A new method for a lattice calculation of $\eta_c \rightarrow 2\gamma$

TL;DR

This paper introduces a novel lattice calculation method for hadron decay to two photons, exemplified by $ ext{eta}_c ightarrow 2 ext{gamma}$, simplifying finite-volume effect analysis and providing precise decay width results.

Contribution

A new direct lattice method for calculating hadron decay widths to two photons, reducing reliance on off-shell form factor extrapolations and enabling finite-volume effect examination.

Findings

Decay width $ ext{Gamma}_{ ext{eta}_c ightarrow 2 ext{gamma}}$ = 6.57(15)(8) keV

Method successfully applied to $ ext{eta}_c$ decay with controlled systematic errors

Potential applicability to other leptonic or radiative decay processes

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 $\eta_c\rightarrow 2\gamma$. Using three $N_f=2$ twisted-mass gauge ensembles with different lattice spacings, we obtain the final decay width $\Gamma_{\eta_c\gamma\gamma}=6.57(15)_{\textrm{stat}}(8)_{\textrm{syst}}$ 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.