Derivating a Yukawa theory loop-integral

[Ace10]

Hello fellow physicists,

during some calculations for a project regarding Renormalization, I had a difficulty in computing a derivative of a loop integral in Yukawa theory. The thing I'm reffering to can be found in Peskin and Schroeder's book, Introduction to QFT , in Chapter 10 page 329-330.

Question #1:

How the gamma function's argument changes from "1-d/2" (10.33) to "2-d/2" (10.35) ?

Question #2:

Could please somebody show me a detailed calculation of the derivation? I cannot get the finel form, with "x(1-x)" in the numerator and plus the denominator has power "2-d/2" and i think that normally the power should be "-d/2"


Thank you very much in advance..

 

[Bill_K]

How the gamma function's argument changes from "1-d/2" (10.33) to "2-d/2" (10.35) ?

When you take the derivative of the denominator, a factor of 1-d/2 comes out, and then use the identity zΓ(z) = Γ(z+1).