Dark matter annihilation cross section What is the meaning of upper limit of annihilation cross section? Sometimes I have seen that $\langle\sigma v\rangle = 3.0 \times 10^{-26}\,{\rm cm}^{3}\,{\rm s}^{-1}$ or $2.0 \times 10^{-25}\,{\rm cm}^{3}\,{\rm s}^{-1}$.
Which is the better value and why? 
 A: By "which is better" I assume that you mean "which is most constraining".
First, $\langle\sigma v\rangle$ refers to the cross section per unit velocity. This is important because it is conjectured that dark matter scattering with a velocity independent cross section has several problems that it seems to be possible to resolve by assuming the cross section changes with velocity. This explains the units of $\langle\sigma v\rangle$: it relates how big a target the particle represents (${\rm cm}^{2}$) and how fast it is traveling (${\rm cm}\,{\rm s}^{-1}$).
The scattering/annihilation cross section of DM (work on both types of interactions uses similar language) has never been measured, which is a bit of a given since DM scattering/annihilation have never been detected (well, there are claims, but none generally accepted at the moment). A smaller upper limit represents a more constraining non-detection. Basically, the limit says "if the scattering/annihilation cross section were larger than $<{\rm value}>$, we would have seen it in our detector, so it must be smaller". The limit only applies to the types of interactions the detector is designed to be sensitive to, and the design is motivated by some theoretical candidate particle, such as a WIMP.
