Leptonic unitarity triangles

Sebastian A R Ellis,Shirley Weishi Li,Kevin J Kelly

doi:10.1103/physrevd.102.115027

Abstract

We present a comprehensive analysis of leptonic unitarity triangles, using both current neutrino oscillation data and projections of next-generation oscillation measurements. Future experiments, sensitive to the degree of CP violation in the lepton sector, will enable the construction of precise triangles. We show how unitarity violation could manifest in the triangles and discuss how they serve as unitarity tests. We also propose the use of Jarlskog factors as a complementary means of probing unitarity. This analysis highlights the importance of testing the unitarity of the leptonic mixing matrix, an understanding of which is crucial for deciphering the nature of the neutrino sector.

Highlights

The discovery of neutrino oscillations confirmed that lepton flavor and mass eigenstates are distinct
Predictions of neutrino masses, e.g., those involving righthanded neutrinos, often lead to a nonunitary 3 × 3 leptonic mixing matrix (LMM), which is a submatrix of a larger unitary matrix
We present a comprehensive analysis of leptonic unitarity triangles using current neutrino oscillation data and projections of future experiments

Summary

Introduction

The discovery of neutrino oscillations confirmed that lepton flavor and mass eigenstates are distinct. Their mixing is canonically parameterized by the 3 × 3 unitary Pontecorvo-Maki-Nakagawa-Sakata (PMNS) matrix [1,2], analogous to the Cabibbo-Kobayashi-Maskawa (CKM) matrix [3,4] for quarks. The misalignment of the flavor and mass eigenstates in the lepton sector, i.e., the origin of the PMNS matrix, remains an open question. Predictions of neutrino masses, e.g., those involving righthanded neutrinos, often lead to a nonunitary 3 × 3 leptonic mixing matrix (LMM), which is a submatrix of a larger unitary matrix (see e.g., [5,6,7,8,9,10,11,12,13]). Throughout this work, we refer to a general 3 × 3 LMM as ULMM and one assumed to be unitary as UPMNS

Objectives

Results

Conclusion