scholarly journals 𝜃23 = π/4 and δ = −π/2 in neutrino mixing, which convention?

2019 ◽  
Vol 34 (35) ◽  
pp. 1950235
Author(s):  
Junxing Pan ◽  
Jin Sun ◽  
Xiao-Gang He
Keyword(s):  
Phase Change ◽  
The Other ◽  
Particle Data Group ◽  
Neutrino Mixing ◽  
Mixing Angle ◽  
Mixing Angles ◽  
Mixing Matrix ◽  
Physical Effects ◽  
Data Group

Considerable information has been obtained about neutrino mixing matrix. Present data show that in the particle data group (PDG) parametrization, the 2–3 mixing angle and the CP violating phase are consistent with [Formula: see text] and [Formula: see text], respectively. A lot of efforts have been devoted to constructing models in realizing a mixing matrix with these values. However, the particular angles and phase are parametrization convention dependent. The meaning about the specific values for mixing angle and phase needs to be clarified. Using the well-known nine independent ways of parametrizing the mixing matrix, we show in detail how the mixing angles and phase change with conventions even with the 2–3 mixing angle to be [Formula: see text] and the CP violating phase to be [Formula: see text]. The original Kobayashi–Maskawa and an additional one belong to such a category. The other 6 parametrizations have mixing angles and phase very different values from those in the PDG parametrization although the physical effects are the same. Therefore one should give the specific parametrization convention when making statements about values for mixing angles and phase.

scholarly journals A systematic analysis of perturbations for hexagonal mixing matrix

2019 ◽  
Vol 34 (01) ◽  
pp. 1950005
Author(s):  
Sumit K. Garg
Keyword(s):  
Neutrino Mixing ◽  
Inverted Hierarchy ◽  
Systematic Analysis ◽  
Mixing Angle ◽  
Mixing Angles ◽  
Angle Data ◽  
Mixing Matrix ◽  
Global Fit ◽  
Pmns Matrix ◽  
The Impact

We present a systematic analysis of perturbative Hexagonal (HG) mixing for describing recent global fit neutrino mixing data with normal and inverted hierarchy. The corrections to unperturbed mixing are parametrized in terms of small orthogonal rotations [Formula: see text] with modified PMNS matrix of the forms [Formula: see text]. Here, [Formula: see text] is rotation in [Formula: see text] sector and [Formula: see text] is unperturbed Hexagonal mixing matrix. The detailed numerical investigation of all possible cases is performed with scanning of parameter space using [Formula: see text] approach. We found that the perturbative schemes governed by single rotation are unable to fit the mixing angle data even at [Formula: see text] level. The mixing schemes which involve two rotation matrices only [Formula: see text] are successful in fitting all neutrino mixing angles within [Formula: see text] range for normal hierarchy (NH). However for inverted hierarchy (IH), only [Formula: see text] is most preferable as it can fit all mixing angles at [Formula: see text] level. The remaining perturbative cases are either excluded at [Formula: see text] level or successful in producing mixing angles only at [Formula: see text] level. To study the impact of phase parameter, we also looked into CP violating effects for single rotation case. The predicted value of [Formula: see text] lies in the range [Formula: see text] for [Formula: see text] and [Formula: see text] case with normal (inverted) hierarchy.

scholarly journals Perturbation to TBM mixing and its phenomenological implications

2016 ◽  
Vol 31 (38) ◽  
pp. 1650207 ◽  
Author(s):  
M. Sruthilaya ◽  
Srinu Gollu
Keyword(s):  
Neutrino Mass ◽  
Mass Formula ◽  
Electron Neutrino ◽  
Leading Order ◽  
Mixing Angle ◽  
Mixing Angles ◽  
Neutrino Sector ◽  
Upper Limit ◽  
Mixing Matrix ◽  
Reactor Mixing

To accommodate the recently observed nonzero reactor mixing angle [Formula: see text], we consider the lepton mixing matrix as tri-bimaximal mixing (TBM) form in the leading order along with a perturbation in neutrino sector. The perturbation is taken to be a rotation in 23 plane followed by a rotation in 13 plane, i.e. [Formula: see text]. We obtain the allowed values of the parameters [Formula: see text], [Formula: see text] and [Formula: see text], which can accommodate all the observed mixing angles consistently and calculate the phenomenological observables such as the Dirac CP violating phase [Formula: see text], Jarlskog invariant [Formula: see text], effective Majorana mass [Formula: see text] and [Formula: see text], the electron neutrino mass. We find that [Formula: see text] can take any values between [Formula: see text] and [Formula: see text] and [Formula: see text] always comes below its experimental upper limit.

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.

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 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.

scholarly journals Standard versus non-standard CP phases in neutrino oscillation in matter with non-unitarity

2020 ◽  
Vol 2020 (6) ◽  
Author(s):  
Ivan Martinez-Soler ◽  
Hisakazu Minakata
Keyword(s):  
Neutral Current ◽  
Phase Correlation ◽  
Charged Current ◽  
Unitary Matrix ◽  
Particle Data Group ◽  
Unitary Evolution ◽  
First Order ◽  
Flavor Mixing ◽  
Mixing Matrix ◽  
Data Group

Abstract We formulate a perturbative framework for the flavor transformation of the standard active three neutrinos but with a non-unitary flavor mixing matrix, a system which may be relevant for the leptonic unitarity test. We use the $\alpha$ parametrization of the non-unitary matrix and take its elements $\alpha_{\beta \gamma}$ ($\beta,\gamma = e,\mu,\tau$) and the ratio $\epsilon \simeq \Delta m^2_{21} / \Delta m^2_{31}$ as the small expansion parameters. Two qualitatively new features that hold in all the oscillation channels are uncovered in the probability formula obtained to first order in the expansion: (1) The phases of the complex $\alpha$ elements always come into the observable in the particular combination with the $\nu$SM CP phase $\delta$ in the form $[e^{- i \delta } \bar{\alpha}_{\mu e}, ~e^{ - i \delta} \bar{\alpha}_{\tau e}, ~\bar{\alpha}_{\tau \mu}]$ under the Particle Data Group convention of a unitary $\nu$SM mixing matrix. (2) The diagonal $\alpha$ parameters appear in particular combinations $\left( a/b - 1 \right) \alpha_{ee} + \alpha_{\mu \mu}$ and $\alpha_{\mu \mu} - \alpha_{\tau \tau}$, where $a$ and $b$ denote, respectively, the matter potential due to charged current and neutral current reactions. This property holds only in the unitary evolution part of the probability, and there is no such feature in the genuine non-unitary part, while the $\delta$–$\alpha$ parameter phase correlation exists for both. The reason for such remarkable stability of the phase correlation is discussed.

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.

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 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 CP, T AND CPT VIOLATIONS IN THE $K^0-\overline{K^0}$ SYSTEM: PRESENT STATUS

2003 ◽  
Vol 18 (09) ◽  
pp. 1551-1571 ◽  
Author(s):  
YOSHIHIRO TAKEUCHI ◽  
S. Y. TSAI
Keyword(s):  
Present Status ◽  
The Other ◽  
Time Dependent ◽  
Numerical Analyses ◽  
Particle Data Group ◽  
Cpt Symmetry ◽  
Mixing Parameters ◽  
Data Group ◽  
Na48 Collaboration

The possible violation of CP, T and CPT symmetries in the [Formula: see text] system is studied in a way as phenomenological and comprehensive as possible. For this purpose, we first introduce parameters which represent violation of these symmetries in mixing parameters and decay amplitudes in a convenient and well-defined way and, treating these parameters as small, derive formulas which relate them to the experimentally measured quantities. We then perform numerical analyses to derive constraints to these symmetry-violating parameters, with the latest data reported by KTeV Collaboration, NA48 Collaboration and CPLEAR Collaboration, along with those compiled by Particle Data Group, used as inputs. The result obtained by CPLEAR Collaboration from an unconstrained fit to a time-dependent leptonic asymmetry, aided by the Bell–Steinberger relation, enables us to determine or constrain most of the parameters separately. It is shown among the other things that (1) CP and T symmetries are violated definitively at least at the level of 10-4in 2π decays, (2) CP and T symmetries are violated at least at the level of 10-3in the [Formula: see text] mixing, and (3) CPT symmetry is at present tested to the level of 10-5at the utmost.

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