We compute the vector analyzing power (VAP) for the elastic scattering of transversely polarized electrons from protons at low energies using an effective theory of electrons, protons, and photons. We study all contributions through second order in E / M, where E and M are the electron energy and nucleon mass, respectively. The leading-order VAP arises from the imaginary part of the interference of one-and two-photon exchange amplitudes. Subleading contributions are generated by the nucleon magnetic moment and charge radius as well as recoil corrections to the leading-order amplitude. Working to O͑E / M͒ 2 , we obtain a prediction for A n that is free of unknown parameters and that agrees with the recent measurement of the VAP in backward angle ep scattering.

The longitudinal asymmetry due to Z 0 exchange is calculated in quasi-elastic electron-deuteron scattering at momentum transfers |Q 2 | ≃ 0.1 GeV 2 relevant for the SAMPLE experiment. The deuteron and pn scattering-state wave functions are obtained from solutions of a Schrödinger equation with the Argonne v 18 potential. Electromagnetic and weak neutral one-and two-nucleon currents are included in the calculation. The two-nucleon currents of pion range are shown to be identical to those derived in Chiral Perturbation Theory. The results indicate that two-body contributions to the asymmetry are small (≃ 0.2%) around the quasi-elastic peak, but become relatively more significant (≃ 3%) in the high-energy wing of the quasielastic peak.pacs: 13.10.+q, 21.45.+v, 25.30.Fj

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