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 $\mathcal{B}(\eta_c\rightarrow 2\gamma)= 1.29(3)(18)\times 10^{-4}$ 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.
Highlights
The charmonium two-photon decay process ηc → 2γ has long been an ideal testing ground for the understanding of nonperturbative nature of quantum chromodynamics (QCD) [1] due to the medium energy scale of charmonium systems in strong interactions [2]
We obtain the results for two-photon decay of ηc as Bðηc → 2γÞ 1⁄4 1.29ð3Þð18Þ × 10−4 where the first error is statistical and the second is our estimate for the systematic error caused by the finite lattice spacing
We verify that the Ward identity is violated for local current with a finite lattice spacing, it will be restored after the continuum limit is taken
Summary
The charmonium two-photon decay process ηc → 2γ has long been an ideal testing ground for the understanding of nonperturbative nature of quantum chromodynamics (QCD) [1] due to the medium energy scale of charmonium systems in strong interactions [2]. [11] have computed the next-to-next-toleading order QCD corrections to this process, yielding a value for Bðηc → 2γÞ that is about twice the one quoted by PDG. In some sense, this discrepancy might indicate that NRQCD breaks down for such processes due to substantial nonperturbative effects. The first quenched LQCD calculation of ηc → 2γ was presented in 2006 [8] and unquenched results followed in recent years [9,10]. In previous lattice calculations of charmonia double gamma decay, the relevant hadronic matrix elements are decomposed into form factors which are functions of photon virtualities Q2i ; i 1⁄4 1, 2. The large deviations between the experiments and lattice results in Refs. [8,9,10] indicate that such methods might suffer from rather severe lattice
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