Résumé
We devise a new semi-analytical method dedicated to the propagation of Galactic electrons and positrons from MeV to TeV energies: the pinching method. It is essentially based on the pinching of inverse Compton and synchrotron energy losses from the magnetic halo, where they take place, inside the Galactic disc. This new tool is fast and allows to carry out extensive scans over parameters. We strongly constrain the cosmic ray propagation parameters by requiring that the secondary component of positrons does not overshoot the AMS-02 measurements. We find that only models with a large diffusion coefficient and a large magnetic halo size are selected by this test. Therefore, we find that the positron excess appears from 1 GeV. We then explore the possibility to explain the positron excess with a component coming from the annihilation of dark matter particles. We show that the pure dark matter interpretation of the AMS-02 positron data is strongly disfavoured. This conclusion is based solely on the positron data, and no other observation, such as the antiproton and gamma ray fluxes or the CMB anisotropies, needs to be invoked. MeV dark matter particles annihilating or decaying to electron-positron pairs cannot, in principle, be observed via local cosmic ray measurements because of the shielding solar magnetic field. We take advantage of spacecraft Voyager-I's capacity for detecting interstellar cosmic rays since it crossed the heliopause in 2012. This opens up a new avenue to probe dark matter particles in the sub-GeV energy/mass range that we exploit here for the first time.