1. The problem statement, all variables and given/known data ( This question is from the textbook of Introduction to Elementary Particle Physics, written by Griffiths, on the problem set of Chapter 3 ) Particle A (energy E) hits particle B (at rest), producing particles C1, C2, ...: A + B → C1 + C2 + ... + CN. Calculate the threshold (i.e. minimum E) for this reaction, in terms of the various particle masses. [ Answer: ( M2 - m2A - m2B ) / ( 2mB ), where M = m1 + m2 + ... + mn ] 2. Relevant equations Assuming that c = 1 and h = 1, Before collision: pμ i = ( EA + mB , pA ) After collision: pμ f = ( M , 0 ) , where M = m1 + m2 + ... + mn , and subsctibe i and f represents initial and final state of collision. pμpμ = m2 3. The attempt at a solution I calculated the answer but I do not understand why momentum pA seems to be not conserved if I want to get the answer. (a). I assumed that the energy-momentum four vector is conserved. (b). I simply calculate ( pμi )2 = ( pμf )2, then I solve for EA . ⇒ ( EA + mB )2 - pA2 = M 2 , then I solved for EA by subsituting pA2 with EA2 = mA2 + pA2 (c) My question is: why should I consider the final momentum state as: pμf = ( M, 0 ) , but not something like: pμf = ( Ej + M , pCj ) for M = M - mj Shouldn't the momentum be conserved, just like a ball hitting a bunch of balls when playing snooker?