Abstract
We propose a μ − τ reflection symmetric Littlest Seesaw (μτ -LSS) model. In this model the two mass parameters of the LSS model are fixed to be in a special ratio by symmetry, so that the resulting neutrino mass matrix in the flavour basis (after the seesaw mechanism has been applied) satisfies μ − τ reflection symmetry and has only one free adjustable parameter, namely an overall free mass scale. However the physical low energy predictions of the neutrino masses and lepton mixing angles and CP phases are subject to renormalisation group (RG) corrections, which introduces further parameters. Although the high energy model is rather complicated, involving (S4 × U(1))2 and supersymmetry, with many flavons and driving fields, the low energy neutrino mass matrix has ultimate simplicity.
Highlights
In a recent paper, the LSS model was shown to respect an approximate μ − τ reflection symmetry, near the best fit region of parameter space, which was responsible for its approximate predictions of maximal atmospheric mixing and maximal CP violation in the lepton sector [31]
In this model the two mass parameters of the LSS model are fixed to be in a special ratio by symmetry, so that the resulting neutrino mass matrix in the flavour basis satisfies μ − τ reflection symmetry and has only one free adjustable parameter, namely an overall free mass scale
The physical low energy predictions of the neutrino masses and lepton mixing angles and CP phases are subject to renormalisation group (RG) corrections, which introduces further parameters
Summary
There are two cases of the LSS neutrino mass matrix [29] (after the seesaw mechanism has been implemented) namely, Case I: Case II: 131. One transforms the mass matrix from one case to the other Both cases predict the same mixing angles (θ13, θ12, θ23), the same Dirac-type CP-violating phase (δ) θ13 = arcsin. Without respecting the Majorana phase and unphysical phases, the PMNS matrix in both cases takes the same form as. The mixing matrix respects μ − τ reflection symmetry and is a special case of tri-maximal. TM1 mixing [32,33,34,35,36,37,38], with a fixed reactor angle and a fixed solar angle This model is not fully consistent with the oscillation data since both the predicted θ13 and ratio of mass square differences ∆m221/∆m231 are smaller than the current global data of neutrino oscillation in 3σ ranges. Different from [31], where only case II is listed, here we write out both cases explicitly since radiative corrections have different contributions to μ and τ flavours
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