Global restrictions to the Mixing Angle $θ_W$

Abstract

We provide the theoretic value 1/2 for the quantity $\sin**2θ_W=e**2/g**2$, as opposite to the experimental value of $\sin**2θ_W=1-M_W**2/M_Z**2 \sim 0.23$, 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 $\sin**2θ_W$ 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.