Neutrino mixing angles and eigenstates; CP properties and mass hierarchies

In the presence of independent generations of leptons, I show that the same type of ambiguity in the mass spectrum arises as was discussed in ref.[1] for neutral kaons. It results from the freedom to add to their Majorana mass matrix, usually taken to be symmetric, an antisymmetric term which vanishes as soon as fermions belonging to different generations anticommute. In the simple examples proposed, dealing with two generations, this procedure introduces an extra (mass) parameter $\rho$, which is shown to connect the (CP violating) mixing angle to the hierarchy of neutrino masses. We use this opportunity to investigate the relations between the two; in particular, large hierarchies are no longer preferentially attached to small mixing angles; this can be relevant for the ``Large Mixing Angle'' solution strongly advocated by recent experiments on neutrinos oscillations. I discuss how the $\rho$ parameter could be fixed, which appears, in the absence of a substructure for leptons, still more delicate than for kaons.Comment: LaTeX 19 pages, 15 postscript figures + 1 Log

The Coupling of the Pion to Two Gauge Fields and to Leptons in a Dynamically Broken Gauge Theory

We show how a spontaneously broken gauge theory of fermions endowed with a composite scalar multiplet becomes naturally anomaly-free, and yet describes the correct couplings of the pion to two gauge fields and to leptons: the first coupling is the same as computed from the chiral anomaly, and the second identical with that obtained from the `Partially Conserved Axial Current' hypothesis. For the sake of simplicity, we only study here the abelian case.Comment: 10 pages. Latex file, 5 postscript figures included. Preprint PAR-LPTHE 93/35. The file for the figures had been badly transmitted. The new uuencoded compressed tarred file should be now correc

Gauge bosons in an SU(2)right x SU(2)left x G(leptonique) electroweak model

By considering its generalization to composite J=0 mesons proposed in a previous work [1], I show how and why a chiral extension of the Glashow-Salam-Weinberg standard model of electroweak interactions calls, there, for right-handed charged W_R's coupled with g_R = e/cos(theta_W), and the masses of which are related to the ones of the left-handed W_L's through the relation M_L^2 + M_R^2 = M_Z^2. The mesonic sector, having vanishing baryonic and leptonic number, is neutral with respect to the corresponding U(1) symmetries, making the natural chiral gauge group to be [SU(2)left x SU(2)right], blind to the presence of extra Z's. The W_R gauge bosons cannot have been detected in hadronic colliders and can be very elusive in electroweak processes involving, in particular, pseudoscalar mesons. Present data select one among two possible extensions for which, in the right sector: - a specific breaking of universality occurs between families of quarks, which belong to inequivalent representations of SU(2)right; - the mixing angle is a free parameter, constrained to be smaller than the Cabibbo angle by the box diagrams controlling the K_L-K_S mass difference; this also minimizes contributions to muon -> electron + photon. The relation g_L^2/M_L^2 = g_R^2/M_R^2 implements left-right symmetry for low energy charged effective weak interactions. For the sake of simplicity, this study is performed for two generations only.Comment: LaTeX, 18 pages, 4 postscript figures + 1 logo automatically include

Leptonic Custodial Symmetry, Quantization of the Electric Charge and the Neutrino in the Standard Model

I study, in the leptonic sector, the role of the $SU(2)_V$ custodial symmetry \ti{\cal G} which was shown in ref. [1] to control the quantization of the electric charge in the $J=0$ mesonic sector. The electroweak theory is considered, according to ref. [2], as a purely vectorial model which interacts with a ``hidden'' sector of composite scalars. \ti{\cal G} can only be a symmetry of the former if the neutrino is a Majorana particle; the latter provides a dynamical modification of the leptonic weak couplings, reconstructing those of the Standard Model with a massless Majorana neutrino.Comment: 11 pages, Late

Extending the Standard Model: an upper bound for a neutrino mass from the rare decay K+ -> Pi+ neutrino antineutrino

The standard model seeming at a loss to account for the present experimental average rate for the rare decay K+ -> Pi+ neutrino antineutrino, I tackle the question with the extension of the Glashow-Salam-Weinberg model to an SU(2)left x U(1) gauge theory of J=0 mesons proposed by the author in [Phys. Lett. B 385 (1996) 198], in which, in addition, the neutrinos are given Dirac masses from Yukawa couplings to the Higgs boson. The latter triggers a new contribution to this decay through flavor changing neutral currents that arise in the quartic term of the symmetry breaking potential; it becomes sizeable for a neutrino mass in the $MeV$ range; the experimental upper limit for the decay rate translates into an upper bound of 5.5 MeV for the mass of the neutrino, three times lower than present direct bounds.Comment: 7 pages LaTeX, 2 postscript figures + 1 logo (epsfig). The discussion about the see-saw mechanism has been modified. Version to appear in Mod. Phys. Lett.

The emergence of the Cabibbo angle in non-degenerate coupled systems of fermions

Investigating, in direct continuation of our previous paper hep-ph/0606303 the implications of the non-unitarity of mixing matrices for non-degenerate coupled systems that we demonstrated there, we examine more accurately the vicinity of Cabibbo-like mixing in quantum field theory. We show that it is possible to preserve one of its main features, namely that, in the space of mass eigenstates, the two requirements -- of universality for weak diagonal currents and -- of the absence of their non-diagonal counterparts, although not fulfilled separately any more, can however reduce to a single condition for a unique mixing angle theta\_c. This leads to tan (2 theta\_c)=+/- 1/2, or cos theta\_c \approx 0.9732, only 7/10000 away from experimental results. No mass ratio appears in the argumentation.Comment: This is a different version of hep-ph/0607193, with a simplified argumentation, a clearer connection with hep-ph/0606303. The solution for the Cabibbo angle is also expressed in terms of the golden number. To appear in Phys. Lett.