When reading about why SM neutrinos are not a candidate for DM, it was stated:

"Neutrinos are involved in weak interactions that keep them in thermal equilibrium in the early Universe down to the temperatures of few MeV."

A similar statement can be found here.

I don't understand how these interactions could maintain a thermal equilibrium. Could someone give me an example of such an interaction?

My "guess" is that in a weak interaction, such as $\mu^- + W^+ \to \nu_\mu$ this would be exothermal and release heat to compensate the clear mass difference between the neutrino (lighter) and the other SM particles.

But to keep an equilibrium wouldn't there need to be isothermic interactions? How could this be done if neutrinos don't decay?


You have to give the time in the early universe. Before the electroweak symmetry breaking mechanism is activated as the universe cools, all particles in the standard model are massless, so there are no decays, just interactions. As the neutrinos are neutral and do not interact with gluons, only the weak interaction could give rise to the energy loss or increase of neutrino energies due to scatterings.

I don't understand how these interactions could maintain a thermal equilibrium.

The term "thermal" implies that thermodynamics is used in modeling the neutrinos during this epoch, like an ideal gas the scatterings happening with the weak interaction.

  • $\begingroup$ Really nice answer. $\endgroup$ Aug 31 '20 at 15:47
  • $\begingroup$ "are massless, so there are no decays", can you please tell me, is rest mass required for decay? Is rest mass a reason for decay? $\endgroup$ Aug 31 '20 at 15:49
  • $\begingroup$ "neutrinos are neutral and do not interact with gluons", can you please tell me why neutrinos do not interact with gluons (outside confinement)? $\endgroup$ Aug 31 '20 at 15:50
  • $\begingroup$ gluons are the carriers of the strong force. there are no first order diagrams connecting weak vertices with strong ones. For a decay to happen there should be a lower energy state , the decaying elementary particle has to have enough rest mass to be able to decay into something. if all rest masses are zero there is no energy left over to be taken by the decay products. $\endgroup$
    – anna v
    Aug 31 '20 at 16:23
  • $\begingroup$ Thank you, so is it impossible for example for a massless photon to decay into a lower energy massless particle (gluon)? $\endgroup$ Aug 31 '20 at 18:58

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