scholarly journals DIRAC NEUTRINO MASSES AND MIXING PARAMETERS IN A LEFT–RIGHT MODEL WITH MIRROR FERMIONS

2007 ◽  
Vol 22 (16n17) ◽  
pp. 2935-2943 ◽  
Author(s):  
R. GAITÁN ◽  
A. HERNÁNDEZ-GALEANA ◽  
J. M. RIVERA-REBOLLEDO ◽  
P. FERNÁNDEZ DE CÓRDOBA ◽  
S. RODRIGUEZ-ROMO
Keyword(s):  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Neutrino Masses ◽  
Neutrino Mixing ◽  
Mixing Angles ◽  
Expectation Value ◽  
Mixing Parameters ◽  
Order Of Magnitude ◽  
Free Parameters ◽  
The Masses

In this work we consider a left–right model containing mirror fermions with gauge group SU (3)C ⊗ SU (2)L ⊗ SU (2)R ⊗ U (1)Y′. The model has several free parameters which here we have calculated by using the recent values for the squared-neutrino mass differences. Lower bound for the mirror vacuum expectation value helped us to obtain crude estimations for some of these parameters. Also we estimate the order of magnitude of the masses of the standard and mirror neutrinos and numerical values for neutrino mixing angles.

scholarly journals Modulus τ linking leptonic CP violation to baryon asymmetry in A4 modular invariant flavor model

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Hiroshi Okada ◽  
Yusuke Shimizu ◽  
Morimitsu Tanimoto ◽  
Takahiro Yoshida
Keyword(s):  
Cp Violation ◽  
Effective Mass ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Baryon Asymmetry ◽  
Neutrino Masses ◽  
Normal Hierarchy ◽  
Modular Invariant ◽  
Mixing Angles ◽  
Expectation Value

Abstract We propose an A4 modular invariant flavor model of leptons, in which both CP and modular symmetries are broken spontaneously by the vacuum expectation value of the modulus τ. The value of the modulus τ is restricted by the observed lepton mixing angles and lepton masses for the normal hierarchy of neutrino masses. The predictive Dirac CP phase δCP is in the ranges [0°, 50°], [170°, 175°] and [280°, 360°] for Re [τ] < 0, and [0°, 80°], [185°, 190°] and [310°, 360°] for Re [τ] > 0. The sum of three neutrino masses is predicted in [60, 84] meV, and the effective mass for the 0νββ decay is in [0.003, 3] meV. The modulus τ links the Dirac CP phase to the cosmological baryon asymmetry (BAU) via the leptogenesis. Due to the strong wash-out effect, the predictive baryon asymmetry YB can be at most the same order of the observed value. Then, the lightest right-handed neutrino mass is restricted in the range of M1 = [1.5, 6.5] × 1013 GeV. We find the correlation between the predictive YB and the Dirac CP phase δCP. Only two predictive δCP ranges, [5°, 40°] (Re [τ] > 0) and [320°, 355°] (Re [τ] < 0) are consistent with the BAU.

scholarly journals Theoretical and Phenomenological Status of Neutrino Physics: A Brief Review

2015 ◽  
Vol 2015 ◽  
pp. 1-15 ◽  
Author(s):  
Surender Verma
Keyword(s):  
Neutrino Mass ◽  
Particle Physics ◽  
Recent Observation ◽  
New Physics ◽  
Neutrino Masses ◽  
Mixing Angles ◽  
Mixing Parameters ◽  
Phenomenological Studies ◽  
The Status ◽  
Free Parameters

We present an overview of recent progress in the theoretical and phenomenological studies of neutrino masses, lepton avor mixing, and CP violation. Firstly, We discuss the status of neutrino mass with in the Standard Model (SM) of particle physics. Then the possible ways in which neutrino mass terms can be included in the SM are discussed. The inclusion of new physics beyond the SM inevitably brings new parameters which are not constrained by the present experimental data on neutrino masses and mixing angles and, thus, are free parameters of the theory. We, also, discuss various theoretically motivated phenomenological approaches which can be used to reduce the number of free parameters and, thus, provide an excellent tool to understand the underlying physics of neutrino masses and mixings. Current experimental constraints on the neutrino mass spectrum and the lepton avor mixing parameters, including the recent observation of nonzeroθ13, have been summarized. Finally, We discuss the renewed interest in the possible existence of one or more sterile neutrinos and their phenomenology.

scholarly journals Spontaneous CP violation by modulus τ in A4 model of lepton flavors

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Hiroshi Okada ◽  
Morimitsu Tanimoto
Keyword(s):  
Cp Violation ◽  
Confidence Level ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
The Other ◽  
Neutrino Masses ◽  
Normal Hierarchy ◽  
Expectation Value ◽  
Invariant Model ◽  
Cp Symmetry

Abstract We discuss the modular A4 invariant model of leptons combining with the generalized CP symmetry. In our model, both CP and modular symmetries are broken spontaneously by the vacuum expectation value of the modulus τ. The source of the CP violation is a non-trivial value of Re[τ] while other parameters of the model are real. The allowed region of τ is in very narrow one close to the fixed point τ = i for both normal hierarchy (NH) and inverted ones (IH) of neutrino masses. The CP violating Dirac phase δCP is predicted clearly in [98°, 110°] and [250°, 262°] for NH at 3 σ confidence level. On the other hand, δCP is in [95°, 100°] and [260°, 265°] for IH at 5 σ confidence level. The predicted ∑mi is in [82, 102] meV for NH and ∑mi = [134, 180] meV for IH. The effective mass 〈mee〉 for the 0νββ decay is predicted in [12.5, 20.5] meV and [54, 67] meV for NH and IH, respectively.

GENERALIZED FUKUGITA–TANIMOTO–YANAGIDA NEUTRINO MASS ANSATZ

2007 ◽  
Vol 16 (05) ◽  
pp. 1405-1416 ◽  
Author(s):  
MIDORI OBARA ◽  
ZHI-ZHONG XING
Keyword(s):  
Beta Decay ◽  
Neutrinoless Double Beta Decay ◽  
Double Beta Decay ◽  
Neutrino Masses ◽  
Neutrino Mixing ◽  
Mixing Angles ◽  
Effective Masses ◽  
Majorana Neutrinos ◽  
Mass Degeneracy ◽  
The Masses

We generalize the Fukugita–Tanimoto–Yanagida ansatz by allowing the masses of three heavy right-handed Majorana neutrinos, Mi (i = 1,2,3), to be partially non-degenerate and search for the parameter space which can be consistent with the current neutrino oscillation data, for three non-degenerate mass cases (A) M3 = M2 ≠ M1, (B) M2 = M1 ≠ M3 and (C) M1 = M3 ≠ M2. We also examine the effect of the deviation from the complete mass degeneracy in each case. Finally, we obtain the numerical constraints on three light neutrino masses, three neutrino mixing angles and three CP-violating phases, together with the predictions for the Jarlskog invariant of CP violation and the effective masses of the tritium beta decay and the neutrinoless double-beta decay.

scholarly journals Modular invariant A4 models for quarks and leptons with generalized CP symmetry

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Chang-Yuan Yao ◽  
Jun-Nan Lu ◽  
Gui-Jun Ding
Keyword(s):  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Modular Invariant ◽  
Quark Masses ◽  
Mass Matrices ◽  
Flavor Mixing ◽  
Mixing Matrix ◽  
Free Parameters ◽  
The Masses ◽  
Cp Symmetry

Abstract We perform a systematical analysis of the A4 modular models with generalized CP for the masses and flavor mixing of quarks and leptons, and the most general form of the quark and lepton mass matrices is given. The CP invariance requires all couplings real in the chosen basis and thus the vacuum expectation value of the modulus τ uniquely breaks both the modular symmetry and CP symmetry. The phenomenologically viable models with minimal number of free parameters and the results of fit are presented. We find 20 models with 7 real free parameters that can accommodate the experimental data of lepton sector. We then apply A4 modular symmetry to the quark sector to explain quark masses and CKM mixing matrix, the minimal viable quark model is found to contain 10 free real parameters. Finally, we give two predictive quark-lepton unification models which use only 16 real free parameters to explain the flavor patterns of both quarks and leptons.

Global symmetries and Noether’s theorem

2018 ◽  
Author(s):  
Michael Kachelriess
Keyword(s):  
Global Symmetries ◽  
Symmetry Transformation ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Quantum Field ◽  
Expectation Value ◽  
Minkowski Space Time ◽  
Integral Measure ◽  
Colour Charge ◽  
Internal Symmetries

Noethers theorem shows that continuous global symmetries lead classically to conservation laws. Such symmetries can be divided into spacetime and internal symmetries. The invariance of Minkowski space-time under global Poincaré transformations leads to the conservation of the four-momentum and the total angular momentum. Examples for conserved charges due to internal symmetries are electric and colour charge. The vacuum expectation value of a Noether current is shown to beconserved in a quantum field theory if the symmetry transformation keeps the path-integral measure invariant.

scholarly journals THE TACHYON FIELD BELOW THE MASS BARRIER

1994 ◽  
Vol 09 (20) ◽  
pp. 3497-3502 ◽  
Author(s):  
D.G. BARCI ◽  
C.G. BOLLINI ◽  
M.C. ROCCA
Keyword(s):  
Green Function ◽  
Eigenvalue Problem ◽  
Plane Wave ◽  
Time Evolution ◽  
Mass Parameter ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Tachyon Field ◽  
Expectation Value ◽  
Wave Solutions

We consider a tachyon field whose Fourier components correspond to spatial momenta with modulus smaller than the mass parameter. The plane wave solutions have then a time evolution which is a real exponential. The field is quantized and the solution of the eigenvalue problem for the Hamiltonian leads to the evaluation of the vacuum expectation value of products of field operators. The propagator turns out to be half-advanced and half-retarded. This completes the proof4 that the total propagator is the Wheeler Green function.4,7

scholarly journals Minimal scoto-seesaw mechanism with spontaneous CP violation

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
D. M. Barreiros ◽  
F. R. Joaquim ◽  
R. Srivastava ◽  
J. W. F. Valle
Keyword(s):  
Dark Matter ◽  
Cp Violation ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Discrete Symmetry ◽  
Double Beta Decay ◽  
Neutrino Masses ◽  
Seesaw Mechanism ◽  
Cosmological Observations ◽  
Scalar Singlet

Abstract We propose simple scoto-seesaw models to account for dark matter and neutrino masses with spontaneous CP violation. This is achieved with a single horizontal $$ {\mathcal{Z}}_8 $$ Z 8 discrete symmetry, broken to a residual $$ {\mathcal{Z}}_2 $$ Z 2 subgroup responsible for stabilizing dark matter. CP is broken spontaneously via the complex vacuum expectation value of a scalar singlet, inducing leptonic CP-violating effects. We find that the imposed $$ {\mathcal{Z}}_8 $$ Z 8 symmetry pushes the values of the Dirac CP phase and the lightest neutrino mass to ranges already probed by ongoing experiments, so that normal-ordered neutrino masses can be cornered by cosmological observations and neutrinoless double beta decay experiments.

THE TWISTED EUCLIDEAN GREEN’S FUNCTION IN THE SPACETIME OF A COSMIC STRING

1992 ◽  
Vol 01 (02) ◽  
pp. 371-377 ◽  
Author(s):  
B. LINET
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Minkowski Spacetime ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Massive Scalar ◽  
Elementary Functions ◽  
Integral Expression ◽  
Massive Scalar Field ◽  
Expectation Value

In a conical spacetime, we determine the twisted Euclidean Green’s function for a massive scalar field. In particular, we give a convenient form for studying the vacuum averages. We then derive an integral expression of the vacuum expectation value <Φ2(x)>. In the Minkowski spacetime, we express <Φ2(x)> in terms of elementary functions.

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