| Using the Eikonal approximation, we study single spin azimuthal asymmetry in elastic and in-elastic lepton-nucleon scattering for the case of transversely polarized nucleons with unpolarized lepton beam. We follow two different approaches to evaluate the asymmetry. In the first approach we utilize the convolution theory of Fourier transforms to express the nucleon potential that appears in the Coulomb phase formula in terms of the nucleon's Dirac and Pauli form factors in the nucleon current density for transversely polarized nucleons. In the second approach, we explicitly evaluate the potential due to transversely polarized nucleons in impact parameter space. The result shows that this potential is asymmetric about an axis normal to the transverse plane; a result that is consistent with the fact that the nucleon charge density (or the unpolarized impact parameter dependent parton distribution function) is transversely distorted for transverse nucleon polarization, which is not the case for longitudinal polarization of the nucleon. To further confirm this fact, we calculate the average transverse momentum experienced by the scattered electron. This quantity is zero considering scattering from a classical dipole moment while our results show a non-zero average transverse momentum even for scattering from a neutron; there we get a negative value for the average momentum, and a positive one (and larger in magnitude) for the case of a proton. The sign of the average transverse momentum is directly related to the sign of the single spin asymmetry, where it is negative in the case of a neutron target and positive for a proton. The expansion of the Eikonal amplitude reveals that the asymmetry is due to the interference of the one and two photon exchange Eikonal amplitudes. In both of the above mentioned approaches, we evaluate the one and two photon exchange amplitudes, from which the asymmetry is found for different parametrizations of the form factors. |
