How can I calculate the sterile neutrino frequency by Boltzmann equation and dY/dT ?
T is temperature
Radiative decay channel and decay rate are attached.
Boltzmann is false: one of his hypothesis is:: a closed System! closed Systems (in cosmos) do not exist!!
Define a variable z=M/T, where M is the mass of the lightest RH neutrino (sterile with respect to S.M). Then you can calculate B-L asymmetry NB-L which is related to Baryon asymmetry by a numerical factor (Harvey & Turner 1990) by solving a set of two coupled differential equations where independent variables are NB-L and and NN where NN is the number density of the lightest right handed neutrino. For that we have to define three rescaled variables, D= ΓD/(H z), S=ΓS/(H z), and W= ΓW /(H z). Denominators have nothing to do with frequency, however, it is a product of Hubble constant and the variable z defined above. Then, the Boltzmann equations are,
- d NN/dz = -(D+S) (NN - NNeq)
- d NB-L/dz = -ε1 D (NN - NNeq) - W NB-L
ε1 is the CP asymmetry parameter. I will be happy to answer further questions on this if you wish. Best and the most standard reference for this is the book The Early Universe by Kolb and Turner. What I have written here is given in sufficient details there.
Right hand side of Boltzmann equation has a very clear physical interpretation. D term accounts for decays and inverse decays, S term represents ΔL=1 scattering and W term represents an effect with tends to erase B-L asymmetry.
- Badges
- Science topic
- Similar topics
- Physical Sciences
- Particle Physics