The Impact of Different Parameterizations on the Interpretation of CP Violation in Neutrino Oscillations

TL;DR

This paper examines how different parameterizations of the lepton mixing matrix affect the interpretation of CP violation measurements in neutrino oscillations, highlighting the advantages of the Jarlskog invariant for clarity.

Contribution

It analyzes the impact of various parameterizations on CP violation interpretation and advocates for using the Jarlskog invariant as a parameterization-independent measure.

Findings

Different parameterizations can lead to varying conclusions about CP violation.

The small value of |U_{e3}| influences the scale of parameterization effects.

The Jarlskog invariant provides a clearer measure of CP violation.

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 $\delta_{\rm PDG}$ 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 $\delta$. We demonstrate how the smallness of $|U_{e3}|$ governs the scale of these results. We then demonstrate how $\delta$ 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.