Determining the Dirac CP Violation Phase in the Neutrino Mixing Matrix from Sum Rules

Abstract

Using the fact that the neutrino mixing matrix $U=U_e^{†}{U}_{\nu }$, where $U_e$ and $U_{\nu }$ result from the diagonalisation of the charged lepton and neutrino mass matrices, we analyse the sum rules which the Dirac phase $\delta$ present in $U$ satisfies when $U_{\nu }$ has a form dictated by flavour symmetries and $U_e$ has a "minimal" form (in terms of angles and phases it contains) that can provide the requisite corrections to $U_{\nu }$, so that reactor, atmospheric and solar neutrino mixing angles ${\theta }_{13}$, ${\theta }_{23}$ and ${\theta }_{12}$ have values compatible with the current data. The following symmetry forms are considered: i) tri-bimaximal (TBM), ii) bimaximal (BM) (or corresponding to the conservation of the lepton charge $L^{\prime }=L_e-L_{\mu }-L_{\tau }$ (LC)), iii) golden ratio type A (GRA), iv) golden ratio type B (GRB), and v) hexagonal (HG). We investigate the predictions for $\delta$ in the cases of TBM, BM (LC), GRA, GRB and HG forms using the exact and the leading order sum rules for $\cos \delta$ proposed in the literature, taking into account also the uncertainties in the measured values of ${\sin }^2{\theta }_{12}$, ${\sin }^2{\theta }_{23}$ and ${\sin }^2{\theta }_{13}$. This allows us, in particular, to assess the accuracy of the predictions for $\cos \delta$ based on the leading order sum rules and its dependence on the values of the indicated neutrino mixing parameters when the latter are varied in their respective 3$\sigma$ experimentally allowed ranges.

37 pages, includes 18 figures and 10 tables; results in v.4 unchanged; typos corrected; matches published version.

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Cited by in corpus (10)

• Predicting the Values of the Leptonic CP Violation Phases
• A Bottom-Up Approach to Lepton Flavor and CP Symmetries
• Leptogenesis in an SU(5) x A5 Golden Ratio Flavour Model
• Towards the minimal seesaw model via CP violation of neutrinos
• Predictions for the Dirac CP Violation Phase in the Neutrino Mixing Matrix
• Renormalisation Group Corrections to Neutrino Mixing Sum Rules
• Neutrino CP violation and sign of baryon asymmetry in the minimal seesaw model
• A hybrid setup for fundamental unknowns in neutrino oscillations using T2HK ($\nu$) and $\mu$-DAR ($\bar{\nu }$)
• Theory Review of Neutrino Models and CP Violation
• A neutrino mixing model based on an $A_4\times Z_3\times Z_4$ flavour symmetry