C. Bouchiat

An anomaly-free version of Weinberg's model

Abstract We discuss the difficulties of carrying the renormalization program in a theory containing Adler anomalies. We present some models of weak and electromagnetic interactions, involving both lepton and quark fields, in which the troublesome anomalies cancel.

A theoretical analysis of parity violation induced by neutral currents in atomic cesium

Abstract In this paper we give a theoretical analysis of the parity violation phenomena in n S − n ′S transitions in atomic cesium induced by the electron-nucleus neutral-current interaction. The actual observation of parity violation consists in the measurement of an interference between the p.v. electric dipole amplitude E l pv with the electric amplitude induced by a static electric field. Our theoretical work must then include a calculation of the diagonal and non-diagonal polarizabilities of the states of atomic cesium. We have used a one-electron model proposed by Norcross which incorporates some many-body effects like the electric screening induced by the core polarization in a semi-empirical way. Our calculated values of the diagonal and non-diagonal polarizabilities of the n S states are in good agreement with the existing measurements; this confirms the already well-established success of the model in predicting the radiative transitions in cesium. We present theoretical arguments supported by detailed numerical computations showing that the one-particle matrix element of the parity-violating electron-nucleus interaction and the parity-violating electric dipole amplitude E l pv itself weakly depend on the shape of the one-electron potential provided the binding energies of the valence states are reproduced accurately. Furthermore it turns out that because of a compensation mechanism, the parity-violating transition is induced by the radiation field outside the ion core region where the screening can be described simply in terms of the measurable cesium ion polarizability. Our results are then used to extract, from the Ecole Normale Superieure experiment, a value of the weak charge Q w = −57.1 ± 9.4 (r.m.s. statistical deviation) ± 4.7 (systematic uncertainty). This number is to be compared with the prediction of the Weinberg-Salam model with electro-weak radiative corrections: Q w = −68.6 ± 3.0. A general discussion of the uncertainties of the atomic physics calculations leads to the conclusion that the theoretical error which affects the determination of Q w is not likely to exceed 10 to 15%.

Algebra currents and the deviation from the |ΔI| = 1/2 rule in K → 3π decay

Abstract Starting from the usual current-current weak Lagrangian and using current algebra, the deviations from the |ΔI| = 1/2 rule in K→ 3π decays are determined in terms of the K → 2π rates. The need for better data on K → 2π and K → 3π decays is stressed in order to arrive at a possible discrimination between a fundamental or a dynamic |ΔI| = 1/2 rule. As a by-product the PC conserving 3π decay of Ko1 is calculated in the linear approximation.

The algebra of currents and the ∣ ΔI ∣ = 12 rule for K-meson non-leptonic decay

Abstract The difficulties occuring in a recent derivation of the ∣ ΔI ∣ = 1 2 rule for the K meson decay into zero energy-momentum pions are removed by a suitable definition of the unphysical amplitude. The selection rule is shown to be valid only in the limit of zero pion mass or in special models.

Inclusive observables and hard gluon emission in neutrino deep inelastic scattering

We derive the predictions of perturbative QCD together with non-perturbative corrections for a set of inclusive observables connected with the angular distribution of light-cone energy in deep inelastic neutrino scattering. Our particular choice of observables has been made in order to meet important physical requirements besides the necessary condition of infrared regularity. Our inclusive observables receive their dominant contribution from the quark fragmentation region. The non-perturbative contribution is calculable in a rather model-independent way and stays at an acceptable level in realistic experimental conditions. The QCD perturbative contribution, which takes the simple form of a convolution product, exhibits a strongly decreasing behaviour as a function of the Bjorken scaling variable x, superimposed on a constant background associated with the non-perturbative terms, allowing a rather clean separation of the two effects. The perturbative term being dominated by the process of hard-gluon emission, an experimental investigation of the observables discussed here may be a good way to detect the effect of gluon emission in deep inelastic neutrino scattering.