Two-loop next-to-leading $\text{mt}$ corrections to the $\rho$ parameter

Abstract

The $O(G_{\mu }^2{m}_t^4)$ correction to the $\rho$ parameter is computed within the Standard Model using the current algebra formulation of radiative corrections. This approach is proved to be equivalent to the effective Lagrangian method proposed by Barbieri {\em et al.} Using the same framework, the $O(G_{\mu }^2{m}_t^2{m}_z^2)$ correction to the ratio of neutral-to-charged current amplitudes is analysed in an $SU(2)$ model. The $O(G_{\mu }^2{m}_t^2{m}_z^2)$ contribution is shown to be numerically comparable to the leading $O(G_{\mu }^2{m}_t^4)$ term for realistic values of the top mass. The resummation of higher-order effects is discussed.

Comments: CERN-TH.7180/94, DFPD 94/TH/12 and NYU-Th-94/02/01, 26 pages (LaTeX + PS figures, needs psfig (optional to include figures), doublespace, equations, and cite styles)