W-pair production near threshold in unstable particle effective theory

In this thesis we present a dedicated study of the four-fermion production process e- e+ ---> mu- nubar_mu u dbar X near the W-pair production threshold, in view of its importance for a precise determination of the W-boson mass at the ILC. The calculation is performed in the framework of unstable-particle effective theory, which allows for a gauge-invariant inclusion of instability effects, and for a systematic approximation of the full cross section with an expansion in the coupling constants, the ratio Gamma_W/M_W, and the non relativistic velocity v of the W boson. The effective-theory result, computed to next-to-leading order in the expansion parameters Gamma_W/M_W ~ alpha_ew ~ v^2, is compared to the full numerical next-to-leading order calculation of the four-fermion production cross section, and agreement to better than 0.5 % is found in the region of validity of the effective theory. Furthermore, we estimate the contributions of missing higher-order corrections to the four-fermion process, and how they translate into an error on the W-boson mass determination. We find that the dominant theoretical uncertainty on M_W is currently due to an incomplete treatment of initial-state radiation, while the remaining combined uncertainty of the two NLO calculations translates into dM_W ~ 5 MeV. The latter error is removed by an explicit computation of the dominant missing terms, which originate from the expansion in v of next-to-next-to leading order Standard Model diagrams. The effect of resummation of logarithmically enhanced terms is also investigated, but found to be negligible