Context. Secondary positrons are produced by spallation of cosmic rays within the interstellar gas. Measurements have been typicallyexpressed in terms of the positron fraction, which exhibits an increase above 10 GeV. Many scenarios have been proposed to explainthis feature, among them some additional primary positrons originating from dark matter annihilation in the Galaxy.Aims. The PAMELA satellite has provided high quality data that has enabled high accuracy statistical analyses to be made, showingthat the increase in the positron fraction extends up to about 100 GeV. It is therefore of paramount importance to constrain theoreticallythe expected secondary positron flux to interpret the observations in an accurate way.Methods. We focus on calculating the secondary positron flux by using and comparing different up-to-date nuclear cross-sectionsand by considering an independent model of cosmic ray propagation. We carefully study the origins of the theoretical uncertainties inthe positron flux.Results. We find the secondary positron flux to be reproduced well by the available observations, and to have theoretical uncertaintiesthat we quantify to be as large as about one order of magnitude. We also discuss the positron fraction issue and find that our predictionsmay be consistent with the data taken before PAMELA. For PAMELA data, we find that an excess is probably present after consideringuncertainties in the positron flux, although its amplitude depends strongly on the assumptions made in relation to the electron flux.By fitting the current electron data, we show that when considering a soft electron spectrum, the amplitude of the excess might be farlower than usually claimed.Conclusions. We provide fresh insights that may help to explain the positron data with or without new physical model ingredients.PAMELA observations and the forthcoming AMS-02 mission will allow stronger constraints to be aplaced on the cosmic-ray transportparameters, and are likely to reduce drastically the theoretical uncertainties.
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