Μτ Symmetry Research Articles

Mu-tau symmetry and the Littlest Seesaw

Motivated by the latest neutrino oscillation data which is consistent with maximal atmospheric mixing and maximal leptonic CP violation, we review various results in μτ symmetry, then include several new observations and clarifications, including identifying a new general form of neutrino mass matrix with μτ symmetry. We then apply the new results to the neutrino mass matrix associated with the Littlest Seesaw model, and show that it approximately satisfies the new general form with μτ symmetry, and that this is responsible for its approximate predictions of maximal atmospheric mixing and maximal CP violation in the lepton sector.

Maximal zero textures of the inverse seesaw with broken μτ symmetry

The inverse neutrino seesaw, characterised by only one source of lepton number violation at an ultralight $O$(keV) scale and observable new phenomena at TeV energies accessible to the LHC, is considered. Maximal zero textures of the $3\times 3$ lighter and heavier Dirac mass matrices of neutral leptons, appearing in the Lagarangian for such an inverse seesaw, are studied within the framework of $\mu\tau$ symmetry in a specified weak basis. That symmetry ensures the identity of the positions of maximal zeros of the heavy neutrino mass matrix and its inverse. It then suffices to study the maximal zeros of the lighter Dirac mass matrix and those of the inverse of the heavier one since they come in a product. The observed absence of any unmixed neutrino flavour and the assumption of no strictly massless physical neutrino state allow only eight $4$-zero $\times$ $4$-zero, eight $4$-zero $\times$ $6$-zero and eight $6$-zero $\times$ $4$-zero combinations. The additional requirement of leptogenesis is shown to eliminate the last sixteen textures. The surviving eight $4$-zero $\times$ $4$-zero textures are subjected to the most general explicit $\mu\tau$ symmetry breaking terms in the Lagrangian in order to accommodate the nonzero value of $\theta_{13}$ in the observed range. A full diagonalisation is then carried out. On numerical comparison with all extant and relevant neutrino (antineutrino) data, seven of these eight combination textures in five neutrino matrix forms are found to be allowed, leading to five distinct neutrino mass matrices. Two of these permit only a normal (and the other three only an inverted) mass ordering of the light neutrinos.

θ13, μτ SYMMETRY BREAKING AND NEUTRINO YUKAWA TEXTURES

Within the type-I seesaw and in the basis where charged lepton and heavy neutrino mass matrices are real and diagonal, μτ symmetric four and three zero neutrino Yukawa textures are perturbed by lowest order μτ symmetry breaking terms. These perturbations are taken to be the most general ones for those textures. For quite small values of those symmetry breaking parameters, permitting a lowest order analysis, current best-fit ranges of neutrino mass squared differences and mixing angles are shown to be accommodable, including a value of θ13 in the observed range, provided all the light neutrinos have an inverted mass ordering.

NEUTRINO MASSES, COSMOLOGICAL BOUND AND FOUR ZERO YUKAWA TEXTURES

Four zero neutrino Yukawa textures in a specified weak basis, combined with μτ symmetry and type-I seesaw, yield a highly constrained and predictive scheme. Two alternately viable 3×3 light neutrino Majorana mass matrices mνA/mνBresult with inverted/normal mass ordering. Neutrino masses, Majorana in character and predicted within definite ranges with laboratory and cosmological inputs, will have their sum probed cosmologically. The rate for 0νββ decay, though generally below the reach of planned experiments, could approach it in some parameter region. Departure from μτ symmetry due to RG evolution from a high scale and consequent CP violation, with a Jarlskog invariant whose magnitude could almost reach 6×10-3, are explored.

TRIBIMAXIMAL MIXING IN NEUTRINO MASS MATRICES WITH TEXTURE ZEROS OR VANISHING MINORS

We study the existence of one/two texture zeros or one/two vanishing minors in the neutrino mass matrix with μτ symmetry. In the basis where the charged lepton mass matrix and the Dirac neutrino mass matrix are diagonal, the one/two zeros or one/two vanishing minors on the right-handed Majorana mass matrix having μτ symmetry will propagate via seesaw mechanism as one/two vanishing minors or one/two texture zeros in the neutrino mass matrix with μτ symmetry respectively. It is found that only five such texture structures of the neutrino mass matrix are phenomenologically viable. For tribimaximal mixing, these texture structures reduce the number of free parameters to one. Interesting predictions are obtained for the effective Majorana mass Mee, the absolute mass scale and the Majorana-type CP violating phases.

Baryon asymmetry from leptogenesis with four zero neutrino Yukawa textures

The generation of the right amount of baryon asymmetry η of the Universe from supersymmetric leptogenesis is studied within the type-I seesaw framework with three heavy singlet Majorana neutrinos Ni (i = 1,2,3) and their superpartners. We assume the occurrence of four zeroes in the neutrino Yukawa coupling matrix Yν, taken to be μτ symmetric, in the weak basis where Ni (with real masses Mi > 0) and the charged leptons lα (α = e,μ,τ) are mass diagonal. The quadrant of the single nontrivial phase, allowed in the corresponding light neutrino mass matrix mν, gets fixed and additional constraints ensue from the requirement of matching η with its observed value. Special attention is paid to flavor effects in the washout of the lepton asymmetry. We also comment on the role of small departuresfrom high scale μτ symmetry due to RG evolution.

μτ symmetry, tribimaximal mixing and four zero neutrino Yukawa textures

Within the type-I seesaw framework with three heavy right chiral neutrinos and in the basis where the latter and the charged leptons are mass diagonal, a near `mu-tau' symmetry in the neutrino sector is strongly suggested by the neutrino oscillation data. There is further evidence for a close to the tribimaximal mixing pattern which subsumes `mu-tau' symmetry. On the other hand, the assumption of a (maximally allowed) four zero texture in the Yukawa coupling matrix Y_nu in the same basis leads to a highly constrained and predictive theoretical scheme. We show that the requirement of an exact `mu-tau' symmetry, coupled with observational constraints, reduces the `seventy two' allowed textures in such a `Y_nu' to 'only four' corresponding to just two different forms of the light neutrino mass matrix `m_nu'. The effect of each of these on measurable quantities can be described, apart from an overall factor of the neutrino mass scale, in terms of two real parameters and a phase angle all of which are within very constrained ranges. The additional input of a tribimaximal mixing reduces these three parameters to `only one' with a very nearly fixed value. Implications for both flavored and unflavored leptogenesis as well as radiative lepton flavor violating decays are discussed. We also investigate the stability of these conclusions under small deviations due to renormalization group running from a high scale where the four zero texture as well as `mu-tau' symmetry or the tribimaximal mixing pattern are imposed.