Florian Scheck

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.

Analysis of Leptonic Charged Weak Interactions

Abstract Motivated by the desire to test the limits of the standard model via the Lorentz structure of charged weak interactions we perform an extended and systematic analysis of charge-changing leptonic vertices. Based on a helicity projection form of the effective hamiltonian, the analysis yields improved limits on noncanonical couplings from recent, high-precision measurements in muon decay. We also give limits on possible, charge-neutral exchanges with intrinsic electron and muon number.

Quantum gauge models without (classical) Higgs mechanism

We examine the status of massive gauge theories, such as those usually obtained by spontaneous symmetry breakdown, from the viewpoint of causal (Epstein–Glaser) renormalization. The BRST formulation of gauge invariance in this framework, starting from canonical quantization of massive (as well as massless) vector bosons as fundamental entities, and proceeding perturbatively, allows one to rederive the reductive group symmetry of interactions, the need for scalar fields in gauge theory, and the covariant derivative. Thus the presence of higgs particles is understood without recourse to a Higgs(–Englert–Brout–Guralnik–Hagen–Kibble) mechanism. Along the way, we dispel doubts about the compatibility of causal gauge invariance with grand unified theories.

Muon Decay: Measurement of the Transverse Positron Polarization and General Analysis

Abstract The components of the transverse polarization of the positrons in the decay μ + → e + ν ν have been measured as a function of the positron total energy. Their energy average is〈PT1〉=0.016±0.023, 〈PT2〉=0.007±0.023 (statistical plus systematic errors). The energy dependence of PT1 and PT2 yields the μ decay parameters α A , β A (with their linear combination η= (α−2β) A ) and α′ A , β′ A , respectively. In an analysis based only on the most general, local, derivative-free four-fermion point interaction, and including all corresponding measurements, the complete set of parameters describing muon decay is determined for the first time.

Amplitude and trace reduction using Weyl-Van der Waerden spinors: Pion pair decay π+ → e+e−e+νe

Abstract Feynman diagram calculations are considerably simpler in the framework of Weyl-Van der Waerden spinors than in the standard formalism. We collect the basic formulae and illustrate the method by a few examples. We study pion pair decay in considerable detail and find that the long-standing ambiguity in determining the ratio of axial vector to vector structure term that hampered pion radiative decay can be resolved in the pair decay.

The Lorentz structure of leptonic charged weak interactions

We analyze all available data on leptonic, charge changing, weak interactions in terms of more general Lorentz structures than V-A. For this purpose we construct classes of models which follow the pattern of unified gauge theories but which are general enough so as to make use of the nearly complete experimental information. In a first class of models we assume the interactions to be mediated by the exchange of charged bosons whose couplings to leptons fulfill either strict universality or modified universality (for spin-zero exchanges). In a second class of models we investigate to which extent the data admit or require unconventional couplings in addition to V-A. A χ2 analysis is presented for nine typical cases and limits on non-canonical couplings are given. As expected the data admit relatively large deviations from V-A. A few per mill measurement of the parameter ξ in μ decay as well as an absolute measurement of the muon neutrino helicity from pion decay would help to remedy this unsatisfactory situation.

Can (noncommutative) geometry accommodate leptoquarks

We investigate the geometric interpretation of the Standard Model based on noncommutative geometry. Neglecting the

Only three flavours

S_0

Quadrupole interactions in pionic and kaonic atoms

-reality symmetry one may introduce leptoquarks into the model. We give a detailed discussion of the consequences (both for the Connes-Lott and the spectral action) and compare the results with physical bounds. Our result is that in either case one contradicts the experimental results.

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

Abstract It is shown that it is possible to account for all the experimental indications for neutrino oscillations with just three flavours. In particular we suggest that the atmospheric neutrino anomaly and the LSND result can be explained by the same mass difference and mixing. Possible implications and future test of the resulting mass and mixing pattern are given.