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.     

Weighing neutrinos in dynamical dark energy models

正The discovery of neutrino oscillation indicates that neutrinos have masses and each flavor state is actually a superposition of three mass states with masses m_1,m_2,and m_3.However,the neutrino oscillation experiments are not able to measure the absolute masses of neutrinos,but can only measure the squared mass differences between the neutrino mass eigenstates—The solar and reactor experiments gave Δm~2_(21)? 7.5×10~(-5), and the atmospheric and accelerator beam experiments gave|?m~2_(31)|?2.5×10~(-3),which indicates that there are two possible mass orders,i.e.,the normal hierarchy (NH) with m_1m_2?m_3 and the inverted hierarchy(IH) with m_3 ? m_1 m_2.     

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.     

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.     

Neutrino masses,leptonic flavor mixing,and muon(g−2)in the seesaw model with the U(1)Lμ-Lrgauge symmetry

The latest measurements of the anomalous muon magnetic moment a_μ≡(g_μ-2)/2show a 4:2σdiscrepancy between the theoretical prediction of the Standard Model and the experimental observations.To account for such a discrepancy,we consider a possible extension of the type-(I+II)seesaw model for neutrino mass generation with a gauged L_μ-L_rsymmetry.By explicitly constructing an economical model with only one extra scalar singlet,we demonstrate that the gauge symmetry U(1)L_μ-L_rand its spontaneous breaking are crucial not only for explaining the muon result but also for generating the neutrino masses and leptonic flavor mixing.Various phenomenological implications and experimental constraints on the model parameters are also discussed.     

Implications of fermionic dark matter on recent neutrino oscillation data

We investigate flavor phenomenology and dark matter in the context of the scotogenic model.In this model,the neutrino masses are generated through radiative corrections at the one-loop level.Considering the neutrino mixing matrix to be of tri-bimaximal form with additional perturbations to accommodate the recently observed nonzero value of the reactor mixing angle θ_(13),we obtain the relation between various neutrino oscillation parameters and the model parameters.Working in a degenerate heavy neutrino mass spectrum,we obtain light neutrino masses obeying the normal hierarchy and also study the relic abundance of fermionic dark matter candidates,including coannihilation effects.A viable parameter space is thus obtained,consistent with neutrino oscillation data,relic abundance and various lepton flavor violating decays such as 1_α→1_(βγ) and 1_α→31_β.     

Multiscalar B-L extension based on S4flavor symmetry for neutrino masses and mixing

A multiscalar and nonrenormalizable B-L extension of the standard model(SM)with S₄symmetry which successfully explains the recently observed neutrino oscillation data is proposed.The tiny neutrino masses and their hierarchies are generated via the type-I seesaw mechanism.The model reproduces the recent experiments of neutrino mixing angles and Dirac CP violating phase in which the atmospheric angle(θ₂₃)and the reactor angle(θ₁₃)get the best-fit values while the solar angle(θ₁₂)and Dirac CP violating phase(δ)are in 3σrange of the best-fit value for the normal hierarchy(NH).For the inverted hierarchy(IH),θ13 gets the best-ft value andθ₂₃together withδare in the lσrange,whileθ12 is in 3δrange of the best-fit value.The effective neutrino masses are pre-dicted to be(m_ee)=6.81 meV for the NH and(m_ee)=48.48 meV for the IH,in good agreement with the most re-cent experimental data.     

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.     

A Model of Fermion Masses and Flavor Mixings with Family Symmetry SU(3)U(1)

The family symmetry SU(3)U(1) is proposed to solve flavor problems about fermion masses and flavor mixings.It is breaking is implemented by some flavon fields at the high-energy scale.In addition a discrete group Z 2 is introduced to generate tiny neutrino masses,which is broken by a real singlet scalar field at the middle-energy scale.The low-energy effective theory is elegantly obtained after all of super-heavy fermions are integrated out and decoupling.All the fermion mass matrices are regularly characterized by four fundamental matrices and thirteen parameters.The model can perfectly fit and account for all the current experimental data about the fermion masses and flavor mixings,in particular,it finely predicts the first generation quark masses and the values of θ l 13 and J l CP in neutrino physics.All of the results are promising to be tested in the future experiments.     

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.     

Neutrino Phenomenology of a High Scale Supersymmetry Model

CP violation in the lepton sector, and other aspects of neutrino physics, are studied within a high scale supersymmetry model. In addition to the sneutrino vacuum expectation values(VEVs), the heavy vector-like triplet also contributes to neutrino masses. Phases of the VEVs of relevant fields, complex couplings, and Zino mass are considered.The approximate degeneracy of neutrino masses m_(ν1) and m_(ν2) can be naturally understood. The neutrino masses are then normal ordered, ～ 0.020 eV, 0.022 eV, and 0.054 eV. Large CP violation in neutrino oscillations is favored. The effective Majorana mass of the electron neutrino is about 0.02 eV.     

Diagonal reflection symmetries and universal four-zero texture

In this paper,we consider a set of new symmetries in the SM:diagonal reflection symmetries Rm_u,v^*,R=m_u,v,m_d,e^*=mde with R=diag(-1,1,1).These generalized CP symmetries predict the Majorana phases to beα_2.3/2-0π/2.Realization of diagonal reflection symmetries implies a broken chiral U(1)po symmetry only for the first generation.The axion scale is suggested to be(θ_u,d)~△GuT√m_{u,dm_(c,s})/v-10¹²[GeV].By combining the symmetries with the four-zero texture,the mass eigenvalues and mixing matrices of quarks and leptons are reproduced well.This scheme predicts the normal hierarchy,the Dirac phase ocp≈203°,and|ml|≈2.5 or 6.2[meV].In this scheme,the type-I seesaw mechanism and a given neutrino Yukawa matrix Y_ycompletely determine the structure of the right-handed neutrino mass M_R.A u-y unification predicts the mass eigenvalues to be(M_RI,M_R2,M_R3)=(O(10⁵).O(10⁹),O(10¹⁴)[Gev].     

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.     

Light Flavor Vector and Pseudo Vector Mesons from a Light-Cone QCD Inspired Effective Hamiltonian Model with SU（3） Flavor Mixing Interactions

Based on the light-cone effective Hamiltonian with confining potential and SU （3） flavor mixing interactions, the flavor mixing mesons on the u, d, and s quark sectors are investigated. The mass eigen equations of the flavor mixing vector and pseudo vector mesons are solved. The calculated masses are in good agreement with the experimental data.     

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.     

Neutrino mixing matrix and masses from a particular two-zero texture based on A4 symmetry

The current study aims to investigate the particular case of two zeros in a Majorana neutrino mass matrix based on A₄ symmetry,where charged lepton mass matrix is diagonal.The texture is ■ with(μ,μ) and(τ,τ) vanishing element of the neutrino mass matrix.The texture ■ has magic and μ-τ symmetry,with a tribimaximal form of the mixing matrix,which leads to θ₁₃=0 that it is not consistent with experimental data and at first,does not seem to be allowed.Since θ₁₃ a sma...     

Towards the meV limit of the effective neutrino mass in neutrinoless double-beta decays

We emphasize that it is extremely important for future neutrinoless double-beta(0νββ)decay experiments to reach the sensitivity to the effective neutrino mass|mββ|≈1 meV.With such a sensitivity,it is highly possible to discover the signals of 0νββ decays.If no signal is observed at this sensitivity level,then either neutrinos are Dirac particles or stringent constraints can be placed on their Majorana masses.In this paper,assuming the sensitivity of|mββ|≈1 meV for future 0νββ decay experiments and the precisions on neutrion oscillation parameters after the JUNO experiment,we fully explore the constrained regions of the lightest neutrino mass m1 and two Majorana-type CP-violating phases{ρ,σ}.Several important conclusions in the case of normal neutrino mass ordering can be made.First,the lightest neutrino mass is severely constrained to a narrow range m1∈[0.7,8]meV,which together with the precision measurements of neutrino mass-squared differences from oscillation experiments completely determines the neutrino mass spectrum m2∈[8.6,11.7]meV ing phases is limited to ρ∈[130°,230°],which cannot be obtained from any other realistic experiments.Third,the sum of three neutrino masses is found to beΣ≡m1+m2+m3∈[59.2,72.6]meV,while the effective neutrino mass for beta decays turns out to be mβ≡(|Ue1|2m1^2+|Ue2|2m2^2+|Ue3|2m3^2)1/2∈[8.9,12.6]meV.These observations clearly set up the roadmap for future non-oscillation neutrino experiments aiming to solve the fundamental problems in neutrino physics.