Lattice determination of the neutrino background for $J/\psi \rightarrow \gamma + \textrm{invisible}$
Searching for dark matter is a primary goal of modern astronomy and particle physics. Invisible decays of heavy quarkonia are particularly promising for probing light dark matter, attracting broad interest due to their unique sensitivity. Experiments searching for radiative invisible decays of the $J/\psi$ have steadily improved upper limits, and upcoming facilities will push sensitivity further--making the precise determination and subtraction of the neutrino background indispensable. Here, we present the first lattice QCD calculation of the Standard Model decay $J/\psi \to \gamma\nu\bar{\nu}$, an irreducible background to $J/\psi \rightarrow \gamma + \textrm{invisible}$. Our result for the branching fraction is $\operatorname{Br}(J/\psi \rightarrow \gamma\nu\bar{\nu})=1.04(7)(8)\times 10^{-10}$, where the first uncertainty is statistical and the second is our systematic estimate. This work advances lattice-based determinations of neutrino backgrounds to quarkonium invisible decays, delivering an ab initio benchmark for $J/\psi \rightarrow \gamma + \textrm{invisible}$. Our approach generalizes to other quarkonium channels (e.g., $\Upsilon/\phi \rightarrow \gamma+\textrm{invisible}$) and provides critical theoretical support for dark matter searches at colliders.