Heavy top effects in the standard electroweak model.

Abstract

We investigate heavy top quark effects in the standard model with two different approaches. The first approach is through the KM suppressed rare decays. Particularly, we find that, without QCD corrections, the branching ratio $B(B\sb s \to \gamma\gamma)$ is estimated to be of the order of 10$\sp{-7}$ and the photon spin orientations are found to be fairly sensitive to the top quark mass. In addition, we show that the calculation of $b \to s\gamma\gamma$ can be greatly simplified by extending Low's low-energy theorem to a case involving non-soft-bremsstrahlung. In the second approach, we show that in the standard model, when the mass of the top quark becomes very large, compared to other mass scales and external momenta, contraints develop in the field system. The top field becomes nonlinearly realized. $SU(2)\ \otimes\ U(1)$ remains a symmetry at the S-matrix level. A general formulation for the one light particle irreducible Green's functional $\Gamma\sb{1LPI}$ is presented in the setting of the external field technique and derivative expansion. The bosonic part of $\Gamma\sb{1LPI}$ is explicitly contructed. With $\Gamma\sb{1LPI}$, we then determine the effective Lagrangian $L\sb{eff}$ which encompasses all the top effects for all the low energy bosonic processes. Examples are given to show that our approach easily reproduce known results. Wess-Zumino terms arisen from chiral anomalies are also discussed.