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General Helicity Formalism for Polarized Semi-Inclusive Deep Inelastic Scattering

We study polarized Semi-Inclusive Deep Inelastic Scattering (SIDIS) processes, within the QCD parton model and a factorization scheme, taking into account all transverse motions, of partons inside the initial proton and of hadrons inside the fragmenting partons. We use the helicity formalism. The elementary interactions are computed at LO with non collinear exact kinematics, which introduces phases in the expressions of their helicity amplitudes. Several Transverse Momentum Dependent (TMD) distribution and fragmentation functions appear and contribute to the cross sections and to spin asymmetries. Our results agree with those obtained with different formalisms, showing the consistency of our approach. The full expression for single and double spin asymmetries is derived. Simplified, explicit analytical expressions, convenient for phenomenological studies, are obtained assuming a factorized Gaussian dependence on intrinsic momenta for the TMDs.