- #1
gobbles
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Homework Statement
I'm trying to understand dimensional regularization with Peskin. There is a transitions that is not clear.
Homework Equations
On page 250, the general expression for the d-dimensional integral is given:
##\int \frac{d^d l_E}{(2\pi)^d}\frac{1}{(l_E^2+\Delta)^2}=\frac{1}{(4\pi)^{d/2}}\frac{\Gamma(2-\frac{d}{2})}{\Gamma(2)}\left(\frac{1}{\Delta}\right)^{2-\frac{d}{2}}##.
So far everything is clear. But then, in 7.84 he writes
##\int \frac{d^d l_E}{(2\pi)^d}\frac{1}{(l_E^2+\Delta)^2}\rightarrow\frac{1}{(4\pi)^2}\left(\frac{2}{\epsilon}-\log\Delta-\gamma+\log(4\pi)+\mathcal{O}(\epsilon)\right),##
when ##d\rightarrow4##.
The Attempt at a Solution
I understand where the ##\frac{2}{\epsilon}## and ##-\gamma## factors come from, but where did the terms involving the logarithm function came from? Even if I take the eventual integration over the Feynman parameters into account I don't get the correct answer.