The electroweak form factor \hatκ(q^2) and the running of \sin^2 \hatθ_W

Abstract

Gauge independent form factors ρ^(e; e) and \hatκ^(e; e)(q^2) for Moller scattering at s << m_W^2 are derived. It is pointed out that \hatκ^(e; e) is very different from its counterparts in other processes. The relation between the effective parameter \hatκ^(e; e)(q^2,μ) \sin^2 \hatθ_W(μ) and \sin^2 θ_eff is derived in a scale-independent manner. A gauge and process-independent running parameter \sin^2 \hatθ_W (q^2), based on the pinch-technique self-energy a_{γZ} (q^2), is discussed for all q^2 values. At q^2=0 it absorbs very accurately the Czarnecki-Marciano calculation of the Moller scattering asymmetry at low s values, and at q^2 = m^2_Z it is rather close to \sin^2 θ_eff. The q^2 dependence of \sin^2 \hatθ_W (q^2) is displayed in the space and time-like domains.