Necessary KE of particles to create a resulting particle in a collision

[HarryO]

Homework Statement

The intermediate vector boson Z with rest mass energy of 91.187 GeV is produced in a collision of positrons and electrons e-+e->Z

a.how much KE, must positrons in colliding symmetric beams have to produce the Z

b.suppose that a beam of positrons strike electrons that are at rest, what must the KE of the positrons be?

Relevant Equations

E^2 = p^2c^2 + m^2c^4

So I am making the assumption that the resulting particle Z is emitted at rest.
For part a I believe that since the two positron beams are symmetric they would each provide half of the energy to create the Z particle so the KE of each positron would be 91.187GeV/2, I am ignoring the rest energy of the positrons because it is so small.

for part b all of the energy would have to come from the KE of the positrons, once again ignoring the rest energy provided by the positrons and electrons, so would the KE just need to be 91.187GeV?

This makes sense to me but seems too easy.

 

[PeroK]

Homework Statement:: The intermediate vector boson Z with rest mass energy of 91.187 GeV is produced in a collision of positrons and electrons e-+e->Z

a.how much KE, must positrons in colliding symmetric beams have to produce the Z

b.suppose that a beam of positrons strike electrons that are at rest, what must the KE of the positrons be?
Homework Equations:: E^2 = p^2c^2 + m^2c^4

So I am making the assumption that the resulting particle Z is emitted at rest.
For part a I believe that since the two positron beams are symmetric they would each provide half of the energy to create the Z particle so the KE of each positron would be 91.187GeV/2, I am ignoring the rest energy of the positrons because it is so small.

for part b all of the energy would have to come from the KE of the positrons, once again ignoring the rest energy provided by the positrons and electrons, so would the KE just need to be 91.187GeV?

This makes sense to me but seems too easy.

For part b), by conservation of momentum the resultant Z boson cannot be at rest (in the lab frame).

 

[Abhishek11235]

Try writing 4-vector of Energy-momentum in CM frame.