Lattice determination of the neutrino background for $J/ψ\rightarrow γ+ \textrm{invisible}$

TL;DR

This work presents the first lattice QCD determination of the neutrino background in the SM radiative decay $J/\psi \to \gamma \nu \bar{\nu}$, computing the full $q^2$-dependence of the hadronic amplitude via the scalar-function method. By using three lattice spacings and controlling excited-state and finite-volume effects through multi-state fits and volume checks, the authors obtain a continuum-extrapolated branching fraction $\operatorname{Br}[J/\psi \to \gamma\nu\bar{\nu}]=1.00(9)(7)\times10^{-10}$. This ab initio benchmark provides crucial input for upcoming collider searches of invisible decays and helps subtract the SM neutrino background at the $10^{-10}$ sensitivity level, with a clear path to extensions to other quarkonia such as $\Upsilon$ and $\phi$. The methodology combines nonperturbative lattice calculations with a scalar-function extraction to deliver precise, model-independent results that support dark-matter searches at current and future facilities.

Abstract

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 $J/ψ$ 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 $J/ψ\to γν\barν$, an irreducible background to $J/ψ\to γ+ \textrm{invisible}$. Our result for the branching fraction is $\operatorname{Br}(J/ψ\to γν\barν)=1.00(9)(7)\times 10^{-10}$, 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 $J/ψ\to γ+ \textrm{invisible}$. Our approach generalizes to other quarkonium channels (e.g., $Υ/φ\to γ+\textrm{invisible}$) and provides critical theoretical support for dark matter searches at colliders.

Figures (6)

• Figure 1: An example of the feynman diagram for the decay $J/\psi\rightarrow \gamma\nu\bar{\nu}$ with the photon emitted from the charm quark.
• Figure 2: The lattice results of $\Gamma_{\gamma\nu\bar{\nu}}/f_{J/\psi}$ for ensemble a67, a85 and a98, which are shown as a function of $t$ with various choices of $\Delta t$. The vertical dashed line denotes a conservative choice of $t \simeq 1.2$ fm, where the ground-state saturation is realized.
• Figure 3: The lattice results of $\Gamma_{\gamma\nu\bar{\nu}}/f_{J/\psi}$ with the cut $t\simeq 1.2$ fm in Fig.\ref{['fig:F_th']} are shown as a function of $\Delta t$ together with a fit to the form (\ref{['eq:th_fit']}).
• Figure 4: Lattice values of $\Gamma_{\gamma\nu\bar{\nu}}/f_{J/\psi}$ as a function of lattice spacing together with a continuous extrapolation with a linear behavior $a^2$. The errors of lattice spacing are included in the fitting and presented by the horizontal error bars. The symbol of the red circle denotes the lattice results from ensemble a67,a85, and a98 from left to right. The statistical error of $Z_A$ is included by error propagation.
• Figure 5: Lattice results of $f_{J/\psi}$ as a function of lattice spacing. The errors of lattice spacing are included in the fitting and presented by the horizontal error bars. The symbol of the red circle denotes the lattice results from ensemble a67,a85, and a98 from left to right. The black triangle is the result in continuum limit $a^2\rightarrow 0$ and circle blue is obtained using the experimental average of $\Gamma_{e+e-}$ and $\alpha_{QED}(m_{J/\psi}^2)=1/134.02$.