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

In this paper we study the double longitudinal spin asymmetry of dihadron production in semi-inclusive deep inelastic scattering (SIDIS). We calculate a unknown twist-3 dihadron fragmentation function $\widetilde{D}^\sphericalangle$ within a spectator model which has been used successfully in describing the dihadron production in both the unpolarized and the single polarized processes. The collinear picture, in which the transverse momentum of the final state hadron pair is integrated out, has been considered. The $\cos\phi_R$ azimuthal asymmetry arises from the coupling $e_L H_1^\sphericalangle$ and the coupling $g_1 \widetilde{D}^\sphericalangle$ is studied. We estimate the $\cos\phi_R$ asymmetry at the kinematics of COMPASS and compare with the data. The prediction at the future Electron Ion Collider (EIC) has also been presented.