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 $\ms$ 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 $Δ\hatα(\mz^2)$ parameter, obtaining $\hatα^{-1}(\mz)= 128.12 \pm 0.05$ for $Δα_{had}(\mz^2) =0.027572 \pm 0.000359$.

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

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