Kinematical contributions to the transverse asymmetry in semi-inclusive DIS

In the studies of semi-inclusive charged and neutral pion production off a longitudinally polarized protons, the HERMES collaboration has observed a single target-spin asymmetry (SSA) [1]. This asymmetry could either result from twist-3 chiral-odd effects [2,3] and/or could be a reflection of the Collins effect [4]. Which of the two is relevant is an open issue. For a further understanding of “transverse asymmetry contribution” we discuss here the double-spin and double-spin azimuthal asymmetries, where those contributions are well defined. A target with an anti-parallel (parallel) polarization with respect to the beam has a transverse spin component in the virtual photon frame which can only have azimuthal angle π (0) (Fig.1). The value of this transverse spin component is