Theory prospective on leptonic CP violation

The phenomenology of 3-neutrino mixing, the current status of our knowledge about the 3-neutrino mixing parameters, including the absolute neutrino mass scale, and of the Dirac and Majorana CP violation in the lepton sector are reviewed. The problems of CP violation in neutrino oscillations and of determining the nature – Dirac or Majorana – of massive neutrinos are discussed. The seesaw mechanism of neutrino mass generation and the related leptogenesis scenario of generation of the baryon asymmetry of the Universe are considered. The results showing that the CP violation necessary for the generation of the baryon asymmetry of the Universe in leptogenesis can be due exclusively to the Dirac and/or Majorana CP-violating phase(s) in the neutrino mixing matrix U are briefly reviewed. The discrete symmetry approach to understanding the observed pattern of neutrino mixing and the related predictions for the leptonic Dirac CP violation are also reviewed

predictions for the dirac phase in the neutrino mixing matrix and sum rules

Using the fact that the neutrino mixing matrix U = U†eUν, where Ue and Uv result from the diagonalisation of the charged lepton and neutrino mass matrices, we analyse the sum rules which the Dirac phase δ present in U satisfies when Uv has a form dictated by, or associated with, discrete symmetries and Ue has a "minimal" form (in terms of angles and phases it contains) that can provide the requisite corrections to Uv, so that reactor, atmospheric and solar neutrino mixing angles θ13, θ23 and θ12 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' = Le — Lμ — Lτ (LC)), iii) golden ratio type A (GRA), iv) golden ratio type B (GRB), and v) hexagonal (HG). We investigate the predictions for 5 in the cases of TBM, BM (LC), GRA, GRB and HG forms using the exact and the leading order sum rules for cos δ proposed in the literature, taking into account also the uncertainties in the measured values of sin2 θ12, sin2 θ23 and sin2 θ13. This allows us, in particular, to assess the accuracy of the predictions for cos δ 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 3σ experimentally allowed ranges

High precision measurements of theta(circle dot) in the solar and reactor neutrino experiments

We discuss the possibilities of high precision measurement of the solar neutrino mixing angle $\theta_\odot \equiv \theta_{12}$ in solar and reactor neutrino experiments. The improvements in the determination of $\sin^2\theta_{12}$, which can be achieved with the expected increase of statistics and reduction of systematic errors in the currently operating solar and KamLAND experiments, are summarised. The potential of LowNu $\nu-e$ elastic scattering experiment, designed to measure the $pp$ solar neutrino flux, for high precision determination of $\sin^2\theta_{12}$, is investigated in detail. The accuracy in the measurement of $\sin^2\theta_{12}$, which can be achieved in a reactor experiment with a baseline $L \sim (50-70)$ km, corresponding to a Survival Probability MINimum (SPMIN), is thoroughly studied. We include the effect of the uncertainty in the value of $\sin^2\theta_{13}$ in the analyses. A LowNu measurement of the $pp$ neutrino flux with a 1\% error would allow to determine $\sin^2\theta_{12}$ with an error of 14\% (17\%) at 3$\sigma$ from a two-generation (three-generation) analysis. The same parameter $\sin^2\theta_{12}$ can be measured with an uncertainty of 2\% (6\%) at 1$\sigma$ (3$\sigma$) in a reactor experiment with $L \sim60$ km, statistics of $\sim$60 GWkTy and systematic error of 2\%. For the same statistics, the increase of the systematic error from 2\% to 5\% leads to an increase in the uncertainty in $\sin^2\theta_{12}$ from 6\% to 9\% at 3$\sigma$. The inclusion of the $\sin^2\theta_{13}$ uncertainty in the analysis changes the error on $\sin^2\theta_{12}$ to 3\% (9\%). The effect of $\sin^2\theta_{13}$ uncertainty on the $\sin^2\theta_{12}$ measurement in both types of experiments is considerably smaller than naively expected