Which fraction of the measured cosmic-ray antiprotons might be due to neutralino annihilation in the galactic halo?

We analyze the data of the low-energy cosmic-ray $\overline{p}$ spectrum, recently published by the BESS Collaboration, in terms of newly calculated fluxes for secondary antiprotons and for a possible contribution of an exotic signal due to neutralino annihilation in the galactic halo. We single out the relevant supersymmetric configurations and discuss their explorability with experiments of direct search for dark matter particles and at accelerators. We discuss how future measurements with the alpha magnetic spectrometer on the shuttle flight may disentangle the possible neutralino-induced contribution from the secondary one.