Global restrictions to the Mixing Angle ${\theta }_W$

Abstract

We provide the theoretic value 1/2 for the quantity $\sin \ast \ast 2{\theta }_W=e\ast \ast 2/g\ast \ast 2$, as opposite to the experimental value of $\sin \ast \ast 2{\theta }_W=1-M_W\ast \ast 2/M_Z\ast \ast 2\sim 0.23$, in the electro-weak gauge group $SU(2)\otimes U(1{)}_Y$. The arguments we use are of topological nature and have to do with natural requirements of globality in the transformations of the gauge algebra. This results supports the idea that the two definitions of $\sin \ast \ast 2{\theta }_W$ cannot be simultaneously identified except, maybe, in an asymptotic limit corresponding to an earlier stage of the Universe, before the spontaneous symmetry breaking had taken place.

3 pages, Latex2e, Presented at 21st International Colloquium on Group Theoretical Methods in Physics, Goslar, Germany, 15-20 Jul 1996