scholarly journals Three-Neutrino Mass Matrices with Two Texture Zeros

2003 ◽  
Vol 18 (20) ◽  
pp. 1355-1365 ◽  
Author(s):  
Bipin R. Desai ◽  
Alexander R. Vaucher ◽  
D. P. Roy
Keyword(s):  
Neutrino Oscillation ◽  
Neutrino Mass ◽  
Charged Lepton ◽  
Quark Mass ◽  
Atmospheric Neutrino ◽  
Neutrino Masses ◽  
Inverted Hierarchy ◽  
Mixing Angle ◽  
Mass Matrices

Out of the 15 3 × 3 neutrino mass matrices with two texture zeros, seven are compatible with the neutrino oscillation data. While two of them correspond to hierarchical neutrino masses and 1 to an inverted hierarchy, the remaining four correspond to degenerate masses. Moreover only the first three of the seven mass matrices are compatible with the maximal mixing angle of atmospheric neutrino and hence favored by data. We give compact expressions for mass matrices in terms of mass eigenvalues and study phenomenological implications for the seven cases. Similarity of the textures of the neutrino, charged-lepton mass matrices with those of quark mass matrices is also discussed.

scholarly journals Relating lepton mixing angles with lepton mass hierarchy

2016 ◽  
Vol 31 (04n05) ◽  
pp. 1650002
Author(s):  
Debasish Borah
Keyword(s):  
Neutrino Mass ◽  
Charged Lepton ◽  
Mass Matrix ◽  
Neutrino Masses ◽  
Mass Hierarchy ◽  
Mixing Angle ◽  
Mixing Angles ◽  
Mass Matrices ◽  
Model Independent ◽  
The Difference

We revisit the possibility of relating lepton mixing angles with lepton mass hierarchies in a model-independent way. Guided by the existence of such relations in the quark sector, we first consider all the mixing angles, both in charged lepton and neutrino sectors to be related to the respective mass ratios. This allows us to calculate the leptonic mixing angles observed in neutrino oscillations as functions of the lightest neutrino mass. We show that for both normal and inverted hierarchical neutrino masses, this scenario does not give rise to correct leptonic mixing angles. We then show that correct leptonic mixing angles can be generated with normal hierarchical neutrino masses if the relation between mixing angle and mass ratio is restricted to 1–2 and 1–3 mixing in both charged lepton and neutrino sectors leaving the 2–3 mixing angles as free parameters. We then restrict the lightest neutrino mass as well as the difference between 2–3 mixing angles in charged lepton and neutrino sectors from the requirement of producing correct leptonic mixing angles. We constrain the lightest neutrino mass to be around 0.002 eV and leptonic Dirac CP phase [Formula: see text] such that [Formula: see text]. We also construct the leptonic mass matrices in terms of 2–3 mixing angles and lightest neutrino mass and briefly comment on the possibility of realizing texture zeros in the neutrino mass matrix.

scholarly journals Towards unification of quark and lepton flavors in $$A_4$$ modular invariance

2021 ◽  
Vol 81 (1) ◽  
Author(s):  
Hiroshi Okada ◽  
Morimitsu Tanimoto
Keyword(s):  
Neutrino Mass ◽  
Modular Forms ◽  
Quark Mass ◽  
Mass Matrix ◽  
Neutrino Masses ◽  
Inverted Hierarchy ◽  
Mass Matrices ◽  
The Common ◽  
Charged Leptons ◽  
The One

AbstractWe study quark and lepton mass matrices in the $$A_4$$ A 4 modular symmetry towards the unification of the quark and lepton flavors. We adopt modular forms of weights 2 and 6 for quarks and charged leptons, while we use modular forms of weight 4 for the neutrino mass matrix which is generated by the Weinberg operator. We obtain the successful quark mass matrices, in which the down-type quark mass matrix is constructed by modular forms of weight 2, but the up-type quark mass matrix is constructed by modular forms of weight 6. The viable region of $$\tau $$ τ is close to $$\tau =i$$ τ = i . Lepton mass matrices also work well at nearby $$\tau =i$$ τ = i , which overlaps with the one of the quark sector, for the normal hierarchy of neutrino masses. In the common $$\tau $$ τ region for quarks and leptons, the predicted sum of neutrino masses is 87–120 meV taking account of its cosmological bound. Since both the Dirac CP phase $$\delta _{CP}^\ell $$ δ CP ℓ and $$\sin ^2\theta _{23}$$ sin 2 θ 23 are correlated with the sum of neutrino masses, improving its cosmological bound provides crucial tests for our scheme as well as the precise measurement of $$\sin ^2\theta _{23}$$ sin 2 θ 23 and $$\delta _{CP}^\ell $$ δ CP ℓ . The effective neutrino mass of the $$0\nu \beta \beta $$ 0 ν β β decay is $$\langle m_{ee}\rangle =15$$ ⟨ m ee ⟩ = 15 –31 meV. It is remarked that the modulus $$\tau $$ τ is fixed at nearby $$\tau =i$$ τ = i in the fundamental domain of SL(2, Z), which suggests the residual symmetry $$Z_2$$ Z 2 in the quark and lepton mass matrices. The inverted hierarchy of neutrino masses is excluded by the cosmological bound of the sum of neutrino masses.

scholarly journals PERTURBED INVARIANT UNDER A CYCLIC PERMUTATION WITH TRACE OF NEUTRINO MASS MATRIX REMAIN CONSTANT

2011 ◽  
Vol 26 (08) ◽  
pp. 567-574 ◽  
Author(s):  
ASAN DAMANIK
Keyword(s):  
Neutrino Mass ◽  
Mass Matrix ◽  
Cyclic Permutation ◽  
Neutrino Mass Matrix ◽  
Neutrino Masses ◽  
Inverted Hierarchy ◽  
Seesaw Mechanism ◽  
Mixing Parameters ◽  
Difference Formula ◽  
Mass Matrices

We construct a neutrino mass matrix Mν via a seesaw mechanism with perturbed invariant under a cyclic permutation by introducing a parameter δ into the diagonal elements of Mν with the assumption that trace of the perturbed Mν is equal to trace of the unperturbed Mν. We found that the perturbed neutrino mass matrices Mν can predict the mass-squared difference [Formula: see text] with the possible hierarchy of neutrino mass is normal or inverted hierarchy. By using the advantages of the mass-squared differences and mixing parameters data from neutrino oscillation experiments, we then have neutrino masses in inverted hierarchy with masses: |m1| = 0.101023 eV , |m2| = 0.101428 eV and |m3| = 0.084413 eV .

scholarly journals MODEL INDEPENDENT CONSTRAINTS OF THE AVERAGED NEUTRINO MASSES REVISITED

2013 ◽  
Vol 28 (39) ◽  
pp. 1350186
Author(s):  
TAKESHI FUKUYAMA ◽  
HIROYUKI NISHIURA
Keyword(s):  
Lower Bound ◽  
Beta Decay ◽  
Neutrino Oscillation ◽  
Neutrino Mass ◽  
Upper Bounds ◽  
Neutrino Masses ◽  
Normal Hierarchy ◽  
Inverted Hierarchy ◽  
Model Independent ◽  
Cosmological Constraint

Averaged neutrino masses defined by [Formula: see text] are reanalyzed using up-to-date observed MNS parameters and neutrino masses by the neutrino oscillation experiments together with the cosmological constraint on neutrino masses. The values of 〈mν〉ab are model-independently evaluated in terms of effective neutrino mass defined by [Formula: see text] which is observable in the single beta decay. We obtain lower bound for 〈mν〉ee in the inverted hierarchy (IH) case, 17 meV ≤〈mν〉ee and one for 〈mν〉τμ in the normal hierarchy (NH) case, 5 meV ≤〈mν〉τμ. We also obtain that all the averaged masses 〈mν〉ab have upper bounds which are at most 80 meV.

scholarly journals What if θ13 is small?

2006 ◽  
Vol 84 (6-7) ◽  
pp. 621-623
Author(s):  
C S Lam
Keyword(s):  
Mass Spectrum ◽  
Neutrino Mass ◽  
Charged Lepton ◽  
Mass Matrix ◽  
Neutrino Mass Matrix ◽  
Inverted Hierarchy ◽  
Seesaw Mechanism ◽  
Mixing Angle ◽  
Left Handed ◽  
The Right

In the basis where the charged lepton mass matrix is diagonal, the left-handed neutrino mass matrix is invariant under the permutation of the second and third generations if, and only if, the reactor angle θ13 is zero and the atmospheric mixing angle θ23 is maximal. In the presence of the seesaw mechanism, this symmetry leads to an inverted hierarchy, with m3 = 0. This inverted mass spectrum is doubly protected if the right-handed neutrinos also have a 2–3 symmetry.PACS No.: 14.60Pq

scholarly journals Deviations from tribimaximal neutrino mixing using a model with Δ(27) symmetry

2014 ◽  
Vol 29 (18) ◽  
pp. 1450095 ◽  
Author(s):  
P. F. Harrison ◽  
R. Krishnan ◽  
W. G. Scott
Keyword(s):  
Neutrino Mass ◽  
Charged Lepton ◽  
Diagonal Form ◽  
Mass Hierarchy ◽  
Neutrino Mixing ◽  
Neutrino Mass Hierarchy ◽  
Mixing Angle ◽  
Mass Matrices ◽  
Mixing Patterns ◽  
Reactor Mixing

We present a model of neutrino mixing based on the flavor group Δ(27) in order to account for the observation of a nonzero reactor mixing angle (θ13). The model provides a common flavor structure for the charged-lepton and the neutrino sectors, giving their mass matrices a "circulant-plus-diagonal" form. Mass matrices of this form readily lead to mixing patterns with realistic deviations from tribimaximal mixing, including nonzero θ13. With the parameters constrained by existing measurements, our model predicts an inverted neutrino mass hierarchy. We obtain two distinct sets of solutions in which the atmospheric mixing angle lies in the first and the second octants. The first (second) octant solution predicts the lightest neutrino mass, m3~29 meV (m3~65 meV ) and the CP phase, [Formula: see text], offering the possibility of large observable CP violating effects in future experiments.

scholarly journals Maximal CP violation in flavor neutrino masses

2016 ◽  
Vol 31 (09) ◽  
pp. 1650043 ◽  
Author(s):  
Teruyuki Kitabayashi ◽  
Masaki Yasuè
Keyword(s):  
Cp Violation ◽  
Neutrino Mass ◽  
Atmospheric Neutrino ◽  
Neutrino Masses ◽  
Neutrino Mixing ◽  
Mutual Dependence ◽  
Mass Matrices

Since flavor neutrino masses [Formula: see text] can be expressed in terms of [Formula: see text], mutual dependence among [Formula: see text] is derived by imposing some constraints on [Formula: see text]. For appropriately imposed constraints on [Formula: see text] giving rise to both maximal CP violation and the maximal atmospheric neutrino mixing, we show various specific textures of neutrino mass matrices including the texture with [Formula: see text] derived as the simplest solution to the constraint of [Formula: see text], which is required by the constraint of [Formula: see text] for [Formula: see text]. It is found that Majorana CP violation depends on the phase of [Formula: see text].

scholarly journals Nonzero |U e3| from charged lepton corrections and the atmospheric neutrino mixing angle

2013 ◽  
Vol 2013 (5) ◽  
Author(s):  
David Marzocca ◽  
S. T. Petcov ◽  
Andrea Romanino ◽  
M. C. Sevilla
Keyword(s):  
Charged Lepton ◽  
Atmospheric Neutrino ◽  
Neutrino Mixing ◽  
Mixing Angle

scholarly journals Investigating the Hybrid Textures of Neutrino Mass Matrix for Near Maximal Atmospheric Neutrino Mixing

2018 ◽  
Vol 2018 ◽  
pp. 1-16
Author(s):  
Madan Singh
Keyword(s):  
Neutrino Mass ◽  
Mass Matrix ◽  
Atmospheric Neutrino ◽  
Zero Element ◽  
Majorana Neutrino ◽  
Neutrino Mixing ◽  
Mixing Angle ◽  
The Comparative Study ◽  
Reactor Mixing ◽  
Majorana Neutrino Mass

We have studied that the implication of a large value of the effective Majorana neutrino mass in case of neutrino mass matrices has either two equal elements and one zero element (popularly known as hybrid texture) or two equal cofactors and one zero minor (popularly known as inverse hybrid texture) in the flavor basis. In each of these cases, four out of sixty phenomenologically possible patterns predict near maximal atmospheric neutrino mixing angle in the limit of large effective Majorana neutrino mass. This feature remains irrespective of the experimental data on solar and reactor mixing angles. In addition, we have also performed the comparative study of all the viable cases of hybrid and inverse hybrid textures at 3σ CL.

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