BRST QUANTIZATION OF SU(2/1) ELECTROWEAK THEORY IN THE SUPERCONNECTION APPROACH, AND THE HIGGS MESON MASS

Abstract

A superconnection, in which a scalar field enters as a zero-form in the odd part of the superalgebra, is used in the BRST quantization of the SU (2/1) “internally superunified” electroweak theory. A quantum action is obtained, by applying symmetric BRST/anti-BRST invariance. Evaluating the mass of the Higgs field, we exhibit the consistency between two approaches: (a) applying the supergroup’s (gauge) value for λ, the coupling of the scalar field’s quartic potential, to the conventional (spontaneous symmetry breakdown) evaluation; (b) dealing with the superconnection components as a supermultiplet of an (global) internal supersymmetry. This result thus provides a general foundation for the use of “internal” supergauges. With SU (2/1) broken by the negative squared mass term for the Higgs field and with the matter supermultiplets involving added “effective” ghost states, there is no reason to expect the symmetry’s couplings not to be renormalized. This explains the small difference between predicted and measured values for sin2θw, namely the other coupling fixed by SU (2/1) beyond the Standard Model’s SU(2)×U(1), and where the experimental results are very precise. Using the renormalization group equations and those experimental data, we thus evaluate the energy E8 at which the SU (2/1) predicted value of 0.25 is expected to correspond to the experimental values. With SU (2/1) precise at that energy Es=5 TeV , we then apply the renormalization group equations again, this time to evaluate the corrections to the above λ, the quartic coupling of the scalar fields; as a result we obtain corrections to the prediction for the Higgs meson’s mass. Our result predicts the Higgs’ mass [170 GeV, according to unrenormalized SU (2/1)] to be as low as 130±6 GeV , using for the top quark mass the recently measured value of 174 GeV .