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

Unlocking the Standard Model. I. 1 generation of quarks. Symmetries

A very specific two-Higgs-doublet extension of the Glashow-Salam-Weinberg model for one generation of quarks is advocated for, in which the two doublets are parity transformed of each other and both isomorphic to the Higgs doublet of the Standard Model. The chiral group U(2)_L X U(2)_R gets broken down to U(1) X U(1)_{em}. In there, the first diagonal U(1) is directly connected to parity through the U(1)_LX U(1)_R algebra. Both chiral and weak symmetry breaking can be accounted for, together with their relevant degrees of freedom. The two Higgs doublets are demonstrated to be in one-to-one correspondence with bilinear quark operators.Comment: A misprint in eq. (13) has been corrected (h^3 -> h^2

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 Cabibbo angle : an algebraic calculation

We show that the Cabibbo angle theta\_c satisfies the relation tan(2 theta\_c)=-+/- 1/2 when universality for diagonal neutral currents of mass eigenstates is satisfied at the same level of accuracy as the absence of their off-diagonal counterparts. The predicted value is cos theta\_c \approx 0.9732, only 7/10000 away from experimental results. No mass ratio appears in the calculation. theta\_c occurs a priori for both quark species, and, showing that one recovers the standard dependence of leptonic and semi-leptonic decays of pseudoscalar mesons, we advocate, like for neutrinos and charged leptons, for a symmetrical treatment of u and d-type quarks.Comment: The Cabibbo angle can be positive or negative, which was overlooked in the first version. Minor addend

The neighborhood of the Standard Model: mixing angles and quark-lepton complementarity for three generations of non-degenerate coupled fermions

We investigate the potential (small) deviations from the unitarity of the mixing matrix that are expected to occur, because of mass splittings, in the Quantum Field Theory of non-degenerate coupled systems. We extend our previous analysis concerning mixing angles, which led to a precise determination of the Cabibbo angle, to the case of three generations of fermions. We show that the same condition for neutral currents of mass eigenstates, i.e. that universality of diagonal currents is violated with the same strength as the absence of non-diagonal ones, is satisfied: on one hand, by the three CKM mixing angles with a precision higher than the experimental uncertainty; on the other hand, by a neutrino-like mixing pattern in which theta_{23} is maximal, and tan (2 theta_{12})=2. This last pattern turns out to satisfy exactly the "quark-lepton complementarity condition" theta_c + theta_{12}= pi/4. Moreover, among all solutions, two values for the third neutrino mixing angle arise which satisfy the bound sin^2(theta_{13}) < 0.1: theta_{13} = +/- 5.7 10^{-3} and theta_{13} = +/- 0.2717. The so-called "Neighborhood of the Standard Model" is thus confirmed to exhibit special patterns which presumably originate in physics "Beyond the Standard Model"

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.

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