Predictions of effective Majorana neutrino mass under radiative corrections to $μ-τ$ reflection symmetry

The search for neutrinoless double beta decay ($0νββ$) is currently one of the key objectives in neutrino physics research. The decay rate of $0νββ$ decay depends on the effective Majorana neutrino mass $|\langle m \rangle_{ee}|$. In this work we study the numerical prediction of $|\langle m \rangle_{ee}|$ in the scenario of deviation from the $μ$-$τ$ reflection symmetry due to radiative corrections, as an extension of our earlier work \cite{pegu}. In \cite{pegu}, we consider an exact $μ$-$τ$ reflection symmetry in the light effective Majorana neutrino mass matrix and in the corresponding lepton mixing matrix as well at the seesaw scale. We choose numerical values of all the mixing parameters and neutrino mass eigenvalues at the seesaw scale as inputs and estimate the values of mass eigenvalues and mixing parameters at the electroweak scale due to radiative corrections. We find these low energy predictions consistent with global $3σ$ oscillation data. In the present work, we compute the effective Majorana neutrino mass $|\langle m \rangle_{ee}|$ using these low energy values at the electroweak scale. We find that the low energy predictions of $|\langle m \rangle_{ee}|$ are consistent with the latest upper bound $|\langle m \rangle_{ee}|<(0.028-0.122)\ eV$ provided by KamLAND-Zen Collaboration.

💡 Research Summary

The paper investigates how radiative corrections affect the μ‑τ reflection symmetry and consequently the effective Majorana neutrino mass relevant for neutrinoless double‑beta decay (0νββ). Starting from the premise that the μ‑τ reflection symmetry is exact at a high flavor‑symmetry scale (taken to be the seesaw scale Λ_μτ ≈ 10¹⁴ GeV), the authors embed the neutrino sector in the Minimal Supersymmetric Standard Model (MSSM) and study the one‑loop renormalization‑group evolution (RGE) of the effective Majorana mass matrix down to the electroweak scale Λ_EW ≈ m_t. The RGE introduces a small parameter ε, driven mainly by the τ‑Yukawa coupling, which breaks the exact μ‑τ symmetry in the low‑energy mass matrix. By expanding to first order in ε, analytical relations are derived linking high‑energy parameters (mass eigenvalues, mixing angles, CP phases) to their low‑energy counterparts. These relations show that θ_23 deviates from the maximal value π/4 by O(ε), while θ_13, θ_12 and the CP phases acquire ε‑dependent corrections expressed through arctangent functions.

Numerical analyses are performed for three supersymmetry‑breaking scales (Λ_s = 1, 7, 14 TeV) and two values of tan β (30 and 58). The high‑energy inputs include the three neutrino masses and the two free mixing angles (θ_12, θ_13); the other parameters (θ_23, δ, α, β) are fixed by the μ‑τ reflection symmetry (θ_23 = π/4, δ = π/2 or 3π/2, α = β = π/2 or 3π/2). The inputs are tuned so that the low‑energy predictions satisfy the global 3σ oscillation data, the cosmological bound Σ m_i < 0.12 eV, and the measured Dirac CP phase. Using the low‑energy masses, mixing angles, and CP phases, the effective Majorana mass |m_ee| = |m₁c₁₂²c₁₃²e^{2iα}+m₂s₁₂²c₁₃²e^{2iβ}+m₃s₁₃²e^{-2iδ}| is computed.

The results show that for both normal and inverted mass orderings, |m_ee| lies in the range roughly 0.015–0.09 eV, depending on the chosen SUSY scale and tan β. This interval comfortably respects the most stringent experimental upper bound from KamLAND‑Zen, |⟨m⟩_ee| < 0.028–0.122 eV. Larger tan β enhances ε, leading to slightly larger symmetry‑breaking effects, but the predictions remain within experimental limits. The study demonstrates that an exact μ‑τ reflection symmetry at high energies, modestly broken by radiative corrections, naturally yields an effective Majorana mass compatible with current 0νββ constraints.

In conclusion, the work provides a concrete quantitative link between high‑energy flavor symmetries, their radiative breaking, and low‑energy observables relevant for neutrinoless double‑beta decay. It shows that μ‑τ reflection symmetry, even when slightly violated by RG effects in the MSSM, can accommodate the present experimental bounds on |⟨m⟩_ee|, offering a testable framework for future, more sensitive 0νββ experiments and for model‑building efforts that aim to embed such symmetries in realistic theories.