Speaker
Description
We calculate the decay rate for the $\eta_b$ meson to two photons for the first time in lattice QCD, building on our previous accurate calculation of the rate for $\eta_c\to\gamma\gamma$. Using the Highly Improved Staggered Quark formalism for valence and sea quarks, we work at lattice spacings from 0.12 fm down to 0.03 fm. Gluon configurations with the effect of $u,$ $d,$ $s$ and $c$ quarks in the sea were provided by the MILC Collaboration. Extracting a form factor, $F(0,0)$, for two on-shell photons over a range of heavy quark masses $m_h$ between that of the $b$ and $c$ quarks, we can accurately determine the value of the ratio $f_{\eta_h}/(F_{\eta_h}(0,0)M^2_{\eta_h})$, with $f_{\eta_h}$ and $M_{\eta_h}$ the pseudoscalar meson decay constant and mass. This can be compared to the approximate value of 0.5 from leading order nonrelativistic QCD. We determine the decay rate $\Gamma(\eta_b\to\gamma\gamma)$ at the $b$ quark mass, providing a precise prediction for searches by the Belle II Collaboration.
