Two-loop next-to-leading $\mt$ corrections to the $ρ$ parameter

The $O(G^2_μm_t^4)$ correction to the $ρ$ 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 $O(G^2_μm_t^2 m_z^2)$ correction to the ratio of neutral-to-charged current amplitudes is analysed in an $SU(2)$ model. The $O(G^2_μm_t^2 m_z^2)$ contribution is shown to be numerically comparable to the leading $O(G^2_μm_t^4)$ term for realistic values of the top mass. The resummation of higher-order effects is discussed.

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