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When we work out the relativistic general two-body scattering in the CM frame (like two elementary particles producing two other P1 +P2 -P3 -P4) , the cross section is proportional to absolute final momentum by absolute initial momentum (Pf/Pi). But that makes no sense to me, since for relativistic collisions the momentum, as well as the energy, is conserved.

Could anyone point to the flaw of my thought?

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  • $\begingroup$ Yes. The cross section is proportional to Pf/Pi. Tks AFT. $\endgroup$
    – Patrick
    Commented Jan 15, 2016 at 14:22
  • $\begingroup$ Could you tell us where you got that result about the cross section? $\endgroup$
    – ignacio
    Commented Jan 15, 2016 at 14:43
  • $\begingroup$ Sure, that's David Griffths, Introductuion to Elemtary Particles p.200. Exp. 6.7, eq 6.42. $\endgroup$
    – Patrick
    Commented Jan 15, 2016 at 16:15

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Check out Halzen & Martin page 91. electron-muon scattering cross section formula

Supose you're doing electron-muon scattering. Pf is the electron momentum in the final state, and Pi electron momentum in the initial state. You are correct that the total momentum is conserved (it is 0 before and after, in the CM frame), but the momentum of each particle changes.

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