Z Boson, Posiron-Electron Annihilation.

[Matteus92]

Suppose I want to find the minimum velocity of the electron and positron required to make a Z boson during annihilation. How would I go about this? I had an attempt which came out at 422ms^-1. This doesn't really seem right... so I'm guessing i made a big mistake...

 

[Bob_for_short]

If Z-boson is much heavier than electron, then the initial particles should be highly relativistic: with v ≈ c (to create a real Z-boson, not virtual).

 

[hamster143]

You need kinetic energy of the two ($$2 \gamma m_e c^2$$) to add up to rest energy of the Z boson. That gives you $$\gamma$$ around 90 thousand. Velocity $$v = c \sqrt{1-1/\gamma^2} \approx c(1-1/2\gamma^2)$$