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

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 ${\delta }_{\mathrm{PDG}}$ 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.

26 pages, 6 figures, 5 tables, 3 appendices, discussion expanded, matches published version, comments welcome

References in corpus (15)

• The Reactor Antineutrino Anomaly
• Statistical Significance of the Gallium Anomaly
• Unitarity of the Leptonic Mixing Matrix
• Comparing Trimaximal Mixing and Its Variants with Deviations from Tri-bimaximal Mixing
• CP-Violating Neutrino Non-Standard Interactions in Long-Baseline-Accelerator Data
• Nonstandard neutrino interactions at DUNE, T2HK and T2HKK
• The gallium anomaly revisited
• Sensitivity of the T2HKK experiment to the non-standard interaction
• Capabilities of long-baseline experiments in the presence of a sterile neutrino
• The Discovery reach of $CP$ violation in neutrino oscillation with non-standard interaction effects
• Type-I Seesaw with eV-Scale Neutrinos
• Leptonic Sum Rules from Flavour Models with Modular Symmetries
• Quasidegeneracy of Majorana Neutrinos and the Origin of Large Leptonic Mixing
• Exponential parameterization of neutrino mixing matrix with account for CP-violation data
• Parametric enhancement of flavor oscillation in a three-neutrino framework

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• The framework for a common origin of ${\delta }_{\mathrm{CKM}}$ and ${\delta }_{\mathrm{PMNS}}$
• Symmetry Finder: A method for hunting symmetry in neutrino oscillation
• Leptonic CP violation from the seesaw
• Signals of eV-scale sterile neutrino at long baseline neutrino experiments
• Neutrino Oscillations in the Three Flavor Paradigm