Klaus Sibold

Gauge independence in ordinary Yang-Mills theories

Abstract Dependence on the gauge parameter α is detected by means of BRS transformations which act also on α. Establishing the corresponding Slavnov identity means controlling gauge dependence at the same time. Simple algebraic manipulation thereby replace the use of Wilson expansions and complete the renormalization scheme independent treatment.

Time-ordered perturbation theory on non-commutative spacetime: Basic rules

Abstract. Assuming that the S-matrix on non-commutative (NC) spacetime can still be developed perturbatively in terms of the time-ordered exponential of the interaction Lagrangian, we investigate the perturbation theory of NC field theory. We first work out with care some typical Green functions starting from the usual concepts of time-ordering and commutation relations for free fields. The results are found to be very different from those in the naive approach pursued in the literature. A simple framework then appears naturally which can incorporate the new features of our results and which turns out to be the usual time-ordered perturbation theory extended to the NC context. We provide the prescriptions for computing S-matrix elements and Green functions in this framework. We also emphasize that the naive seemingly covariant approach cannot be reproduced from the current one, in contrast to the field theory on ordinary spacetime. We attribute this to the phase-like non-local interaction intrinsic in NC field theory which modifies the analyticity properties of the Green functions significantly.

Higgs and top mass from reduction of couplings

Abstract We reduce the couplings in the standard model with one Higgs doublet and n generations and obtain for three generations 61 GeV and 81 GeV for the mass of the Higgs particle and the top quark respectively. The error is estimated to be about 10–15%.

The Anomaly in the Slavnov Identity for

Abstract We solve the consistency conditions of the BRS symmetry in a general N = 1 sypersymmetric Yang-Mills theory with semi-simple gauge group. As a result we find uniquely the supersymmetric extension of the chiral anomaly. Its coefficient is calculated in one loop and does not, in general, vanish. This corrects our earlier statement on the absence of this anomaly.

N=1

The renormalization of the Minimal Supersymmetric Standard Model is discussed. In particular we focus on the soft-supersymmetry breaking sector of the MSSM and comment on non-renormalization theorems.

Supersymmetric {Yang-Mills} Theories

Abstract. We examine the unitarity issue in the recently proposed time-ordered perturbation theory on noncommutative (NC) spacetime. We show that unitarity is preserved as long as the interaction Lagrangian is explicitly hermitian. We explain why it makes sense to distinguish the hermiticity of the Lagrangian from that of the action in perturbative NC field theory and how this requirement fits in this framework.

Renormalization of the minimal supersymmetric standard model

Abstract An axial current is defined in supersymmetric QED and its anomalous Ward identity equations are derived. The anomaly is shown to have no radiative corrections.

Time-ordered perturbation theory on non-commutative spacetime II: Unitarity

Abstract We construct, in the tree approximation, the complete off-shell supercurrent, including Faddeev-Popov fields and gauge contributions for a general supersymmetric Yang-Mills theory maintaining parity. Due to the conformally non-covariant character of the Faddeev-Popov procedure this supercurrent cannot be improved. The other currents of the superconformal group can therefore no longer be obtained by simply forming moments.

The absence of radiative corrections to the axial current anomaly in supersymmetric QED

Abstract If the matter self-couplings in SYM theories are certain uniquely determined power series of the coupling then it is necessary and sufficient, for the vanishing of all β-functions to all orders, that the gauge β-function and the anomalous dimensions of the matter fields vanish at the one-loop order.

The supercurrent in N = 1 supersymmetric Yang-Mills theories: (I). The classical case

Abstract We show to all orders of perturbation theory that in a general N = 1 supersymmetric Yang-Mills theory maintaining parity there exists a supercurrent. Since all Faddeev-Popov fields and gauge contributions are taken into account, the relation between supercurrent anomalies and the Callan-Symanzik equation can be established. The connection with the axial anomaly coefficient is somewhat obscured by the fact that the supercurrent cannot be improved.