I want to do two tests:

1) W boson t-channel exchange: Work in a simple model which consists of the SM with only one generation of leptons and nothing else (I might have to add a RH neutrino as well, for the moment I haven't reached this point yet). The role of the dark matter will be played by the neutrino (gauge-charged, but I don't care if it's a viable freeze-in model, I'm interested in the general behaviour of the cross-section and that of the yields). This model contains DM (identified as the SM neutrino) production through e+ e- → nu nubar, which also proceeds through W

FB In your example, take nu_e

AG: Yes, I'll only be taking a single lepton generation, so there's only nu_e

exchange. Then I want to:

- Reproduce the pathologic behaviour (large contributions from high temperatures).

- Figure out around which temperature the cross-section obtains an asymptotic value.

- Compute the relic with T-dependent masses (my idea is to do that by introducing a T-dependent vev) and no cut on the integration (I don't think this is doable with MO, so I'll have to do it externally by myself).

FB For GI this may do as discussed but check that (since you are most probably going to give nu_e a Temp. dep. mass as if the latter are in the bath …what will you be assuming for v(T) the scale has to match the one introduced by the cut. Of course this should have no impact if the Yukawa of the neutrino =0

AG: I'm not sure I understand the comment. I think that I'll have to add a RH neutrino (otherwise the neutrino will be massless, at least from the point of view of a Higgs-induced mass) with a small Yukawa. For v(T), I'm sure people have already computed its expression in the SM and I'll use that. As for the temperature, I was thinking of just integrating the Boltzman equation up to T_RH and compute the yield. This is the point of the whole exercise: compare the cut method with a more “proper” calculation in which thermal masses are taken into account. Or am I misunderstanding your comment?

- Compute the relic with T-independent masses and the cut Sasha has implemented, and compare the results.

2) Exchange of a fermion in the t-channel: Here I think that I can work with the 3rd model that we had in the micromegas paper and repeat the steps described previously (it has the advantage that several masses are not vev-induced, so they can be changed independently).

My goal is to check the cut method in two different models, involving exchange of different particles in the t-channel.

FB (a reminder) Of course the limitations of MO5 is that a model is not defined through the different stages of SB, ie SB phase, Symmetric phase,…the temperature implementation is just a “limit”of integration. Yes?

AG: Yes, this is one of the limitations, and this also applies to the previous model. I see three options: i) Just use the broken model ii) Just use the unbroken model iii) Write down two models, one broken and one unbroken, run the code with the unbroken model down to T_EWSB, get a result, continue with the broken model below T_EWSB, get another result and add the two (here it would also be interesting to compare the results obtained through the three options). In passing, I'm wondering if this is actually already doable with MO (of course with no T-dependent masses), one just needs to stop integrating at T_EWSB (or whatever SB temperature), then run the code with a different model below T_EWSB and (externally) add up the two results. If this is a correct procedure, then even using the current MO version one should be able to handle both phases.