What CM frame to take in this case?

1. Mar 10, 2015

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 $$p_{\bar{f}}=q_2$$

2. Mar 11, 2015

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 $q_1+q_2=(E_1^\prime+E_2^\prime, \vec{0})$.

3. Mar 11, 2015

Staff: Mentor

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.

4. Mar 11, 2015

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?

5. Mar 12, 2015

Einj

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