General helicity formalism for semi-inclusive deep inelastic scattering

Abstract

We study polarized and unpolarized semi-inclusive deep inelastic scattering processes, $\ensuremath{\ell}({S}_{\ensuremath{\ell}})+p(S)\ensuremath{\rightarrow}{\ensuremath{\ell}}^{\ensuremath{'}}hX$, within a QCD parton model motivated by a generalized QCD factorization scheme. We take into account all transverse motions, of partons inside the initial proton and of hadrons inside the fragmenting partons and use the helicity formalism. The elementary interactions are computed at leading order with noncollinear exact kinematics, which introduces phases in the expressions of their helicity amplitudes. Several transverse momentum dependent 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 ${A}_{{S}_{\ensuremath{\ell}}S}$ is derived. Simplified, explicit analytical expressions, convenient for phenomenological studies, are obtained assuming a factorized Gaussian dependence on intrinsic momenta for transverse momentum dependent functions.