Using the fact that the neutrino mixing matrix $U = U^\dagger_{e}U_{\nu}$, 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, or associated with, discrete 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 $L' = L_e - L_\mu - L_{\tau}$ (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.

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

Girardi, Ivan;Petkov, Serguey Todorov;Titov, Arsenii
2015-01-01

Abstract

Using the fact that the neutrino mixing matrix $U = U^\dagger_{e}U_{\nu}$, 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, or associated with, discrete 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 $L' = L_e - L_\mu - L_{\tau}$ (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.
2015
894
733
768
Girardi, Ivan; Petkov, Serguey Todorov; Titov, Arsenii
File in questo prodotto:
File Dimensione Formato  
NPB8942015733v3.pdf

accesso aperto

Tipologia: Versione Editoriale (PDF)
Licenza: Creative commons
Dimensione 1.69 MB
Formato Adobe PDF
1.69 MB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/12607
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 76
  • ???jsp.display-item.citation.isi??? 65
social impact