The particle antiparticle pair (e⁺ and e^-) collide and annihilate to produce a virtual photon with zero momentum and total energy equal to the sum of the e⁺ and e^- total energies. The 'virtual photon' then materialises into a new e⁺ and e^- pair or any other heavier particle antiparticle pair, such as μ⁺ and μ^-, provided sufficient energy is available. If a μ⁺ and μ^- pair is created they will move off with equal and opposite momenta (remember that momentum is conserved and the total momentum before or after is zero).

Let the total energy of each positron and electron be E_e.

(1)

The total energy of each electron and positron in the colliding beams must be greater than the mass energy of a particle. The mass of a μ particle is 105 MeV/c² and it follows that:

(2)

Derivation of this result