GRADED ALGEBRA AND NONCOMMUTATIVE GEOMETRY VERSION TO L–R SYMMETRIC MODEL

Abstract

A left–right symmetric model based on graded Lie algebra and noncommutative geometry is constructed. In this approach, the two Higgs fields H R and H L — responsible for the first stage symmetry breaking — transform as [Formula: see text] and [Formula: see text] under SU (2) L , SU (2) R and U(1). Their vacuum expectation values happen to be equal. A bi-doublet ɸ with zero U(1) charge for the second stage is also obtained. Enlarging the Higgs sector with the introduction of the triplets <δ L,R > and singlet <δ0> make parity spontaneously broken at a mass higher than that of the standard charged gauge boson. A fixed value for the Weinberg angle [Formula: see text] and a simple relation between neutral gauge bosons masses [Formula: see text] are predicted.