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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 ΛH to the electroweak scale ΛEW 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 μ-τ reflection symmetry breaking analytically and numerically. [ABSTRACT FROM AUTHOR]

We have performed a theoretical study on the process χc0(1P)→¯ΛΣπ, by taking into account the final-state interactions of πΣ and π¯Λ based on the chiral unitary approach. As the isospin filters of I=0 in the πΣ channel and I=1 in the π¯Λ channel, this process can be used to study the molecular structure of the Λ(1405) resonance and to test the existence of the predicted states Σ(1380) and Σ(1430) with spin parity JP=1/2-. Our results show that there is a peak around 1350-1400 MeV and a cusp around the ¯KN threshold in the πΣ invariant mass distribution, which should be the important feature of the molecular state Λ(1405). We also find a peak around 1380 MeV and a cusp around the ¯KN threshold in the π¯Λ invariant mass distribution, which are associated to the Σ(1380) and Σ(1430) resonances. [ABSTRACT FROM AUTHOR]