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The contributions to the electron-electron-photon vertex of two-loopelectroweak corrections are calculated. The relative correction to theparity-violating asymmetry of M{\o}ller scattering for the case of 11 GeVelectron scattered off the electron at rest is found to be about -0.0034 andshould be taken into account at future experiment MOLLER at JLab.

Two-loop electroweak vertex corrections for polarized M{\o}ller scattering