[Paper Review] Tribimaximal mixing and leptogenesis in a seesaw model

Riazuddin|ArXiv.org|Sep 22, 2008

Neutrino Physics Research6 citations

TL;DR

This paper proposes a seesaw model with μ–τ symmetry and conserved total lepton number L = Le + Lμ + Lτ, which naturally produces tribimaximal neutrino mixing. It demonstrates that leptogenesis can generate the observed baryon asymmetry when two heavy right-handed neutrinos are nearly degenerate, with CP violation arising solely from Majorana phases, yielding a lepton asymmetry of order 10⁻⁹–10⁻⁶ depending on mass degeneracy.

ABSTRACT

It is pointed out that if a neutrino mass matrix for right-handed neutrinos in seesaw mechanism has mu -tau symmetry and total lepton number L_{e}+L_{μ}+L_τ remains constant (not zero), exact tribimaximal neutrino mixing in this sector is produced. The same follows for the effective Majorana light neutrino mass matrix provided that Yukawa couplings (multiplied by the corresponding Higgs vacuum expectation values) in Dirac mass matrix satisfy some constraints which in general implies zero leptongenesis asymmetry. However this can be avoided when two of the heavy right-hand neutrinos [the third one is irrelevant when mu -tau symmetry is assumed] are (nearly) degenerate.

Motivation & Objective

• To explain the observed tribimaximal neutrino mixing pattern in a seesaw mechanism with μ–τ symmetry.
• To investigate whether leptogenesis can generate the observed baryon asymmetry of the universe in this symmetric framework.
• To determine the conditions under which a non-zero lepton asymmetry arises despite constraints from μ–τ symmetry and conserved total lepton number.
• To identify the role of Majorana phases in generating CP violation for successful leptogenesis.

Proposed method

• Imposes μ–τ symmetry on the right-handed neutrino mass matrix and assumes conservation of total lepton number L = Le + Lμ + Lτ.
• Derives the Dirac and Majorana mass matrices from Yukawa couplings to Higgs fields with specific U(1) quantum numbers.
• Uses a seesaw mechanism to compute the effective Majorana neutrino mass matrix, diagonalizing it via a mixing matrix with sin²θ₂₃′ = 1/2 and θ₁₃′ = 0.
• Applies the condition of non-zero conserved L to constrain the Majorana mass matrix, leading to tribimaximal mixing via tan²θ₁₂′ = 1/2.
• Calculates the leptogenesis asymmetry ε₁ using the one-loop formula involving the imaginary part of (R₁₂)², with R defined via the matrix R = m_D†m_D.
• Evaluates the asymmetry in the limit of near-degenerate heavy neutrinos (M₁ ≈ M₂), showing that CP violation arises only from Majorana phases.

Experimental results

Research questions

• RQ1 Can tribimaximal neutrino mixing be derived from μ–τ symmetry and conserved total lepton number in a seesaw model?
• RQ2 Does the constraint of conserved total lepton number L = Le + Lμ + Lτ forbid leptogenesis in such a model?
• RQ3 Under what conditions can a non-zero lepton asymmetry be generated despite μ–τ symmetry and conserved L?
• RQ4 What is the role of Majorana phases in generating CP violation for successful leptogenesis in this framework?

Key findings

• Tribimaximal mixing arises naturally when μ–τ symmetry and conserved total lepton number L are imposed, leading to tan²θ₁₂′ = 1/2.
• The effective Majorana neutrino mass matrix M_ν is diagonalized by a tribimaximal mixing matrix, consistent with neutrino oscillation data.
• Leptogenesis asymmetry ε₁ vanishes unless the two lightest heavy right-handed neutrinos are nearly degenerate, i.e., ΔM/M ≈ 10⁻³.
• The asymmetry ε₁ ≈ 10⁻⁹ × {1 + (Δm/m)/(ΔM/M)}² is of the right order (10⁻⁹ to 10⁻⁶) for successful leptogenesis when ΔM/M ≈ (1–3)×10⁻³.
• The CP violation responsible for baryogenesis originates entirely from Majorana phases Δ, not from Dirac phases.
• With sinΔ ≈ 0.14 and Δm_solar² = 8×10⁻⁵ eV², the asymmetry reaches the required magnitude for baryogenesis when the mass degeneracy condition is satisfied.