Sivers Effect in Dihadron Semi-Inclusive Deep Inelastic Scattering

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 ($\varphi_h$ and $\varphi_S$, respectively). It has been recently suggested that the Sivers effect can also be measured in two hadron SIDIS process as sine modulations involving the azimuthal angles $\varphi_T$ and $\varphi_R$ 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 $\sin(\varphi_R-\varphi_S)$ and $\sin(\varphi_T-\varphi_S)$ modulations are non-zero. Further, we derive the cross section expressions for single hadron production in the two hadron sample. Finally, we employ a modified version of the $\tt{LEPTO}$ 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.