Weak mixing angle in the Thomson limit

We present a calculation of the weak mixing angle in the MS¯\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \overline{\mathrm{MS}} $$\end{document} renormalization scheme which is relevant for experiments performed at very low energies or momentum transfers. We include higher orders in the perturbative QCD expansion, as well as updated phenomenological and theoretical input, and obtain the result sin2θ^W0=0.2386852\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ { \sin}^2{\widehat{\theta}}_W(0)=0.23868(5)(2) $$\end{document} for the reference values α^sMZ=0.1182\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\widehat{\alpha}}_s\left({M}_Z\right)=0.1182 $$\end{document} and m^cm^c=1.272GeV\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\widehat{m}}_c\left({\widehat{m}}_c\right)=1.272\ \mathrm{GeV} $$\end{document}. The first quoted error is from the current Standard Model evaluation of the mixing angle at the Z boson mass scale. The second error represents the theoretical and parametric uncertainties induced by the evolution to the Thomson limit and is discussed in detail.