6533b7d0fe1ef96bd125b71a

RESEARCH PRODUCT

Group-Theoretic analysis of the mixing angle in the electroweak gauge group

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In this paper the authors provide strong mathematical support for the idea that the experimentally measured magnitude 1 - M{sub W}{sup 2}/M{sub Z}{sup 2} associated with sin{sup 2}{theta}{sub w} in the standard model of electroweak interactions cannot be simultaneously identified with the squared quotient of the electric charge by the SU(2) charge, e{sup 2}/g{sup 2}. In fact, the natural, mathematical requirement that the Weinberg rotation between the gauge fields associated with the third component of the {open_quotes}weak isospin{close_quotes} (T{sub 3}) and the hypercharge (Y) proceeds from a global Lie-group homomorphism of the SU(2) {circle_times} U(1){sub y} gauge group in some locally isomorphic Lie group [which then proves to be U(2)], and not from a local (Lie algebra) isomorphism, imposes strong restrictions so as to fix the single value e{sup 2}/g{sup 2} = 1/2. The two definitions of sin{sup 2}{theta}{sub w} can only be identified in the asymptotic limit corresponding to an earlier stage of the universe before the spontaneous symmetry breaking had taken place.