Weak mixing angle at low energies

We determine the weak mixing angle in the $\overline{\mathrm{MS}}$ scheme, ${sin}^2{\widehat{\theta }}_W(\mu )$, at energy scales $\mu$ relevant for present and future low-energy electroweak measurements. We relate the renormalization group evolution of ${sin}^2{\widehat{\theta }}_W(\mu )$ to the corresponding evolution of $\widehat{\alpha }(\mu )$ and include higher-order terms in ${\alpha }_s$ and $\alpha$ that had not been treated in previous analyses. We also update the analysis of nonperturbative, hadronic contributions and argue that the associated uncertainty is small compared to anticipated experimental errors. The resulting value of the low-energy $\overline{\mathrm{MS}}$ weak mixing angle is ${sin}^2{\widehat{\theta }}_W(0)=0.23867\pm 0.00016$.

Figure 1

Scale dependence of the weak mixing angle in the $\overline{\mathrm{MS}}$ renormalization scheme.