Invisible Decays of Hyperons Could Reveal Dark Matter’s Baryonic Twin

Physicists have long wondered whether the dark matter that binds galaxies together might be a kind of mirror image of ordinary matter, carrying its own hidden baryon number. A new theoretical study published in The European Physical Journal C takes this idea seriously at the level of individual particles, calculating how often hyperons, the strange cousins of protons and neutrons, might decay into ordinary pions or photons plus an invisible dark baryon. The work, led by Lai Jiang, Ye Xing, Yu Zhou and Xiao-hui Hu of the China University of Mining and Technology, provides the most detailed treatment to date of these so-called semi-invisible hyperon decays, and its conclusions are striking: quantum loop effects that earlier analyses ignored can be just as important as the leading contributions themselves.

The theoretical backdrop is a family of low-scale baryogenesis scenarios collectively known as Mesogenesis. In these models, the matter-antimatter asymmetry of the universe and the dark matter abundance are generated together, at energy scales below the electroweak scale. That is a tantalizing feature, because it means the underlying interactions could be probed directly in laboratory experiments rather than only inferred from cosmology. The mechanism works through heavy colored mediators, scalar fields or vector fields, that couple Standard Model quarks to a dark baryon called psi, a fermion that is a complete singlet under the Standard Model gauge group. Because the mediators are heavy, with collider searches by ATLAS and CMS pushing their masses above roughly 0.52 teraelectronvolts, they can be integrated out, leaving behind compact effective interactions described by a handful of Wilson coefficients.

Experiments have already begun to squeeze those coefficients. The BABAR Collaboration has set upper limits of order ten to the minus six on B-meson decays into a baryon plus the invisible psi particle, while Belle has reached limits around ten to the minus five for a range of invisible B decays. More relevant for the new work, the BESIII Collaboration has searched for invisible decays of hyperons such as the Lambda and the Xi, establishing upper limits also at the level of ten to the minus five. Each null result translates directly into a tighter bound on the effective couplings that control how strongly quarks talk to the dark sector. The new analysis folds these constraints into a systematic calculation of what branching ratios the Mesogenesis framework actually predicts for hyperons.

The technical heart of the paper is an effective Lagrangian matched onto chiral perturbation theory, the standard framework for describing the low-energy interactions of light quarks, baryons and the pseudo-Goldstone mesons that encode chiral symmetry breaking. The three-quark operators that survive in the Mesogenesis model form a flavor octet, and the authors construct the most general flavor-invariant Hamiltonian for hyperon decays into a meson plus psi, or a photon plus psi. Angular momentum conservation plays a crucial role: in the Lambda hyperon the up-down quark pair carries spin zero, while in the Sigma-zero it carries spin one, so scalar and vector mediators predict different patterns of amplitudes for the radiative channels. The framework also yields approximate relations among decay rates that follow from SU(3) flavor symmetry, relations that the full calculation later shows to be only roughly obeyed.

Where the study departs from earlier work is in its treatment of one-loop triangle diagrams, which encode final-state interactions among ordinary hadrons. At first glance such loop processes should be suppressed, since every additional vertex typically costs a factor of the strong coupling divided by some large scale. But the authors point out that a triangle diagram has only one or two more strong vertices than the tree-level invisible decay, and the strong couplings among hadrons are vastly larger than the couplings between hadrons and the dark baryon. The loops are further regulated by phenomenological form factors that account for the internal structure of the exchanged particles, with a cutoff parameterized in terms of the QCD scale. The result is that these rescattering effects, far from being negligible, contribute corrections comparable in size to the tree diagrams.

The numerical consequences are laid out for a dark baryon mass near one gigaelectronvolt, within the kinematic window of roughly 0.94 to 1.18 gigaelectronvolts where all hyperon decays into psi plus a pion or photon remain allowed. For the hadronic channels, the branching ratios cluster around ten to the minus five. In the process Sigma-minus going to pi-minus plus psi, the tree diagrams alone give a branching ratio of 1.83 times ten to the minus five, while the triangle loops alone give 0.94 times ten to the minus five, and the combined result with interference is 1.25 times ten to the minus five. For Xi-zero going to pi-zero plus psi, the tree contribution is 5.24 times ten to the minus five and the loop contribution 1.05 times ten to the minus five. The loops are thus not a footnote but a co-star, and for Sigma-minus and Xi-zero they simply cannot be ignored.

The radiative channels, in which the hyperon emits a photon alongside the invisible dark baryon, fare considerably worse. Because the leading-order process requires radiative couplings of light hadrons, the predicted branching ratios fall below ten to the minus seven, at least two orders of magnitude smaller than the hadronic modes. The authors also extend the analysis to the neutron, which, if it can decay into a photon and a dark baryon, would offer a possible explanation for the well-known discrepancy between bottle and beam measurements of the neutron lifetime. That discrepancy, however, amounts to only about one percent, which constrains the decay width of the neutron into photon plus psi to roughly 7.41 times ten to the minus thirty gigaelectronvolts and forces the corresponding Wilson coefficient down to 6.87 times ten to the minus eleven inverse gigaelectronvolts squared, an extraordinarily tight bound.

One of the most interesting byproducts of the calculation is a stress test of SU(3) flavor symmetry. Simple symmetry arguments predict, for example, that the rate for Xi-minus decays should be exactly twice that for Xi-zero decays, and that the Sigma-minus rate should be a small fraction of the Xi-zero rate. The full effective Lagrangian calculation tells a different story: the Xi-minus to Xi-zero ratio comes out near 1.04 rather than 2, and the Sigma-minus to Xi-zero ratio near 0.40 rather than 0.07. The tree-level ratios by themselves agree well with the symmetry predictions, which pinpoints the deviation on the final-state interaction effects and the interference between tree and loop amplitudes. Flavor-symmetry breaking, in other words, is sizable in these decays, and analyses that rely on exact SU(3) may be misleading.

The practical upshot is a roadmap for experiments. The branching ratios decrease as the dark baryon mass increases across the allowed window, with Xi-zero going to pi-zero plus psi reaching the largest value, about 7.0 times ten to the minus five, at the lowest allowed mass, while Lambda decays give the smallest at 1.16 times ten to the minus five. Most channels are fairly insensitive to the cutoff parameter governing the form factors, but the Xi-zero and Sigma-minus modes grow strongly with it, a signature of their large loop contributions. Since current BESIII limits already sit at the same order of magnitude as these predictions, a modest improvement in sensitivity could either catch the first glimpse of a dark baryon or push the Mesogenesis parameter space into a much narrower corner. Either outcome would mark real progress in connecting the darkest question in cosmology to the humble decays of strange particles.

Subject of Research: Semi-invisible decays of hyperons into pions or photons plus a dark baryon in Mesogenesis models, computed with an effective Lagrangian approach

Article Title: Semi-invisible hyperon decays in the effective Lagrangian approach

Article References: Jiang, L., Xing, Y., Zhou, Y., & Hu, X.-H. (2026). Semi-invisible hyperon decays in the effective Lagrangian approach. The European Physical Journal C, 86(9), Article 1034. https://doi.org/10.1140/epjc/s10052-026-16292-w

Image Credits: AI Generated

DOI: 10.1140/epjc/s10052-026-16292-w

Keywords: hyperon decays, dark matter, Mesogenesis, dark baryon, effective Lagrangian, chiral perturbation theory, branching ratios, BESIII, baryogenesis, final-state interactions, SU(3) flavor symmetry, neutron lifetime