The impact of different parameterizations on the interpretation of CP violation in neutrino oscillations

Peter B Denton,Rebekah Pestes

doi:10.1007/jhep05(2021)139

Abstract

CP violation in the lepton mass matrix will be probed with good precision in upcoming experiments. The amount of CP violation present in oscillations can be quantified in numerous ways and is typically parameterized by the complex phase δPDG in the standard PDG definition of the lepton mixing matrix. There are additional parameterizations of the lepton mixing matrix as well. Through various examples, we explore how, given the current data, different parameterizations can lead to different conclusions when working with parameterization dependent variables, such as δ. We demonstrate how the smallness of |Ue3| governs the scale of these results. We then demonstrate how δ can be misleading and argue that the Jarlskog is the cleanest means of presenting the amount of CP violation in the lepton sector. We also confirm that, among the different parameterizations considered, the standard PDG parameterization has a number of convenient features.

Highlights

JHEP05(2021)139 the constraint on the complex phase can be quite different
We show the values of the three mixing angles in the different parameterizations in figure 2, along with bands representing the region covered by these curves when the mixing angles in UPDG are allowed to vary independently within their 3 σ ranges
We find that in different parameterizations of the lepton mixing matrix, a precision on δPDG of 15◦ will lead to extremely different precision in different parameterizations, in particular in the three parameterizations with complicated expressions for Ue3

Summary

Introduction

JHEP05(2021)139 the constraint on the complex phase can be quite different. This means that interpreting results and goals of experiments in terms of the complex phase of one parameterization is not a fundamental description of our understanding of CPV. The addition of non-standard neutrino interactions (with or without additional CP violating phases), sterile neutrinos ( with or without additional CP violating phases), or unitary violation can all lead to confusion related to the extraction of the standard CP violating three-flavor phase [8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32] Some of these degeneracies can be differentiated by combining measurements from different experiments.

Objectives

Findings

Discussion

Conclusion