Towards a \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$Z\prime $$ \end{document} Gauge Boson in Noncommutative Geometry

We study all possible U(1)-extensions of the standard model within the framework of noncommutative geometry with the algebra \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathbb{H} \oplus \mathbb{C} \oplus \mathbb{C} \oplus M_3 (\mathbb{C}) $$ \end{document}. Comparison to experimental data about the mass of a hypothetical \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$Z\prime $$ \end{document} gauge boson leads to the necessity of introducing at least one new family of heavy fermions.