Thermal Leptogenesis in the BNT Model of Neutrino Mass

Technical Summary: Thermal Leptogenesis in the BNT Model of Neutrino Mass

Problem Statement
The paper addresses two fundamental open problems in particle physics and cosmology: the origin of small, non-zero neutrino masses and the generation of the observed baryon asymmetry of the Universe (BAU). While the Standard Model (SM) predicts massless neutrinos, oscillation experiments confirm they possess mass. The canonical seesaw mechanism explains this via heavy Majorana fermions but typically requires a lepton number violation (LNV) scale near $10^{14}$ GeV, rendering it inaccessible to current or near-future experiments. Conversely, models with lower mass scales (TeV) often struggle to generate sufficient CP asymmetry for successful thermal leptogenesis without fine-tuning Yukawa couplings. The authors investigate whether the Babu-Nandi-Tavartkiladze (BNT) model, which generates neutrino masses via higher-dimensional operators involving a scalar quadruplet ($\Phi$) and vector-like fermion triplets ($\Sigma$), can simultaneously accommodate TeV-scale neutrino mass generation and viable thermal leptogenesis.

Methodology
The authors analyze the BNT model, which extends the SM with a scalar quadruplet $\Phi \sim (1, 4, 3/2)$ and two generations of vector-like fermion triplets $\Sigma_{L,R} \sim (1, 3, 1)$.

1. Neutrino Mass Generation: They examine two contributions to neutrino mass:
   • A tree-level dimension-7 operator ($LLHH(H^\dagger H)/\Lambda^3$) mediated by the exchange of $\Phi$ and $\Sigma$.
   • A one-loop dimension-5 Weinberg operator ($LLHH/\Lambda$) generated via the same particle content.
     The authors utilize a Generalized Casas-Ibarra (GCI) parameterization to relate the Yukawa couplings ($Y_H, Y_\Phi$) to low-energy neutrino data, allowing for large Yukawa couplings not suppressed by the small neutrino mass scale.
2. Leptogenesis Framework: They study thermal leptogenesis driven by the out-of-equilibrium decays of the heavy fermion triplets $\Sigma$. The analysis distinguishes between two LNV scenarios based on the lepton number assignment of $\Phi$:
   • Case 1: $\Phi$ carries $L=-2$. LNV arises from the scalar potential ($\lambda_5$ term). The $\Sigma$ decays conserve lepton number, but asymmetry is generated via interference between tree and loop diagrams due to different scalar final states.
   • Case 2: $\Phi$ carries $L=0$. LNV arises directly from the Yukawa interactions.
3. Dynamical Evolution: The authors solve a set of coupled Boltzmann equations (BEs) to track the evolution of number densities and asymmetries for $\Sigma$, $\Phi$, $H$, and leptons ($L$). The BEs include:
   • Decay and inverse decay rates.
   • Gauge scattering and annihilation processes (which are significant due to the non-zero hypercharge of $\Sigma$).
   • $\Delta L = 2$ scatterings mediated by $\Sigma$.
   • Scalar interactions ($\Phi \to HHH$ and $2 \leftrightarrow 2$ scatterings) driven by the $\lambda_5$ coupling, which wash out scalar asymmetries.
4. Scenarios: They explore two mass spectra for the fermion triplets:
   • Hierarchical: $M_{\Sigma_2} \gg M_{\Sigma_1}$.
   • Quasi-degenerate: $M_{\Sigma_1} \approx M_{\Sigma_2}$, allowing for resonant enhancement of CP asymmetry.

Key Contributions and Results

• Viability of Leptogenesis: The study demonstrates that thermal leptogenesis is viable in the BNT model. The presence of vector-like fermions and the specific structure of the scalar potential allow for significantly larger Yukawa couplings compared to canonical seesaw models, as the suppression of neutrino masses is attributed to the small induced vacuum expectation value (VEV) of the quadruplet ($v_\Phi$) rather than tiny Yukawas.
• Hierarchical Spectrum: For a hierarchical mass spectrum ($r = M_{\Sigma_2}/M_{\Sigma_1} \ge 2$), the authors find that successful leptogenesis requires a lower bound on the lightest triplet mass of $M_{\Sigma_1} \gtrsim 3.5 \times 10^7$ GeV. This is lower than the Davidson-Ibarra bound for Type-I seesaw ($10^9$ GeV) but remains above the TeV scale, potentially limiting the model's testability at colliders for this specific regime.
• Resonant Leptogenesis: In the quasi-degenerate regime ($r \simeq 1$), the CP asymmetry is resonantly enhanced. This lowers the viable scale for leptogenesis to $M_{\Sigma_1} \gtrsim 1.7$ TeV. This result reconciles the model's original motivation (TeV-scale phenomenology) with the requirement to explain the BAU.
• CP Asymmetry Mechanism: The paper highlights that the CP asymmetry ($\epsilon_\Sigma$) can be of order $\mathcal{O}(1)$ because the factors suppressing neutrino masses (loop factors and $\lambda_5$) do not appear in the CP asymmetry expressions. The asymmetry is maximized when the branching ratios to the scalar quadruplet and Higgs doublet are comparable ($Y_\Phi \sim Y_H$).
• Scalar Dynamics: The authors emphasize the critical role of the $\lambda_5$-induced scalar interactions ($\Phi \to HHH$). These interactions rapidly wash out scalar asymmetries, modifying the final lepton asymmetry and the sphaleron conversion factor. The analysis shows that for $\lambda_5 > 10^{-6}$, these interactions are in equilibrium at the relevant temperatures.
• Benchmark Points: Two benchmark points (BP1 and BP2) are identified. BP1 corresponds to the hierarchical case ($M_{\Sigma_1} \sim 3.5 \times 10^7$ GeV) with a small $\lambda_5 \sim 10^{-5}$, while BP2 corresponds to the resonant case ($M_{\Sigma_1} \sim 1.7$ TeV) with a larger $\lambda_5 \sim 0.01$. In BP2, the larger $\lambda_5$ compensates for smaller Yukawa couplings, and the dominant decay channel of the quadruplet shifts from dileptons to gauge bosons.

Significance and Claims
The paper claims to be the first detailed study of thermal leptogenesis within the BNT model and, more broadly, in a framework where both fermionic and scalar multiplets larger than SU(2)$_L$ triplets participate in neutrino mass generation.

• Distinct Mechanism: The authors argue that the BNT model offers a distinct leptogenesis mechanism compared to canonical Type-I or Type-III seesaws. The LNV source can be either the scalar potential or the Yukawa sector, and the vector-like nature of the fermions allows for CP violation even if the decays themselves do not violate lepton number (in the $L_\Phi = -2$ scenario).
• Reconciliation of Scales: The primary significance lies in the demonstration that resonant leptogenesis can lower the required new physics scale to the TeV range ($\sim 1.7$ TeV). This restores the model's testability at the Large Hadron Collider (LHC) and future colliders, addressing the tension between generating neutrino masses and the BAU at experimentally accessible scales.
• Robustness: The results suggest that the lower bound on the triplet mass in the resonant case is extremely close to the absolute theoretical lower bound for triplet fermions and scalars, implying that flavor effects (not included in this analysis) are unlikely to lower the bound significantly further.

The authors conclude that while the hierarchical case pushes the scale beyond current experimental reach, the quasi-degenerate case successfully realizes the BNT model's promise of a testable, TeV-scale origin for both neutrino masses and the baryon asymmetry.