A Minimal Dark SU(2) Origin of a Massless Dirac Neutrino

The paper proposes a minimal theoretical framework, A Minimal Dark SU(2) Origin of a Massless Dirac Neutrino, to explain why one neutrino is exactly massless, protected by gauge symmetry, while remaining consistent with current oscillation and cosmological data.

Motivation and Theoretical Context

The observation of neutrino oscillations has increased the number of free parameters in the Standard Model (SM). While oscillation experiments are precise, none of the oscillation experiments are sensitive to the absolute neutrino mass scale, leaving this as an open question. Constraints on sum m i come from cosmological observations, such as DESI BAO and Planck. The paper notes that current cosmological bounds are close to the minimum value of m i allowed by oscillation data for Normal Ordering (NO), suggesting a timely motivation to consider theories in which the lightest neutrino remains exactly massless.

Existing models that rely on a minimal field content or texture zeros often fail to protect this zero mass from higher-order corrections. The authors propose an alternative: a gauge selection rule.

The Minimal Dark SU(2) Model

The mechanism is based on introducing a minimal dark SU(2) D gauge symmetry. To ensure the theory is anomaly-safe, the global Witten anomaly must be prevented, which requires including an even number of SU(2) D doublets. The model introduces two key components:

1. ** N 1 **: A right-handed-neutrino-like Weyl fermion that transforms as an SU(2) D doublet, making it the charged state responsible for the masslessness.

2. ** xi **: Another SU(2) D doublet Weyl-fermion field, required for anomaly cancellation.

The SM fields and two other right-handed neutrinos (N 2, N 3 are singlets under the dark gauge group). A discrete Z 4 symmetry is imposed to keep the neutrino sector Dirac.

Mechanism of Masslessness

The masslessness of one neutrino is enforced by the dark gauge charge, which forbids one Dirac Yukawa column. The allowed renormalizable Yukawa interactions with the SM lepton and Higgs sector are:

L Yukawa = - (Y e) ij L i H e Rj - (Y nu) i alpha L i H N alpha

A crucial interaction is the vectorlike mass term L mass = -m D epsilon ab N 1a xi b + h.c., which controls the dark infrared dynamics.

Neutrino Mass Matrix and Predictions

The resulting Dirac neutrino mass matrix, after electroweak symmetry breaking, is:

Y nu = 0 & y 12 & y 13 v

The first column of Y nu is identically zero because N 1 has the requisite dark gauge charge. This results in M nu = 0, meaning one physical Dirac neutrino mass vanishes.

This model predicts a zero lightest neutrino mass, leading to specific absolute mass predictions:

• Normal Ordering (NO): m 1 = 0, m 2 = m 221, m 3 = m 231. The predicted sum of neutrino masses (sum m nu) is 58.79+1.07-0.57 meV.

• Inverted Ordering (IO): m 3 = 0, m 1 = m 231, m 2 = m 231 + m 221. The predicted sum of neutrino masses (sum m nu) is 98.92+2.06-1.65 meV.

Phenomenology and Dark Sector Dynamics

The dark gauge theory is strong in the infrared, generating a confinement scale D via dimensional transmutation:

D = mu (-2(mu)/b 0 g D)

In the minimal model (n W=2, n S=0), b 0 = 2/3 > 0, meaning the theory is asymptotically free and confines.

Dark Matter Candidate: If the lightest confined states are stable, they provide a natural Dark Matter candidate. The dark sector's interactions with the SM occur primarily through higher-dimensional portals (e.g, L theta D = theta D g D over 2 pi squared epsilon mu nu rho sigma G mu nu G rho sigma).

Dark Sector Phenomenology and Constraints:

• The dark confinement transition occurs at a temperature T D about D.

• The model predicts that neutrinoless double beta decay should not be observed.

• The relic neutrino capture rate is smaller by a factor of two compared to the Majorana case, providing specific targets for detectors like PTOLEMY.

Flavor Completion and Correlations

Using the D76 texture as a representative case, the model predicts correlations between oscillation parameters and CP violation. The required zero-mass condition leads to specific predictions in the (squared theta 23, delta CP) plane (Figure A1), which can be tested by imposing flavor symmetries, such as a right-handed dihedral D N symmetry.

Conclusion

The model provides a minimal, gauge-protected mechanism for a massless Dirac neutrino. The predictions for the absolute mass sum (sum m nu) are testable using future direct beta-decay searches (e.g., Project 8) and cosmological surveys, while the dark sector offers potential targets for gravitational-wave and compact-object studies.

Based on my rigorous analysis of this scientific paper, I have identified several critical areas for improvement in advanced AI research systems. These improvements transform the model from a static piece of literature into a dynamic, predictive framework capable of cross-disciplinary scientific inquiry.

Improvement: Implement an AI system designed to build and maintain a multi-layered knowledge graph (KGC) that links the specific parameters, symmetries, and physical predictions of this model to external experimental data sources.

What the improved AI system can do:

• Trace Causal Pathways: The system can trace how a specific symmetry (SU(2) D and Z 4) leads to a specific mathematical property (the zero-column in the mass matrix, M nu) and then predict observable outcomes.

• Contextual Cross-Referencing: It can instantly cross-reference the predicted values for sum m i (e.g., <64 meV for DESI) against real-time updates from the DESI collaboration, identifying areas of tension or confirmation with unprecedented speed and granularity.

• Model Validation: The AI can detect if a specific flavor completion (e.g a right-handed dihedral D N symmetry) leads to a predicted correlation between squared theta 23 and delta CP that contradicts the current NuFIT best-fit values, allowing researchers to immediately discard unphysical parameter spaces.

We propose a gauge-symmetry origin of a rank-two Dirac neutrino mass matrix that enforces one exactly massless neutrino, while being consistent with the oscillation data, as well as cosmological constraints. The mechanism relies on a minimal dark SU(2) D gauge symmetry under which one right-handed-neutrino-like Weyl fermion is charged, thereby forbidding its Standard Model Yukawa coupling. Quantum consistency then fixes the minimal dark-sector completion: Cancellation of the Witten anomaly requires a second fermionic SU(2) D doublet, while a discrete Z 4 symmetry that forbids Majorana masses allows the two dark doublets to form a vectorlike pair. This anomaly-free completion gives rise to a secluded, confining dark sector with a viable dark matter candidate, linking the protected neutrino texture to dark infrared dynamics.