Belle Experiment Sets Toughest Constraints on Invisible Hidden-Sector Particles

Crucially, three of the five decay channels (B⁺ → π⁺ X, B⁺ → Dₛ⁺ X, and B⁺ → p X) had never been directly searched for before this study . To identify the invisible recoil, the team employed a B-tagging technique, completely reconstructing one B meson in the pair to precisely infer the properties of the other, which decayed into a known track plus missing energy .

No significant excess over the expected background was observed in any channel. As a result, the collaboration set 90% confidence level (CL) upper limits on the branching fractions that range between 10⁻⁴ and 10⁻⁶—meaning the probability of these decays is at most one in ten thousand to one in a million, depending on the mass of the hypothetical particle .

Immediate squeeze on axion-like particles and dark scalars

The null result has immediate implications for a broad class of theoretical models. Invisible feebly interacting particles, including axion-like particles (ALPs) and dark scalars, are a common prediction of theories that attempt to explain dark matter. The strength of their interaction with Standard Model particles directly dictates how often they would appear in B decays. By finding no signal, the Belle analysis translates directly into tighter limits on the coupling constants of these particles .

These new limits do not rule out ALPs or dark scalars entirely—they could still exist with interactions too weak to have been seen—but they substantially narrow the allowed parameter space, guiding future experimental efforts toward the most promising theoretical targets .

First direct constraint on B-mesogenesis

One of the study's most impactful results comes from the channel involving a proton: B⁺ → p X. This provides the first direct experimental constraint on the "B-mesogenesis" mechanism, a theoretical scenario in which the decays of B mesons in the early universe generated an excess of antimatter funneled into a dark sector, helping to explain why our universe is dominated by matter .

The Belle collaboration's upper limits on this decay rule out the mechanism for a range of dark-sector particle masses, placing significant pressure on the model. However, a recent theoretical paper notes that experimental limits on the branching fraction of B⁺ → p + missing energy would need to be pushed down to the level of 10⁻⁷ or 10⁻⁸ to provide a definitive test of B-mesogenesis .

The path forward with Belle II

These constraints are groundbreaking, but they are largely statistically limited—meaning the Belle data sample is simply not large enough to probe extremely rare decays. The upgraded Belle II experiment, operating at the SuperKEKB collider, has already accumulated a data sample many times larger than Belle's and is expected to eventually collect 50 times more data .

With this much larger dataset, Belle II will be able to improve the sensitivity on these invisible decay channels by orders of magnitude, probing much deeper into the allowed parameter space for all the models covered by this search. The Belle results therefore serve as a critical benchmark and launchpad for the next generation of searches, pointing Belle II toward the mass ranges and theoretical models where a discovery could be hiding .