Why in scattering processes q^2 is negative?

[Mesmerized]

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 ?

 

[M Quack]

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.

 

[Mesmerized]

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.

 

[Mesmerized]

In other words, why is the virtual photon in the electron-electron scattering process spacelike?

 

[Mesmerized]

ok, eventually found the answer in an old thread of this great site. here's a long discussion https://www.physicsforums.com/showthread.php?t=372021 , particularly on the second page there's an answer why that photon should be spacelike.

 

[Bill_K]

Indeed! It's the triangle inequality.