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Impact of the spectral hardening of TeV cosmic rays on the prediction of the secondary positron flux

The rise in the cosmic-ray positron fraction measured by the PAMELA satellite is likely due to the presence of astrophysical sources of positrons, e.g. pulsars, on the kpc scale around the Earth. Nevertheless, assessing the properties of these sources from the positron data requires a good knowledge of the secondary positron component generated by the interaction of cosmic rays with the interstellar gas. In this paper, we investigate the impact of the spectral hardening in the cosmic-ray proton and helium fluxes recently reported by the ATIC2 and CREAM balloon experiments, on the predictions of the secondary positron flux. We show that the effect is not negligible, leading to an increase of the secondary positron flux by up to $\sim$60% above $\sim$100 GeV. We provide fitting formulae that allow a straightforward utilization of our results, which can help in deriving constraints on one's favorite primary positron source, e.g. pulsars or dark matter.