Flavor-deconstructed neutrinos

Abstract: A tentative approach to explain the flavor puzzle consists of embedding the Standard Model in a larger gauge symmetry that contains a separate gauge group for each fermion family. In such gauge non-universal (or flavor-deconstructed) theories, neutrinos pose some challenges. I will discuss existing ideas in the literature and present a simple model in which flavor deconstruction naturally leads to sequential dominance for both neutrinos and charged leptons, thus providing a viable explanation for the flavor structure of the lepton sector.

• The paper introduces a modified tri-hypercharge framework that utilizes sequential dominance to naturally generate hierarchical neutrino mass textures with one massless state.
• It constructs a type-I seesaw mechanism where hierarchical Dirac matrices and nearly diagonal Majorana matrices yield large lepton mixing angles consistent with experimental data.
• The model employs O(1) parameters and moderate VEV hierarchies to achieve realistic neutrino masses and mixing, offering concrete targets for neutrinoless double beta decay and collider searches.

Sequential Dominance in Flavor-Deconstructed Neutrino Models

Introduction: The Flavor Puzzle and Limitations of the Standard Model

The origin of fermion masses and mixings, particularly the hierarchical patterns and differing mixing matrices between quarks and leptons, remains one of the central outstanding puzzles in particle physics. Traditional approaches, primarily based on horizontal (flavor) symmetries—whether continuous, discrete, global, or gauged—strive to impose flavor structures dynamically during symmetry breaking. However, alternative frameworks such as "flavor deconstruction" have emerged, wherein the Standard Model (SM) is embedded within a product gauge symmetry, assigning distinct gauge factors to each fermion family.

Flavor-deconstructed (gauge non-universal) theories naturally accommodate charged fermion mass hierarchies and the observed approximate diagonality of the CKM matrix. Nonetheless, extensions to the lepton sector, especially with mechanisms for neutrino masses, introduce significant tension—these frameworks typically yield small lepton mixing angles, at odds with experimental results for the PMNS matrix.

Review of Tri-Hypercharge and the Challenge of Neutrino Mixing

The tri-hypercharge construction, as a minimal instance of flavor deconstruction, replaces the SM hypercharge $U(1)_Y$ with a product $U(1)_{Y_1} \times U(1)_{Y_2} \times U(1)_{Y_3}$, assigning specific charge assignments per family. Scalar fields ("hyperons") mediate the breaking to the universal hypercharge at a high scale. In the minimal tri-hypercharge model for the lepton sector, the hierarchical Dirac and nearly diagonal charged-lepton mass matrices are generated automatically. However, right-handed neutrinos—being gauge singlets—produce anarchic Majorana mass matrices, and the overall lepton mixing remains highly suppressed unless dimensionless couplings are finely tuned.

Several proposals attempt to circumvent this issue, such as introducing additional family-dependent scalars for the neutrino sector, embedding the complete model within an ultraviolet (UV) completion, or invoking family-non-universal charge assignments for the lepton doublets. Despite these interventions, such models predominantly yield anarchical neutrino mass matrices, reducing predictivity and failing to explain large lepton mixing without ad-hoc parameter choices.

The Proposed Extension: Flavor Decomposition with Sequential Dominance

The work proposes a systematic modification of the tri-hypercharge structure: instead of maintaining singlet right-handed neutrinos, the gauge group is enlarged such that right-handed neutrinos of the second and third families are distinguished by $U(1)_R \times U(1)_{(B-L)/2}$ charges. This extension modifies the lepton field content and charge assignments, ensuring that the Dirac mass matrix $m_D$ becomes hierarchical by columns, while the heavy Majorana mass matrix $M_M$ remains nearly diagonal.

The resultant textures support a type-I seesaw realization with strong sequential dominance. Here, one right-handed neutrino drives the generation of the heaviest neutrino mass eigenstate, with the subdominant right-handed neutrino generating the second eigenstate, while the lightest is massless ($m_1=0$), enforcing a normal mass ordering. The PMNS matrix acquires large mixing angles from structured, rather than anarchic, Yukawa couplings—charged lepton and neutrino sectors both contribute appreciably to the leptonic mixing, consistent with experimental data.

A key result is that all mass and mixing hierarchies can be generated with $\mathcal{O}(1)$ parameters and moderate VEV hierarchies for the breaking scalars (e.g., $\langle\chi_2\rangle \sim 10^{13}$ GeV, $\langle\chi_3\rangle \sim 10^{14}$ GeV), and realistic choices of suppression parameters ($\epsilon_{12,23}^{R,L}$ and their analogues). The model predicts suppressed right-handed charged lepton mixing, hierarchical charged lepton masses, and provides analytic relations governing the PMNS entries and neutrino masses at leading order.

Implications and Theoretical Extensions

The model offers a systematic pathway to address the flavor puzzle within a deconstructed gauge framework, in particular circumventing the typical reliance on parameter anarchy in the lepton sector. The structured mass matrices enable testable predictions: a normal ordering for neutrino masses and a vanishing lightest neutrino mass, in contrast with anarchic models that have less sharp outcomes.

The formalism is compatible with further UV model building, and the gauge structure admits unification with extensions such as $U(1)_{Y_1} \times U(1)_{Y_2} \times U(1)_{Y_3}$0 or $U(1)_{Y_1} \times U(1)_{Y_2} \times U(1)_{Y_3}$1, provided appropriate anomaly cancellations are built in—possibly demanding extra high-scale vectorlike fermions. Experimentally, the sequential dominance scenario offers robust targets for neutrinoless double beta decay searches and direct neutrino mass measurements.

From a model-building perspective, this sequential dominance prediction can be extended to larger frameworks, providing a template for addressing flavor in grand unified or string-inspired constructions. The presence of new gauge bosons and scalar degrees of freedom may also yield phenomenologically accessible signatures in precision flavor or collider observables, subject to the high scale of flavor symmetry breaking.

Conclusion

By refining the gauge structure of flavor-deconstructed models and avoiding the unsatisfactory anarchy of the neutrino sector, the proposed scheme derives sequential dominance as a structural outcome of the gauge group and field content. The consequence is a predictive and economical description of lepton masses and mixings consistent with experimental data, with normal ordering and a massless lightest neutrino. This construction strengthens the theoretical case for flavor deconstruction as a viable strategy for addressing the SM flavor puzzle in both quark and lepton sectors, and motivates further investigation in model extensions and related experimental signatures.