Four-fermion production near the W pair-production threshold

We perform a dedicated study of the four-fermion production process e−e+→μ−ν¯μud¯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, ΓW/MWΓW/MW, and the non-relativistic velocity v of the W   boson up to next-to-leading order in ΓW/MW∼αew∼v2ΓW/MW∼αew∼v2. We find that the dominant theoretical uncertainty in MWMW is currently due to an incomplete treatment of initial-state radiation. The remaining uncertainty of the NLO EFT calculation translates into δMW≈10–15 MeVδMW≈10–15 MeV, and to about 5 MeV with additional input from the NLO four-fermion calculation in the full theory.