Beam single spin asymmetry $A_{LU}^{\sin \phi_R}$ of the dihadron production in SIDIS process

We study the longitudinal beam single-spin asymmetry $A_{LU}^{\sin \phi_R}$ of dihadron production in semi-inclusive deep inelastic scattering process with a polarized electron beam scattering off an unpolarized proton target. The asymmetry arises from the convolutions of twist-3 PDF $e(x)$ and twist-2 DiFF $H_1^\sphericalangle$ as well as twist-2 PDF $f_1(x)$ and twist-3 DiFF $\widetilde{G}^{\sphericalangle}$. Using the spectator model calculations for the twist-3 PDF $e(x)$, the DiFFs $D_1 , H_1^\sphericalangle$, and $\widetilde{G}^{\sphericalangle}$, we estimate the BSA $A^{\sin \phi_R}_{LU}$ at the kinematical configuration of CLAS and CLAS12. We find good agreement with $z$- and $M_h$-dependencies data, though $x$- and $Q^2$- dependencies show discrepancies. We include DGLAP evolution of $e(x)$ and provide predictions for COMPASS, EIC, and EicC. The negligible contribution from $f_1(x) \otimes \widetilde{G}^{\sphericalangle}$ supports the Wandzura-Wilczek approximation, while our results highlight the importance of QCD evolution in twist-3 PDF analyses.