Abstract
Inspired by the neutrino oscillations data, we consider the exact $\mu-\tau$ symmetry, implemented at the level of the neutrino mass matrix, as a good initial framework around which to study and describe neutrino phenomenology. Working in the diagonal basis for the charged leptons, we deviate from $\mu-\tau$ symmetry by just modifying the phases of the neutrino mass matrix elements. This deviation is enough to allow for a non-vanishing neutrino mixing entry $|V_{e3}|$ (i.e. $\theta_{13}$) but it also gives a very stringent (and eventually falsifiable) prediction for the atmospheric neutrino mixing element $|V_{\mu3}|$ as a function of $|V_{e3}|$. The breaking by phases is characterized by a single phase and is shown to lead to interesting lower bounds on the allowed mass of the lightest neutrino depending on the ordering of neutrino masses (normal or inverted) and on the value of the Dirac ${\cal CP}$ violating phase $\delta_{CP}$. The allowed parameter space for the effective Majorana neutrino mass $m_{ee}$ is also shown to be non-trivially constrained.
Highlights
Neutrinos are some of the most elusive particles of the Standard Model since they interact mainly through weak processes
The mixing angles jVe3j and jVe2j have been allowed to range in their 1-σ experimental range and we have fixed the value of the solar and atmospheric neutrino mass differences to their central experimental values. In this case we observe that even though δCP remains fixed at 1⁄4 −π=2, the relaxation of the Majorana phases does open an allowed parameter space region that was closed in the μ − τ reflection symmetry limit studied in the previous section
In this paper we have considered deviations from the usual μ − τ symmetry framework by adding general phases to a μ − τ symmetric neutrino mass matrix
Summary
Neutrinos are some of the most elusive particles of the Standard Model since they interact mainly through weak processes. We propose to modify the symmetric structure of the neutrino mass matrix of Eq (1) by adding phases that will break the exact 2–3 permutation symmetry. Within the paradigm of μ − τ symmetry, we can implement minimal deviations at the level of the effective neutrino mass matrix Mν given in Eq (1) by adding phases to its elements [12] (while maintaining its complex symmetric nature).. The phenomenological effects of this texture should depart smoothly from the usual μ − τ symmetry predictions, which correspond to the limit θ → 0 We have dubbed this ansatz as phase-broken μ − τ symmetry and it can obviously be described by the two conditions jMeμj 1⁄4 jMeτj and jMμμj 1⁄4 jMττj on the elements of the neutrino mass matrix. Choosing jVe2j, jVe3j, jVμ3j, δCP, η and ξ as our six independent parameters, we shall parametrize the VPMNS mixing matrix as
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