Using two different approaches, we perform updated and detailed calculationsof the complete one-loop (Next-to-Leading Order (NLO)) set of electroweakradiative corrections to the parity violating e- e- -> e- e- (gamma) scatteringasymmetry. Our first approach, more classical, relies on calculations "by hand"with reasonable approximations. Our second approach relies on program packagesFeynArts, FormCalc, LoopTools, and FORM. The detailed numerical analysis of thevarious contributions is provided for a wide range of energies relevant for theultra-precise 11 GeV MOLLER experiment planned at the Jefferson Laboratory, aswell as future experiments at the International Linear Collider (ILC). Thenumerical results obtained within the on-shell renormalization scheme using twodifferent sets of renormalization conditions are in excellent agreement. Wealso calculate the total NLO correction in the Constrained DifferentialRenormalization (CDR) scheme. Analysis of the results, along with theincreasing experimental precision, shows that it is feasible that thecorrections at the Next-to-Next-to-Leading Order (NNLO) level may be importantfor the next generation of high-precision experiments.
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