Small Dirac neutrino mass and left-right symmetry

We analyze the possibility of generating light Dirac neutrinos at the tree level in a left-right symmetric scenario. We present a minimal extension of the standard SU(2) _L × SU(2) _R × U(1) _Y′ model where the above result is achieved through a “see-saw” like mechanism induced by the minimization of the Higgs potential. The Dirac neutrinos thus obtained are naturally light; indeed we show that the scheme is stable under radiative corrections. The neutrino mass is inversely related to the scale of parity breaking, which may naturally be in the TeV range, leading to new phenomenology in an interesting energy domain.     

The singular seesaw mechanism with hierarchical Dirac neutrino mass

We evaluate the one-loop fermion self-energy for the gauged Thirring model in (2+1) dimensions, with one massive fermion flavor. We do this in the framework of the causal perturbation theory. In contrast to QED, the corresponding two-point function turns out to be infrared finite on the mass shell. Then, by means of a Ward identity, we derive the on-shell vertex correction and discuss the role played by causality for non-renormalizable theories. Received: 5 May 1999 / Published online: 27 January 2000     

Majorana mass term,Dirac neutrinos and selective neutrino oscillations

In a theory of neutrino mixing via a Majorana mass term involving only the left-handed neutrinos there exist selection rules for neutrino oscillations if true Dirac and/or exactly zero mass eigenstates are present. In the case of three neutrino flavours no oscillation is allowed if the mass spectrum contains one Dirac and one nondegenerate Majorana massive neutrino. The origin of these selection rules and their implications are discussed and the number of possible CP-violating phases in the lepton mixing matrix when Dirac and Majorana mass eigenstates coexist is given.     

Majorana mass of the electron-muon Dirac neutrino and the fermion masses

The left-handed electron and muon neutrinos are considered to be Majorana neutrinos with equal mass. They have oppositeCP parities and are equivalent to a single Dirac neutrino. These neutrinos are shown to have a Majorana mass of about 6.5 eV. The relatively large mass of their charged leptons is due to their γ₅ coupling with the Higgs scalars By expressing the Higgs scalars as Clebsch-Gordon type of combinations ofZ andD neutral vector bosons with appropriate quantum numbers, it is shown that 2m _e m _μ /(m _e ² +m _μ ² )=(g_{v/g A}) _eμ ² , whereg _v andg _A are the vector and axial vector coupling constants, respectively, ofZ (orD) with the leptonse and μ. Weinberg mixing parametersx _L =e²/g _L ² andx _R =e ²/g _R ² are determined to be 0.2254 and 0.2746, respectively. In the quark sector the Cabibbo angle is about 13°11′ and the masses oft andb quarks are found to be respectively 134.2 and 4.69 GeV.     

Complex scaling and residual flavour symmetry in the neutrino mass matrix

We present an instance from nonequilibrium statistical mechanics which combines increase in entropy and finite Poincaré recurrence time. The model we consider is a variation of the well-known Kac’s ring where we consider balls of four colours. As is known, Kac introduced this model where balls arranged between lattice sites, in each time step, move one step clockwise. The colour of the balls change as they cross marked sites. This very simple example rationalize the increase in entropy and recurrence. In our variation, the interesting quantity which counts the difference in the number of balls of different colours is shown to reduce to a set of linear equations if the probability of change of colour is symmetric among a pair of colours. The transfer matrix turns out to be non-Hermitian with real eigenvalues, leading to all colours being equally likely for long times, and a monotonically varying entropy. The new features appearing due to four colours is very instructive.     

The one-loop neutrino contribution to the gravitation propagator

The one-loop neutrino correction to the gravitation propagator is calculated using the technique of dimensional regularization. The resulting amplitude satisfies Slavnov-Ward identities and the divergent part can be cancelled by a pole term of the form

$\text{Δ}\text{L}\text{=}\text{√?g}\text{(2?ω)(4π)}{}^2\text{120}\text{[R}{}^2\text{?3R}{}_{\mathrm{\mu \nu }}\text{R}{}^{\mathrm{\mu \nu }}\text{]}$

. If, however, we are to avoid the appearance of a somewhat unusual anomaly it is essential that the counterterm be in a continuous (2ω) number of dimensions rather than 4, in which case

$\text{Δ}\text{L}\text{=}\text{√?g2}{}^{\mathrm{\omega }}\text{(2?ω)(4π)}{}^2\text{32(4ω}{}^2\text{?1)}\text{[}\text{1}\text{2}\text{ω′R}{}^2\text{?(2ω?1)R}{}_{\mathrm{\mu \nu }}\text{R}{}^{\mathrm{\mu \nu }}\text{0]}$

.     

Extended scaling and residual flavor symmetry in the neutrino Majorana mass matrix

The European Physical Journal C - We consider the flavor-changing decays of the Higgs boson in a grand unified theory framework which is based on the SU(5) gauge group and implements the principle...     

O(3) flavor symmetry and an empirical neutrino mass matrix

Based on a new approach to quark and lepton masses, where the mass spectra originate in vacuum expectation values of O(3)-flavor 1+5$\mathbf{1}+\mathbf{5}$ (gauge singlet) scalars, a neutrino mass matrix of a new type is speculated. The mass matrix is described in terms of the up-quark and charged lepton masses, and, by assuming a special flavor basis, it can be accommodated to a nearly tribimaximal mixing without explicitly assuming a discrete symmetry. Quark mass relations are also discussed based on the new approach.     

Zero textures of the neutrino mass matrix from cyclic family symmetry

We present the symmetry realization of the phenomenologically viable Frampton-Glashow-Marfatia (FGM) two zero texture neutrino mass matrices in the flavor basis within the framework of the type (I+II) seesaw mechanism natural to SO(10) grand unification. A small Abelian cyclic symmetry group Z₃ is used to realize these textures except for class C for which the symmetry is enlarged to Z₄. The scalar sector is restricted to the Standard Model (SM) Higgs doublet to suppress the flavor changing neutral currents. Other scalar fields used for symmetry realization are at the most two scalar triplets and, in some cases, a complex scalar singlet. Symmetry realization of one zero textures has, also, been presented.     

Left-right symmetry breaking scale and supersymmetry in unified theories

We propose a class of supersymmetric grand unified models where parity and SU(2)_R breaking scales are widely separated and compatible with a low-lying mass for the right-handed gauge boson W_R. The intermediate symmetry SU(4)_c×SU(2)_L×SU(2)_R and Higgs content are uniquely fixed if m_WR < 10⁹ GeV. The unification scale lies within an order of magnitude below the Planck mass.     

On the massive Dirac neutrino radiative decay

The presence of right-handed currents and left-right mixing contributes to the neutrino radiative decay amplitude a term that is directly proportional to the charged lepton mass. This has led to the suggestion that observable decays of relic neutrinos might occur in the left-right model or the mirror model. Explicit calculations in these models are carried out including a careful analysis of the origin of neutrino mass, here assumed to be a Dirac mass. It is found that the amplitude is proportional to the neutrino mass and thus too small to be of interest. A brief comment on the neutrino magnetic moment in anSU(2) _L ×U(1) _Y model, which contains an iso-singlet charged scalar η⁺, is also presented.