N.A. Papadopoulos

SU(2|1) symmetry, algebraic superconnections and a generalized theory of electroweak interactions☆

We discuss an extension of the standard model of electroweak interactions which incorporates the usual gauge fields and the Higgs fields in one generalized Yang-Mills field (or superconnection). It is shown that both this Yang-Mills field and the corresponding field strength (supercurvature) take their values in the real, graded Lie algebra SU(2|1). The lagrangian as obtained from this superconnection yields the standard model with interesting predictions for masses and couplings. The primordial, larger symmetry is realized as a hidden symmetry. The odd part survives in relations between couplings and masses, while the even part is broken to U(1)em, as usual, though in “reverse order” as compared to the standard model.

The QCD non-perturbative contribution to the axial form factor in radiative pion decay

Abstract We show that QCD non-perturbative terms a la Shifman-Vainshtein-Zakharov are crucial for understanding the radiative pion decay. We obtain for the axial-vector form factor γ = 0.0 ± 0.3 which is in very good agreement with one of the two experimental values γ exp = 0.15 ± 0.11 and excludes the other one γ exp = −2.1 ± 0.11.

Model independent determination of QCD quark masses

Abstract The method of approximate analytic continuation by duality (ACD), which permits to extrapolate a two-point function from its asymptotic QCD form down to Q2 = 0, is used to determine the value of the light quark masses in QCD. For the value of the four-quark condensate advocated by Shifman, Vainshtein and Zakharov we obtain (mu + md) = (21 ± 2) MeV at Q2 = 1 GeV2.

Structure of the space of reducible connections for Yang-Mills theories

Abstract The geometrical structure of the gauge equivalence classes of reducible connections are investigated. The general procedure to determine the set of orbit types (strata) generated by the action of the gauge group on the space of gauge potentials is given. In the so obtained classification, a stratum, containing generically certain reducible connections, corresponds to a class of isomorphic subbundles given by an orbit of the structure and gauge group. The structure of every stratum is completely clarified. A nonmain stratum can be understood in terms of the main stratum corresponding to a stratification at the level of a subbundle.

Hadronic part of the muon's (g − 2) from QCD

Abstract The hadronic part of the taus ( g - 2), a H ( τ ) , is relatively important due to the large mass of the lepton. A purely theoretical calculation of a H ( τ ) , using QCD and the analytic properties of the vacuum polarization tensor is presented. We obtain a H ( τ ) ≅ 3 × 10 −6 as compared to the pure QED contribution a QED ( τ ) = 1.17319 × 10 −3 .

Anomalies from nonfree action of the gauge group

Abstract The question whether new anomalies appear, connected with the finite dimensional part of the gauge group isomorphic to the structure group of the theory, is investigated in a systematical way. The stability groups from the stratification of the gauge group on the space of connections lead to anomalies. The detection of these anomalies within the equivariant approach pursued here is extremely simple. For a large class of theories it is shown that no new anomalies appear.

The vector boson masses in the standard model: Hadronic contributions to the mass shifts from the ACD method

Abstract We calculate the hadronic contributions to the W-and Z-mass shifts from QCD, taking account of the correct asymptotic QCD two-point functions and using a dispersive method to relate them (via duality) to the values at small momentum transfer. The method is well defined and free of ambiguities in the choice of quark masses. The resulting shifts are found to be large and positive, and dominate the total radiative mass corrections.

Light quark condensates from QCD sum rules

The light quark condensates have been determined by two different methods: By Laplace transformed QCD sum rules together with an improved hadronic continuum from extended PCAC and by analytic continuation by duality (ACD) of the asymptotic QCD amplitude. Both methods yield compatible results. The PCAC corrections are considerably large: for theu, d quarks near 8% and for theu, s quarks of order 60%.

THE ELECTROMAGNETIC MASS DIFFERENCE OF PIONS FROM ASYMPTOTIC QCD

AbstractWe show how the asymptotic behaviour of an analytic amplitude can yield information on the amplitude at small space-like momenta. Applying this to QCD two-point functions, we are able to obtain low energy parameters without using resonance saturation. In the special case considered here, we have calculated the electromagnetic mass difference of pions using only the asymptotic QCD amplitude. The result, in very good agreement with experiment is