Split Seesaw Mechanism in Neutrino Physics

• Split Seesaw Mechanism is a framework where active neutrino masses remain small by splitting the right-handed neutrino spectrum across keV to high scales.
• It utilizes extra-dimensional models and tailored flavor symmetries to generate exponential hierarchies in Yukawa couplings and Majorana masses without fine tuning.
• The mechanism offers a unified explanation for neutrino mass, baryogenesis via leptogenesis, and sterile neutrino dark matter, with observable signals like X-ray lines and collider signatures.

The Split Seesaw Mechanism is a class of extensions to the canonical seesaw scenario that enables small neutrino masses and potentially light sterile neutrino dark matter by “splitting” the right-handed neutrino mass spectrum across several orders of magnitude. It achieves suppressed active neutrino masses with new physics at accessible energy scales (keV–TeV), while maintaining testable predictions for leptogenesis and dark matter. Often realized in models with extra dimensions, tailored flavor symmetries, or nested seesaw constructions, split seesaw frameworks are at the intersection of neutrino physics, collider phenomenology, cosmology, and dark sector investigations.

1. Theoretical Motivation and Definition

The standard seesaw mechanism accounts for tiny active neutrino masses via heavy right-handed (sterile) neutrinos with masses $M_R \sim 10^{10-15}$ GeV, yielding active neutrino masses $m_\nu \sim \frac{\lambda^2 v^2}{M_R}$ for Yukawa coupling $\lambda$ and Higgs vacuum expectation value $v$. The split seesaw mechanism modifies this picture by arranging a sharply hierarchical spectrum for right-handed neutrinos—typically, two at very high scale for leptogenesis and one with a mass in the keV range for dark matter (Kusenko et al., 2010), allowing the realization of

• $M_{R,1} \sim {\rm keV}$ (sterile neutrino DM)
• $M_{R,2,3} \sim 10^{11-12}$ GeV (for leptogenesis)

In extra-dimensional constructions (notably five-dimensional models compactified on $S^1/Z_2$), wavefunction localization yields exponential hierarchies in both effective Yukawa couplings and Majorana masses, but the suppression cancels out in the seesaw formula so that active neutrino masses remain naturally small regardless of the value of $M_{R,1}$ (Kusenko et al., 2010).

2. Core Formalism and Mechanisms

2.1. Canonical Seesaw Formula

The generic seesaw formula is

$$(m_\nu)_{\alpha\beta} = \sum_i \frac{\lambda_{i\alpha}\lambda_{i\beta} v^2}{M_{R,i}}$$

where $\lambda_{i\alpha}$ are Yukawa couplings, $v$ is the Higgs VEV, and $M_{R,i}$ are the right-handed neutrino Majorana masses.

2.2. Split Seesaw Realization in Extra Dimensions

Split seesaw in 5D models uses bulk mass parameters $m_i$ to localize right-handed neutrino zero modes. The 4D zero-mode profile is (see (Kusenko et al., 2010), Eq. (7)): $$\nu_{R}^{(0)}(y,x) = \sqrt{\frac{2m_i}{e^{2m_i\ell}-1}} e^{m_i y} \psi_R^{4D}(x)$$ Majorana mass and Yukawa couplings are exponentially suppressed, but their ratio (appearing in the seesaw formula) is not: $$(m_\nu)_{\alpha\beta} \sim \text{(order 1)}\times v^2 / v_{B-L}$$ with $v_{B-L}$ the B–L breaking scale (Kusenko et al., 2010). Thus, splitting $M_{R,1}$ to the keV scale does not enhance $m_\nu$, preserving eV-scale active neutrino masses.

3. Dark Matter and Leptogenesis Implications

3.1. Sterile Neutrino Dark Matter

A sterile right-handed neutrino with $M_{R,1}\sim 1-10$ keV is extremely long-lived (small mixing with active neutrinos) and is an excellent candidate for warm dark matter. Its decay produces a monochromatic X-ray line; observations such as Chandra’s 2.5 keV feature are consistent with the predicted sterile neutrino decay (Kusenko et al., 2010, Ishida et al., 2014).

3.2. Leptogenesis

The two heavier right-handed neutrinos ($M_{R,2,3}\sim 10^{11-12}$ GeV) decay out-of-equilibrium, generating lepton number asymmetry eventually converted to baryon asymmetry via sphaleron processes (Kusenko et al., 2010, Adulpravitchai et al., 2011). Split seesaw frameworks naturally accommodate this standard leptogenesis scenario.

4. Flavor Structure and Embedding

4.1. Flavor Symmetry Solutions

Embedding in discrete flavor groups (e.g., $A_4$ symmetry (Adulpravitchai et al., 2011)) allows realistic mixing angles and mass hierarchies. Assigning right-handed neutrinos to distinct nontrivial $A_4$ singlets overcomes degeneracy problems in triplet assignments—the bulk mass terms for different right-handed neutrinos become independent, enabling the split spectrum.

4.2. Flavon Vacuum Alignment

Orbifold compactification with flavon fields and controlled vacuum alignment yields desired textures for neutrino Dirac and Majorana matrices, leading at leading order to the mu–tau symmetric limit: $\theta_{13} = 0$, $\theta_{23} = \pi/4$ (Adulpravitchai et al., 2011).

5. Phenomenology and Experimental Signatures

5.1. Astrophysical Signals

The sterile neutrino DM candidate predicts X-ray lines at energies determined by $M_{R,1}$, compatible with Chandra and other X-ray observatory results (Kusenko et al., 2010, Ishida et al., 2014).

5.2. Collider Signatures

Split seesaw with TeV-scale heavy neutrinos and scalar triplets leads to possible direct production at colliders, including signatures such as same-sign dileptons and displaced vertices for the heavier (but still TeV-scale) right-handed neutrinos and scalar states (Cogollo et al., 2010, Mohapatra et al., 2011).

5.3. Constraints from Neutrino Mixing and Non-unitarity

Split seesaw frameworks must respect constraints from neutrino oscillation data and non-unitarity of the PMNS matrix, especially if heavy neutrinos mix sizably with active states.

6. Extensions: Split Flavor Mechanisms and Cosmology

The split flavor mechanism generalizes the split seesaw idea to suppress Yukawa couplings of the lightest sterile neutrino via flavor symmetry breaking tied to B–L breaking, naturally ensuring both small mass ($\sim$ keV) and ultra-suppressed mixing ($\sin^2 2\theta \sim 10^{-10}$) for longevity, as required by X-ray bounds (Ishida et al., 2014). Supersymmetric versions impose relations such as

$m_s \sim m_{3/2} \left( \frac{M}{M_{Pl}} \right)^3$

linking sterile neutrino and gravitino masses.

7. Models, Limitations, and Outlook

Split seesaw mechanisms—whether realized in extra dimensions, via nested seesaw chains, or through flavor symmetry engineering—provide a framework where the smallness of active neutrino masses, matter–antimatter asymmetry, and dark matter composition are unified and potentially accessible to experiment. Key limitations include the requirement of specific flavor assignments and vacuum alignments, the stability against radiative corrections, and the necessity to avoid fine-tuning in parameter choices.

Further directions involve direct searches for sterile neutrino dark matter, precise measurements of leptogenesis parameters, and collider searches for TeV-scale seesaw mediators. Future cosmological observations (e.g., the sum of neutrino masses, structure formation signatures of warm DM) and improved X-ray astronomy will critically test the split seesaw paradigm.