Heavy Quarkonium from Lattice QCD

We discuss recent progress in radiative decays of heavy quarkonium from $2+1+1$ flavour lattice QCD using the Highly Improved Staggered Quark formalism for all quarks. In particular, we summarise our recent calculations of the decay of heavyonium mesons to on-shell photons. Our calculation of the form factor for the decay $\eta_c\to\gamma\gamma$ and the determination of its decay width has changed the theoretical picture of the process. By calculating the decay width for the process $\eta_b\to\gamma\gamma$ we have provided a robust and timely prediction for experimental searches possible at, for example, Belle II. We then explore Beyond the Standard Model physics by studying $J/\psi\to\gamma a$ where $a$ is an axion-like particle. Our fully relativistic calculation using lattice QCD leads to precise branching fractions and exclusion limits that can now be used in place of nonrelativistic perturbative expansion results that do not fully take nonperturbative effects of hadron decays into account.