Abstract
We propose a generalized version of the Tri-Bi-Maximal (TBM) ansatz for lepton mixing, leading to non-zero reactor angle $\theta_{13}$ and CP violation. The latter is characterized by two CP phases. The Dirac phase affecting neutrino oscillations is nearly maximal ($\delta_{CP} \sim \pm \pi/2$), while the Majorana phase implies narrow allowed ranges for the neutrinoless double beta decay amplitude. The solar angle $\theta_{12}$ lies nearly at its TBM value, while the atmospheric angle $\theta_{23}$ has the TBM value for maximal $\delta_{CP}$. Neutrino oscillation predictions can be tested in present and upcoming experiments.
Highlights
We propose a generalized version of the tribimaximal (TBM) ansatz for lepton mixing, leading to a nonzero reactor angle θ13 and CP violation
Ever since the discovery of neutrino oscillations, the structure of the leptonic mixing matrix has been an active topic of research
Solar and atmospheric data, confirmed by accelerator and reactor data, made it clear that the structure of lepton mixing is quite at odds with that of quarks, given the large values of θ12 and θ23. These observations were soon encoded in the tribimaximal mixing (TBM) ansatz proposed by Harrison, Perkins, and Scott [1], described by
Summary
Ever since the discovery of neutrino oscillations, the structure of the leptonic mixing matrix has been an active topic of research. Motivated by the need for departing from the simplest “first-order” form for the TBM ansatz, Eq (1), here, we propose a generalized version of the TBM ansatz (GTBM), which correctly accounts for the nonzero value of θ13 and introduces the CP violation as follows: U peiρffiffi ffiffi eipðρþσÞ e−iρpcffioffi s θ cposffiffiθ − ie−ipσ sffiffiin θ eiσpcoffiffis θ i spinffiffiθ ie−ipρ sffiffiin e−iσpcffioffi s θ − i θ psinffiffiθ ð2Þ cposffiffiθ þ ieiσpsffiiffin θ. This new ansatz is characterized by just one angle θ and two phases ρ and σ. We turn to the several interesting limiting cases of the above GTBM matrix in Eq (2)
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