Natural Hierarchical Flavor Mixing

Lemke, E.

doi:10.1142/s0217732392003633

Cited by 10 publications

(7 citation statements)

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“…The greatest simplicity occurred with x q = 0 and x ℓ = 0.93 corresponding to diagonal up quark and Dirac neutrino mass matrices and leading to from the seesaw formula [16] with use of M N Dirac and the reconstructed light neutrino mass matrix, exhibits a nearly geometrical structure [17] given by…”

Section: Phenomenological Matrices From a Bottom-up Approachmentioning

confidence: 99%

Construction of anSO(10)×U(1)Fmodel of the Yukawa interactions

Albright

Nandi

1996

Phys. Rev. D

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We construct a supersymmetric SO(10)×U (1) F model of the Yukawa interactions at the grand unification scale from knowledge of a phenomenological set of mass matrices obtained by a previous bottom-up approach. The U (1) F family symmetry determines the textures for the Majorana and generic Dirac mass matrices, while the SO(10) symmetry relates each particular element of the up, down, neutrino and charged lepton Dirac matrices. The dominant second and third family contributions in the Dirac sector are renormalizable, while the remaining contributions to the Dirac mass matrices are of higher order, restricted by the U (1) F family symmetry to a small set of tree diagrams, and mainly complex-symmetric. The tree diagrams for the Majorana mass matrix are all non-renormalizable and of progressively higher-order, leading to a nearly * Permanent address † Electronic address: ALBRIGHT@FNALV ‡ Electronic address: PHYSSNA@OSUCC I. INTRODUCTIONThe standard model (SM) of strong and electroweak interactions, while providing excellent agreement with experiment todate, is known to be woefully inadequate to explain the mass spectrum and mixings of the three families of quarks and leptons. One needs to go beyond the standard model in order to relate the independent Yukawa couplings to each other.Of the various possibilities, supersymmetric grand unified theories and superstring theories seem to hold the most promise for successfully incorporating the Yukawa interactions in a more satisfactory fashion. In this paper we shall restrict our attention to supersymmetric SO(10) grand unification, which has been shown [1] to unify the gauge couplings successfully at a scale of Λ SGU T ∼ 10 16 GeV.It is a generally held opinion that knowledge of the mass matrices in the weak flavor basis can provide insights into the dynamical mass-generating mechanism.[2] This follows from the fact that the mass eigenvalues are obtained by diagonalization of the mass matrices, while the mixing matrices in the mass eigenbasis can be constructed from knowledge of the diagonalizing matrices connecting the two bases. By starting from the correct mass matrices, one should then be able to deduce the observed quark and lepton masses and mixings after evolving the results down to the present "low energy" scales.Generally two procedures are at one's disposal for the identification of the "correct" mass matrices. One can attempt to postulate a particular structure or "texture" for the mass matrices based on some well-defined and presumably simple theoretical concepts such as the unification group and/or the number of texture zeros present.[3] This procedure has been employed by most researchers in the past twenty years. Alternatively, one can make use of the known low energy mass and mixing data, supplemented by reasonable guesses for data which is not yet well determined, in order to extract mass matrices within some framework at the unification scale which yield the low energy data in question. Of special -3-FERMILAB-Pub-95/236-T interest are neutrino s...

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Section: Phenomenological Matrices From a Bottom-up Approachmentioning

confidence: 99%

Construction of anSO(10)×U(1)Fmodel of the Yukawa interactions

Albright

Nandi

1996

Phys. Rev. D

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“…The 10's contribute equally to (M U , M D ) and (M N Dirac , M E ), while the 126's weight (M U , M D ) and (M N Dirac , M E ) in the ratio of 1 : -3. The Majorana neutrino mass matrix M R , determined from the seesaw formula [16] with use of M N Dirac and the reconstructed light neutrino mass matrix, exhibits a nearly geometrical structure [17] given by…”

Section: Phenomenological Matrices From a Bottom-up Approachmentioning

confidence: 99%

AN EXPLICIT SO(10)×U(1)_F MODEL OF THE YUKAWA INTERACTIONS

Albright

Nandi

1996

Mod. Phys. Lett. A

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We construct an explicit SO (10)× U (1)F model of the Yukawa interactions by using as a guide previous phenomenological results obtained from a bottom-up approach to quark and lepton mass matrices. The U (1)F family symmetry group sets the textures for the Majorana and generic Dirac mass matrices by restricting the type and number of Higgs diagrams which can contribute to each matrix element, while the SO(10) group relates each particular element of the up, down, neutrino and charged lepton Dirac matrices. The Yukawa couplings and vacuum expectation values associated with pairs of 1, 45, 10 and 126 Higgs representations successfully correlate all the quark and lepton masses and mixings in the scenario incorporating the nonadiabatic solar neutrino and atmospheric neutrino depletion effects.

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“…Subsequently, investigations 8 indicated that certain degeneracies of the Hessian matrix, thought to be necessary for a viable theory, appeared to lead to difficulties with the initial value problem. Then a shock-wave analysis 9,10 concluded that these same degeneracies allowed tachyonic propagating modes. These difficulties were more recently reconsidered 11 .…”

Section: Introductionmentioning

confidence: 99%

Hamiltonian Analysis of Poincaré Gauge Theory Scalar Modes

Nester

1999

Int. J. Mod. Phys. D

109

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The Hamiltonian constraint formalism is used to obtain the first explicit complete analysis of nontrivial viable dynamic modes for the Poincaré gauge theory of gravity. Two modes with propagating spin-zero torsion are analyzed. The explicit form of the Hamiltonian is presented. All constraints are obtained and classified. The Lagrange multipliers are derived. It is shown that a massive spin-0 − mode has normal dynamical propagation but the associated massless 0 − is pure gauge. The spin-0 + mode investigated here is also viable in general. Both modes exhibit a simple type of "constraint bifurcation" for certain special field/parameter values.

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Natural Hierarchical Flavor Mixing

Cited by 10 publications

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Construction of anSO(10)×U(1)Fmodel of the Yukawa interactions

Construction of anSO(10)×U(1)Fmodel of the Yukawa interactions

AN EXPLICIT SO(10)×U(1)_F MODEL OF THE YUKAWA INTERACTIONS

Hamiltonian Analysis of Poincaré Gauge Theory Scalar Modes

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Natural Hierarchical Flavor Mixing

Cited by 10 publications

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Construction of anSO(10)×U(1)Fmodel of the Yukawa interactions

Construction of anSO(10)×U(1)Fmodel of the Yukawa interactions

AN EXPLICIT SO(10)×U(1)F MODEL OF THE YUKAWA INTERACTIONS

Hamiltonian Analysis of Poincaré Gauge Theory Scalar Modes

Contact Info

Product

Resources

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AN EXPLICIT SO(10)×U(1)_F MODEL OF THE YUKAWA INTERACTIONS