What CM frame to take in this case?

[physciencer]

If an electron-positron is decaying into Higgs and then from Higgs into fermions. What is CM frame in this case?

Let us say that electron has momentum $$p_{e^-}=p_1$$ The positron has a momentum $$p_{e^+}=p_2$$ The fermion has momentum $$ p_{f} = q_1$$ and the other one has momentum $$p_{\bar{f}}=q_2$$

 

[Einj]

The CM frame is always the same, i.e. the one where the total spatial momentum is zero. In this frame you have that the initial e+e- pair have total four-momentum $p_1+p_2=(E_1+E_2, \vec{0})$. However, by conservation of four-momentum it must also be $q_1+q_2=(E_1^\prime+E_2^\prime, \vec{0})$.

 

[mfb]

If an electron-positron is decaying into Higgs

That does not make sense - neither the electron nor the positron can decay to a Higgs, and a combined object (positronium) cannot do either.

You can produce a Higgs in a high-energetic collision of electrons and positrons, but the direct production (a Higgs and nothing else) is very unlikely due to the small mass of the particles.

 

[physciencer]

SO yes that is what I meant, that you can produce a Higgs in that way. If so, then the CM is how @Einj posted, no?

@Einj, how would I find invariants in this case?

 

[Einj]

It depends on what invariants you want to find. What do you have in mind?