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

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

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

Mixing angles of quarks and leptons as an outcome of SU(2) horizontal symmetries

We show that all mixing angles are determined, within experimental uncertainty, by a product of SU(2) horizontal symmetries intimately linked to the algebra of weak neutral currents. This concerns: on one hand, the three quark mixing angles; on the other hand, a neutrino-like pattern in which theta_{23} is maximal and tan (2 theta_{12}) = 2. The latter turns out to exactly satisfy 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}) \leq 0.1: theta_{13} = +/- 5.7 10^{-3} and theta_{13} = +/- 0.2717.Comment: While calculations are unchanged w.r.t. arXiv:0705.1237, the horizontal symmetries controlling the mixing angles have been uncovered, motivating a change of title and a new entry in the arXiv. A new point of view about which angles are measured has also been adopte

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"

Mixing and 1-loop flavor structure of fermionic currents in the Standard Model of electroweak interactions

8 pagesWe show that, unlike mass matrices, the fermionic gauge currents of the Standard Model exhibit, at the quantum level, remarkable SU(2)_f flavor properties at the observed values of the mixing angles. They accommodate all measured mixing for three families of quarks, and, for neutrinos, maximal theta_{23}, quark-lepton complementarity tan(2 theta_c)=1/2 \tan (2 theta_{12})=2, and a not so small sin^2(2 theta_{13}) = .267 within the present 90% c.l. interval of the T2K experiment

Unlocking the Standard Model. IV. N=1 AND 2 generations of quarks : spectrum and mixing

86 pages, 12 pdf figures. The previous version has been largely extended. The case of 1 generation has been included. The importance of both u-c and d-s mixing angles for 2 generations is emphasized. 1/2 leptonic decays are investigated. Several figures and references have been added. Some misprints have be corrected.Using a one-to-one correspondence between its complex Higgs doublet and very specific quadruplets of bilinear quark operators, the Glashow-Salam-Weinberg model for 2 generations is extended, without adding any extra fermion, to 8 composite Higgs multiplets. 8 is the minimal number required to suitably account, simultaneously, for the pseudoscalar mesons that can be built with 4 quarks and for the mass of the W gauge bosons. Their masses being used as input, together with elementary low energy considerations for the pions, we calculate all other parameters, masses and couplings. We focus in this work on the spectrum of the 8 Higgs bosons, and on the two u-c and d-s mixing angles, showing that this is very fine-tuned physics. We show in particular that the u-c mixing angle cannot be safely tuned to 0. Symmetries are investigated in detail. We leave the study of couplings and of their content of non-standard physics to a forthcoming work

Large mixing angles in a SU(2)_L gauge theory of weak interactions as a resonant effect of 1-loop transitions between quasi-degenerate fermions

We show that 1-loop transitions between two quasi-degenerate fermions can induce a potentially large renormalization of their mixing angle, and a large renormalized Cabibbo (or PMNS) angle when the second fermion pair in the same two generations is far from degeneracy. At the resonance, the "Cabibbo angle" gets maximal and simply connected to masses without invoking any new physics beyond the standard model. This solution appears as the only one "perturbatively stable" (mixing angles are then renormalized with respect to their classical values by small amounts).Comment: 8 pages, 1 figur