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

TL;DR

This paper derives analytical integral solutions to the one-loop RGEs for lepton flavor mixing parameters and the Jarlskog invariant, enabling efficient and accurate analysis of their evolution in the standard model and its extensions.

Contribution

The paper provides the first analytical integral solutions to the one-loop RGEs for lepton flavor parameters, validated against exact numerical results.

Findings

Integral solutions match exact numerical results

Solutions accurately describe parameter evolution in most cases

Analytical approach simplifies RGE analysis for lepton flavor mixing

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.