A new method for a lattice calculation of ${\eta }_c\to 2\gamma$

Abstract

We propose a direct method to calculate the decay width of a hadron decaying to two photons, which is conventionally obtained by an extrapolation for various off-shell form factors. The new method provides an simple way to examine the finite-volune effects. As an example, we apply the method to ${\eta }_c\to 2\gamma$. Using three $N_f=2$ twisted-mass gauge ensembles with different lattice spacings, we obtain the final decay width ${\Gamma }_{{\eta }_c\gamma \gamma }=6.57(15{)}_{\text{stat}}(8{)}_{\text{syst}}$ keV, where the systematic error accounts for the fine-tuning of the charm quark mass. This method can also be applied for other processes which involve the leptonic or radiative particles in the final states.

The 38th International Symposium on Lattice Field Theory, LATTICE2021 26th-30th July, 2021 Zoom/Gather@Massachusetts Institute of Technology. New submission with references added

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