Evaluate radiative corrections to small-angle Bhabha scattering for alpha(mZ) extraction

Evaluate the impact of vertex and box radiative corrections in e^+e^- → e^+e^- at the Z pole on the extraction of the time-like electromagnetic coupling α(m_Z) from differential Bhabha-scattering measurements.

Background

A proposed determination of α(t) uses the differential cross section for e+e- → e+e- at √s = m_Z, exploiting the dominance of t-channel photon exchange at small scattering angles. The extracted space-like coupling must then be translated to the time-like coupling α(m_Z).

The analysis also requires radiative corrections to Bhabha scattering, particularly vertex and box contributions. Their impact on the proposed extraction, and therefore the associated theory uncertainty, has not yet been assessed.

References

Theory uncertainties enter through the need to translate $\alpha(t)$ to the time-like $\alpha(m_Z)$, and through radiative corrections to the process $e+ e- \to e+ e-$, in particular vertex and box contributions, whose impact on this analysis has not been evaluated so far.

— Theoretical and phenomenological aspects of the Electroweak physics WG studies for the 2026 ESPPU Physics Briefing Book  (2609.18607 - Blas et al., 16 Sep 2026) in Section 2.2, subsection “SM parameters,” paragraph beginning “Ref.~\cite{Riembau:2025ppc} proposes”