Four-fermion production near the W pair-production threshold

We perform a dedicated study of the four-fermion production process e^- e⁺ → μ^- over(ν, ̄)_μ u over(d, ̄) X near the W pair-production threshold in view of the importance of this process for a precise measurement of the W boson mass. Accurate theoretical predictions for this process require a systematic treatment of finite-width effects. We use unstable-particle effective field theory (EFT) to perform an expansion in the coupling constants, Γ_W / M_W, and the non-relativistic velocity v of the W boson up to next-to-leading order in Γ_W / M_W ∼ α_ew ∼ v². We find that the dominant theoretical uncertainty in M_W is currently due to an incomplete treatment of initial-state radiation. The remaining uncertainty of the NLO EFT calculation translates into δ M_W ≈ 10 - 15   MeV, and to about 5 MeV with additional input from the NLO four-fermion calculation in the full theory.