First-principle calculation of $\eta_c\rightarrow 2\gamma$ decay width from lattice QCD

We perform a lattice QCD calculation of the $\eta_c\to2\gamma$ decay width using a model-independent method that requires no momentum extrapolation of the off-shell form factors. This method also provides a straightforward and simple way to examine the finite-volume effects. The calculation is accomplished using $N_f=2$ twisted mass fermion ensembles. The statistically significant excited-state effects are observed and eliminated using a multi-state fit.The impact of fine-tuning the charm quark mass is also examined and confirmed to be well-controlled. Finally, using three lattice spacings for the continuum extrapolation, we obtain the decay width $\Gamma_{\eta_c\gamma\gamma}=6.67(16)_{\mathrm{stat}}(6)_{\mathrm{syst}}$ keV, which differs significantly from the Particle Data Group's reported value of $\Gamma_{\eta_c\gamma\gamma}=5.4(4)$ keV (2.9~$\sigma$ tension). We provide insight into the comparison between our findings, previous theoretical predictions, and experimental measurements.