Invisible Quarkonium Decays as a Sensitive Probe of Dark Matter
Bob McElrath
TL;DR
This work proposes a model-independent strategy to search for light dark matter through invisible decays of quarkonium states at B-factories, leveraging ISR-tagged production and radiative transitions to access the spin and CP properties of the SM–DM mediator. By connecting relic-density calculations to expected invisible branching fractions, it provides concrete targets such as $BR(\Upsilon(1S)\to \chi\chi) \approx 0.41\%$, and shows that with about $400\ \text{fb}^{-1}$ one can reach $BR(\Upsilon(1S)\to invisible) \lesssim 0.1\%$, enabling discovery or strong constraints for $m_\chi < M_\Upsilon/2$. The approach relies on careful kinematic tagging, ISR formalism, and background control (photon fusion, di-$\tau$, two-body decays, Drell–Yan) to exploit bottomonium transitions like $\Upsilon(nS)\to \Upsilon(1S)\pi^+\pi^-$. Overall, the method provides a complementary probe of light dark matter and mediator scenarios, with the potential to determine mediator spin/CP and expand sensitivity beyond direct detection in the sub-GeV to few-GeV mass range.
Abstract
We examine in a model-independent manner the measurements that can be performed at B-factories with sensitivity to dark matter. If a singlet scalar, pseudo-scalar, or vector is present and mediates the Standard Model - dark matter interaction, it can mediate invisible decays of quarkonium states such as the $Υ$, $J/Ψ$, and $η$. Such scenarios have arisen in the context of supersymmetry, extended Higgs sectors, solutions the supersymmetric $μ$ problem, and extra U(1) gauge groups from grand unified theories and string theory. Existing B-factories running at the $Υ(4S)$ can produce lower $Υ$ resonances by emitting an Initial State Radiation (ISR) photon. Using a combination of ISR and radiative decays, the initial state of an invisibly decaying quarkonium resonance can be tagged, giving sensitivity to the spin and CP-nature of the particle that mediates standard model-dark matter interactions. These measurements can discover or place strong constraints on dark matter scenarios where the dark matter is approximately lighter than the $b$-quark. For the decay chains $Υ(nS) \to π^+ π^- Υ(1S)$ (n=2,3) we analyze the dominant backgrounds and determine that with $400 fb^{-1}$ collected at the $Υ(4S)$, the B-factories can limit $BR(Υ(1S) \to invisible) \lsim 0.1%$.