Simplified Unitarity Triangles for the Lepton Sector

Bjorken, James D.; Harrison, P. F.; Scott, W. G.

doi:10.2172/878004

Cited by 4 publications

(10 citation statements)

References 20 publications

(29 reference statements)

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“…This parametrization was first obtained in [13] with 2/3ξ = u. The Jarlskog invariant is − 2/3 Im(ξ).…”

Section: C1mentioning

confidence: 99%

“…Eqs. ( 12), (13), and ( 14) are subject to phase conventions. Since we may alter the phase of each column and each row at will, we may always pre-multiply each unitary matrix in these equations by a ∆(δ 1 , δ 2 , δ 3 ) .…”

Section: Diagonalization Matrixmentioning

confidence: 99%

“…A similar discussion can be carried out for the CKM mixing matrix. However, since U CKM has no zero element, in order to obtain an approximate symmetry, not only do we have to assume a two-fold mass degeneracy for the u or the d quarks, we must also be willing to approximate the small (13) or the (31) elements of the CKM matrix to be zero.…”

Section: Similarly If We Choosementioning

confidence: 99%

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Mass independent textures and symmetry

Lam

2006

Phys. Rev. D

103

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A mass-independent texture is a set of linear relations of the fermion mass-matrix elements which imposes no constraint on the fermionic masses nor the Majorana phases. Magic and 2-3 symmetries are examples. We discuss the general construction and the properties of these textures, as well as their relation to the quark and neutrino mixing matrices. Such a texture may be regarded as a symmetry, whose unitary generators of the symmetry group can be explicitly constructed. In particular, the symmetries connected with the tri-bimaximal neutrino mixing matrix are discussed, together with the physical consequence of breaking one symmetry but preserving another.

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“…This parametrization was first obtained in [13] with 2/3ξ = u. The Jarlskog invariant is − 2/3 Im(ξ).…”

Section: C1mentioning

confidence: 99%

Section: Diagonalization Matrixmentioning

confidence: 99%

Section: Similarly If We Choosementioning

confidence: 99%

See 1 more Smart Citation

Mass independent textures and symmetry

Lam

2006

Phys. Rev. D

103

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“…Refs. [13,14,15,16]. In the case c = s = 1/ √ 2 and ρ = 0, the mixing matrix reduces to the tri-bimaximal form.…”

Section: Introductionmentioning

confidence: 99%

Minimal modification to the tri-bimaximal neutrino mixing

Zee²

2007

Physics Letters B

153

122

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We explore some ways of minimally modifying the neutrino mixing matrix from tribimaximal, characterized by introducing at most one mixing angle and a CP violating phase thus extending our earlier work. One minimal modification, motivated to some extent by group theoretic considerations, is a simple case with the elements V α2 of the second column in the mixing matrix equal to 1/ √ 3. Modifications by keeping one of the columns or one of the rows unchanged from tri-bimaximal mixing all belong to the class of minimal modification. Some of the cases have interesting experimentally testable consequences. In particular, the T2K and MINOS collaborations have recently reported indications of a non-zero θ 13 . For the cases we consider,the new data sharply constrain the CP violating phase angle δ, with δ close to 0 (in some cases) and π disfavored.PACS numbers:

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“…One such clue is the fact that the leptonic mixing matrix is now known to be somewhat close to what is called the "tribimaximal" form; actually a number of interesting discussions [9,10,11,12,13,14,15,16,17,18] of this form have been presented over a period of years.…”

Section: Introductionmentioning

confidence: 99%

An Approach to Permutation Symmetry for the Electroweak Theory

Jora

Nasri

Schechter

2006

Int. J. Mod. Phys. A

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The form of the leptonic mixing matrix emerging from experiment has, in the last few years, generated a lot of interest in the so-called tribimaximal type. This form may be naturally associated with the possibility of a discrete permutation symmetry (S 3 ) among the three generations.However, trying to implement this attractive symmetry has resulted in some problems and it seems to have fallen out of favor. We suggest an approach in which the S 3 holds to first approximation, somewhat in the manner of the old SU (3) flavor symmetry of the three flavor quark model. It is shown that in the case of the neutrino sector, a presently large experimentally allowed region can be fairly well described in this first approximation. We briefly discuss the nature of the perturbations which are the analogs of the Gell-Mann Okubo perturbations but confine our attention for the most part to the S 3 invariant model. We postulate that the S 3 invariant mass spectrum consists of non zero masses for the (τ, b, t) and zero masses for the other charged fermions but approximately degenerate masses for the three neutrinos. The mixing matrices are assumed to be trivial for the charged fermions but of tribimaximal type for the neutrinos in the first approximation. It is shown that this can be implemented by allowing complex entries for the mass matrix and spontaneous breakdown of the S 3 invariance of the Lagrangian. ‡

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Simplified Unitarity Triangles for the Lepton Sector

Cited by 4 publications

References 20 publications

Mass independent textures and symmetry

Mass independent textures and symmetry

Minimal modification to the tri-bimaximal neutrino mixing

An Approach to Permutation Symmetry for the Electroweak Theory

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