Parametrization of seesaw models and light sterile neutrinos

The recent recomputation of the neutrino fluxes from nuclear reactors relaxes the tension between the LSND and MiniBooNE anomalies and disappearance data when interpreted in terms of sterile neutrino oscillations. The simplest extension of the Standard Model with such fermion singlets is the addition of right-handed sterile neutrinos with small Majorana masses. Even when introducing three right-handed neutrinos, this scenario has less free parameters than the 3 + 2 scenarios studied in the literature. This begs the question whether the best fit regions obtained can be reproduced by this simplest extension of the Standard Model. In order to address this question, we devise an exact parametrization of Standard Model extensions with right-handed neutrinos. Apart from the usual 3×3 neutrino mixing matrix and the 3 masses of the lightest neutrinos, the extra degrees of freedom are encoded in another 3×3 unitary matrix and 3 additional mixing angles. The parametrization includes all the correlations among masses and mixings and is valid beyond the usual seesaw approximation. Through this parametrization we find that the best fit regions for the LSND and MiniBooNE anomalies in a 3 + 2 scenario can indeed be reproduced despite the smaller number of degrees of freedom.     

Oscillation properties of active and sterile neutrinos and neutrino anomalies at short distances

A generalized phenomenological (3 + 2 + 1) model featuring three active and three sterile neutrinos that is intended for calculating oscillation properties of neutrinos for the case of a normal activeneutrino mass hierarchy and a large splitting between the mass of one sterile neutrino and the masses of the other two sterile neutrinos is considered. A new parametrization and a specific form of the general mixing matrix are proposed for active and sterile neutrinos with allowance for possible CP violation in the lepton sector, and test values are chosen for the neutrino masses and mixing parameters. The probabilities for the transitions between different neutrino flavors are calculated, and graphs representing the probabilities for the disappearance of muon neutrinos/antineutrinos and the appearance of electron neutrinos/antineutrinos in a beam of muon neutrinos/antineutrinos versus the distance from the neutrino source for various values of admissible model parameters at neutrino energies not higher than 50 MeV, as well as versus the ratio of this distance to the neutrino energy, are plotted. It is shown that the short-distance accelerator anomaly in neutrino data (LNSD anomaly) can be explained in the case of a specific mixing matrix for active and sterile neutrinos (which belongs to the a₂ type) at the chosen parameter values. The same applies to the short-distance reactor and gallium anomalies. The theoretical results obtained in the present study can be used to interpret and predict the results of ground-based neutrino experiments aimed at searches for sterile neutrinos, as well as to analyze some astrophysical observational data.     

Leptogenesis and bi-unitary parametrization of neutrino Yukawa matrix

We analyze the neutrino Yukawa matrix by considering three constraints: the out-of-equilibrium condition of the lepton number-violating process responsible for leptogenesis, the upper bound of the branching ratio of the lepton flavor violating decay, and the prediction of large mixing angles using the see-saw mechanism. In a certain parametrization with a bi-unitary transformation, it is shown that the structure which satisfies the constraints can be characterized by only seven types of Yukawa matrices. The constraint of the branching ratio of LFV turns out to be redundant after applying the other two constraints. We propose that this parametrization can be the framework in which the CP asymmetry of a lepton number-violating process can be predicted in terms of observable neutrino parameters at low energy, if necessary, under assumptions following from a theory with additional symmetries. There is an appealing model of the neutrino Yukawa matrix considering the CP asymmetry for leptogenesis, giving a theoretical motivation to reduce the number of free parameters.Arrival of the final proofs: 24 June 2003     

Semileptonic b-->u decays: lepton invariant mass spectrum

We compute O(alpha(2)(s)) QCD corrections to the lepton invariant mass spectrum in the decay b-->ulnu(l), relevant for the determination of the Cabibbo-Kobayashi-Maskawa matrix element /V(ub)/. Our method can also be used to evaluate moments of the lepton energy distribution with an O(alpha(2)(s)) accuracy. The Abelian part of our result gives the neutrino invariant mass spectrum in the muon decay and, upon integration, the O(alpha(2)) correction to the muon lifetime.     

Neutrino oscillations in the O(10) model with radiatively induced Majorana masses

We analyse the structure of the neutrino mass matrix and the pattern of neutrino oscillations in the O(10) model with radiatively induced Majorana masses. In particular, we show that the possibility of experimentally interesting neutrino oscillations is left open.     

Unitary parametrization of perturbations to tribimaximal neutrino mixing

Current experimental data on neutrino mixing are very well described by tribimaximal mixing. Accordingly, any phenomenological parametrization of the Maki-Nakagawa-Sakata-Pontecorvo matrix must build upon tribimaximal mixing. We propose one particularly natural parametrization, which we call "triminimal." The three small deviations of the Particle Data Group angles from their tribimaximal values, and the PDG phase, parametrize the triminimal mixing matrix. As an important example of the utility of this new parametrization, we present the simple resulting expressions for the flavor-mixing probabilities of atmospheric and astrophysical neutrinos. As no foreseeable experiment will be sensitive to more than second order in the small parameters, we expand these flavor probabilities to second order.     

New type of seesaw mechanism for neutrino masses

In a wide class of unified models there is an additional (and possibly dominant) term in the neutrino mass formula that under the simplest assumption takes the form M(nu)=(M(N)+M(T)(N))u/M(G), where M(N) is the neutrino Dirac mass matrix, and u=O(M(W)). This makes possible highly predictive models. A generalization of this form yields realistic neutrino masses and mixings more readily than the usual seesaw formula in some models. The conditions for resonant enhancement of leptogenesis can occur naturally in such models.     

Stability of the lepton-flavor mixing matrix against quantum corrections

Recent neutrino experiments suggest strong evidence of tiny neutrino masses and the lepton-flavor mixing. Neutrino-oscillation solutions for the atmospheric neutrino anomaly and the solar neutrino deficit can determine the texture of the neutrino mass matrix according to the neutrino mass hierarchies as Type A: , Type B: , and Type C: , where is the i-th generation neutrino mass. In this paper we study the stability of the lepton-flavor mixing matrix against quantum corrections for all three types of mass hierarchy in the minimal supersymmetric Standard Model with an effective dimension-five operator which gives the Majorana masses of neutrinos. The relative sign assignments of neutrino masses in each type play crucial role for the stability against quantum corrections. We find that the lepton-flavor mixing matrix of Type A is stable against quantum corrections, and that of Type B with the same (opposite) signs of and are unstable (stable). For Type C, the lepton-flavor-mixing matrix approaches the definite unitary matrix according to the relative sign assignments of the neutrino mass eigenvalues as the effects of quantum corrections become large enough to neglect the squared mass differences of neutrinos. Received: 24 June 1999 / Revised version: 23 December 1999 / Published online: 17 March 2000     

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.     

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 parametrization-independent 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 at 39° (in the P_a parametrization) which will be tested in the future experiments.     

Naumov- and Toshev-like relations in the renormalization-group evolution of quarks and Dirac neutrinos

In an analytical way of studying matter effects on neutrino oscillations, the Naumov and Toshev relations have been derived to respectively link the Jarlskog invariant of CP violation and the Dirac phase in the standard parametrization of the 3×3 flavor mixing matrix to their matter-corrected counterparts. Here we show that there exist similar relations for Dirac neutrinos and charged leptons evolving with energy scales via the one-loop renormalizationgroup(RG) equations in the tau-dominance approximation, and for the running behaviors of up-and down-type quarks in the top-dominance approximation, provided a different parametrization is taken into account.     

The effects of Majorana phases in three-generation neutrinos

Neutrino-oscillation solutions for the atmospheric neutrino anomaly and the solar neutrino deficit can determine the texture of the neutrino mass matrix according to three types of neutrino mass hierarchy: Type A: , Type B: , and Type C: , where is the absolute mass of the ith generation neutrino. The relative sign assignments of the neutrino masses in each type of mass hierarchy play crucial roles in the stability against quantum corrections. Actually, two physical Majorana phases in the lepton flavor mixing matrix connect the relative sign assignments of the neutrino masses. Therefore, in this paper we analyze the stability of the mixing angles against quantum corrections according to three types of neutrino mass hierarchy (Type A, B, C) and two Majorana phases. The two phases play crucial roles in the stability of the mixing angles against quantum corrections. Received: 9 May 2000 / Revised version: 23 May 2000 / Published online: 8 September 2000     

Neutrino mass anarchy

What is the form of the neutrino mass matrix which governs the oscillations of the atmospheric and solar neutrinos? Features of the data have led to a dominant viewpoint where the mass matrix has an ordered, regulated pattern, perhaps dictated by a flavor symmetry. We challenge this viewpoint and demonstrate that the data are well accounted for by a neutrino mass matrix which appears to have random entries.     

Neutrino masses and lepton-flavor-violating τ decays in the supersymmetric left-right model

In the supersymmetric left-right model, the light neutrino masses are given by the Type-Ⅱ seesaw mechanism. A duality property of this mechanism indicates that there exist eight possible Higgs triplet Yukawa couplings which result in the same neutrino mass matrix. In this paper, we work out the one-loop renormalization group equations for the effective neutrino mass matrix in the supersymmetric left-right model. The stability of the Type-Ⅱ seesaw scenario is briefly discussed. We also study the lepton-flavor-violating processes (τ→ μγ and τ→eγ) by using the reconstructed Higgs triplet Yukawa couplings.     

Massive and massless neutrinos on unbalanced seesaws

The observation of neutrino oscillations requires new physics beyond the standard model (SM).A SM-like gauge theory with p lepton families can be extended by introducing q heavy right-handed Majorana neutrinos but preserving its SU(2)L x U(1)y gauge symmetry.The overall neutrino mass matrix M turns out to be a symmetric (p+q) x (p+q) matrix.Given p＞q,the rank of M is in general equal to 2q,corresponding to 2q non-zero mass eigenvalues.The existence of (p-q) massless left-handed Majorana neutrinos is an exact consequence of the model,independent of the usual approximation made in deriving the Type-I seesaw relation between the effective p x p light Majorana neutrino mass matrix M,and the q x q heavy Majorana neutrino mass matrix MR.In other words,the numbers of massive left- and right-handed neutrinos are fairly matched.A good example to illustrate this "seesaw fair play rule"is the minimal seesaw model with p ＝ 3 and q ＝ 2,in which one masslese neutrino sits on the unbalanced seesaw.     

Two-texture zeros and near-maximal atmospheric neutrino mixing angle

We study the implications of a large value of the effective Majorana neutrino mass for a class of two-texture zero neutrino mass matrices in the flavour basis. We find that these textures predict near-maximal atmospheric neutrino mixing angle in the limit of large effective Majorana neutrino mass. We present the symmetry realization of these textures using the discrete cyclic group Z₃. It is found that the texture zeros realized in this work remain stable under the renormalization group running of the effective neutrino mass matrix at one-loop level.     

Texture zeros and majorana phases of the neutrino mass matrix

We present the generic formulas to calculate the ratios of neutrino masses and the Majorana phases of CP violation from the neutrino mass matrix with two independent vanishing entries in the flavor basis where the charged lepton mass matrix is diagonal. An order-of-magnitude illustration is given for seven experimentally acceptable textures of the neutrino mass matrix, and some analytical approximations are made for their phenomenological consequences at low energy scales.     

General neutrino mass spectrum and mixing properties in seesaw mechanisms

Neutrinos stand out among the elementary particles because of their unusually small masses.Various seesaw mechanisms attempt to explain this fact.In this work,applying insights from matrix theory,we are in a position to treat variants of seesaw mechanisms in a general manner.Specifically,using Weyl's inequalities,we discuss and rigorously prove under which conditions the seesaw framework leads to a mass spectrum with exactly three light neutrinos.We find an estimate of the mass of heavy neutrinos to be the mass obtained by neglecting light neutrinos,shifted at most by the maximal strength of the coupling to the light neutrino sector.We provide analytical conditions allowing one to prescribe that precisely two out of five neutrinos are heavy.For higher-dimensional cases the inverse eigenvalue methods are used.In particular,for the CP-invariant scenarios we show that if the neutrino sector has a valid mass matrix after neglecting the light ones,i.e.if the respective mass submatrix is positive definite,then large masses are provided by matrices with large elements accumulated on the diagonal.Finally,the Davis-Kahan theorem is used to show how masses affect the rotation of light neutrino eigenvectors from the standard Euclidean basis.This general observation concerning neutrino mixing,together with results on the mass spectrum properties,opens directions for further neutrino physics studies using matrix analysis.     

Discrimination of neutrino mass models

We consider the Majorana CP violating phases derived from right-handed Majorana mass matrices to estimate the baryon asymmetry of the universe, for different neutrino mass models, namely degenerate, inverted hierarchical and normal hierarchical models, with tri-bimaximal mixings. Considering three possible diagonal forms of Dirac neutrino mass matrix as charged-lepton, up-quark or down-quark mass matrix within the framework of left-right symmetric GUT models, the right-handed Majorana mass matrices are constructed from the light Majorana neutrino mass matrix through the inverse seesaw formula. These light neutrino mass matrices have already been tested to provide good predictions on neutrino mass parameters and mixing angles. They are again applied to predict baryon asymmetry of the universe in the present work. The normal hierarchical model gives the best prediction for baryon asymmetry, consistent with observation. The analysis may serve as additional information in the discrimination of the presently available neutrino mass models.