  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).
