{..everything that follows is in the domain of relativistic kinematics..}
Say a particle A collides with a particle B at rest and produces particles C and D.
What exactly is the definition of "threshold energy" for a reaction ?
Is it the energy that A should have so that so that the heavier of C and D is produced at rest?
Given the masses of all the particles, how does one calculate the threshold energy that A must have to cause this reaction ?
I intuitively feel that a threshold energy scenario would mean that C and D are moving along the same direction in which A was coming in. I think it is an unnecessary "waste" of energy for C and D to develop momentum in the two transverse directions of A's motion. But I can't prove this in general.
I would like to know how this situation is analyzed.
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