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.

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