Particle decoupling during Universe's evolution Studying cosmology, I've seen that when you want to calculate the number of degrees of freedom of the thermal bath before and after the decoupling of some species, it is used the mass of that particle as the temperature (actually, $k_B T = m$) at which the decoupling happpens. E.g.: electron-positron annhilation is suppose to happen at $T = 500 \ \mbox{keV} = \mbox{mass of the electron}$ - using $k_B= 1$ units for simplicity.
Nonetheless, I don't understand this clearly. For electron-positron annhilation you will always have at least a total energy of twice the electron's mass, so even when bath energy is below once that mass that means that your electron and positron will have its mass plus a 'little' kinetic energy and therefore the interaction 
$$
e^+ + e^- \leftrightarrow \gamma + \gamma
\tag1$$
is possible. I imagine it will have an interaction rate $\Gamma$ very low so I guess that's what 'decoupling' means: not that the interactions are banned, but that they are very suppressed. Nevertheless, I don't get yet why to use the mass of the electron instead of, for example, a less value.
Moreover, photon deocupling happens after electron-positron annhilation so we were saying that electrons decoupled but phtons didn't, how is that possible if due to interction (1) they should be already decoupled?
Can anyone clarify this to me?
 A: When people say a specific process "decouples", they mean that it doesn't happen often enough to stay in equilibrium. The reaction
$$e^+ + e^- \leftrightarrow \gamma + \gamma$$
can always occur whenever an electron and positron meet, regardless of their energies. But for $T \ll m_e$, the equilibrium number of electrons and positrons is very small, because it's suppressed by the Boltzmann factor $e^{-m_e/T}$. So they just don't meet each other often enough to annihilate as much as they need to, to stay in equilibrium. 
Photon decoupling is a different idea, and has to do with the scattering process
$$e^\pm + \gamma \leftrightarrow e^\pm + \gamma$$
which transfers energy between the electrons/positrons and photons. The reason this process decouples at $T \ll m_e$ is just because there are fewer electrons/positrons around, so photons can't find any of them to scatter off of. The reason we don't call this "electron decoupling" is because most electrons do still find photons to scatter off of, because there are so many more photons. That is, most photons don't interact after "photon decoupling", but most electrons do. 
A: This article in wikipedia may help:

In cosmology, decoupling refers to a period in the development of the universe when different types of particles fall out of thermal equilibrium with each other. This occurs as a result of the expansion of the universe, as their interaction rates decrease (and mean free paths increase) up to this critical point. The two verified instances of decoupling since the Big Bang which are most often discussed are photon decoupling and neutrino decoupling, as these led to the cosmic microwave background and cosmic neutrino background, respectively.

Note the italics I have put to emphasize.Photons in thermodynamic equillibrium before they decouple means that the probability of interacting with the matter existing there was very high, due to the  small mean free path. As the expansion continued the targets the photons can interact with are very few, so no thermodynamic equilibrium holds. 
Maybe you should give a link where this estimate for pair production decoupling is made, as it is the first time I hear of it. I suppose that if the photon energies in the primordial heat bath is smaller than two electron masses, no equilibrium between annihilation and creation can exist, but that is not usually described by "decoupling"
