[Paper Review] Minimal predictive see-saw model with normal neutrino mass hierarchy

Stephen F. King|arXiv (Cornell University)|Apr 23, 2013

Neutrino Physics Research16 references16 citations

TL;DR

This paper proposes a minimal two-right-handed-neutrino see-saw model with normal neutrino mass hierarchy, where a dominant texture zero (zero coupling to the electron neutrino) links leptogenesis and CP violation. It derives a master formula connecting Yukawa couplings to physical observables, identifying a simple, predictive pattern: atmospheric neutrino mass from couplings (0,1,1) and solar from (1,1,3) or (1,3,1), with relative phase ±π/3, leading to Tri-bimaximal-Cabibbo mixing with δ ≈ ±π/2 and m₁ = 0.

ABSTRACT

We consider the type I see-saw model with two right-handed neutrinos and a normal neutrino mass hierarchy and impose a zero coupling between the right-handed neutrino mainly responsible for the atmospheric neutrino mass and the electron neutrino. We derive a master formula which relates see-saw input parameters in a one to one correspondence with physical neutrino observables. Using the master formula we search for simple ratios of couplings consistent with current data on neutrino mass and lepton mixing. We discover a minimal predictive example in which the right-handed neutrino mainly responsible for the atmospheric neutrino mass has couplings to (nu_e, nu_mu, nu_tau) proportional to (0,1,1) and the right-handed neutrino mainly responsible for the solar neutrino mass has couplings to (nu_e, nu_mu, nu_tau) proportional to (1,1,3) or (1,3,1), with a relative phase eta = -/+ pi/3, providing the link between leptogenesis and CP violation in neutrino oscillation experiments. We show how these patterns of couplings could arise from an A_4 family symmetry model of leptons which predicts all the PMNS parameters in terms of the neutrino mass ratio m_2/m_3, corresponding to approximate Tri-bimaximal-Cabibbo mixing, accurate to one degree, with the prediction delta = +/- pi/2.

Motivation & Objective

• To construct a minimal two-right-handed-neutrino see-saw model with normal neutrino mass hierarchy that explains current neutrino oscillation data.
• To identify simple Yukawa coupling ratios consistent with observed neutrino masses and mixing angles.
• To link leptogenesis and CP violation in neutrino oscillations through a specific relative phase.
• To realize the model via an A₄×Z₃¹⁰ family symmetry with spontaneous CP violation.
• To predict all PMNS parameters from a single input parameter, the neutrino mass ratio m₂/m₃.

Proposed method

• Derives a master formula relating see-saw input parameters to physical neutrino observables in a two-right-handed-neutrino model.
• Imposes a dominant texture zero (zero coupling to electron neutrino) to reduce parameters and link to physical constraints.
• Uses the master formula to search for simple coupling ratios consistent with current data on θ₁₃, θ₂₃, θ₁₂, and m₂/m₃.
• Identifies a minimal solution with couplings (0,1,1) and (1,1,3) or (1,3,1) and relative phase η = ∓π/3.
• Constructs an A₄×Z₃¹⁰ family symmetry model using F-term alignment to realize the flavon alignments (0,1,1) and (1,3,1).
• Shows that spontaneous CP violation fixes the phase η = ∓π/3, leading to δ ≈ ±π/2 and m₁ = 0.

Experimental results

Research questions

• RQ1 Can a minimal two-right-handed-neutrino see-saw model with normal hierarchy predict all PMNS parameters from a single input?
• RQ2 What simple Yukawa coupling patterns are consistent with current neutrino oscillation data and the texture zero condition?
• RQ3 How can the observed CP violation in neutrino oscillations be linked to leptogenesis in a minimal see-saw model?
• RQ4 Can the Tri-bimaximal-Cabibbo mixing pattern be realized via a family symmetry model with spontaneous CP violation?
• RQ5 What are the cosmological and phenomenological implications of the model’s prediction of m₁ = 0 and δ ≈ ±π/2?

Key findings

• The model identifies a minimal predictive solution with Yukawa couplings (0,1,1) and (1,1,3) or (1,3,1), and relative phase η = ∓π/3, consistent with current data.
• The model predicts Tri-bimaximal-Cabibbo mixing to within one degree, with θ₁₂ ≈ 34°, θ₂₃ ≈ 45°, and θ₁₃ ≈ 9.15°.
• It predicts the CP phase δ ≈ ±π/2, which is testable in upcoming neutrino experiments.
• The model realizes the PMNS matrix entirely from the neutrino mass ratio m₂/m₃, with m₁ = 0.
• The A₄×Z₃¹⁰ family symmetry model realizes the required flavon alignments via F-term alignment and spontaneous CP violation.
• The model predicts a very small neutrinoless double beta decay matrix element, mββ ≈ 2.5×10⁻³ eV, which could be excluded by future experiments.