Two-loop renormalization of the electric charge in the Standard Model

Abstract

We discuss the renormalization of the electric charge at the two-loop level in the Standard Model of the electroweak interactions. We explicitly calculate the expression of the complete on-shell two-loop counterterm using the Background Field Method and discuss the advantages of this computational approach. We consider the related quantity $\hat{e}(\mu )$, defined in the $\text{ms}$ renormalization scheme and present numerical results for different values of the scale $\mu$. We find that the full 2-loop electroweak corrections contribute more than 10 parts in units $10^{-5}$ to the $\Delta \hat{\alpha }({\text{mz}}^2)$ parameter, obtaining ${\hat{\alpha }}^{-1}(\text{mz})=128.12\pm 0.05$ for $\Delta {\alpha }_{had}({\text{mz}}^2)=0.027572\pm 0.000359$.

Comments: 13 pages; 1 figure; version to appear on Physical Review D