Phenomenological aspects of possible vacua of a neutrino flavor model

We discuss a supersymmetric model with discrete flavor symmetry A_4×Z_3. The additional scalar fields which contribute masses of leptons in the Yukawa terms are introduced in this model. We analyze their scalar potential and find that they have various vacuum structures. We show the relations among 24 different vacua and classify them into two types. We derive expressions of the lepton mixing angles, Dirac CP violating phase and Majorana phases for the two types. The model parameters which are allowed by the experimental data of the lepton mixing angles are different for each type. We also study the constraints on the model parameters which are related to Majorana phases. The different allowed regions of the model parameters for the two types are shown numerically for a given region of two combinations of the CP violating phases.     

Neutrino mass ordering and μ-τ reflection symmetry breaking

If the neutrino mass spectrum turns out to be m_3 m_1 m_2, it may be relabeled as m_1 m_2 m_3 such that all the masses of fundamental fermions with the same electrical charges are in order. In this case the columns of the 3×3 lepton flavor mixing matrix U should be reordered accordingly, and the resulting pattern U may involve one or two large mixing angles in the standard parametrization or its variations. Since the Majorana neutrino mass matrix remains unchanged in such a mass relabeling, a possible μ-τ reflection symmetry is respected in this connection and its breaking effects are model-independently constrained at the 3σ level by using current experimental data.     

Update on two-zero textures of the Majorana neutrino mass matrix in light of recent T2K,Super-Kamiokande and NOνA results

The latest results from atmospheric and accelerator neutrino experiments indicate that the normal neutrino mass ordering m_1 m_2 m_3, a maximal leptonic CP-violating phase δ = 270° and the second octant of neutrino mixing angle θ_23 45° are favored. In light of new experimental results, we update previous phenomenological studies on two-zero textures of the Majorana neutrino mass matrix M-_ν, in the flavor basis where the charged-lepton mass matrix M_l is diagonal. When the 1σ ranges of neutrino mixing parameters are taken into account, only four(i.e., A_(1,2)and B_(2,4)) among seven two-zero patterns of Mνshow the aforementioned features of neutrino mass spectrum, mixing angle θ_23and CP-violating phase δ, and thus are compatible with the latest neutrino oscillation data. The correlative relations among neutrino masses and mixing parameters have been derived analytically for these four patterns, and the allowed regions of neutrino mixing angles and the CP-violating phase are also given. Possible realizations of four viable two-zero textures via non-Abelian discrete flavor symmetries are discussed.     

Calculation of Decay μ → eγ in R ξ Gauge in a Model of Electroweak-Scale Right-Handed Neutrinos

The lepton flavor violating process μ - eγ has been previously studied in a model of electroweak-scale right-handed neutrinos. In that work the decay amplitude was computed in unitarity gauge, augmented by some technical considerations that correct the leading term thus obtained. This complication arises because the mixing matrices appearing in the weak charged currents are not unitary in the model. In this paper, we recalculate the amplitude in Re gauge. The cancellation of the ξ dependence in the final result serves as a useful check to both the obtained amplitude and the technical points made in the previous work.     

The lepton flavor violating signal of the extra gauge boson Z′in photon-photon collision at the ILC

The hitherto unconstrained lepton flavor mixings,induced by the new gauge boson Z ,which are the prediction of many new physics models,such as topcolor-assisted technicolor (TC2) models and flavor-universal TC2 models,may lead to the lepton flavor violating productions of τμˉ,τeˉ and μeˉ in photon-photon collision at the proposed International Linear Collider (ILC).Through a comparative analysis of these processes,we find that the better channel to probe the new physics models is the production of τμˉ or τeˉ which occurs at a much higher rate than μeˉ production due to the large mixing angle and the large flavor changing coupling,and may reach the detectable level of the ILC for a large part of the parameter space.Since the rates predicted by the Standard Model are far below the detectable level,these processes may serve as a sensitive probe for such new physics models.     

T2K indication of relatively large θ13 and a natural perturbation to the democratic neutrino mixing pattern

The T2K Collaboration has recently reported a remarkable indication of the ν→ν oscillation which is consistent with a relatively large value of θ₁₃ in the three-flavor neutrino mixing scheme. We show that it is possible to account for such a result of θ₁₃ by introducing a natural perturbation to the democratic neutrino mixing pattern, without or with CP violation. A testable correlation between θ₁₃ and θ₂₃ is predicted in this ansatz. We also discuss the Wolfenstein-like parametrization of neutrino mixing, and comment on other possibilities of generating sufficiently large θ₁₃ at the electroweak scale.     

Broken S_(3L)×S_(3R) flavor symmetry and leptonic CP violation

In the framework of the canonical seesaw model,we present a simple but viable scenario to explicitly break an S_(3L)×S_(3R) flavor symmetry in the leptonic sector.It turns out that the leptonic flavor mixing matrix is completely determined by the mass ratios of the charged leptons(i.e.,me/mμand mμ/mτ) and those of light neutrinos(i.e.,m_1/m_2 and m_2/m_3).The latest global-fit results of the three neutrino mixing angles {θ_(12),θ_(13),θ_(23)}and two neutrino mass-squared differences {?m_(21)~2,?m_(31)~2} at the 3σ level are used to constrain the parameter space of {m_1/m_2,m_2/m_3}.The predictions for the mass spectrum and flavor mixing are highlighted:(1) the neutrino mass spectrum shows a hierarchical pattern and a normal ordering,e.g.,m_1≈2.2meV,m_2≈8.8 meV and m_3≈52.7 meV;(2) only the first octant of θ_(23) is allowed,namely,41.8? θ_(23) 43.3?;(3) the Dirac C P-violating phase δ≈-22?deviates significantly from the maximal value-90?.All these predictions are ready to be tested in ongoing and forthcoming neutrino oscillation experiments.Moreover,we demonstrate that the cosmological matter-antimatter asymmetry can be explained via resonant leptogenesis,including the individual lepton-flavor effects.In our scenario,leptonic C P violation at low-and high-energy scales is closely connected.     

Phenomenology of Friedberg-Lee Texture in Left-Right Symmetric Model

We consider that the Higgs triplet Yukawa coupling takes the Friedberg-Lee texture, and the Higgs doublet Yukawa coupling simply identifies with the diagonal Yutawa coupling of charged lepton in the context of left-right symmetric model. In this scenario, the phenomenology, including effective neutrino masses, mixings, and thermal flavor-dependent leptogenesis and lepton flavor violation decays are studied. We investigate the combined constrain of the parameters in this scenario and test its consistency with present data.     

Far-field divergence of a vectorial plane wave diffracted by a circular aperture from the vectorial structure

Based on the vectorial structure of an electromagnetic wave, the analytical and concise expressions for the TE and TM terms of a vectorial plane wave diffracted by a circular aperture are derived in the far-field. The expressions of the energy flux distributions of the TE term, the TM term and the diffracted plane wave are also presented. The ratios of the power of the TE and TM terms to that of the diffracted plane wave are examined in the far-field. In addition, the far-field divergence angles of the TE term, the TM term and the diffracted plane wave, which are related to the energy flux distribution, are investigated. The different energy flux distributions of the TE and TM terms result in the discrepancy of their divergence angles. The influences of the linearly polarized angle and the radius of the circular aperture on the far-field divergence angles of the TE term, the TM term and the diffracted plane wave are discussed in detail. This research may promote the recognition of the optical propagation through a circular aperture.vspace1mm     

Measurements of D~0-~0 mixing and searches for CP violation:HFAG combination of all data

We present world average values for D~0-~0 mixing parameters x and y,CP violation parameters |q/P|and Arg(q/p),and strong phase differencesδandδ_(Kππ)These values are calculated by the Heavy Flavor Averaging Group(HFAG)by performing a global fit to relevant experimental measurements.The results for x and y differ significantly from zero and are inconsistent with no mixing at the level of 6.7a.The results for |q/P|and Arg(q/p)are consistent with no CP violation.The strong phase differenceδis less than 45°at 95%C.L.     

Deviations of the lepton mapping matrix from the Harrison-Perkins- Scott form

We propose a simple set of hypotheses governing the deviations of the leptonic mapping matrix from the Harrison-Perkins-Scott （HPS） form. These deviations are supposed to arise entirely from a perturbation of the mass matrix in the charged lepton sector. The perturbing matrix is assumed to be purely imaginary （thus maximally T-violating） and to have a strength in energy scale no greater （but perhaps smaller） than the muon mass. As we shall show, it then follows that the absolute value of the mapping matrix elements pertaining to the tau lepton deviate by no more than O（（mμ/mτ）^2） ≈ 3.5 ×10^-3 from their HPS values. Assuming that （mμ/mτ）^2 can be neglected, we derive two simple constraints on the four parameters θ12,θ23, θ31, and δ of the mapping matrix. These constraints are independent of the details of the imaginary T-violating perturbation of the charged lepton mass matrix. We also show that the e and μ parts of the mapping matrix have a definite form governed by two parameters α and β; any deviation of order mμ/mτ can be accommodated by adjusting these two parameters.     

Control of chaos in Frenkel–Kontorova model using reinforcement learning

It is shown that we can control spatiotemporal chaos in the Frenkel–Kontorova(FK) model by a model-free control method based on reinforcement learning. The method uses Q-learning to find optimal control strategies based on the reward feedback from the environment that maximizes its performance. The optimal control strategies are recorded in a Q-table and then employed to implement controllers. The advantage of the method is that it does not require an explicit knowledge of the system, target states, and unstable periodic orbits. All that we need is the parameters that we are trying to control and an unknown simulation model that represents the interactive environment. To control the FK model, we employ the perturbation policy on two different kinds of parameters, i.e., the pendulum lengths and the phase angles. We show that both of the two perturbation techniques, i.e., changing the lengths and changing their phase angles, can suppress chaos in the system and make it create the periodic patterns. The form of patterns depends on the initial values of the angular displacements and velocities. In particular, we show that the pinning control strategy, which only changes a small number of lengths or phase angles, can be put into effect.     

Implications of the RK and R_(K*) anomalies

We discuss the implications of the recently reported R_K and R_(K*) anomalies, the lepton flavor nonuniversality in the B → Kl~+l~-and B → K~*l~+~l- decay channels. Using two sets of hadronic inputs of form factors, we perform a fit of new physics to the R_K and R_(K*) data, and significant new physics contributions are found. We suggest the study of lepton flavor universality in a number of related rare B,Bs,Bc and Λb decay channels, and in particular we give predictions for the μ-to-e ratios of decay widths with different polarizations of the final state particles, and of the b → dl~+l~- processes, which are presumably more sensitive to the structure of the underlying new physics. With the new physics contributions embedded in the Wilson coefficients, we present theoretical predictions for lepton flavor non-universality in these processes.     

Correlation of normal neutrino mass ordering with upper octant of θ_(23) and third quadrant of δ via RGE-induced μ-τ symmetry breaking

The recent global analysis of three-flavor neutrino oscillation data indicates that the normal neutrino mass ordering is favored over the inverted one at the 3σ level, and the best-fit values of the largest neutrino mixing angle θ_(23) and the Dirac CP-violating phase δ are located in the higher octant and third quadrant, respectively. We show that all these important issues can be naturally explained by the μ-τ reflection symmetry breaking of massive neutrinos from a superhigh energy scale down to the electroweak scale owing to the one-loop renormalization-group equations(RGEs) in the minimal supersymmetric standard model(MSSM). The complete parameter space is explored for the first time in both the Majorana and Dirac cases, by allowing the smallest neutrino mass m1 and the MSSM parameter tanβ to vary within their reasonable regions.     

Terrestrial matter effects on reactor antineutrino oscillations at JUNO or RENO-50: how small is small?

We have carefully examined, in both analytical and numerical ways, how small the terrestrial matter effects can be in a given medium-baseline reactor antineutrino oscillation experiment like JUNO or RENO-50. Taking the forthcoming JUNO experiment as an example, we show that the inclusion of terrestrial matter effects may reduce the sensitivity of the neutrino mass ordering measurement by ?χ_(MO)~2■0.6, and a neglect of such effects may shift the best-fit values of the flavor mixing angle θ_(12) and the neutrino mass-squared difference ?21 by about 1σ to 2σ in the future data analysis. In addition, a preliminary estimate indicates that a 2σ sensitivity of establishing the terrestrial matter effects can be achieved for about 10 years of data taking at JUNO with the help of a suitable near detector implementation.     

The Majorana neutrino mass matrix indicated by the current data

The Majorana neutrino mass matrix combines information from the neutrino masses and the leptonic mixing in the flavor basis. Its invariance under some transformation matrices indicates the existence of certain residual symmetry. We offer an intuitive display of the structure of the Majorana neutrino mass matrix, using the whole set of the oscillation data. The structure is revealed depending on the lightest neutrino mass. We find that there are three regions with distinct characteristics of structure. A group effect and the-τ exchange symmetry are observed. Six types of texture non-zeros are shown. Implications for flavor models are discussed.     

An Underlying Symmetry Determines all Elements of CKM and PMNS up to a Universal Constant?

Observing the CKM matrix elements written in different parametrization schemes,one can notice obvious relations among the sine-values of the CP phases in those schemes.Using the relations,we establish a few parametrizationindependent equations,by which the matrix elements of the CKM matrix can be completely fixed up to a universal parameter.If it is true,we expect that there should exist a hidden symmetry in the nature,which determines the relations.Moreover,it requires a universal parameter,naturally it would be the famous Jarlskog invariant,which is also parametrization independent.Thus the four parameters(three mixing angles and one CP phase) of the CKM matrix are not free,but determined by the symmetry and the universal parameter.As we generalize the rules to the PMNS matrix for neutrino mixing,the CP phase of the lepton sector is predicted to be within a range of 0 ~ 59° centered at39°(in the P_a parametrization) which will be tested in the future experiments.