Integral solutions to the one-loop renormalization-group equations for lepton flavor mixing parameters and the Jarlskog invariant

Abstract

Working in the basis where the charged-lepton Yukawa matrix is diagonal and making the $\tau$-dominance approximations, we analytically derive integral solutions to the one-loop renormalization-group equations (RGEs) for neutrino masses, flavor mixing angles, CP-violating phases and the Jarlskog invariant under the standard parametrization of the PMNS matrix in the standard model or its minimal supersymmetric extension for both Majorana and Dirac neutrinos. With these integral solutions, we carry out numerical calculations to investigate the RGE running of lepton flavor mixing parameters and the Jarlskog invariant, and also compare these integral solutions with the exact results obtained by numerically solving the one-loop RGEs. It is shown that these integral solutions coincide with the exact results and can well describe the evolution of lepton flavor mixing parameters and the Jarlskog invariant in most cases. Some important features of our integral solutions and the evolution behaviors of relevant flavor parameters are also discussed in detail both analytically and numerically.

arXiv comment36 pages, 6 figures, 6 tables, and the version accepted for publication in NPB

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• Sufficient and Necessary Conditions for CP Conservation in the Case of Degenerate Majorana Neutrino Masses
• Complete One-loop Renormalization-group Equations in the Seesaw Effective Field Theories
• The translational $\mu$-$\tau$ reflection symmetry of Majorana neutrinos
• Small ${\theta }_{13}$ and solar neutrino oscillation parameters from $\mu -\tau$ symmetry
• Predictions of effective Majorana neutrino mass under radiative corrections to $\mu -\tau$ reflection symmetry
• Minimal structure for neutrino mass matrix