Applications of unitarity in the standard model.

Abstract

Unitarity is a crucial ingredient of any quantum field theory. The requirement that the sum of probalities of all possible consequences resulting out of a given initial situation equals 100% is inescapable. We study the practical consequences that can be derived from the unitarity requirement. We show how unitarity can be proved in a quantum field theory. First the old proof by Veltman is reviewed. Next a new derivation of the Cutkosky-Veltman cutting rules is given. As an application, we discuss the constraints on the photon self energy and the resulting effect on the photon propagator. Next the decomposition of transition amplitudes into partial wave amplitudes is discussed. Bounds on these partial waves are derived. The concept of 'partial wave unitarity' is explained. Assuming that for weak interactions the lowest order Feynman diagrams will always dominate the higher order diagrams, bounds can be put on certain parameters in the standard model Lagrangian. An upper limit for the Higgs mass is derived, and the four vector boson vertex is constrained. Finally we study the partial wave decomposition for off-shell scattering processes. We find that such off-shell partial waves cannot be constrained, as opposed to the on-shell partial waves.