Parity violating Moller scattering asymmetry up to the two-loop level

The paper investigates contributions of $Z$, $W$ and $\gamma$ intermediate states to the parity-violating Moller scattering asymmetry up to two-loop level. Using the Yennie--Frautschi--Suura factorization form for amplitudes, we demonstrate that QED corrections, with an exception of vacuum-polarization effects, cancel at the asymmetry level. We obtain chiral amplitudes at Born, one-loop and partially at two-loop level: boxes with lepton self-energies, ladder boxes and decorated boxes. Our calculations are relevant for the ultra-precise 11 GeV MOLLER experiment planned at Jefferson Laboratory and future ILC experiments. The numerical comparision of the two-loop contributions with the experimental accuracy of MOLLER is provided.