Systematic Uncertainties In Constraining Dark Matter Annihilation From
  The Cosmic Microwave Background
  Anisotropies of the cosmic microwave background (CMB) have proven to be a
very powerful tool to constrain dark matter annihilation at the epoch of
recombination. However, CMB constraints are currently derived using a number of
reasonable but yet un-tested assumptions that could potentially lead to a
misestimation of the true bounds. In this paper we examine the potential impact
of these systematic effects. In particular, we separately study the propagation
of the secondary particles produced by annihilation in two energy regimes;
first following the shower from the initial particle energy to the keV scale,
and then tracking the resulting secondary particles from this scale to the
absorption of their energy as heat, ionization, or excitation of the medium. We
improve both the high and low energy parts of the calculation, in particular
finding that our more accurate treatment of losses to sub-10.2 eV photons
produced by scattering of high-energy electrons weakens the constraints on
particular DM annihilation models by up to a factor of two. On the other hand,
we find that the uncertainties we examine for the low energy propagation do not
significantly affect the results for current and upcoming CMB data. We include
the evaluation of the precise amount of excitation energy, in the form of
Lyman-alpha photons, produced by the propagation of the shower, and examine the
effects of varying the Helium fraction and Helium ionization fraction. In the
recent literature, simple approximations for the fraction of energy absorbed in
different channels have often been used to derive CMB constraints: we assess
the impact of using accurate versus approximate energy fractions. Finally we
check that the choice of recombination code (between RECFAST v1.5 and
COSMOREC), to calculate the evolution of the free electron fraction in the
presence of dark matter annihilation, introduces negligible differences.
