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Direct constraints on diffusion models from cosmic-ray positron data: Excluding the Minimal model for dark matter searches

Galactic Cosmic-ray (CR) transport parameters are usually constrained by the boron-to-carbon ratio. This procedure is generically plagued with degeneracies between the diffusion coefficient and the vertical extent of the Galactic magnetic halo. The latter is of paramount importance for indirect dark matter (DM) searches, because it fixes the amount of DM annihilation or decay that contributes to the local antimatter CR flux. These degeneracies could be broken by using secondary radioactive species, but the current data still have large error bars, and this method is extremely sensitive to the very local interstellar medium (ISM) properties. Here, we propose to use the low-energy CR positrons in the GeV range as another direct constraint on diffusion models. We show that the PAMELA data disfavor small diffusion halo ($L\lesssim 3$ kpc) and large diffusion slope models, and exclude the minimal ({\em min}) configuration (Maurin et al. 2001, Donato et al. 2004) widely used in the literature to bracket the uncertainties in the DM signal predictions. This is complementary to indirect constraints (diffuse radio and gamma-ray emissions) and has strong impact on DM searches. Indeed this makes the antiproton constraints more robust while enhancing the discovery/exclusion potential of current and future experiments, like AMS-02 and GAPS, especially in the antiproton and antideuteron channels.