COMPUTING THE WEAK MIXING ANGLE FROM ANOMALY CANCELLATION

I remark that the weak mixing angle in the standard model may be computed even in the absence of a grand unification symmetry. In particular, if there is an additional gauged U(1) symmetry at some large scale which can be made anomaly-free only by a Green-Schwarz (GS) mechanism, this typically results in a prediction for the weak angle. In the case of the standard model one can see that the standard Peccei-Quinn symmetry may be gauged and the anomalies cancelled through a GS mechanism. Remarkably enough, cancellation of anomalies works only for the ''canonical'' value sin2theta(w)=3/8. In the case of the supersymmetric standard model one can also find U(1) currents which may be made anomaly-free through a GS mechanism but the canonical value is only obtained in the absence of any Higgs multiplet. If the analysis is extended to include U(1) R-symmetries, there is a unique class of U(1)'s which give rise to the canonical value. The R-symmetry is only anomaly-free for sin2theta(w)=(4N(g)-3)/(10N(g)-3N(D)-3), where N(g), N(D) are the number of generation and Higgs pairs. The natural context in which the above scenario may naturally arise is string theory. I also emphasize other interesting possibilities offered by the GS mechanism to model-building.