Abstract
There are six leptonic unitarity triangles (LUTs) defined by six orthogonality conditions of the three-family lepton flavor mixing matrix in the complex plane. In the framework of the standard model or the minimal supersymmetric standard model, the evolutions of sides and inner angles of the six LUTs from a superhigh energy scale $\Lambda_{\rm H}^{}$ to the electroweak scale $\Lambda_{\rm EW}^{}$ due to the renormalization-group equation (RGE) running are derived in the integral form for both Dirac and Majorana neutrinos. Furthermore, the LUTs as an intuitively geometrical language are applied to the description of the RGE-induced $\mu$-$\tau$ reflection symmetry breaking analytically and numerically.
Highlights
In the recent twenty years, a series of neutrino oscillation experiments have definitely proved that neutrinos have masses and lepton flavors mix with one another [1]
We aim to study how the sides and inner angles of the leptonic unitarity triangles (LUTs) evolve in the integral form due to the renormalization-group equation (RGE) running from an arbitrary superhigh energy scale ΛH to the electroweak scale ΛEW in the framework of the standard model (SM) or the minimal supersymmetric standard model (MSSM)
The neutrino physics has promisingly entered the era of precision measurements, providing us more information to understand the large-angle lepton favor mixing pattern and potentially big CP-violating phases
Summary
In the recent twenty years, a series of neutrino oscillation experiments have definitely proved that neutrinos have masses and lepton flavors mix with one another [1]. We aim to study how the sides and inner angles of the LUTs evolve in the integral form due to the RGE running from an arbitrary superhigh energy scale ΛH to the electroweak scale ΛEW in the framework of the standard model (SM) or the minimal supersymmetric standard model (MSSM) Both the cases of Dirac and Majorana neutrinos will be considered.
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