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We present a study on the beam single spin asymmetries $A_{LU}^{\sin\phi_h}$of $\pi^+$, $\pi^-$ and $\pi^0$ production in semi-inclusive deep inelasticscattering process, by considering Collins effect and the $g^\perp D_1$ termsimultaneously. We calculate the twist-3 distributions $e(x, \bm k_T^2)$ and$g^\perp(x,\bm k_T^2)$ for the valence quarks inside the proton in a spectatormodel. We consider two different options for the form of diquark propagator, aswell as two different choices for the model parameters in the calculation.Using the model results, we estimate the beam spin asymmetries$A_{LU}^{\sin\phi_h}$ for the charged and neutral pions and compare the resultswith the measurement from the HERMES Collaboration. We also make predictions onthe asymmetries at CLAS with a $5.5 \,\textrm{GeV}$ beam using the same modelresults. It is found that different choices for the diquark propagator will notonly lead to different expressions for the distribution functions, but alsoresult in different sizes of the asymmetries. Our study also shows that,although the spectator model calculation can describe the asymmetries forcertain pion production in some kinematic regions, it seems difficult toexplain the asymmetries of pion production for all three pions in a consistentway from the current versions.

Beam Spin Asymmetries of Charged and Neutral Pion Productions in Semi-inclusive DIS