Weak Mixing Angle in the Thomson Limit

Understand

We present a calculation of the weak mixing angle in the $\overline{\rm\small MS}$ 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 $\sin^{2}{\theta}_W(0) = 0.23868(5)(2)$ for the reference values $\alpha_s(M_Z) = 0.1182$ and $m_c(m_c) = 1.272$ GeV.
• 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.