Weak Mixing Angle in the Thomson Limit

TL;DR

This paper calculates the weak mixing angle at very low energies using advanced perturbative QCD methods, providing precise theoretical predictions relevant for low-energy experiments.

Contribution

It offers a refined calculation of the weak mixing angle in the Thomson limit including higher-order QCD corrections and updated input parameters.

Findings

Calculated ng in the Thomson limit with high precision.

Quantified uncertainties from theoretical and parametric sources.

Provided a result applicable to low-energy experimental analyses.

Abstract

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.