[Paper Review] Neutrino mass matrix in the standard parametrization with texture two zeros

Rukmani Mohanta, G. Kranti+1 more|ArXiv.org|Aug 28, 2006

Neutrino Physics Research3 citations

TL;DR

This paper investigates texture two-zero neutrino mass matrices within the standard parametrization of the PMNS mixing matrix, analyzing how the presence or absence of a Dirac CP-violating phase affects the viability of different mass matrix structures. It finds that only two of seven possible forms (A1, A2) are compatible with current data when the Dirac phase is zero—both favoring normal neutrino mass hierarchy—while nonzero Dirac phases allow all forms, most of which prefer inverted hierarchy and a Dirac phase near π/2.

ABSTRACT

We study the texture two zeros neutrino mass matrices using the standard parametrization for the neutrino mixing matrix. We find that if the origin of CP violation in the leptonic sector is not due to the Dirac-type complex phase of the mixing matrix but because of some non-standard phenomena then some of the possible texture two mass matrices, which are allowed by standard parametrization, are found to be unsuitable to accommodate the observed data in the neutrino sector. Furthermore, incorporating nonzero Dirac phase in our analysis we find that many of them do not exhibit normal hierarchy.

Motivation & Objective

• To assess the viability of texture two-zero neutrino mass matrices under the standard parametrization of the PMNS mixing matrix.
• To investigate the impact of the Dirac CP-violating phase on the allowed mass matrix structures and neutrino mass hierarchy.
• To determine which texture-zero patterns are consistent with current experimental data on neutrino mixing angles and mass-squared differences.
• To compare analytical results for mass ratios and Majorana phases with experimental constraints, especially regarding normal vs. inverted hierarchy.

Proposed method

• The PMNS mixing matrix is parameterized using standard PDG conventions with three mixing angles (θ₁₂, θ₂₃, θ₁₃) and a Dirac CP phase δ.
• The neutrino mass matrix is constructed under the assumption of two texture zeros, leading to seven possible forms (A1–A7, C), each with specific vanishing matrix elements.
• Analytical expressions for mass ratios (m₁/m₃, m₂/m₃), the rephasing invariants Rν and |Mₑₑ|, and Majorana phases (ρ, σ) are derived in terms of mixing angles and δ.
• Lowest-order approximations are used to simplify expressions, enabling comparison with experimental data.
• Numerical evaluations are performed using best-fit mixing angles and varying δ (e.g., 0°, 60°, 89°) to test consistency with observed neutrino parameters.
• The results are cross-checked against current 2σ experimental constraints on mixing angles and mass-squared splittings.

Experimental results

Research questions

• RQ1 Which texture two-zero neutrino mass matrix forms are consistent with current experimental data when the Dirac CP phase δ is zero?
• RQ2 How does the inclusion of a nonzero Dirac phase δ affect the viability of different texture-zero mass matrix structures?
• RQ3 Do the texture-zero mass matrices prefer normal or inverted neutrino mass hierarchy, and how does this preference depend on δ?
• RQ4 What are the predicted values of the rephasing invariants Rν and |Mₑₑ| for each texture-zero form under standard parametrization?
• RQ5 How sensitive are the mass ratios and Majorana phases to variations in the Dirac phase δ?

Key findings

• When δ = 0°, only two texture-zero forms (A1 and A2) are viable, both predicting normal neutrino mass hierarchy.
• With δ ≠ 0, all seven texture-zero forms are allowed by current data, but most favor inverted hierarchy.
• For δ ≈ 89°, the ratio Rν ≈ 0.04 and |Mₑₑ|/m₃ ≈ 1.24, consistent with experimental constraints.
• Pattern C (Mμμ = Mττ = 0) is viable only for δ ≈ 60°, yielding m₁/m₃ ≈ 1.55 and m₂/m₃ ≈ 1.57, indicating inverted hierarchy.
• The mass ratio m₁/m₃ − m₂/m₃ ≈ 0.008 and ρ − σ ≈ 0.024 for δ = 89°, showing small deviations from degeneracy.
• The Dirac phase δ strongly influences Rν in pattern C, making it sensitive to δ, especially when s_z is small.