From a conservative point of view, the measurements of the positron flux or fraction
allow one to set limits on the dark matter annihilation cross section and decay width in a
given dark matter scenario. Many studies have derived limits on the dark matter parameters
employing measurements of the positron fraction under the assumption that the positron
background vanishes or that the only source of background is secondary production due to
spallations of cosmic rays in the interstellar medium (see e.g. Refs. [8–15]). This approach
was recently improved in Ref. [16], where a search was undertaken in the positron fraction
for spectral features which are predicted to arise in certain final states of dark matter
annihilations. We will consider in this paper the limits that can be obtained from the
positron flux and which, in contrast to the positron fraction, do not require knowledge of
the electron flux and are therefore cleaner from the theoretical point of view. These limits
are complementary (and as we will show, competitive) to those derived from the positron
fraction. We will also include in our calculation a plausible background model to take into
account a possible primary component of astrophysical origin in the positron flux, which is
likely to exist and which presumably provides the additional source of positrons when the
dark matter annihilations or decays cannot totally explain the rise in the positron fraction
(for example, when the dark matter mass is smaller than 300 GeV or when the annihilation
cross section or decay rate is too small). Besides, most analyses neglect the positron data at
low energies (see however recent analyses [16,17] where the low energy data of the positron
fraction was used). Nevertheless, the exquisite measurements provided by experiments,
together with the excellent agreement of the observations with the expectations from nonexotic
physics which leave little room for an exotic component in the positron fraction, allow
us to set very stringent bounds on the dark matter properties.