Hadronic effects in Møller scattering at NNLO

Abstract

Two-loop electroweak corrections to polarized Møller scattering are studied in two different schemes at low energies. We find the finite Q2 corrections to be well under control. The hadronic and perturbative QCD corrections to the γZ two-point function are incorporated through the weak mixing angle at low energies, which introduce an error of 0.08 × 10−3 in the weak charge of the electron {Q}_W^e . Furthermore, by studying the scheme dependence, we obtain an estimate of the current perturbative electroweak uncertainty, delta {Q}_W^e ≈ 0.23 × 10−3, which is five times smaller than the precision estimated for the MOLLER experiment ( delta {Q}_W^e = 1.1 × 10−3). Future work is possible to reduce the theory error further.