Single-spin asymmetry in dihadron production in SIDIS off the longitudinally polarized nucleon target

We study the single longitudinal-spin asymmetry of dihadron production in semi-inclusive deep inelastic scattering process. We consider the collinear picture in which the transverse momentum of the final-state hadron pair is integrated out, such that the $\sin \phi_R$ azimuthal asymmetry arises from the coupling $h_L\, H_{1}^{\sphericalangle}$ as well as the coupling $g_1 \,\widetilde{G}^{\sphericalangle}$. We calculate the unknown twist-3 dihadron fragmentation function $\widetilde{G}^{\sphericalangle}$ using a spectator model which is successful in describing the dihadron production in the unpolarized process. Using the spectator model results for the quark distributions and dihadron fragmentation functions, we estimate the $\sin \phi_R$ asymmetry of dihadron production in SIDIS at the kinematics of COMPASS and compare it with the COMPASS preliminary data. In addition, the prediction on the $\sin \phi_R$ asymmetry at the typical kinematics of the future Electron Ion Collider is also presented. In order to test the reliability of the spectator model estimate, we compare the model result for the distribution $h_L$ with the Wandzura-Wilczek approximation for that distribution, and compare $H_{1}^{\sphericalangle}$ with the existing parametrization. Although the asymmetry is dominated by the $h_L H_{1}^{\sphericalangle}$ term, we find that the contribution from the $g_1\, \widetilde{G}^{\sphericalangle}$ term should also be taken into account in certain kinematical region.