The Sivers effect describes the correlation of the unpolarized parton’s transverse momentum with the transverse spin of the nucleon. It manifests as a sine modulation of the cross section for single-hadron semi-inclusive deep inelastic scattering (SIDIS) on a transversely polarized nucleon with the azimuthal angle between the produced hadron’s transverse momentum and the nucleon spin (${\phi }_h$ and ${\phi }_S$, respectively). It has been recently suggested that the Sivers effect can also be measured in a two-hadron SIDIS process as sine modulations involving the azimuthal angles ${\phi }_T$ and ${\phi }_R$ of both the total and the relative transverse momenta of the hadron pair. Here we present the detailed derivation of the two-hadron SIDIS cross section using simple parton-model inspired functional forms for both the parton distribution and the fragmentation functions. We show explicitly that the terms corresponding to the $\sin ({\phi }_R-{\phi }_S)$ and $\sin ({\phi }_T-{\phi }_S)$ modulations are nonzero. Further, we derive the cross section expressions for single-hadron production in the two-hadron sample. Finally, we employ a modified version of the lepto Monte Carlo event generator that includes the Sivers effect to estimate the size of single spin asymmetries corresponding to these modulations independent of the formalism developed.

• Received 20 May 2014

DOI:https://doi.org/10.1103/PhysRevD.90.074006