In this work, a flavour theory of a neutrino mass model based on <math><msub><mrow><mi>A</mi></mrow><mrow><mn>4</mn></mrow></msub></math> symmetry is considered to explain the phenomenology of neutrino mixing. The spontaneous symmetry breaking of <math><msub><mrow><mi>A</mi></mrow><mrow><mn>4</mn></mrow></msub></math> symmetry in this model leads to tribimaximal mixing in the neutrino sector at a leading order. We consider the effect of <math><msub><mrow><mi>Z</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>×</mo><msub><mrow><mi>Z</mi></mrow><mrow><mn>2</mn></mrow></msub></math> invariant perturbations in neutrino sector and find the allowed region of correction terms in the perturbation matrix that is consistent with 3σ ranges of the experimental values of the mixing angles. We study the entanglement of this formalism on the other phenomenological observables, such as <math><msub><mrow><mi>δ</mi></mrow><mrow><mi>C</mi><mi>P</mi></mrow></msub></math> phase, the neutrino oscillation probability <math><mi>P</mi><mo>(</mo><msub><mrow><mi>ν</mi></mrow><mrow><mi>μ</mi></mrow></msub><mo>→</mo><msub><mrow><mi>ν</mi></mrow><mrow><mi>e</mi></mrow></msub><mo>)</mo></math>, the effective Majorana mass <math><mo>|</mo><msub><mrow><mi>m</mi></mrow><mrow><mi>e</mi><mi>e</mi></mrow></msub><mo>|</mo></math> and <math><mo>|</mo><msubsup><mrow><mi>m</mi></mrow><mrow><mi>ν</mi><mi>e</mi></mrow><mrow><mi>e</mi><mi>f</mi><mi>f</mi></mrow></msubsup><mo>|</mo></math>. A <math><msub><mrow><mi>Z</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>×</mo><msub><mrow><mi>Z</mi></mrow><mrow><mn>2</mn></mrow></msub></math> invariant perturbations in this model is introduced in the neutrino sector which leads to testable predictions of <math><msub><mrow><mi>θ</mi></mrow><mrow><mn>13</mn></mrow></msub></math> and CP violation. By changing the magnitudes of perturbations in neutrino sector, one can generate viable values of <math><msub><mrow><mi>δ</mi></mrow><mrow><mi>C</mi><mi>P</mi></mrow></msub></math> and neutrino oscillation parameters. Next we investigate the feasibility of charged lepton flavour violation in type-I seesaw models with leptonic flavour symmetries at high energy that leads to tribimaximal neutrino mixing. We consider an effective theory with an <math><msub><mrow><mi>A</mi></mrow><mrow><mn>4</mn></mrow></msub><mo>×</mo><msub><mrow><mi>Z</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>×</mo><msub><mrow><mi>Z</mi></mrow><mrow><mn>2</mn></mrow></msub></math> symmetry, which after spontaneous symmetry breaking at high scale which is much higher than the electroweak scale leads to charged lepton flavour violation processes once the heavy Majorana neutrino mass degeneracy is lifted either by renormalisation group effects or by a soft breaking of the <math><msub><mrow><mi>A</mi></mrow><mrow><mn>4</mn></mrow></msub></math> symmetry. In this context the implications for charged lepton flavour violation processes like <math><mi>μ</mi><mo>→</mo><mi>e</mi><mi>γ</mi></math>, <math><mi>τ</mi><mo>→</mo><mi>e</mi><mi>γ</mi></math>, <math><mi>τ</mi><mo>→</mo><mi>μ</mi><mi>γ</mi></math> are discussed.

India

Gayatri Ghosh

Non-zero And Phase With Flavor Symmetry and Deviations to Tri-bi-maximal Mixing via × Invariant Perturbations in the Neutrino Sector

Leptonic CP violating phase <math id="M5"><msub><mrow><mi>δ</mi></mrow><mrow><mtext>CP</mtext></mrow></msub></math> in the light neutrino sector and leptogenesis via present matter-antimatter asymmetry of the Universe entails each other. Probing CP violation in light neutrino oscillation is one of the challenging tasks today. The reactor mixing angle<math id="M6"><msub><mrow><mi>θ</mi></mrow><mrow><mn>13</mn></mrow></msub></math>measured in reactor experiments, LBL, and DUNE with high precision in neutrino experiments indicates towards the vast dimensions of scope to detect <math id="M7"><msub><mrow><mi>δ</mi></mrow><mrow><mtext>CP</mtext></mrow></msub></math>. The correlation between leptonic Dirac CPV phase <math id="M8"><msub><mrow><mi>δ</mi></mrow><mrow><mtext>CP</mtext></mrow></msub></math>, reactor mixing angle <math id="M9"><msub><mrow><mi>θ</mi></mrow><mrow><mn>13</mn></mrow></msub></math>, lightest neutrino mass <math id="M10"><msub><mrow><mi>m</mi></mrow><mrow><mn>1</mn></mrow></msub></math>, and matter-antimatter asymmetry of the Universe within the framework of <math id="M11"><mi>μ</mi><mo>−</mo><mi>τ</mi></math> symmetry breaking assuming the type I seesaw dominance is extensively studied here. Here, a SO(10) GUT model with flavor <math id="M12"><mi>μ</mi><mo>−</mo><mi>τ</mi></math> symmetry is considered. In this work, the idea is to link baryogenesis through leptogenesis and the hint of CP violation in the neutrino oscillation data to a breaking of the mu-tau symmetry. Small tiny breaking of the<math id="M13"><mi>μ</mi><mo>−</mo><mi>τ</mi></math> symmetry allows a large Dirac CP violating phase in neutrino oscillation which in turn is characterized by awareness of measured value of <math id="M14"><msub><mrow><mi>θ</mi></mrow><mrow><mn>13</mn></mrow></msub></math> and to provide a hint towards a better understanding of the experimentally observed near-maximal value of<math id="M15"><msub><mrow><mi>ν</mi></mrow><mrow><mi>μ</mi></mrow></msub><mo>−</mo><msub><mrow><mi>ν</mi></mrow><mrow><mi>τ</mi></mrow></msub></math>mixing angle<math id="M16"><msub><mrow><mi>θ</mi></mrow><mrow><mn>23</mn></mrow></msub><mo>≃</mo><mfenced><mrow><mi>π</mi><mo>/</mo><mn>4</mn></mrow></mfenced></math>. Precise breaking of the <math id="M17"><mi>μ</mi><mo>−</mo><mi>τ</mi></math> symmetry is achieved by adding a 120-plet Higgs to the<math id="M18"><mn>10</mn><mo>+</mo><mn>1</mn><mover><mn>2</mn><mo>¯</mo></mover><mn>6</mn></math>-dimensional representation of Higgs. The estimated three-dimensional density parameter space of the lightest neutrino mass <math id="M19"><msub><mrow><mi>m</mi></mrow><mrow><mn>1</mn></mrow></msub></math>, <math id="M20"><msub><mrow><mi>δ</mi></mrow><mrow><mtext>CP</mtext></mrow></msub></math>, and reactor mixing angle <math id="M21"><msub><mrow><mi>θ</mi></mrow><mrow><mn>13</mn></mrow></msub></math> is constrained here for the requirement of producing the observed value of baryon asymmetry of the Universe through the mechanism of leptogenesis. Carrying out numerical analysis, the allowed parameter space of <math id="M22"><msub><mrow><mi>m</mi></mrow><mrow><mn>1</mn></mrow></msub></math>, <math id="M23"><msub><mrow><mi>δ</mi></mrow><mrow><mtext>CP</mtext></mrow></msub></math>, and <math id="M24"><msub><mrow><mi>θ</mi></mrow><mrow><mn>13</mn></mrow></msub></math> is found out which can produce the observed baryon to photon density ratio of the Universe.

Significance of Broken Symmetry in Correlating , , Lightest Neutrino Mass, and Neutrinoless Double Beta Decay

Neutrino physics is a mature branch of science with all the three neutrino mixing angles and two mass squared differences determined with high precision. In spite of several experimental verifications of neutrino oscillations and precise measurements of two mass squared differences and the three mixing angles, the unitarity of the leptonic mixing matrix is not yet established, leaving room for the presence of small nonunitarity effects. Deriving the bounds on these nonunitarity parameters from existing experimental constraints, on cLFV decays such as <math id="M1"><mi>μ</mi><mo>→</mo><mi>e</mi><mi>γ</mi></math>, <math id="M2"><mi>μ</mi><mo>→</mo><mi>τ</mi><mi>γ</mi></math>, and <math id="M3"><mi>τ</mi><mo>→</mo><mi>e</mi><mi>γ</mi></math>, we study their effects on the generation of baryon asymmetry through leptogenesis and neutrino oscillation probabilities. We consider a model where see-saw is extended by an additional singlet <math id="M4"><mrow><mi>S</mi></mrow></math> which is very light but can give rise to nonunitarity effects without affecting the form on see-saw formula. We do a parameter scan of a minimal see-saw model in a type I see-saw framework satisfying the Planck data on baryon to photon ratio of the Universe, which lies in the interval <math id="M5"><mn>5.8</mn><mo>×</mo><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mo>-</mo><mn>10</mn></mrow></msup><mo>&lt;</mo><msub><mrow><mi>Y</mi></mrow><mrow><mi>B</mi></mrow></msub><mo>&lt;</mo><mn>6.6</mn><mo>×</mo><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mo>-</mo><mn>10</mn></mrow></msup><mo>(</mo><mi>B</mi><mi>B</mi><mi>N</mi><mo>)</mo></math>. We predict values of lightest neutrino mass and Dirac and Majorana CP-violating phases <math id="M6"><mrow><msub><mrow><mi>δ</mi></mrow><mrow><mi>C</mi><mi>P</mi></mrow></msub></mrow></math>, <math id="M7"><mrow><mi>α</mi></mrow></math>, and <math id="M8"><mrow><mi>β</mi></mrow></math>, for normal hierarchy and inverted hierarchy for one-flavor leptogenesis. It is worth mentioning that all these four quantities are unknown yet, and future experiments will be measuring them.

Kalpana Bora

Effects of Leptonic Nonunitarity on Lepton Flavor Violation, Neutrino Oscillation, Leptogenesis, and Lightest Neutrino Mass

In a recent work by us, we have studied how CP violation discovery potential can be improved at long baseline neutrino experiments (LBNE/DUNE), by combining with its ND (near detector) and reactor experiments. In this work, we discuss how this study can be further analysed to resolve entanglement of the quadrant of leptonic CPV phase and octant of atmospheric mixing angle <math id="M2"><mrow><msub><mrow><mi>θ</mi></mrow><mrow><mn>23</mn></mrow></msub></mrow></math>, at LBNEs. The study is done for both NH (normal hierarchy) and IH (inverted hierarchy), HO (higher octant), and LO (lower octant). We show how baryogenesis can enhance the effect of resolving this entanglement and how possible values of the leptonic CP violating phase <math id="M3"><mrow><msub><mrow><mi>δ</mi></mrow><mrow><mtext>CP</mtext></mrow></msub></mrow></math> can be predicted in this context. With respect to the latest global fit data of neutrino mixing angles, we predict the values of <math id="M4"><mrow><msub><mrow><mi>δ</mi></mrow><mrow><mtext>CP</mtext></mrow></msub></mrow></math> for different cases. In this context we present favoured values of <math id="M5"><mrow><msub><mrow><mi>δ</mi></mrow><mrow><mtext>CP</mtext></mrow></msub></mrow></math> (<math id="M6"><mrow><msub><mrow><mi>δ</mi></mrow><mrow><mtext>CP</mtext></mrow></msub></mrow></math> range at ≥2σ) constrained by the latest updated BAU range and also confront our predictions of <math id="M7"><mrow><msub><mrow><mi>δ</mi></mrow><mrow><mtext>CP</mtext></mrow></msub></mrow></math> with an up-to-date global analysis of neutrino oscillation data. We find that some region of the favoured <math id="M8"><mrow><msub><mrow><mi>δ</mi></mrow><mrow><mtext>CP</mtext></mrow></msub></mrow></math> parameter space lies within the best fit values around <math id="M9"><msub><mrow><mi>δ</mi></mrow><mrow><mtext>CP</mtext></mrow></msub><mo>≃</mo><mn>1.3</mn><mi>π</mi><mtext>–</mtext><mn>1.4</mn><mi>π</mi></math>. A detailed analytic and numerical study of baryogenesis through leptogenesis is performed in this framework within the nonsupersymmetric SO<math id="M10"><mo>(</mo><mn>10</mn><mo>)</mo></math> models.

Debajyoti Dutta

Octant Degeneracy and Quadrant of Leptonic CPV Phase at Long Baseline Experiments and Baryogenesis

Charged Lepton Flavor Violation (cLFV) processes like μ→eγ are rare decay processes that are another signature of physics beyond standard model. These processes have been studied in various models that could explain neutrino oscillations and mixings. In this work, we present bounds on the cLFV decay μ→eγ in a μ – τ symmetric SUSY SO(10) theory, using the type I seesaw mechanism. The updated constraints on BR( μ→eγ ) from the MEG experiment, the recently measured value of Higgs mass at LHC, and the value of θ13 from reactor data have been used. We present our results in mSUGRA, NUHM, NUGM, and NUSM models, and the sensitivity to test these theories at the next run of LHC is also discussed.