Why in scattering processes q^2 is negative?

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Discussion Overview

The discussion revolves around the nature of the four-momentum transfer, denoted as q, in scattering processes, specifically why q^2 is negative when considering the momenta of electrons before and after scattering. The scope includes theoretical aspects of particle physics and the properties of virtual particles.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant questions why q^2 is negative, referencing a specific equation from a textbook.
  • Another participant argues that since p, p', and q are momentum vectors, q^2 should be a positive, real number due to conservation of momentum.
  • A third participant clarifies that p, p', and q are four-momenta and notes that the square of the difference can be negative under certain conditions.
  • There is a specific inquiry about why the virtual photon in electron-electron scattering is spacelike.
  • A later reply references an external thread that discusses why the photon should be spacelike, indicating that the answer was found in previous discussions.
  • Another participant mentions the triangle inequality as a relevant concept in this context.

Areas of Agreement / Disagreement

Participants express differing views on the nature of q^2, with some asserting it must be positive while others acknowledge the conditions under which it can be negative. The discussion remains unresolved regarding the implications of these differing perspectives.

Contextual Notes

Participants note that the conditions for the four-momentum of electrons in scattering processes are not fully explored, and the implications of the triangle inequality are mentioned but not elaborated upon.

Mesmerized
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Hello,

not sure if I'm typing the question in the right place, but I encountered this question when going through Peskin (eq. 6.44, though it's not important). If p and p' are respectively the momentum of electron before and after the scattering, then q=p'-p is the momentum of photon joining the vertex. Why is that q^2<0 ?
 
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I am not familiar with that textbook, but that does not make any sense.

p, p' and q are momentum vectors. Momentum is conserved in the scattering process,
so p = p' + q. q^2 is the (length of the photon's momentum)^2 and has to be a positive, real number.
 
I guess I should've noted that p,p' and q are the four-momentums. Of course, the square of the difference of the two momenta (p'-p)^2 can be negative, but for that purpose p and p' must obey certain conditions. I don't see why the fact that the process describes a scattering puts such conditions on the four-momentum of the electrons.
 
In other words, why is the virtual photon in the electron-electron scattering process spacelike?
 
Indeed! It's the triangle inequality.
 

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