scholarly journals QUARK AND LEPTON MASS MATRICES WITH A4 FAMILY SYMMETRY

2007 ◽  
Vol 16 (05) ◽  
pp. 1383-1393 ◽  
Author(s):  
HIDEYUKI SAWANAKA
Keyword(s):  
Experimental Data ◽  
Neutrino Mixing ◽  
Family Symmetry ◽  
Mixing Angles ◽  
Quark Masses ◽  
Quark Sector ◽  
Mass Matrices ◽  
Mixing Matrix ◽  
Current Experimental Data

Realistic quark masses and mixing angles are obtained applying the successful A4 family symmetry for leptons, motivated by the quark-lepton assignments of SU (5). The A4 symmetry is suitable to give tri-bimaximal neutrino mixing matrix which is consistent with current experimental data. We study new scenario for the quark sector with the A4 symmetry.

GENERAL STUDY OF QUARK MASS MATRICES WITH FULL OFF-DIAGONAL MIXING

1992 ◽  
Vol 07 (25) ◽  
pp. 6357-6370 ◽  
Author(s):  
ROBERT E. SHROCK
Keyword(s):  
Quark Mass ◽  
Mass Matrix ◽  
General Study ◽  
Mixing Angles ◽  
Quark Masses ◽  
Rotation Matrices ◽  
Quark Mixing ◽  
Down Quark ◽  
Mass Matrices ◽  
Mixing Matrix

We study an ansatz for the quark mass matrix in which all of the nondiagonal entries are nonzero, but which still allows the quark mixing angles to be calculated in terms of ratios of quark masses and certain phases. Analytic calculations of the orthogonal rotation matrices in the up and down quark sectors and the resultant observed quark mixing matrix are presented. Comparison with experimental data is given.

scholarly journals CHARGED LEPTON CORRECTION TO TRI-BIMAXIMAL LEPTON MIXING AND ITS IMPLICATIONS TO NEUTRINO PHENOMENOLOGY

2013 ◽  
Vol 28 (31) ◽  
pp. 1350131 ◽  
Author(s):  
SRINU GOLLU ◽  
K. N. DEEPTHI ◽  
R. MOHANTA
Keyword(s):  
Charged Lepton ◽  
Daya Bay ◽  
Neutrino Mixing ◽  
Mixing Angle ◽  
Quark Sector ◽  
Mass Matrices ◽  
Reactor Neutrino ◽  
Mixing Matrix ◽  
Neutrino Experiments ◽  
Reactor Mixing

The recent results from Daya Bay and RENO reactor neutrino experiments have firmly established that the smallest reactor mixing angle θ13 is nonvanishing at the 5 σ level, with a relatively large value, i.e. θ13 ≈ 9°. Using the fact that the neutrino mixing matrix can be represented as [Formula: see text], where Ul and Uν result from the diagonalization of the charged lepton and neutrino mass matrices and Pν is a diagonal matrix containing the Majorana phases and assuming the tri-bimaximal (TBM) form for Uν, we investigate the possibility of accounting for the large reactor mixing angle due to the corrections of the charged lepton mixing matrix. The form of Ul is assumed to be that of CKM mixing matrix of the quark sector. We find that with this modification it is possible to accommodate the large observed reactor mixing angle θ13. We also study the implications of such corrections on the other phenomenological observables.

scholarly journals Theory for Neutrino Mixing

2016 ◽  
Vol 43 ◽  
pp. 1660197
Author(s):  
Xiao-Gang He
Keyword(s):  
Theoretical Model ◽  
Nobel Prize ◽  
Neutrino Mixing ◽  
Oscillation Pattern ◽  
Family Symmetry ◽  
Mixing Angles ◽  
Mixing Matrix ◽  
Nobel Prize In Physics ◽  
Matrix Formula ◽  
Made In

Since the discovery of neutrino oscillations, for which Takaaki Kajita and Arthur B. McDonald were awarded the 2015 Nobel prize in physics, tremendous progresses have been made in measuring the mixing angles which determine the oscillation pattern. A lot of theoretical efforts have been made to understand how neutrinos mix with each other. Present data show that in the standard parameterization of the mixing matrix, [Formula: see text] is close to [Formula: see text] and the CP violating phase is close to [Formula: see text]. In this talk I report results obtained in arXiv:1505.01932 (Phys. Lett. B750(2015)620) and arXive:1404.01560 (Chin. J. Phys.53(2015)100101) and discuss some implications for theoretical model buildings for such mixing pattern. Specific examples for neutrino mixing based on [Formula: see text] family symmetry are given.

scholarly journals BOUNDS ON QUARK MASS MATRICES ELEMENTS DUE TO MEASURED PROPERTIES OF THE MIXING MATRIX AND PRESENT VALUES OF THE QUARK MASSES

2008 ◽  
Vol 23 (11) ◽  
pp. 1729-1746 ◽  
Author(s):  
S. CHATURVEDI ◽  
V. GUPTA ◽  
G. SÁNCHEZ-COLÓN
Keyword(s):  
Energy Scale ◽  
Matrix Elements ◽  
Specific Mass ◽  
Quark Masses ◽  
Quark Sector ◽  
Mass Matrices ◽  
Simple Generalization ◽  
Mixing Matrix ◽  
Extra Parameter

We obtain constraints on possible structures of mass matrices in the quark sector by using as experimental restrictions the determined values of the quark masses at the MZ energy scale, the magnitudes of the quark mixing matrix elements V ud , V us , V cd and V cs , and the Jarlskog invariant J(V). Different cases of specific mass matrices are examined in detail. The quality of the fits for the Fritzsch- and Stech-type mass matrices is about the same with χ2/ d.o.f. = 4.23/3 = 1.41 and χ2/ d.o.f. = 9.10/4 = 2.28, respectively. The fit for a simple generalization (one extra parameter) of the Fritzsch type matrices, in the physical basis, is much better with χ2/ d.o.f. = 1.89/4 = 0.47. For comparison we also include the results using the quark masses at the 2 GeV energy scale. The fits obtained at this energy scale are similar to that at MZ energy scale, implying that our results are unaffected by the evolution of the quark masses from 2 to 91 GeV.

scholarly journals Predictions for the Dirac CP violation phase in the neutrino mixing matrix

2015 ◽  
Vol 30 (13) ◽  
pp. 1530035 ◽  
Author(s):  
S. T. Petcov ◽  
I. Girardi ◽  
A. V. Titov
Keyword(s):  
Cp Violation ◽  
Sum Rules ◽  
Current Data ◽  
Neutrino Mixing ◽  
Mixing Angles ◽  
Flavor Symmetries ◽  
Minimal Form ◽  
Mass Matrices ◽  
Mixing Matrix ◽  
Matrix Formula

Using the fact that the neutrino mixing matrix [Formula: see text], where Ue and Uν result from the diagonalization of the charged lepton and neutrino mass matrices, we analyze the predictions based on the sum rules which the Dirac phase δ present in U satisfies when Uν has a form dictated by, or associated with, discrete flavor symmetries and Ue has a "minimal" form (in terms of angles and phases it contains) that can provide the requisite corrections to Uν, so that the reactor, atmospheric and solar neutrino mixing angles θ13, θ23 and θ12 have values compatible with the current data.

scholarly journals On the CP Violation Phase in a Neutrino Mixing Model with an A4 Flavor Symmetry

2016 ◽  
Vol 26 (1) ◽  
pp. 1
Author(s):  
Phi Quang Van ◽  
Nguyen Thi Hong Van
Keyword(s):  
Experimental Data ◽  
Cp Violation ◽  
Standard Model ◽  
Mixing Model ◽  
Neutrino Masses ◽  
Flavor Symmetry ◽  
Neutrino Mixing ◽  
Normal Ordering ◽  
Mixing Angles ◽  
Mixing Matrix

Neutrino masses and mixing in an extended standard model acquiring an A4 flavour symmetry are considered. The corresponding three-neutrino mixing matrix obtained via a pertur- bative method allows us to determine the Dirac CP violation phase (\delta_{CP}) as a function of the mixing angles (\theta_{12}, \theta_{23}, \theta_{13}). Then, numerical values and distributions of \delta_{CP} are given. The latter values are quite close to the global fits of the experimental data for both the normal ordering and inverse ordering of the neutrino masses.

scholarly journals TETRAHEDRAL FAMILY SYMMETRY AND THE NEUTRINO MIXING MATRIX

2005 ◽  
Vol 20 (34) ◽  
pp. 2601-2605 ◽  
Author(s):  
ERNEST MA
Keyword(s):  
Neutrino Mass ◽  
Mass Matrix ◽  
Neutrino Mass Matrix ◽  
Neutrino Mixing ◽  
Symmetry Limit ◽  
Family Symmetry ◽  
Seesaw Mechanism ◽  
Mixing Angles ◽  
Mixing Matrix ◽  
Natural Symmetry

In a new application of the discrete non-Abelian symmetry A4 using the canonical seesaw mechanism, a three-parameter form of the neutrino mass matrix is derived. It predicts the following mixing angles for neutrino oscillations: θ13=0, sin 2θ23=1/2, and sin 2θ12 close, but not exactly equal to 1/3, in one natural symmetry limit.

scholarly journals QUARK MASS MATRICES IN THE A4 MODEL

2002 ◽  
Vol 17 (10) ◽  
pp. 627-630 ◽  
Author(s):  
ERNEST MA
Keyword(s):  
Gauge Symmetry ◽  
Quark Mass ◽  
Spontaneous Breaking ◽  
Charged Current ◽  
Lepton Sector ◽  
Mixing Angles ◽  
Quark Masses ◽  
Mass Matrices ◽  
The Standard Model ◽  
Mixing Matrix

If the standard model of quark interactions is supplemented by a discrete A4 symmetry (which may be relevant for the lepton sector), the spontaneous breaking of the electroweak gauge symmetry allows arbitrary quark masses, but all mixing angles are predicted to be zero. A pattern of the explicit breaking of A4 is proposed, which results in a realistic charged-current mixing matrix.

scholarly journals IMPLICATIONS OF MEASURED PROPERTIES OF THE MIXING MATRIX ON MASS MATRICES

2007 ◽  
Vol 22 (32) ◽  
pp. 2463-2470 ◽  
Author(s):  
S. CHATURVEDI ◽  
V. GUPTA ◽  
G. SÁNCHEZ-COLÓN
Keyword(s):  
Main Diagonal ◽  
Specific Mass ◽  
Quark Sector ◽  
Mass Matrices ◽  
Mixing Matrix ◽  
The Asymmetry

It is shown how the two experimentally measurable properties of the mixing matrix V, the asymmetry Δ(V) = |V12|2 - |V21|2 of V with respect to the main diagonal and the Jarlskog invariant [Formula: see text], can be exploited to obtain constraints on possible structures of mass matrices in the quark sector. Specific mass matrices are examined in detail as an illustration.

scholarly journals Parametrization of Pontecorvo–Maki–Nakagawa–Sakata mixing matrix based on CP-violating bipair neutrino mixing

2015 ◽  
Vol 30 (05) ◽  
pp. 1550019 ◽  
Author(s):  
Jun Iizuka ◽  
Teruyuki Kitabayashi ◽  
Yuki Minagawa ◽  
Masaki Yasuè
Keyword(s):  
Matrix Element ◽  
Cp Violation ◽  
Numerical Computation ◽  
Neutrino Mixing ◽  
Mixing Angles ◽  
Neutrino Interactions ◽  
Reactor Neutrino ◽  
Mixing Matrix ◽  
Three Phases

CP violation in neutrino interactions is described by three phases contained in Pontecorvo–Maki–Nakagawa–Sakata mixing matrix (U PMNS ). We argue that the phenomenologically consistent result of the Dirac CP violation can be obtained if U PMNS is constructed along bipair neutrino mixing scheme, namely, requiring that |U12| = |U32| and |U22| = |U23| (case 1) and |U12| = |U22| and |U32| = |U33| (case 2), where Uij stands for the i × j matrix element of U PMNS . As a result, the solar, atmospheric and reactor neutrino mixing angles θ12, θ23 and θ13, respectively, are correlated to satisfy cos 2θ12 = sin 2 θ23 - tan 2 θ13 (case 1) or cos 2θ12 = cos 2 θ23 - tan 2 θ13 (case 2). Furthermore, if Dirac CP violation is observed to be maximal, θ23 is determined by θ13 to be: [Formula: see text] (case 1) or [Formula: see text] (case 2). For the case of non-maximal Dirac CP violation, we perform numerical computation to show relations between the CP-violating Dirac phase and the mixing angles.

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