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The self-energy and vertex QED radiative corrections (Z alpha^2 f(Z alpha)) are shown to give a large negative contribution to the parity nonconserving (PNC) amplitude in heavy atoms. The correction -0.7(2)% found for the 6s-7s PNC amplitude in Cs brings the experimental result for this transition into agreement with the standard model. The calculations are based on a new identity that expresses the radiative corrections to the PNC matrix element via corrections to the energy shifts induced by the finite nuclear size.

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