(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A particle physicist seeks to create a new fundamental particle with rest energy

200GeV by colliding electrons and positrons. What is the minimum positron energy

required when electrons and positrons travelling in opposite directions with equal speeds are

collided together?

The new particle is produced using this method with the minimum necessary

energy, and rapidly decays into two identical particles of rest energy 91.2GeV

2. Relevant equations

E^{2}-p^{2}c^{2}=m^{2}c^{4}

3. The attempt at a solution

I am trying to do this question using 4-momentum. For a positron I have it as (E, p1, 0, 0) and for the electron I have it as once again (E, p2, 0, 0) (we are allowed to approximate the mass of a positron to that of an electron), the resultant being (2E, p1+p2, 0, 0).

I then equate (2E)^{2}-(p1+p2)^{2}=(200x10^{3})^{2}(Working in MeV)

However, the problem I get is that as these particles are of essentially equal mass, and moving in opposite directions with the same speed, does p1+p2 in the 4-momentum effectively become 0?

If so, I get 4E^{2}=(200x10^{3})^{2}

giving E=100GeV

I think there's something I am missing, as in the next part it says two particles of rest mass 91.2GeV are produced, which exceeds this energy. Or does this energy translate to kinetic energy for the 200GeV particle?

Any help would be appreciated.

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# Homework Help: Electron-positron collisions and decay in Special Relativity

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