Does the $D^-/D^+$ production asymmetry decrease at large $x_F$?

We have applied the meson cloud model (MCM) to calculate the asymmetries in $D$ and $D_s$ meson production in high energy $Σ^-$-nucleus and $π^-$-nucleus collisions. We find a good agreement with recent data. Our results suggest that the asymmetries may decrease at large $x_F$.