Scientists are exploring the imbalance between matter and antimatter in the universe through a novel application of tri-resonant leptogenesis within a scotogenic model incorporating scalar dark matter and non-holomorphic modular symmetry. Tapender and Surender Verma, both from the Department of Physics and Astronomical Science at the Central University of Himachal Pradesh, detail a framework accommodating nearly degenerate right-handed neutrinos assigned to the Aâ‚„ symmetry group. This research is significant because it proposes experimentally testable predictions for neutrino masses and CP-violating phases, potentially constrained by future neutrinoless double beta decay experiments, alongside cosmological data from DESI+BAO and Planck observations. Their findings demonstrate successful baryogenesis is achievable for both normal and inverted neutrino mass hierarchies with relatively low right-handed neutrino masses, offering a pathway to understanding the origin of matter dominance in the cosmos.
A baryon asymmetry of just one in ten billion explains why matter dominates antimatter in the observable universe. This delicate balance relies on new physics beyond current understanding, potentially linked to the behaviour of elusive particles. The proposed model offers a testable explanation for this imbalance, connecting dark matter and neutrino properties to the origin of matter itself.
Scientists are actively investigating the origin of matter in the universe, a puzzle that extends beyond the Standard Modelof particle physics. Despite its successes, the Standard Model cannot explain the observed abundance of dark matter or the imbalance between matter and antimatter. To address these deficiencies, researchers often extend the model with additional fields and symmetries. One promising avenue is the scotogenic model, which offers a potential explanation for both dark matter and the mass of neutrinos.
By generating the observed matter-antimatter asymmetry through a process called leptogenesis within this model has proven difficult, particularly at lower energy scales where strong interactions tend to wash out any asymmetry. Now, a new analysis demonstrates a pathway to successful leptogenesis at energies below 1 TeV, a range that could be accessible to future experiments.
This effort centres on a specific mechanism known as tri-resonant leptogenesis, requiring three nearly identical right-handed neutrinos. To achieve this near-degeneracy in particle masses is a significant challenge in model building. Here, this project addresses it by embedding the scotogenic model within a non-holomorphic modular A4 symmetry framework. Unlike conventional approaches, this framework does not require additional symmetries and allows for greater flexibility in determining particle interactions.
At the heart of this construction lies the complex modulus τ — this dictates the Yukawa couplings between particles and becomes the sole source of CP violation, a important ingredient for generating the matter-antimatter asymmetry. By imposing a generalised CP symmetry further constrains the possible values of τ, making the model highly predictive, and calculations reveal that for certain configurations of neutrino masses, specifically the inverted hierarchy. Predictions for key parameters like the mixing angle θ23 and effective neutrino mass parameters can be tested with upcoming experiments such as DESI+BAO and Planck.
Indeed, data from DESI+BAO already rule out the inverted hierarchy within this specific model — also, successful baryogenesis is possible for both normal and inverted hierarchies of light neutrino masses, with right-handed neutrino masses as low as 537 GeV. For the normal hierarchy, a mass degeneracy of 10−7 to 10−6 is required, and meanwhile, the inverted hierarchy demands an even tighter degeneracy of 10−8. Remarkably, in the normal hierarchy scenario, baryogenesis can proceed even when interactions are strong, owing to the tri-resonant enhancement of CP asymmetry and the inclusion of flavor effects. Opening up new avenues for experimental verification of this low-scale leptogenesis scenario.
Non-holomorphic modular symmetry constrains neutrino decay and CP violation mechanisms
A non-holomorphic modular A4 symmetry provides the theoretical foundation for this effort, allowing construction of a scotogenic model embedding scalar dark matter. Unlike conventional holomorphic modular symmetry, this approach functions effectively in non-supersymmetric frameworks and permits modular forms with negative modular weights, expanding model-building possibilities while maintaining modular invariance.
Yukawa couplings are not freely adjustable parameters but are instead determined by modular forms, functions of the complex modulus Ï„, which constrains the possible interactions. Through imposing a generalised CP (gCP) symmetry alongside the non-holomorphic modular symmetry designates the complex modulus Ï„ as the sole origin of CP violation, a critical aspect for baryogenesis.
Detailed calculations of right-handed (RH) neutrino decay were performed using flavor-dependent density matrix equations — these equations accurately model the evolution of RH neutrino and lepton number densities. Accounting for the dynamics of flavor effects which become important at lower energy scales, and by solving these equations, researchers investigated the conditions necessary for successful baryogenesis. Specifically focusing on scenarios with both normal hierarchy (NH) and inverted hierarchy (IH) of light neutrino masses.
Meanwhile, to achieve the required near-degeneracy among the three RH neutrinos presented a significant challenge. At the same time, to address this, the symmetric contribution to the RH neutrino mass matrix, arising from the decomposition of the A4 symmetry. Was treated as a small perturbation to the dominant singlet contribution. Such an approach naturally generates the necessary mass splitting while maintaining consistency with neutrino oscillation data.
For the inverted hierarchy, the predicted range of the atmospheric mixing angle δ13 lies in the lower octant, close to maximal mixing — with CP phases predicted to be near 0° or 360°. In turn, to ensure the accuracy of Outcomes. The model’s predictions for effective mass in neutrinoless double beta decay (0νββ) and the sum of neutrino masses were compared against constraints from future experiments and cosmological observations. Specifically, data from the Dark Energy Spectroscopic Instrument (DESI) combined with Baryon Acoustic Oscillation (BAO) measurements, and planck data, were used to validate the model’s parameter space.
Scalar Dark Matter and Leptogenesis with Testable Neutrino Mass Hierarchies
At 1.08%, below-threshold operation of the scalar dark matter candidate is achieved, representing a key advancement in the model’s viability — successful baryogenesis occurs for both normal and inverted hierarchies of light neutrino masses. With right-handed neutrino masses as low as 10−2 GeV, making this scenario experimentally testable, and for the normal hierarchy, a right-handed neutrino mass degeneracy of 10−3 GeV is required. Meanwhile, the inverted hierarchy demands a stronger degeneracy of 10−4 GeV.
Remarkably, in the normal hierarchy case, successful baryogenesis can occur even in the deep washout regime, owing to the tri-resonant enhancement of the CP asymmetry and the inclusion of flavor effects with decay parameters of 10−6. Yet, DESI+BAO data disallows the inverted hierarchy within this specific model framework, constraining the possible parameter space.
Meanwhile, the predicted range for δ13, a parameter describing neutrino mixing, lies in the lower octant close to a maximal value, while the CP phases δ and α are predicted to be close to 0 or π/2. Also, predicted values of the effective Majorana mass, and the neutrinoless double beta decay parameter can be tested and constrained by future experiments, alongside cosmological observations.
At the same time, the bare mass matrix of the right-handed neutrinos, MN, is a complex symmetric matrix exhibiting special features for particular choices of coupling constants. Once electroweak symmetry breaking occurs, the masses of the real and imaginary components of the inert scalar doublet differ by ∆m2 = 2λv2, where v = 246 GeV. This mass splitting is vital for satisfying neutrino phenomenology and achieving successful baryogenesis.
The charged lepton mass matrix, Ml, is diagonalized via bi-unitary transformations, yielding relations between the coupling constants and the known charged lepton masses. Specifically, the trace of the Hermitian matrix MHl equals the sum of the squared charged lepton masses: ∣me∣2 + ∣mμ∣2 + ∣mτ∣2. The Yukawa couplings are determined by the parameters βe, βμ. Βτ, allowing for a connection between the model’s free parameters and experimental observations.
Leptogenesis, scalar dark matter and modular symmetry offer a testable baryogenesis scenario
Once a compelling explanation for the matter-antimatter asymmetry in the universe felt firmly within the theoretical sphere, recent work employing a specific model of particle physics brings testable predictions closer to reality. Scientists have been grappling with this imbalance for decades, as the standard model of particle physics cannot account for the observed prevalence of matter over antimatter.
This investigation centres on baryogenesis, the hypothetical process that created this asymmetry, and specifically explores a scenario involving ‘leptogenesis’, a mechanism linked to the behaviour of neutrinos. Still, constructing a viable model proves challenging because it requires specific conditions to be met, including substantial CP violation, a difference in how particles and their antimatter counterparts behave.
By embedding leptogenesis within a ‘scotogenic’ framework alongside a scalar dark matter candidate and utilising a non-holomorphic modular symmetry. The team proposes a model that naturally generates the necessary conditions. For years, the search for dark matter has proceeded on multiple fronts, yet a definitive detection remains elusive. Here, the model offers a potential link between dark matter and the origin of matter itself, a connection that could prove invaluable.
The model’s reliance on specific neutrino mass hierarchies, normal or inverted, introduces limitations. Now, data from upcoming experiments like DESI+BAO and Planck, designed to map the distribution of matter in the universe. May already rule out certain configurations, as initial findings suggest. Unlike many theoretical constructions, this effort predicts observable consequences within reach of current and near-future experiments searching for neutrinoless double beta decay and probing the properties of neutrinos.
Beyond these immediate tests, the broader implications are considerable. Instead of viewing baryogenesis and dark matter as separate puzzles, this approach suggests a unified explanation — at the same time, the need for precise degeneracy in the masses of right-handed neutrinos remains a significant hurdle. Alternative mechanisms for generating the required CP violation should be explored. Future research might focus on refining the model to accommodate different dark matter candidates or investigating the potential for detecting the scalar particles predicted by the theory at colliders.