# Feynman parameters in one loop contribution for electron vertex

I'm studying one loop contribution for electron vertex function form Peskin and Schroeder's book " An introduction to quantum field theory " Section: 6.3 .. the momentum flow is given as in the following diagram:

I'm stuck in evaluating the dominator to get Equation (6.44) after Feynman parametrization .. Starting from equ. (6.43) :

$D= k^2+ 2k . (yq-zp)+ y q^2 + z p^2 -(x+y)m^2$

after changing the variables $k \to l -(yq-zp)$ I got:

$D = l^2 - 2 l (yq-zp) + (yq-zp)^2 + 2 l (yq-zp) - 2 (yq-zp)^2 + y q^2 + z p^2 -(x+y)m^2 \\ = l^2 - 2 y z q.p -(x+y)m^2$

Then I stop here. I think reaching for (6.44) just comes from evaluting $q.p$ depending on the process kinamtics which i can't figure out now , so any help ?

• $p$ is the $4$-momentum of a real incoming particle. Therefore it is on the mass-shell, $$p^2 = m^2 .$$ Note that in this context $q$ is the momentum of a virtual particle, that's why $q^2 \neq 0$ in general.
• From energy-momentum conservation, $p' = p + q$. Square both sides to obtain $$m^2 = m^2 + 2pq + q^2 \qquad \Rightarrow \qquad 2pq = -q^2$$