CONSTRAINTS ON THE HIGGS AND TOP-QUARK MASSES FROM EFFECTIVE POTENTIAL AND NONCOMMUTATIVE GEOMETRY

We consider the standard model in the formulation.of non-commutative geometry, for a Euclidean space-time consisting of two copies. The electroweak scale is set by the vacuum expectation value of a scalar field and is undetermined at the classical level. By adding the Coleman-Weinberg effective potential, that scale turns out to be fixed. Provided that the renormalized form of the Lagrangian maintains the vanishing of the cosmological constant, we show that the only solutions for the minimization equations of the total potential occur in the narrow band 146.2 less-than-or-equal-to m(t) less-than-or-equal-to 147.4 GeV for the top quark mass, with the corresponding Higgs mass 117.3 less-than-or-equal-to m(H) less-than-or-equal-to 142.6 GeV.