Perturbations to μ-τ Reflection Symmetry Due to Renormalization Group Running Effects

Abstract With the discovery of nonzero $\theta _{13}$ and a near-maximal value of the Dirac CP phase as reflected from the measurements of the T2K and NO$\nu$A experiments, the significance of $\mu \text{-} \tau$ reflection symmetry becomes more prominent. In this work, we study the renormalization group (RG) running effects on neutrino parameters as a perturbation to $\mu \text{-} \tau$ reflection symmetry. Assuming the symmetry to be exact at the seesaw scale, we account the deviations of the parameters at the electroweak scale due to RG running. We solve numerically a set of 19 one-loop RG equations in total, including those of neutrino mixing parameters, mass eigenvalues, and gauge and Yukawa couplings, using a top-down approach. We aim to examine the consistency of the low-energy solutions at the EW scale with the observational data. Working in the Minimal Supersymmetric Standard Model framework, we choose three benchmark values at $1\ \text{TeV},\ 7\ \text{TeV}$, and $14\ \text{TeV}$ for the supersymmetry breaking scale intermediate between the seesaw scale and EW scale. This requires a two-step running procedure to solve the RG equations and it also allows us to study the impact of variation of the supersymmetry breaking scale on the running effects. Our numerical results indicate that the deviations from $\mu \text{-} \tau$ reflection symmetry induced by RG running remain compatible with the current $3\sigma$ global oscillation data.