Ward identity of the vector current and the decay rate of ηc →γγ in lattice QCD

Abstract

Using a recently proposed method [Y. Meng, C. Liu, and K. L. Zhang, arXiv:1910.11597v3], we study the two-photon decay rate of ηc using two Nf=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 ηc as B(ηc→2γ)=1.29(3)(18)×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 verify 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.