I have an electron of 20 GeV and negligible mass that collides with a stationary proton (mc^2 = 9.38 GeV) and deflects at an angle of 5°. I'm asked to find the square of the four-momentum transfer, q2
q = P - P', where P/P' is a 4-momentum vector <px, py, pz, iE>
a "primed" quantity represents a value after the collision with the proton.
The Attempt at a Solution
I took the quantity P-P' and squared it:
q2 = (P-P')*(P-P') = P2 + P'2 -2P*P'
I'm told the first two terms are negligible due to the electron's mass being negligible, but I'm not sure I see the sense in that.
Anyways, continuing on, I then have:
q2 = -2P*P' = -2(px*px' + py*py'+pz*pz' -E*E')
or q2 = -2p*p' + 2E*E'
This is where I'm stuck. Should I also assume the product of the 3-momenta is 0 and carry on with the +2EE' term I'm left with? And what do I even do about the E' since I don't know that quantity?