scholarly journals Model independent analysis of Dirac CP violating phase for some well-known mixing scenarios

2021 ◽  
pp. 2150188
Author(s):  
Sumit K. Garg
Keyword(s):  
Cp Violation ◽  
Numerical Investigation ◽  
Parameter Space ◽  
Neutrino Mixing ◽  
Mixing Angles ◽  
Complex Rotation ◽  
Rotation Matrices ◽  
Independent Analysis ◽  
Model Independent ◽  
Pmns Matrix

In this paper, we present a model independent analysis of Leptonic CP violation for some well-known mixing scenarios. In particular, we considered modified schemes for bimaximal (BM), democratic (DC), hexagonal (HG) and tribimaximal (TBM) mixing for our numerical investigation. These model independent corrections to mixing matrices are parametrized in terms of complex rotation matrices [Formula: see text] with related modified PMNS matrix of the forms [Formula: see text] where [Formula: see text] is a complex rotation in [Formula: see text] sector and [Formula: see text] is unperturbed mixing scheme. We present generic formulae for mixing angles, Dirac CP phase [Formula: see text] and Jarlskog invariant [Formula: see text] in terms of correction parameters. The parameter space of each modified mixing case is scanned for fitting neutrino mixing angles using [Formula: see text] approach and the corresponding predictions for Leptonic CP phase [Formula: see text] and Jarlskog invariant [Formula: see text] has been evaluated from allowed parameter space. The obtained ranges are reported for all viable cases.

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.

WHAT DOES μ - τ SYMMETRY IMPLY ABOUT LEPTONIC CP VIOLATION?

2007 ◽  
Vol 16 (05) ◽  
pp. 1373-1381 ◽  
Author(s):  
TEPPEI BABA
Keyword(s):  
Experimental Data ◽  
Cp Violation ◽  
Symmetry Breaking ◽  
Neutrino Mass ◽  
Mass Matrix ◽  
Mass Difference ◽  
Atmospheric Neutrino ◽  
Symmetric Part ◽  
Neutrino Mixing ◽  
Mixing Angles

The μ - τ symmetry can reproduce the consistent results with experimental data of θ13, and θ23 (θ13, and θ23 respectively denote the νe - ντ, and νμ - ντ, mixing angles). However, we can not address the issue of the leptonic CP violation in μ - τ symmetric models. So we add the μ - τ symmetry breaking part to include the CP violation. We characterize leptonic CP violation in terms of three phases, where one is conventional phase δ and others are additional phases ρ and γ. These δ, ρ and γ are, respectively, the phases of νe - ντ, νe - νμ and νμ - ντ mixings. The ρ and γ are redundant but the effect of ρ remains in the leptonic CP violation which is characterized by δ + ρ. The δ arises from the μ - τ symmetry breaking part of the Meμ and Meτ while ρ arises from of μ - τ symmetric part of the Meμ and Meτ, where Mij stands for ij (i,j = e,μ,τ) element of M(= [Formula: see text] for Mν being a flavor neutrino mass matrix). Moreover, θ23 can be exactly estimated to be: [Formula: see text] ( sin θ ∝ sin θ13 cos (δ + ρ)[Formula: see text], sin ϕ ∝ Mμμ - Mττ, where [Formula: see text] is the solar neutrino mass difference squared). The conditions of maximal atmospheric neutrino mixing are given by [Formula: see text] and Mμμ = Mττ,which indicate maximal Dirac CP violation.

scholarly journals Lepton mass and mixing in a neutrino mass model based onS4flavor symmetry

2016 ◽  
Vol 31 (09) ◽  
pp. 1650039 ◽  
Author(s):  
V. V. Vien
Keyword(s):  
Cp Violation ◽  
Neutrino Mass ◽  
Tree Level ◽  
Neutrino Mixing ◽  
Mass Model ◽  
Mixing Angles ◽  
Neutrino Sector ◽  
Neutrino Mass And Mixing ◽  
Model Based ◽  
Mixing Matrix

We study a neutrino mass model based on [Formula: see text] flavor symmetry which accommodates lepton mass, mixing with nonzero [Formula: see text] and CP violation phase. The spontaneous symmetry breaking in the model is imposed to obtain the realistic neutrino mass and mixing pattern at the tree-level with renormalizable interactions. Indeed, the neutrinos get small masses from one [Formula: see text] doublet and two [Formula: see text] singlets in which one being in [Formula: see text] and the two others in [Formula: see text] under [Formula: see text] with both the breakings [Formula: see text] and [Formula: see text] are taken place in charged lepton sector and [Formula: see text] in neutrino sector. The model also gives a remarkable prediction of Dirac CP violation [Formula: see text] or [Formula: see text] in both the normal and inverted spectrum which is still missing in the neutrino mixing matrix. The relation between lepton mixing angles is also represented.

MU-TAU REFLECTION SYMMETRY AND RADIATIVELY GENERATED LEPTOGENESIS

2009 ◽  
Vol 24 (18n19) ◽  
pp. 3660-3667
Author(s):  
Y. H. AHN ◽  
SIN KYU KANG ◽  
C. S. KIM ◽  
T. PHONG NGUYEN
Keyword(s):  
Renormalization Group ◽  
Cp Violation ◽  
Neutrino Oscillation ◽  
Baryon Asymmetry ◽  
Reflection Symmetry ◽  
Neutrino Mixing ◽  
Mixing Angles ◽  
Neutrino Sector ◽  
Seesaw Model ◽  
Gut Scale

We consider an exact µ-τ reflection symmetry in neutrino sector realized at the GUT scale in the context of the seesaw model with and without supersymmetry. It is shown that the renormalization group (RG) evolution from the GUT scale to the seesaw scale gives rise to breaking of the µ-τ symmetry which is essential to achieve a successful leptogenesis. We show that CP violation responsible for the generation of baryon asymmetry of our universe can be directly linked with CP violation measurable through neutrino oscillation as well as neutrino mixing angles θ12 and θ13.

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 FERMION MASSES, NEUTRINO MIXING AND CP VIOLATION FROM THE ANTI-GRAND-UNIFICATION MODEL

1998 ◽  
Vol 13 (29) ◽  
pp. 5037-5074 ◽  
Author(s):  
C. D. FROGGATT ◽  
M. GIBSON ◽  
H. B. NIELSEN ◽  
D. J. SMITH
Keyword(s):  
Cp Violation ◽  
Mass Scale ◽  
Grand Unification ◽  
Neutrino Mixing ◽  
Mixing Angles ◽  
Quantum Numbers ◽  
Fermion Masses ◽  
The Standard Model ◽  
Higgs Fields ◽  
Fundamental Mass

The fermion masses and mixing angles are fitted using only three free parameters in a nonsupersymmetric extension of the Standard Model, with new, approximately conserved chiral gauge quantum numbers broken by a set of Higgs fields. The fundamental mass scale of this anti-grand-unification model is given by the Planck mass. We also calculate neutrino mixing angles and masses, as well as CP violation from the CKM matrix. A good fit to the observed fermion masses is obtained, but our predictions of the neutrino masses are too small to lead to any observable neutrino oscillation effects claimed today, without introducing another mass scale. We also give some arguments in support of this type of model based on the observed fermion masses.

scholarly journals Radiative decays of charged leptons as constraints of unitarity polygons for active-sterile neutrino mixing and CP violation

2020 ◽  
Vol 80 (12) ◽  
Author(s):  
Zhi-zhong Xing ◽  
Di Zhang
Keyword(s):  
Cp Violation ◽  
Complex Plane ◽  
Sterile Neutrino ◽  
Radiative Decays ◽  
Neutrino Mixing ◽  
Seesaw Mechanism ◽  
Majorana Neutrinos ◽  
Alpha Beta ◽  
Charged Leptons ◽  
Pmns Matrix

AbstractWe calculate the rates of radiative $$\beta ^- \rightarrow \alpha ^- + \gamma $$ β - → α - + γ decays for $$(\alpha , \beta ) = (e, \mu )$$ ( α , β ) = ( e , μ ) , $$(e, \tau )$$ ( e , τ ) and $$(\mu , \tau )$$ ( μ , τ ) by taking the unitary gauge in the $$(3+n)$$ ( 3 + n ) active-sterile neutrino mixing scheme, and make it clear that constraints on the unitarity of the $$3\times 3$$ 3 × 3 Pontecorvo–Maki–Nakagawa–Sakata (PMNS) matrix U extracted from $$\beta ^- \rightarrow \alpha ^- + \gamma $$ β - → α - + γ decays in the minimal unitarity violation scheme differ from those obtained in the canonical seesaw mechanism with n heavy Majorana neutrinos by a factor 5/3. In such a natural seesaw case we show that the rates of $$\beta ^- \rightarrow \alpha ^- + \gamma $$ β - → α - + γ can be used to cleanly and strongly constrain the effective apex of a unitarity polygon, and compare its geometry with the geometry of its three sub-triangles formed by two vectors $$U^{}_{\alpha i} U^*_{\beta i}$$ U α i U β i ∗ and $$U^{}_{\alpha j} U^*_{\beta j}$$ U α j U β j ∗ (for $$i \ne j$$ i ≠ j ) in the complex plane. We find that the areas of such sub-triangles can be described in terms of the Jarlskog-like invariants of CP violation $${{\mathcal {J}}}^{ij}_{\alpha \beta }$$ J α β ij , and their small differences signify slight unitarity violation of the PMNS matrix U.

scholarly journals Aspects of high scale leptogenesis with low-energy leptonic CP violation

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
A. Granelli ◽  
K. Moffat ◽  
S. T. Petcov
Keyword(s):  
Cp Violation ◽  
Low Energy ◽  
Type I ◽  
Neutrino Mixing ◽  
High Scale ◽  
Boltzmann Equations ◽  
Majorana Neutrinos ◽  
Pmns Matrix ◽  
Neutrino Experiments ◽  
Majorana Phases

Abstract Using the density matrix equations (DME) for high scale leptogenesis based on the type I seesaw mechanism, in which the CP violation (CPV) is provided by the low-energy Dirac or/and Majorana phases of the neutrino mixing (PMNS) matrix, we investigate the 1-to-2 and the 2-to-3 flavour regime transitions, where the 1, 2 and 3 leptogenesis flavour regimes in the generation of the baryon asymmetry of the Universe ηB are described by the Boltzmann equations. Concentrating on the 1-to-2 flavour transition we determine the general conditions under which ηB goes through zero and changes sign in the transition. Analysing in detail the behaviour of ηB in the transition in the case of two heavy Majorana neutrinos N1,2 with hierarchical masses, M1 ≪ M2, we find, in particular, that i) the Boltzmann equations in many cases fail to describe correctly the generation of ηB in the 1, 2 and 3 flavour regimes, ii) the 2-flavour regime can persist above (below) ∼ 1012 GeV (∼ 109 GeV), iii) the flavour effects in leptogenesis persist beyond the typically considered maximal for these effects leptogenesis scale of 1012 GeV. We further determine the minimal scale M1min at which we can have successful leptogenesis when the CPV is provided only by the Dirac or Majorana phases of the PMNS matrix as well as the ranges of scales and values of the phases for having successful leptogenesis. We show, in particular, that when the CPV is due to the Dirac phase δ, there is a direct relation between the sign of sin δ and the sign of ηB in the regions of viable leptogenesis in the case of normal hierarchical light neutrino mass spectrum; for the inverted hierarchical spectrum the same result holds for M1 ≲ 1013 GeV. The considered different scenarios of leptogenesis are testable and falsifiable in low-energy neutrino experiments.

scholarly journals CP VIOLATION IN NEUTRINO MIXING MATRIX AND LEPTOGENESIS

2001 ◽  
Vol 16 (09) ◽  
pp. 603-613 ◽  
Author(s):  
YONG LIU ◽  
UTPAL SARKAR
Keyword(s):  
Cp Violation ◽  
Invariant Measures ◽  
Lepton Number ◽  
Effective Theory ◽  
Neutrino Mixing ◽  
Lepton Asymmetry ◽  
Mixing Angles ◽  
Leptonic Sector ◽  
Mixing Matrix ◽  
Lepton Number Violating

The CP violation required in leptogenesis may have different origin, but in an effective theory they are all related to the rephasing invariant CP violating measures in the mixing matrix of the leptonic sector. We point out that with our present knowledge of the mixing angles it is possible to estimate the maximum allowed value for all the rephasing invariant measures of CP violation in the leptonic sector. In the effective three-generation scenario there are three CP violating rephasing invariant measures. We show that only one rephasing invariant measure enters the lepton number conserving processes while the other two enter the lepton number violating processes. In the bimaximal mixing case, the lepton number conserving measure of CP violation vanishes while the two lepton number violating rephasing invariant measures of CP violation remain nonzero, which could contribute to the lepton asymmetry of the universe.

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