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.

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

Mixing at 1-loop in a SU(2)_L gauge theory of weak interactions

Flavor mixing is scrutinized at 1-loop in a SU(2)_L gauge theory of massive fermions. The main issue is to cope with kinetic-like, momentum (p^2) dependent effective interactions that arise at this order. They spoil the unitarity of the connection between flavor and mass states, which potentially alters the standard Cabibbo-Kobayashi-Maskawa (CKM) phenomenology by giving rise, in particular, to extra flavor changing neutral currents (FCNC). We explore the conservative requirement that these should be suppressed, which yields relations between the CKM angles, the fermion and $W$ masses, and a renormalization scale $\mu$. For two generations, two solutions arise: either the mixing angle of the fermion pair the closer to degeneracy is close to maximal while, inversely, the mass and flavor states of the other pair are quasi-aligned, or mixing angles in both sectors are very small. For three generations, all mixing angles of neutrinos are predicted to be large (theta_{23}, close to maximal, is the largest) and the smallness of their mass differences induces mass-flavor quasi-alignment for all charged leptons. The hadronic sector differs in that the top quark is twice as heavy as the W. The situation is, there, bleaker, as all angles come out too large, but, nevertheless, encouraging, because theta_{12} decreases as the top mass increases. Whether other super-heavy fermions could drag it down to realistic values stays an open issue, together with the role of higher order corrections. The same type of counterterms that turned off the 4th order static corrections to the quark electric dipole moment are, here too, needed, in particular to stabilize quantum corrections to mixing angles.Comment: 40 pages, LaTeX, 3 figure

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

The 1-loop self-energy of an electron in a strong external magnetic field revisited

I calculate the 1-loop self-energy of the lowest Landau level an electron of mass m in a strong, constant and uniform external magnetic field B, beyond its always used truncation at (ln L)^2, L=|e|B/m^2. This is achieved by evaluating the integral deduced in 1953 by Demeur and incompletely calculated in 1969 by Jancovici, which I recover from Schwinger's techniques of calculation. It yields \delta m \simeq (\alpha*m/(4*\pi))*[(\ln L -\gamma_E -3/2)^2 -9/4 +\pi/(\beta-1) + \pi^2/6 +\pi*\Gamma[1-\beta]/L^{\beta-1} +(1/L)*(\pi/(2-\beta)-5) +{\cal O}(1/L^{>= 2})] with \beta \approx 1.175 for 75 =< L =< 10000. . The (\ln L)^2 truncation exceeds the precise estimate by 45% at L=100 and by more at lower values of L, due to neglecting, among others, the single logarithmic contribution. This is doubly unjustified because it is large and because it is needed to fulfill appropriate renormalization conditions. Technically challenging improvements look therefore necessary, for example when resumming higher loops and incorporating the effects of large B on the photonic vacuum polarization, like investigated in recent years.Comment: 15 pages, 7 figures. Revised version, more self-contained. To appear in IJMP