A general formula by $LDL^{T}$ decomposition for the type-I seesaw mechanism

Yang, Masaki J. S.

doi:10.48550/arxiv.2112.14402

Cited by 2 publications

(3 citation statements)

References 22 publications

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“…Here we review a formula by LDL T decomposition [86,87] in the minimal seesaw models [88][89][90][91][92]. The Yukawa matrix of neutrinos Y and the mass matrix of right-handed neutrinos M are defined as follows…”

Section: A Formula For the Minimal Type-i Seesaw Model And Conditions...mentioning

confidence: 99%

Conditions of general $Z_{2}$ symmetry and TM$_{1,2}$ mixing for the minimal type-I seesaw mechanism in an arbitrary basis

Yang¹

2022

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In this paper, using a formula for the minimal type-I seesaw mechanism by LDL T decomposition, conditions of general Z 2 -invariance of the neutrino mass matrix m is obtained for Lagrangian parameters in an arbitrary basis. The conditions are found to be (Mand the right-handed neutrino mass matrix M ij . In other words, the symmetric and antisymmetric part of b i must be proportional to those of the quantity (M 22 a i − M 12 b i ).Since the eigenvectors of the generator T are orthogonal, we can analyze the eigenvectors and mass eigenvalues of mm † for a Z 2 -symmetric m. Two eigenvectors u 1,2 of mm † coincide with any of those of T , and the remaining one is a vector (u 1 × u 2 ) * orthogonal to them. Furthermore, if the Yukawa matrix does not have the Z 2 symmetry, two nonzero neutrino masses are concisely represented.These results are applied to three Z 2 symmetries, the µ − τ symmetry, the TM 1 mixing, and the magic symmetry which predicts the TM 2 mixing. In particular, for the TM 2 mixing, the magic (anti-)symmetric Yukawa matrix with S 2 Y = ±Y is phenomenologically rejected because it predicts m 2 = 0 or m 1 , m 3 = 0. I. INTRODUCTIONThe structure of the lepton mixing matrix often involves a certain Z 2 symmetry of the neutrino mass matrix m. The bi-maximal mixing [1] accompanies the µ − τ symmetry [2-22], and the trimaximal mixing [23-30] does the magic symmetry [31]. The tri-bi-maximal (TBM) mixing [32] realized by the combination of these two mixings has the Klein symmetry K 4 ≃ Z 2 × Z 2 [33-35]. And for CP phases, µ − τ reflection symmetry [36-60] predicts the

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Section: A Formula For the Minimal Type-i Seesaw Model And Conditions...mentioning

confidence: 99%

Conditions of general $Z_{2}$ symmetry and TM$_{1,2}$ mixing for the minimal type-I seesaw mechanism in an arbitrary basis

Yang¹

2022

Preprint

Self Cite

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“…However, such a representation obscures symmetries and relationships of the original Lagrangian. Thus, in this letter, we analyze the conditions for CP symmetry of the light neutrino mass matrix m in the minimal seesaw model [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] using a formula by LDL T decomposition [24]. As a result, basis-independent conditions are obtained for the general Lagrangian parameters.…”

Section: Introductionmentioning

confidence: 99%

“…In the beginning, we consider a general formula by LDL T decomposition [24] in the minimal seesaw models [9][10][11][12][13]. By setting the vacuum expectation value of Higgs to one, the two mass matrices of neutrinos are defined as follows…”

Section: Introductionmentioning

confidence: 99%

A formula by $LDL^{T}$ decomposition for the minimal type-I seesaw mechanism and conditions of $CP$ symmetry in an arbitrary basis

Yang¹

2022

Preprint

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In this letter, using a general formula by LDL T decomposition in the minimal seesaw model, we obtain the basis-independent conditions of CP symmetry for Lagrangian parameters of the neutrino mass matrix m. The conditions are found to be Re (M 22 a i −Re b j for the Yukawa matrix Y ij = (a j , b j ) and the right-handed neutrino mass matrix M ij . In other words, the real or imaginary part of b i must be proportional to the real or imaginary part of the quantity (M 22 a i − M 12 b i ).

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A general formula by $LDL^{T}$ decomposition for the type-I seesaw mechanism

Cited by 2 publications

References 22 publications

Conditions of general $Z_{2}$ symmetry and TM$_{1,2}$ mixing for the minimal type-I seesaw mechanism in an arbitrary basis

Conditions of general $Z_{2}$ symmetry and TM$_{1,2}$ mixing for the minimal type-I seesaw mechanism in an arbitrary basis

A formula by $LDL^{T}$ decomposition for the minimal type-I seesaw mechanism and conditions of $CP$ symmetry in an arbitrary basis

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