The electroweak form factor κ̂ ( q 2 ) and the running of sin 2 θ̂

The electroweak form factorˆκ(q 2) and the running of sin 2 ˆ θ W Gauge independent form factors ρ (e; e) andˆκ (e; e) (q 2) for Møller scattering at s ≪ m 2 W are derived. It is pointed out thatˆκ (e; e) is very different from its counterparts in other processes. The relation between the effective parameterˆκ (e; e) (q 2 , µ) sin 2 ˆ θ W (µ) and sin 2 θ lept ef f is derived in a scale-independent manner. A gauge and process-independent running parameter sin 2 ˆ θ 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 Møller scattering asymmetry at low s values, and at q 2 = m 2 Z it is rather close to sin 2 θ lept ef f. The q 2 dependence of sin 2 ˆ θ W (q 2) is displayed in the space and time-like domains.