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Consider the case in which an incoming particle collides with stationary target particle producing new particles through the interaction. For example, $$e^{-}+e^{+}\rightarrow X+\bar{X}$$ My question is, why in general do the particles produced in such an interaction propagate outwards are angles relative to the beam axis?
Can one use the classical analogy of collisions between billiard balls, in the sense that if the incoming ball strikes the stationary target ball the force acting on target ball acts in the direction normal to the contact point (along the line passing through the contact point and the centres of both billiard balls). If the incoming ball strikes the target ball off centre then this results in both balls moving off at angles relative to the original direction of propagation of the incoming billiard ball.
I'm completely unsure in the case where a particle and an anti-particle collide and annihilate, producing another particle anti-particle pair. Why are the momenta of the particle anti-particle pair at angles relative to the direction of propagation of the incident particle?!
Can one use the classical analogy of collisions between billiard balls, in the sense that if the incoming ball strikes the stationary target ball the force acting on target ball acts in the direction normal to the contact point (along the line passing through the contact point and the centres of both billiard balls). If the incoming ball strikes the target ball off centre then this results in both balls moving off at angles relative to the original direction of propagation of the incoming billiard ball.
I'm completely unsure in the case where a particle and an anti-particle collide and annihilate, producing another particle anti-particle pair. Why are the momenta of the particle anti-particle pair at angles relative to the direction of propagation of the incident particle?!