The framework builds on the classic Sakharov conditions, formulated in 1967, which identify three requirements for dynamically generating a matter–antimatter asymmetry: baryon number violation, violation of the charge conjugation and charge–parity symmetries (C and CP), and departure from thermal equilibrium. Kilic and Mathai relax the first condition in an elegant way. Rather than violating baryon number outright, they consider a hidden sector containing baryon-number-carrying particles that is effectively decoupled from ordinary matter at late times. If baryon number is transferred between the two sectors in the early universe, equal and opposite baryon abundances can be sequestered, one in the visible sector and one in the hidden sector, while the net baryon number of the universe remains exactly zero.

The two sectors communicate through a so-called baryon portal, a dimension-six operator coupling right-handed up- and down-type quarks to a new fermionic mediator. In the benchmark model, this portal arises from integrating out a heavy colored scalar, a fundamental of the strong-interaction gauge group with hypercharge −2/3, which couples to pairs of down-type quarks through one set of couplings and to up-type quarks and the portal fermions through another. The hidden sector itself is deliberately minimal: a Majorana fermion and a scalar that carries baryon number, both stable and neutral under the Standard Model, making them plausible dark matter candidates. Crucially, the model contains order-one CP-violating phases in its couplings, satisfying the second Sakharov condition far more generously than the tiny CP violation observed in the Standard Model.

Timing is everything in this scenario. The baryon number transfer must occur below the electroweak scale, at temperatures of roughly 100 GeV or less, so that sphaleron processes cannot wash out the generated asymmetry, yet above the temperatures probed by primordial nucleosynthesis so that the latter’s successful predictions remain intact. That leaves only a narrow energy window in which the entire observed asymmetry must be manufactured. The authors first analyzed the case in which the asymmetry is generated through the decays of top quarks. Setting up a Boltzmann equation for the top quark population as the universe cools from 100 GeV down to 10 GeV, they found that even a loop-suppressed CP asymmetry suffices, with the required branching ratio of the top quark into the hidden sector being a minuscule 10⁻¹⁹, far beyond the reach of any collider constraint. The catch is that the couplings involved are so small that this version of the scenario would be nearly impossible to test experimentally.

The more interesting and more testable case involves bottom quarks, and here the mathematics becomes dramatically tighter. Rare decays of bottom quarks have been searched for at the BaBar and Belle experiments, which bound non-Standard-Model branching ratios at roughly the 10⁻⁵ level. In the mesogenesis variant of the scenario, the universe reheats after inflation to a temperature below the QCD scale, and a reheaton field with a mass of tens of GeV produces a non-thermal population of bottom quarks that hadronize and then decay, seeding the visible plasma and generating the asymmetry through rare CP-violating decays. Combining the existing branching-ratio limits with the required yield shows that a generic loop-level efficiency, of order 10⁻³, is simply not enough. The efficiency of baryon number transfer must be pushed close to unity, and that is where the new paper makes its central contribution.

The mechanism for this boost is resonant enhancement, a phenomenon familiar from studies of leptogenesis involving nearly degenerate heavy neutrinos. In the benchmark model there are two portal fermions, and when their masses are nearly degenerate, the internal propagator in the loop diagram that supplies the CP-odd phase goes on shell. The CP asymmetry then takes a Breit–Wigner shape, peaking when the mass splitting between the two fermions is comparable to their decay widths. In precisely this regime the two portal fermions do not propagate as independent resonances but as a single coherent, mixing pair, and the authors employ a closed-time-path, density-matrix treatment in which the resonant pole is regulated by the coherent sum of the two widths rather than their difference. Their analytical result shows the asymmetry can reach approximately 0.7 at the peak of the resonance, compared with the generic loop-suppressed value of a thousandth.

Importantly, this enhancement does not require any special tuning of flavor structures. The authors performed a Monte Carlo scan over the model parameters, fixing the portal fermion mass at 4 GeV with bottom decays in mind, sampling coupling magnitudes from Gaussian distributions centered on perturbative values, and drawing all CP phases uniformly. They found that roughly ten percent of the sampled parameter points yield an average CP asymmetry of at least 0.5, and that the asymmetry falls to the generic non-resonant value only a vanishing fraction of the time, of order 10⁻⁴ to 10⁻⁵. The two CP asymmetries associated with the two portal flavors are guaranteed to have the same sign, so there is no cancellation of the transferred baryon number. Resonant enhancement, in other words, is generic.

The stakes for experiment are unusually sharp. Even with a maximally efficient CP asymmetry near unity, generating the observed baryon asymmetry through bottom meson decays requires a branching fraction into the hidden sector of at least order 10⁻⁸. Current limits sit at 10⁻⁵, and Belle-II is expected to push them to 10⁻⁷. That means the entire viable parameter space of the mesogenesis scenario lies within a factor of a hundred of existing bounds, and improvements of just two to three orders of magnitude in sensitivity would either discover the rare decay channels or rule the framework out completely. The authors describe this as a final stand for mesogenesis: if the limits drop below about 1.3 × 10⁻⁸, even perfect efficiency cannot save the mechanism, and non-thermal bottom meson decays can be excluded in full as the source of the cosmic matter surplus.

Complementary probes come from other directions. The colored scalar mediator can be produced at the Large Hadron Collider, either resonantly through its couplings to quark pairs or through ordinary strong pair production, with current direct searches requiring its mass to exceed about 1.2 TeV. At that mass the scalar decays promptly on collider timescales, so R-hadron searches do not add further constraints, but future colliders could reach deeper. The authors also examined electric dipole moment constraints, since coupling a maximally CP-violating hidden sector to the visible world risks observable low-energy signatures. Three-loop contributions generate the CP-violating Weinberg operator and shift the neutron electric dipole moment, but the suppression by the fourth power of the mediator mass pushes the effect well below even the Standard Model’s own tiny prediction of 10⁻³² e·cm, making neutron EDM measurements unlikely to probe this scenario.

The broader significance of the work lies in its fusion of two ideas that have largely developed on parallel tracks: resonant enhancement, imported wholesale from the leptogenesis literature with a single substitution in the CP-odd invariant, and mesogenesis, which ties the origin of matter to rare decays of heavy mesons at temperatures far below those usually associated with baryogenesis. By proving that order-one efficiency emerges generically rather than by construction, Kilic and Mathai have transformed a speculative scenario into a sharply falsifiable one. Within the coming decade, as Belle-II and successor experiments grind down the limits on rare bottom decays, the question of whether our matter came from a hidden, CP-violating mirror world may be answered not by better theory but by a simple null result, or by the discovery of a decay that should not exist.

Subject of Research: Resonantly enhanced baryon number transfer from a CP-violating hidden sector as a mechanism for the cosmic matter–antimatter asymmetry

Article Title: Resonant Enhancement for the transfer of baryon number from a CP-violating hidden sector

Article References: Kilic, C., & Mathai, S. (2026). Resonant Enhancement for the transfer of baryon number from a CP-violating hidden sector. The European Physical Journal C, 86(9), Article 1124. https://doi.org/10.1140/epjc/s10052-026-16384-7

Image Credits: AI Generated

DOI: 10.1140/epjc/s10052-026-16384-7

Keywords: baryogenesis, hidden sector, CP violation, mesogenesis, baryon portal, resonant enhancement, bottom quark decays, Belle-II, dark matter, sphalerons, neutron electric dipole moment, Standard Model