Single spin asymmetry $A_{UL}^{\sin(\phi_h-\phi_R)}$ in dihadron semi-inclusive DIS

In this paper we study the single longitudinal spin asymmetry $A_{UL}^{\sin(\phi_h-\phi_R)}$ of dihadron production in semi-inclusive deep inelastic scattering (SIDIS) via helicity-dependent dihadron fragmentation function (DiFF), which describes the correlation of the longitudinal polarization of a fragmenting quark with the transverse momenta of the produced hadron pair. Recently experimental searching for this azimuthal asymmetry in dihadron SIDIS by the COMPASS Collaboration yielded a very small signal. Here we calculate this unknown T-odd DiFF $G_1^\perp$ using a spectator model to access the asymmetry and clarify why the signal is very small. The transverse momentum dependent (TMD) factorization method, in which the transverse momentum of the final state hadron pair leaves unintegrated, has been applied. We estimate the $\sin(\phi_h-\phi_R)$ asymmetry at the kinematics of COMPASS experiments and compare with the data. What's more, the predictions on the same asymmetry are also made at the Electron Ion Collider (EIC).