Parametrizing the Mixing Matrix: A Unified Approach

Chaturvedi, S.; Mukunda, N.

doi:10.1142/s0217751x01003196

Cited by 12 publications

(26 citation statements)

References 22 publications

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“…We thus can easily recover all the existing parameterizations of the CKM matrix [21,[24][25][26][27][28][29]: -the Maiani parameterization [24,27] is obtained from U 1 by setting θ 12 → θ, θ 13 → β, θ 23 → γ, δ 12 → 0, δ 13 → 0, δ 23 → −δ; -the Chau-Keung parameterization [24,28] [24,29] is obtained from U 1 by setting θ 12 ↔ θ 13 , then δ 12 → 0, δ 13 → 0, θ 12 → π + θ 12 , θ 13 → π − θ 13 , θ 23 → 3 2 π + θ 23 , exchanging second and third column and multiplying the last row for (−1). From the above analysis it is clear that a number of new parameterizations of the mixing matrix can be generated and that a clear physical meaning can be attached to each of them, by considering the order in which the generators G ij act and the initial conditions used for getting that particular matrix.…”

Section: The Parameterizations Of the Three Flavor Mixing Matrixmentioning

confidence: 99%

Quantum field theory of three flavor neutrino mixing and oscillations withCPviolation

2002

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We study in detail the Quantum Field Theory of mixing among three generations of Dirac fermions (neutrinos). We construct the Hilbert space for the flavor fields and determine the generators of the mixing transformations. By use of these generators, we recover all the known parameterizations of the three-flavor mixing matrix and we find a number of new ones. The algebra of the currents associated with the mixing transformations is shown to be a deformed su(3) algebra, when CP violating phases are present. We then derive the exact oscillation formulas, exhibiting new features with respect to the usual ones. CP and T violation are also discussed.

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Section: The Parameterizations Of the Three Flavor Mixing Matrixmentioning

confidence: 99%

Quantum field theory of three flavor neutrino mixing and oscillations withCPviolation

2002

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“…Such 3-subgroups might be used as bigger elementary blocks in constructing of a general transformation [25,28]. For instance, for the variant from (8.5): (α 1 , A 2 , A 3 ) =⇒ (a 1 , X 2 , X 3 ) the general multiplication law (7.4) gives…”

Section: On the Multiplication Law For Gl(4 C) In Dirac Basismentioning

confidence: 99%

“…This paper is a contribution to the Proceedings of the Seventh International Conference "Symmetry in Nonlinear Mathematical Physics" (June [24][25][26][27][28][29][30]2007, Kyiv, Ukraine). The full collection is available at http://www.emis.de/journals/SIGMA/symmetry2007.html…”

Section: Introductionmentioning

confidence: 99%

On Parametrization of the Linear GL(4,C) and Unitary SU(4) Groups in Terms of Dirac Matrices

Red'kov¹

2008

SIGMA

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Abstract. Parametrization of 4 × 4-matrices G of the complex linear group GL(4, C) in terms of four complex 4-vector parameters (k, m, n, l) is investigated. Additional restrictions separating some subgroups of GL(4, C) are given explicitly. In the given parametrization, the problem of inverting any 4×4 matrix G is solved. Expression for determinant of any matrix G is found: det G = F (k, m, n, l). Unitarity conditions G + = G −1 have been formulated in the form of non-linear cubic algebraic equations including complex conjugation. Several simplest solutions of these unitarity equations have been found: three 2-parametric subgroups G 1 , G 2 , G 3 -each of subgroups consists of two commuting Abelian unitary groups; 4-parametric unitary subgroup consisting of a product of a 3-parametric group isomorphic SU (2) and 1-parametric Abelian group. The Dirac basis of generators Λ k , being of Gell-Mann type, substantially differs from the basis λ i used in the literature on SU (4) group, formulas relating them are found -they permit to separate SU (3) subgroup in SU (4). Special way to list 15 Dirac generators of GL(4, C) can be usedwhich permit to factorize SU (4) transformations according to S = e i a α e i b β e ikK e ilL e imM , where two first factors commute with each other and are isomorphic to SU (2) group, the three last ones are 3-parametric groups, each of them consisting of three Abelian commuting unitary subgroups. Besides, the structure of fifteen Dirac matrices Λ k permits to separate twenty 3-parametric subgroups in SU (4) isomorphic to SU (2); those subgroups might be used as bigger elementary blocks in constructing of a general transformation SU (4). It is shown how one can specify the present approach for the pseudounitary group SU (2, 2) and SU (3, 1).

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“…Another kind of factorization is that suggested by Chaturvedi and Mukunda in their paper [6] aiming at obtaining a more "suitable" parametrization of the Kobayashi-Maskawa matrix. Although the proposed forms for n = 3, 4 are awfully complicated by comparison with other parametrizations existing in literature, and for this reason it cannot be extended easily to cases n ≥ 5, the paper contains a novel idea namely that that an SU(n) matrix can be parametrized by a sequence of n − 1 complex vectors of dimensions 2, 3, .…”

Section: −Iϕmentioning

confidence: 99%