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

The new analysis, published in The European Physical Journal C by Yin Huang and Xurong Chen, tackles the problem from a fresh angle. Rather than relying on the traditional method of fitting invariant mass spectra, the researchers focus on the transverse momentum of the final-state D mesons produced in electron-positron collisions. Their central insight is deceptively simple but theoretically powerful: if G(3900) is a real resonance, it must imprint a distinctive kinematic fingerprint on the angular distribution of its decay products, a fingerprint that no amount of interference between intermediate states can mimic. This fingerprint is known as a Jacobian peak, and its predicted position can be calculated with extraordinary precision from first principles.

The mathematics behind the proposal rests on the geometry of two-body decays. When a resonance of a given mass decays into a pair of D mesons, kinematics dictate that the transverse momentum of each meson cannot exceed a maximum value determined by the Källén function of the participating masses. When the cross section is re-expressed as a function of the transverse momentum rather than the emission angle, a characteristic singularity appears at this kinematic limit, producing a sharp enhancement called a Jacobian peak. For G(3900), the peak should appear at approximately 520.995 MeV for neutral D meson pairs and 504.018 MeV for charged pairs. Crucially, the position of this peak depends only on the mass of the parent resonance, not on the details of any theoretical model used to describe the production amplitudes.

This model independence is precisely what makes the proposal so compelling. The authors demonstrate that when G(3900) is treated as a genuine resonance alongside the known charmonium states psi(3686), psi(3770), psi(4040), and psi(4160), the calculated transverse momentum distribution displays a clear Jacobian peak at the predicted location. When the G(3900) contribution is removed and the observed enhancement is instead attributed entirely to interference effects and the opening of the D D* threshold, the peak vanishes completely. Because interference between intermediate states cannot produce this kinematic singularity, the presence or absence of the peak in experimental data would constitute direct evidence for or against the existence of G(3900) as a bona fide hadronic state.

The theoretical framework underpinning the study combines an effective Lagrangian approach with loop calculations that account for the opening of the D D* threshold. The coupling constants for the charmonium states are fixed from known decay widths, while other parameters are fitted to the existing body of electron-positron collision data. The authors performed a series of fits using different model assumptions, including scenarios with and without G(3900), and found that all of them describe the measured invariant mass spectra reasonably well. This degeneracy explains why nearly twenty years of fitting mass spectra have failed to settle the debate: the two-body invariant mass distribution alone simply does not contain enough information to discriminate between a genuine resonance and cleverly arranged interference effects.

Intriguingly, the analysis also sheds new light on the internal structure of G(3900). Its measured mass of about 3872.5 MeV sits remarkably close to the D D* threshold, prompting several theoretical groups to interpret it as a P-wave molecular state composed of a D meson and a D* meson bound together. The new study explores this possibility but finds that different, equally reasonable fits lead to contradictory conclusions about the molecular interpretation. In one favored fit, the ratio of the G(3900) decay width into D meson pairs to its width into electron-positron pairs appears incompatible with a molecular assignment, while in another equally successful fit the numbers permit it. The authors emphasize that this ambiguity in classification does not undermine the Jacobian peak criterion, which remains valid regardless of the particle’s ultimate structural identity.

The experimental prospects for testing the prediction appear highly favorable. The authors estimate that the predicted Jacobian peaks have characteristic widths of roughly 14 MeV at a normalized cross section value of 3, narrowing to about 5 MeV at a value of 6, features that are easily resolvable by modern detectors. The momentum resolution of the BESIII detector is approximately 0.5 percent at momenta around 1 GeV, corresponding to uncertainties of only about 2.6 MeV at the relevant transverse momenta. Combined with the beam-energy spread of roughly 1.5 MeV, the total experimental uncertainty amounts to about 3 MeV, far smaller than the width of the predicted peak. Moreover, BESIII has already accumulated large datasets of electron-positron collisions producing D meson pairs, providing ample statistics, and the estimated signal-to-background ratio in the most favorable region reaches approximately 110.

The authors also identify an important caveat that itself constitutes a valuable experimental probe. If the production amplitude for the process carries a purely angular dependence proportional to the cosine of the emission angle, the Jacobian peak could be dynamically suppressed, because the squared amplitude would vanish exactly at the kinematic limit. Measuring the differential cross section at a scattering angle of 90 degrees would therefore provide an important consistency check: a vanishing cross section at that angle would indicate suppression of the peak without negating the underlying kinematic structure. This subtlety underscores the care required in interpreting the proposed measurement, but it does not diminish the power of the criterion when applied with full awareness of the angular dynamics.

Beyond its immediate implications for G(3900), the Jacobian peak method offers a broadly applicable tool for hadron spectroscopy. The field has been flooded in recent years with candidate exotic states whose reality is debated, from tetraquarks to hadronic molecules, and many of these controversies stem from the same fundamental limitation: interference effects can mimic resonance signals in invariant mass spectra. A model-independent observable whose position is fixed purely by the mass of the hypothesized parent state provides exactly the kind of clean discriminator the field needs. The authors suggest that the same transverse momentum analysis can be extended to other hadronic systems, potentially resolving long-standing disputes about the existence of various resonance candidates across the light, strange, charm, and bottom sectors.

The study represents a convergence of precision experiment and incisive theoretical reasoning at a moment when the particle physics community is actively re-examining the census of hadronic matter. With BESIII’s confirmation of the G(3900) structure having reignited interest in the 3.9 GeV region, and with the proposed Jacobian peak test requiring no new instrumentation beyond what existing datasets already permit, the coming analysis of transverse momentum distributions may soon deliver one of the cleanest verdicts in modern hadron physics. Whether G(3900) emerges as a genuine new state of matter or fades into the machinery of quantum interference, the criterion developed by Huang and Chen is poised to become a standard instrument in the ongoing effort to map the true spectrum of strongly interacting particles.

Subject of Research: Criterion for establishing the existence of the G(3900) hadronic resonance through transverse momentum distributions in electron-positron collisions

Article Title: Criterion for the existence of the G(3900) resonance

Article References: Huang, Y., & Chen, X. (2026). Criterion for the existence of the G(3900) resonance. The European Physical Journal C, 86(10), Article 1161. https://doi.org/10.1140/epjc/s10052-026-16432-2

Image Credits: AI Generated

DOI: 10.1140/epjc/s10052-026-16432-2

Keywords: G(3900), BESIII, charmonium, D meson, Jacobian peak, hadron spectroscopy, resonance, electron-positron annihilation, D D* threshold, molecular state, quantum interference, particle physics

The study, published in The European Physical Journal C by Teng Ji and Ulf-G. Meißner of the University of Bonn and Forschungszentrum Jülich, tackles the near-threshold structures that experiments at BESIII in Beijing, BaBar at SLAC, and CMD-3 and SND in Novosibirsk have observed in electron-positron annihilation. These anomalies appear not only in the direct production of proton-antiproton and neutron-antineutron pairs, but also, remarkably, in final states containing no baryons whatsoever: three charged pion pairs, two charged pion pairs plus a neutral pion, an omega meson accompanied by pions, and even kaon-pion combinations. The fact that the same threshold energy shows up in so many different channels is precisely what makes the puzzle so tantalizing, and so resistant to explanations based on a single new particle.

The key insight behind the new work is that when a proton-antiproton pair is produced in the aftermath of an annihilation, the pair does not simply fly apart. The proton and antiproton interact strongly with each other before separating, a phenomenon known as final-state interaction. This interaction is not a weak correction; it is powerful enough to reshape the entire line shape of the production cross section near threshold. Crucially, quantum mechanics dictates that these threshold effects must also leak into other reaction channels, a consequence of the fundamental requirements of unitarity and analyticity that govern all scattering amplitudes. In other words, the opening of the proton-antiproton and neutron-antineutron channels leaves fingerprints everywhere, including in final states made purely of mesons.

To make this idea quantitative, the authors relied on chiral effective field theory, the modern framework that derives nuclear forces from the approximate symmetries of quantum chromodynamics. Chiral effective field theory has been spectacularly successful in describing the ordinary interaction between two nucleons, and it has been extended to the nucleon-antinucleon system, where it must additionally handle the violent annihilation of the pair into mesons. Ji and Meißner used the highest-order available description, complete to next-to-next-to-next-to-leading order, with its parameters fixed entirely by low-energy nucleon-antinucleon scattering data. That fixed interaction was never adjusted to fit the annihilation data, which makes the subsequent agreement all the more meaningful.

The calculation proceeds in three carefully separated steps. First, the strong nucleon-antinucleon interaction is taken as given from the chiral effective field theory description of the coupled spin-triplet S-wave and D-wave system, solved through the coupled-channel Lippmann-Schwinger equation. Second, with this interaction frozen, the electromagnetic production amplitudes for proton-antiproton and neutron-antineutron pairs are determined by fitting only a handful of short-distance source coefficients to the measured cross sections. These sources are assumed to vary slowly with energy, so that all the sharp structure near threshold must come from the final-state interaction itself. Third, the same nucleon-antinucleon amplitudes are used as input for five inelastic mesonic channels, each described by a slowly varying polynomial background plus the universal rescattering response.

The results are striking. For the baryonic channels, the fit achieves a chi-squared per degree of freedom of essentially one, meaning the theory reproduces the data at the level of the experimental uncertainties, using just seven real parameters across fifty-four data points spanning the region from threshold up to two gigaelectronvolts. No additional narrow resonance is needed to explain the rapid rise of the cross sections just above the proton-antiproton and neutron-antineutron thresholds. The framework also incorporates the subtle isospin-breaking effects that matter at this precision, including the small mass difference between the proton and neutron and the Coulomb attraction between the proton and antiproton, treated through the Vincent-Phatak matching method that separates short-range and long-range physics cleanly.

Underlying the line shapes are near-threshold poles of the scattering amplitude, the mathematical signatures that would correspond to physical particles if they sat close enough to the real-energy axis. The chiral interaction generates one such pole in each isospin channel: an isospin-one pole near 2122 megaelectronvolts with a small imaginary part, and an isospin-zero pole near 1840 megaelectronvolts with a larger imaginary part reflecting the strong annihilation into mesons. Because annihilation makes the interaction absorptive, these poles acquire finite widths and sit on different Riemann sheets of the complex energy plane. Their proximity to the physical thresholds is what sculpts the observed enhancements, providing a dynamical origin for structures that might otherwise be misread as evidence for new particles.

The real test comes with the non-baryonic channels, where the same nucleon-antinucleon dynamics is used without modification. The authors allowed each mesonic channel its own slowly varying polynomial background and a small set of complex transition parameters connecting the intermediate baryon-antibaryon state to the final mesons, with the allowed isospin components fixed by the quantum numbers of each final state. A simultaneous fit to all five channels yields a chi-squared per degree of freedom of 1.7, reproducing the main near-threshold features of the data. The message is that the threshold structures in these mesonic channels can be understood as echoes of the same baryon-antibaryon final-state interaction, transmitted through off-shell nucleon-antinucleon amplitudes, rather than as independent resonances requiring separate explanations in each channel.

The implications reach well beyond electron-positron physics. Similar threshold enhancements have been reported in the invariant-mass spectra of proton-antiproton pairs produced in the radiative decays of the J/psi meson and in B-meson decays at Belle and LHCb, and the timelike electromagnetic form factors of the proton and neutron show dramatic rises near the same thresholds. If the unified picture holds, many of these anomalies may share a common dynamical origin, and the widespread habit of labeling every threshold bump as a new particle, from the X(1835) onward, may need systematic re-examination. The authors caution that a naive Breit-Wigner resonance interpretation can be actively misleading in the near-threshold region when the underlying rescattering dynamics is ignored.

The analysis is not without caveats. The chiral effective field theory description is restricted to low energies, so the fits stop at two gigaelectronvolts, and explicit excited vector mesons such as a possible rho state near 2.04 gigaelectronvolts are not included in the framework. The finest experimental points from CMD-3 immediately at the proton-antiproton threshold involve experiment-specific corrections for initial-state radiation and beam-energy spread that the Born-level theory curves do not attempt to replicate point by point. Yet the authors verified that their conclusions are stable under the estimated truncation uncertainties of the chiral expansion: repeating the analysis with lower-order interactions and refitting the short-distance parameters leaves the line shapes essentially unchanged. The next step will be for experimentalists to test the framework’s predictions with precision data, and for theorists to extend the same unified logic to the threshold structures seen in heavy-quark systems. If the pattern holds, physics may have gained something rare and valuable: a case where a flock of apparent new particles dissolves into the familiar, if ferociously complicated, dance of nucleons and antinucleons.

Subject of Research: Near-threshold nucleon-antinucleon final-state interactions in electron-positron annihilation

Article Title: Understanding the near-threshold structures in (e^+e^-) annihilation from a unified (N\bar{N})-interaction perspective

Article References: Understanding the near-threshold structures in (e^+e^-) annihilation from a unified (N\bar{N})-interaction perspective. (n.d.). https://doi.org/10.1140/epjc/s10052-026-16364-x

Image Credits: AI Generated

DOI: 10.1140/epjc/s10052-026-16364-x

Keywords: particle physics, nuclear physics, electron-positron annihilation, nucleon-antinucleon interaction, chiral effective field theory, near-threshold structures, final-state interaction, proton-antiproton, BESIII, CMD-3, hadron spectroscopy, scattering poles