Ward Identity of the Vector Current and the Decay Rate of ${\eta }_c\to \gamma \gamma$ in Lattice QCD

Abstract

Using a recently proposed method arXiv:1910.11597 (Yu Meng et al.), we study the two-photon decay rate of ${\eta }_c$ using two $N_f=2$ twisted mass gauge ensembles with lattice spacings $0.067$fm and $0.085$fm. The results obtained from these two ensembles can be extrapolated in a naive fashion to the continuum limit, yielding a result that is consistent with the experimental one within two standard deviations. To be specific, we obtain the results for two-photon decay of ${\eta }_c$ as $\mathcal{B}({\eta }_c\to 2\gamma )=1.29(3)(18)\times 10^{-4}$ where the first error is statistical and the second is our estimate for the systematic error caused by the finite lattice spacing. It turns out that Ward identity for the vector current is of vital importance within this new method. We find that the Ward identity is violated for local current with a finite lattice spacing, however it will be restored after the continuum limit is taken.

9 pages, 5 figures

References in corpus (3)

• Two Photon Decays of Charmonia from Lattice QCD
• Measurement of the gamma gamma* --> eta_c transition form factor
• Next-to-next-to-leading-order QCD corrections to hadronic width of pseudoscalar quarkonium

Cited by in corpus (6)

• Precise determination of decay rates for ${\eta }_c\to \gamma \gamma$, $J/\psi \to \gamma {\eta }_c$ and $J/\psi \to {\eta }_c{e}^{+}{e}^{-}$ from lattice QCD
• Two-photon transitions of charmonia on the light front
• Observation of the charmonium decay ${\eta }_c\to \gamma \gamma$ in $J/\psi \to \gamma {\eta }_c$
• Self-consistent analysis for the ${\eta }_c\to \gamma \gamma$ process
• Spectroscopy of heavy-heavy flavour mesons and annihilation widths of quarkonia
• Study of the Magnetic Dipole Transition of $J/\psi \to \gamma {\eta }_c$ via ${\eta }_c\to p\bar{p}$