Prediction for Z-mass is a crucial test of the standard model

Abstract

In schemes with oneW boson and twoZ-bosons (mediating the charged and neutral current interactions involving ordinary fermions) based on the direct product and simple groups, SU(2) × U(1) ×u′(1) andG × U(1) (G is a simple group of rank two), the following two questions are discussed. (1) What are the necessary and sufficient conditions for minimal reducibility of the effective four-fermion neutral current interaction (involving ν_μ-hadron, electron-hadron and ν_μ-electron sectors) to the corresponding prediction of the standard model? (2) In what way are the masses of the twoZ-bosons constrained relative to the mass of the neutral boson of standard model? The answers to these questions are given first by keeping the underlying Higgs structure, responsible for gauge-boson (and fermion) mass generation, completely arbitrary (called Higgs-independent case) and then by making a specific choice for the Higgs structure resulting in a natural mass relation for theW andZ-bosons that is an exact counterpart toM ^(S)/2 _W =M ^(S)/2 _Z sec² ϑ _W for the standard model (called Higgs-dependent case). The distinction between these two cases is brought out clearly as also that between the direct product and simple groups. Whether or not any assumption is made about the Higgs structure, with either the direct product or the simple group, it is concluded that in general there is aZ-boson lighter than the neutral boson of the standard model.