$\psi$ production in $\overline{p}N$ and ${\pi }^{-}N$ interactions at 125 GeV/c and a determination of the gluon structure functions of the $\overline{p}$ and the ${\pi }^{-}$

We have measured the cross section for production of $\psi$ and ${\psi }^{\prime }$ in $\overline{p}$ and ${\pi }^{-}$ interactions with Be, Cu, and W targets in experiment E537 at Fermilab. The measurements were performed at 125 GeV/c using a forward dimuon spectrometer in a closed geometry configuration. The gluon structure functions of the $\overline{p}$ and ${\pi }^{-}$ have been extracted from the measured $\frac{d\sigma }{d{x}_F}$ spectra of the produced $\psi \text{'}\mathrm{s}$. From the $\overline{p}\mathrm{W}$ data we obtain, for $\overline{p}$, $\mathrm{xG}\left(x\right)=(2.15\mathrm{}\pm 0.7){\mathrm{}[1-x]\mathrm{}}^{(6.83\mathrm{}\pm 0.5)}[1+(5.85\mathrm{}\pm 0.95\left)x\right]$. In the ${\pi }^{-}$ case, we obtain, from the W and the Be data separately, $\mathrm{xG}\left(x\right)=(1.49\mathrm{}\pm 0.03){\mathrm{}[1-x]\mathrm{}}^{(1.98\mathrm{}\pm 0.06)}$ (for ${\pi }^{-}\mathrm{W}$), $\mathrm{xG}\left(x\right)=(1.10\mathrm{}\pm 0.10){\mathrm{}[1-x]\mathrm{}}^{(1.20\mathrm{}\pm 0.20)}$ (for ${\pi }^{-}\mathrm{Be}$).