# Question on electron-positron scattering

1. Apr 2, 2013

### Morgoth

Well I am sure this is a lame question, but I am stuck over it for hours. I'm working on Bjorken, Drell book, and I'm trying to calculate the extreme relativistic differential cross section for electron-positron scattering.

Well, I have evaluated the cross section up to my attachment's form...

Then it says in order to keep working we choose the center-of-mass frame system, and gives us the inner products of p1,p1',-q1,-q1'

p1p1'=q1q1'=2E2sin2(θ/2)
p1(-q1')=p1'(-q1)=2Ε2
p1(-q1)=p1'(-q1')=2Ε2cos2(θ/2)

However that way I can calculate the quantities on the numerator, but I don't know how to work with the denominator...
could someone just tell me how i can find the 4-components of ps and qs?

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Last edited: Apr 2, 2013
2. Apr 4, 2013

### andrien

why don't you involve the on-shell condition for denominators i.e like p12=m2 also expanding in the denominator you will have the terms which can be filled up by the relation you already wrote

3. Apr 5, 2013

### Hepth

Just to clarify what andrien means:

Take the first term, the denominator is $(p'-p_1)^2 = p'^2 + p_1^2 - 2 (p' \cdot p_1)$.

In the relativistic limit we can ignore the light masses, since the p's are on-shell, which means p^2 = m^2, but in the relativistic limit that goes to zero.
So that denominator becomes $\frac{-1}{2 p' \cdot p_1}$ which you have above in terms of energy.