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     

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 mixing in the seesaw model

In the seesaw model with hierarchical Dirac masses, the neutrino mixing angle exhibits the behavior of a narrow resonance. In general, the angle is strongly suppressed, but it can be maximal for special parameter values. We delineate the small regions in which this happens for the two-flavor problem. On the other hand, the physical neutrino masses are hierarchical, in general, except in a large part of the region in which the mixing angle is sizable, where they are nearly degenerate. Our general analysis is also applicable to the RGE of the neutrino mass matrix, where we find analytic solutions for the running of the physical parameters, in addition to a complex RGE invariant relating them. It is also shown that, if one mixing angle is small, the three-neutrino problem reduces to two two-flavor problems. Received: 16 March 2001 / Revised version: 17 May 2001 / Published online: 19 July 2001     

Effects of the scale-dependent vacuum expectation values in the renormalisation group analysis of neutrino masses

The contribution of scale-dependent vacuum expectation values (VEVs) of Higgs scalars, which gives significant effects in the evolution of the fundamental fermion masses in the minimal supersymmetric standard model (MSSM), is now considered in the derivation of the analytic one-loop expression for the evolution of the left-handed Majorana neutrino masses with energies. The inclusion of such an effect of the running VEV increases the stability of the neutrino masses under quantum corrections even for the low values of at the scale GeV, and leads to a mild decrease of the neutrino masses with higher energies. Such a trend is common with that of other fundamental fermion masses. Received: 18 September 2000 / Published online: 23 February 2001     

The spectrum of the 4-generation Dirac–Kähler extension of the SM

We compute the mass spectrum of the fermionic sector of the Dirac–Kähler extension of the SM (DK-SM) by showing that there exists a Bogoliubov transformation that transforms the DK-SM into a flavor U(4)$U(4)$ extension of the SM (SM-4) with a particular choice of masses and mixing textures. Mass relations of the model allow determination of masses of the 4th generation. Tree level prediction for the mass of the 4th charged lepton is 370 GeV. The model selects the normal hierarchy for neutrino masses and reproduces naturally the near tri-bimaximal and quark mixing textures. The electron neutrino and the 4th neutrino masses are related via a see-saw-like mechanism.     

Vacuum solutions of neutrino anomalies through a softly broken U(1) symmetry

We discuss an extended model which naturally leads to mass scales and mixing angles relevant for understanding both the solar and atmospheric neutrino anomalies in terms of the vacuum oscillations of the three known neutrinos. The model uses a softly broken –– symmetry and contains a heavy scale GeV. The –– symmetric neutrino masses solve the atmospheric neutrino anomaly while breaking of –– generates the highly suppressed radiative mass scale needed for the vacuum solution of the solar neutrino problem. All the neutrino masses in the model are inversely related to , thus providing seesaw-type of masses without invoking any heavy right-handed neutrinos. The possible embedding of the model into an SU(5) grand unified theory is discussed. Received: 5 August 1999 / Revised version: 18 November 1999 / Published online: 6 April 2000     

Numerical consistency check between two approaches to radiative corrections for neutrino masses and mixings

We briefly outline the two popular approaches on radiative corrections to neutrino masses and mixing angles, and then carry out a detailed numerical analysis for a consistency check between them in MSSM. We find that the two approaches are nearly consistent with a discrepancy factor of 4.2% with running vacuum expectation value (VEV) (13% for scale-independent VEV) in mass eigenvalues at low-energy scale but the predictions on mixing angles are almost consistent. We check the stability of the three types of neutrino models, i.e., hierarchical, inverted hierarchical and degenerate models, under radiative corrections, using both approaches, and find consistent conclusions. The neutrino mass models which are found to be stable under radiative corrections in MSSM are the normal hierarchical model and the inverted hierarchical model with opposite CP parity. We also carry out numerical analysis on some important conjectures related to radiative corrections in the MSSM, viz., radiative magnification of solar and atmospheric mixings in the case of nearly degenerate model having same CP parity (MPR conjecture) and radiative generation of solar mass scale in exactly two-fold degenerate model with opposite CP parity and non-zero U_e3 (JM conjecture). We observe certain exceptions to these conjectures. We find a new result that both solar mass scale and U_e3 can be generated through radiative corrections at low energy scale. Finally the effect of scaledependent vacuum expectation value in neutrino mass renormalisation is discussed     

Lepton Flavor Violating Z→lIlJ in SO(3) Gauge Extension of SM

The SO(3) gauge extension of SM, which is proposed to present a successfulexplanation for the observed small masses of neutrino and the nearly tri-bimaximal neutrino mixing, predicted the vector-like SO(3) triplet Majorana neutrinos and SU_L(2) double Higgs bosons. In this work we calculate branching ratios of the charged lepton flavor violating decays l_Il_JV (V=γ,Z) induced by these Majorana neutrinos and Higgs bosons. We find that under the model parameters constrained by experimental bounds on the decays Z→l_Il_J, the branching ratio of decays l_I→l_Jγ can be up to 10^-10, which may be accessible at the future experiments.     

A new three-flavor oscillation solution of the solar neutrino deficit in <Emphasis Type="Italic">R</Emphasis>-parity violating supersymmetry

We present a solution of the solar neutrino deficit using three flavors of neutrinos and R-parity non-conserving supersymmetry. In this model, in vacuum, the is massless and unmixed, mass and mixing being restricted to the - sector only, which we choose in consistency with the requirements of the atmospheric neutrino anomaly. The flavor changing and flavor diagonal neutral currents present in the model and the three-flavor picture together produce an energy dependent resonance-induced - mixing in the sun. This mixing plays a key role in the new solution to the solar neutrino problem. The best fit to the solar neutrino rates and spectrum (1258-day SK and 241-day SNO data) requires a mass square difference of eV² in vacuum between the two lightest neutrinos. This solution cannot accommodate a significant day-night effect for solar neutrinos nor CP violation in terrestrial neutrino experiments. Received: 26 December 2001 / Revised version: 16 February 2002 / Published online: 26 July 2002     

New supersymmetric source of neutrino masses and mixings

Conventionally, neutrino masses in a supersymmetric theory arise from nonrenormalizable lepton-number (L)-violating operators in the superpotential. The alternative possibility of having such operators in the K?hler potential as the dominant source of neutrino masses has very interesting implications and differences with respect to the standard scenario: first, the scale of L violation can be lowered dramatically; second, the renormalization of these operators has remarkable properties: in many cases it improves drastically the stability of neutrino textures against radiative corrections, while in others it makes it possible to generate radiatively large mixing angles in a natural way.     

Majorana neutrinos from inverse seesaw in warped extra dimension

We propose the inverse seesaw mechanism as a way to understand small Majorana masses for neutrinos in warped extra dimension models with seesaw scale in the TeV range. The ultra-small lepton number violation needed in implementing inverse seesaw mechanism in 4D models is explained in this model as a consequence of lepton number breaking occurring on the Planck brane. We construct realistic models based on this idea that fit observed neutrino oscillation data for both normal and inverted mass patterns. We compute the corrections to light neutrino masses from the Kaluza-Klein modes and show that they are small in the parameter range of interest. Another feature of the model is that the absence of global parity anomaly implies the existence of at least one light sterile neutrino with sterile and active neutrino mixing in the range suggested by the LSND and MiniBooNE observations.     

Neutrino textures in light of Super-Kamiokande data and a realistic string model

Motivated by the Super-Kamiokande atmospheric neutrino data, we discuss possible textures for Majorana and Dirac neutrino masses within the see-saw framework. There are two main purposes of this paper: first, to gain intuition into this area from a purely phenomenological analysis, and second, to explore to what extent it may be realized in a specific model. We comment initially on the simplified two-generation case, emphasizing that large mixing is not incompatible with a large hierarchy of mass eigenvalues. We also emphasize that renormalization-group effects may amplify neutrino mixing, and we present semi-analytic expressions for estimating this amplification. Several examples are then given of three-family neutrino mass textures, which may also accommodate the persistent solar neutrino deficit, with different assumptions for the neutrino Dirac mass matrices. We comment on a few features of neutrino mass textures arising in models with a U(1) flavour symmetry. Finally, we discuss the possible pattern of neutrino masses in a “realistic” flipped SU(5) model derived from string theory, illustrating how a desirable pattern of mixing may emerge. Both small- or large-angle MSW solutions are possible, while a hierarchy of neutrino masses appears more natural than near-degeneracy. This model contains some unanticipated features that may be relevant in other models also: The neutrino Dirac matrices may not be related closely to the quark mass matrices, and the heavy Majorana states may include extra gauge-singlet fields. Received: 6 November 1998 / Published online: 18 June 1999     

The heavy neutral Higgs signature in the \gamma \gamma \to Z Z process

If the standard model (SM) Higgs particle is sufficiently heavy, then its contribution to should be largely imaginary, interfering with the also predominantly imaginary SM “background” generated by the W loop. For standard model Higgs masses in the region GeV, this interference is found to be constructive and increasing the Higgs signal. In the minimal SUSY case an interference effect should also appear for the contribution of the heavier CP-even neutral Higgs boson , provided it is sufficiently heavy. The effect is somewhat reduced, though, by the smallness of the width and the and ZZ branching ratios. The interference is again found to be constructive for part of the parameter space corresponding to sfermion masses at the TeV scale and maximal stop mixing. For both the SM and the SUSY case, regions of the parameter space exist, though, where the interference may be destructive. It is therefore essential to take these effects into account when searching for possible scalar Higgs-like candidates. To this aim, we present the complete analytic expressions for both resonance and background amplitudes. Received: 20 October 2000 / Revised version: 5 January 2001 / Published online: 23 February 2001     

New formulas and predictions for running fermion masses at higher scales in SM, 2HDM, and MSSM

Including contributions of scale-dependent vacuum expectation values, we derive new analytic formulas and obtain substantially different numerical predictions for the running masses of quarks and charged leptons at higher scales in the SM, 2HDM and MSSM. These formulas exhibit significantly different behaviours with respect to their dependence on gauge and Yukawa couplings from those derived earlier. At one-loop level, the masses of the first two generations are found to be independent of the Yukawa couplings of the third generation in all three effective theories in the small mixing limit. Analytic formulas are also obtained for the running of in 2HDM and MSSM. Other numerical analyses include a study of the third generation masses at high scales as functions of the low-energy values of and the SUSY scale GeV. Received: 1 October 2000 / Revised version: 11 January 2001 / Published online: 12 April 2001     

Lepton mixing matrix in standard model extended by one sterile neutrino

We consider the simplest extension of the standard electroweak model by one sterile neutrino that allows for neutrino masses and mixing. We find that its leptonic sector contains much less free physical parameters than previously realized. In addition to the two neutrino masses, the lepton mixing matrix in charged current interactions involves (n-1) free physical mixing angles for n generations. The mixing matrix in neutral current interactions of neutrinos is completely fixed by the two masses. Both interactions conserve CP. We illustrate the phenomenological implications of the model by vacuum neutrino oscillations, tritium β decay and neutrinoless double β decay. It turns out that, due to the revealed specific structure in its mixing matrix, the model with any n generations cannot accommodate simultaneously the data by KamLAND, K2K and CHOOZ. PACS 14.60.Pq; 14.60.St; 23.40.-s     

Seesaw neutrino masses with large mixings from dimensional deconstruction

We demonstrate a dynamical origin for the dimension-five seesaw operator in dimensional deconstruction models. Light neutrino masses arise from the seesaw scale which corresponds to the inverse lattice spacing. It is shown that the deconstructing limit naturally prefers maximal leptonic mixing. Higher-order corrections which are allowed by gauge invariance can transform the bimaximal into a bilarge mixing. These terms may appear to be nonrenormalizable at scales smaller than the deconstruction scale.     

A horizontal model for neutrino mixing

We consider a horizontal SU(3)_H × SU(2)_L × U(1) model in which the large Majorana neutrino masses are associated with a large horizontal scale. We find that the charged lepton sector is responsible for the neutrino mixing which we calculate in the present model. We also find that the neutrino oscillation length is related to the horizontal scale.     

Renormalisation group improved leptogenesis in family symmetry models

We study renormalisation group (RG) corrections relevant for leptogenesis in the case of family symmetry models such as the Altarelli–Feruglio A₄$A_4$ model of tri-bimaximal lepton mixing or its extension to tri-maximal mixing. Such corrections are particularly relevant since in large classes of family symmetry models, to leading order, the CP violating parameters of leptogenesis would be identically zero at the family symmetry breaking scale, due to the form dominance property. We find that RG corrections violate form dominance and enable such models to yield viable leptogenesis at the scale of right-handed neutrino masses. More generally, the results of this paper show that RG corrections to leptogenesis cannot be ignored for any family symmetry model involving sizeable neutrino and τ Yukawa couplings.     

Parameterization for Neutrino Mixing Matrix with Deviated Unitarity

Neutrino oscillation experiments provide the first evidence on non-zero neutrino masses and indicate new physics beyond the standard model. With Majorana neutrinos introduced to acquire tiny neutrino masses, it leads to the existence of more than three neutrino species, implying that the ordinary neutrino mixing matrix is only a part of the whole extended unitary mixing matrix and thus no longer unitary. We give a parameterization for a non-unitary neutrino mixing matrix under seesaw framework and further present a method to test the unitarity of the ordinary neutrino mixing matrix.     

Searches for the appearance of \nu_\tau using neutrino beams from muon storage rings

We study the possibilities offered by muon storage rings for appearance experiments in order to determine masses and mixing angles for the and oscillations. The dependence of tau event rates on baseline, forward peaking of decay neutrinos with increasing energies, and average fluxes intercepted by detectors of various sizes is discussed. It is found that the baseline length does not significantly affect the rates for oscillations of such magnitudes as are suggested by the current atmospheric neutrino data. Subsequently, the effects of cuts on hadronic and wrong sign leptonic modes are computed and used to plot 90% CL contours for the parameter regions that can be explored in such experiments. The results show that even for modest muon beam energies, convincing coverage and verification of the Super Kamiokande parameters is possible. In addition, a very significant enlargement of present day bounds on the mixing parameters for neutrino oscillations of all types is guaranteed by these types of searches. Received: 4 April 2000 / Revised version: 22 July 2000 / Published online: 8 December 2000