Relating neutrino masses and mixings by discrete symmetries

Hernández, Daniel E.; Smirnov, A. Yu.

doi:10.1103/physrevd.88.093007

Cited by 30 publications

(39 citation statements)

References 40 publications

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“…In this case with the solution tag C 4 , the seventh root of unity, γ = e 2πi/7 , occurs in the eigenvalues and the mixing matrix reads 18) where the r i are the roots of the equation…”

Section: Jhep09(2014)033mentioning

confidence: 99%

“…In recent years, assuming neutrinos are Majorana particles, much effort has gone into the discussion of the lepton mixing matrices U from residual symmetries. Though a lot of results have been achieved [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24], the present status has not been reached in a systematic way. 1 Thus it is by no means clear if the cases existing in the literature encompass all relevant mixing matrices.…”

Section: Introductionmentioning

confidence: 99%

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Classification of lepton mixing matrices from finite residual symmetries

Fonseca

Grimus

2014

J. High Energ. Phys.

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Assuming that neutrinos are Majorana particles, we perform a complete classification of all possible mixing matrices which are fully determined by residual symmetries in the charged-lepton and neutrino mass matrices. The classification is based on the assumption that the residual symmetries originate from a finite flavour symmetry group. The mathematical tools which allow us to accomplish this classification are theorems on sums of roots of unity. We find 17 sporadic cases plus one infinite series of mixing matrices associated with three-flavour mixing, all of which have already been discussed in the literature. Only the infinite series contains mixing matrices which are compatible with the data at the 3 sigma level.

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“…In this case with the solution tag C 4 , the seventh root of unity, γ = e 2πi/7 , occurs in the eigenvalues and the mixing matrix reads 18) where the r i are the roots of the equation…”

Section: Jhep09(2014)033mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Classification of lepton mixing matrices from finite residual symmetries

Fonseca

Grimus

2014

J. High Energ. Phys.

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“…(1.2) and DSG of SU(3). This was studied for the finite von-Dyck groups in [21] and for all DSG of SU(3) having three dimensional IR in [22]. Here, the third state is not implied to be massless.…”

Section: Jhep11(2015)186mentioning

confidence: 99%

Neutrino masses and mixing from flavour antisymmetry

Joshipura¹

2015

J. High Energ. Phys.

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We discuss consequences of assuming (i) that the (Majorana) neutrino mass matrix M ν displays flavour antisymmetry, S T ν M ν S ν = −M ν with respect to some discrete symmetry S ν contained in SU(3) and (ii) S ν together with a symmetry T l of the Hermitian combination M l M † l of the charged lepton mass matrix forms a finite discrete subgroup G f of SU(3) whose breaking generates these symmetries. Assumption (i) leads to at least one massless neutrino and allows only four textures for the neutrino mass matrix in a basis with a diagonal S ν if it is assumed that the other two neutrinos are massive. Two of these textures contain a degenerate pair of neutrinos. Assumption (ii) can be used to determine the neutrino mixing patterns. We work out these patterns for two major group series ∆(3N 2 ) and ∆(6N 2 ) as G f . It is found that all ∆(6N 2 ) and ∆(3N 2 ) groups with even N contain some elements which can provide appropriate S ν . Mixing patterns can be determined analytically for these groups and it is found that only one of the four allowed neutrino mass textures is consistent with the observed values of the mixing angles θ 13 and θ 23 . This texture corresponds to one massless and a degenerate pair of neutrinos which can provide the solar pair in the presence of some perturbations. The well-known groups A 4 and S 4 provide examples of the groups in respective series allowing correct θ 13 and θ 23 . An explicit example based on A 4 and displaying a massless and two quasi degenerate neutrinos is discussed.

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“…In the semi-direct models a continuous parameter is introduced, derived from the freedom to rotate in the degenerate subspace of the neutrino residual symmetry, allowing the prediction of * jessica.turner@durham.ac.uk a non-zero θ 13 . There are several attractive features of implementing such an approach: firstly a UV-complete theory is not necessary in order to predict leptonic observables [16][17][18][19][20][21][22]. Secondly, correlations between the observables can be derived and provide specific signatures which allow the comparison of a range of models to experimental data [18][19][20][21][22][23][24][25].…”

Section: Introductionmentioning

confidence: 99%

Predictions for leptonic mixing angle correlations and nontrivial DiracCPviolation fromA5with generalizedCPsymmetry

Turner

2015

Phys. Rev. D

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Using discrete flavour group, A5, combined with generalised CP, we study the mixing parameter correlations which arise from breaking to residual symmetries in the neutrino, Gν = Z2 × CP, and charged lepton sectors, Ge = Z2. By focusing on patterns that agree with current experimental data we demonstrate that non-trivial leptonic phases are predicted and discuss a number of distinctive correlations between mixing parameters.

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Relating neutrino masses and mixings by discrete symmetries

Cited by 30 publications

References 40 publications

Classification of lepton mixing matrices from finite residual symmetries

Classification of lepton mixing matrices from finite residual symmetries

Neutrino masses and mixing from flavour antisymmetry

Predictions for leptonic mixing angle correlations and nontrivial DiracCPviolation fromA5with generalizedCPsymmetry

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