussions. Our thanks also go to National Supercomputing Center in Tianjin (NSCC). This work is supported in part by the National Science Foundation of China (NSFC) under the Project No. 12075176 and No. 11705072. This work is also supported by the Scientific Research Program Funded by Shaanxi Provincial Education Department under the Grant No. 19JK0391, and Natural Science Basic Research Plan in Shaanxi Province of China (Program No. 2019JM-001).

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Authors and Affiliations

  1. School of Science, Xi’an Technological University, Xi’an, 710032, People’s Republic of China

    Ning Li, Chao-Chen Liu & Ya-Jie Wu

Authors
  1. Ning Li
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  2. Chao-Chen Liu
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  3. Ya-Jie Wu
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Corresponding author

Correspondence to Ning Li.

Additional information

Communicated by William Detmold

Appendix

Appendix

In this appendix, we provide Tables 5, 6, 7, and 8 to show the data correlation matrices for fitted form factors of \(\eta _c\) and \(\chi _{c0}\).

Table 5 The data correlation matrix for fitted form factors of \(\eta _c\) by using Eq. (13) on Ens.\(B_1\)
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Table 6 The data correlation matrix for fitted form factors of \(\eta _c\) by using Eq. (13) on Ens.\(C_1\)
Full size table
Table 7 The data correlation matrix for fitted form factors of \(\chi _{c0}\) by using Eq. (13) on Ens.\(B_1\)
Full size table
Table 8 The data correlation matrix for fitted form factors of \(\chi _{c0}\) by using Eq. (13) on Ens.\(C_1\)
Full size table

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Li, N., Liu, CC. & Wu, YJ. Lattice study of form factors for charmonium. Eur. Phys. J. A 56, 242 (2020). https://doi.org/10.1140/epja/s10050-020-00253-2

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