The electroweak form factor $\hat{\kappa}(q^2)$ and the running of $\sin^2\hat{\theta}_{\mathrm {W}}$

Abstract

Gauge independent form factors \rho^(e; e) and \hat{\kappa}^(e; e)(q^2) for Moller scattering at s << m_W^2 are derived. It is pointed out that \hat{\kappa}^(e; e) is very different from its counterparts in other processes. The relation between the effective parameter \hat{\kappa}^(e; e)(q^2,\mu) \sin^2 \hat{\theta}_W(\mu) and \sin^2 \theta_eff is derived in a scale-independent manner. A gauge and process-independent running parameter \sin^2 \hat{\theta}_W (q^2), based on the pinch-technique self-energy a_{\gamma Z} (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 \theta_eff. The q^2 dependence of \sin^2 \hat{\theta}_W (q^2) is displayed in the space and time-like domains.