DERIVATION OF A NOVEL RELATION BETWEEN THE MASSES OF THE TOP-QUARK AND AN ELECTROWEAK SCALAR

Abstract

We start with generating the masses of the charged leptons by gap equations. Then we present analogous radiative masses of the electroweak vector-bosons. We derive them from the global SU (2)L× U (1) symmetry without making recourse to any scalar fields or spontaneous breaking of gauge symmetry. Nevertheless, we find the mixing angle relation [Formula: see text]. Moreover, we find that the radiatively generated masses of Z and W require the existence of a cutoff energy of the order of 1014 GeV, which is just the grand-unification energy scale. We then eliminate the cutoff by renormalizing the two coupling constants and arrive at a function between mW and m top if mZ, [Formula: see text] and sin 2θ eff are given. Comparison with the electroweak precision data shows that the predicted value of mW does reproduce the experimental data though the vacuum loops of the leptons, of the light quarks as well as of possible scalar particles have been ignored. Then, we introduce a doublet of scalar bosons to investigate its effect on the mW prediction. We fix its couplings to the photon, to W as well as Z by localizing SU (2)L× U (1). The radiative mZ and mW results interdict a spontaneous breaking of the gauge symmetry. So there are an elementary charged and neutral scalar field. Their masses are identical. We show that there is no radiative effect of these scalars on the masses of W and Z. However, the scalar fields affect the coupling constants and, by this, the relationship between mW and m top alters. We calculate the modifications and find a relatively small effect. It seems to be comparable in magnitude with the QCD-corrections of the loops of vacuum polarization. Substituting the experimental mW value, we get a relation between m top and m scalar . The mass of the top-quark is increasing with increasing m scalar . In the standard model, m top also increases with increasing m Higgs . The effect of the elementary scalar is however much weaker.