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Derivating a Yukawa theory loop-integral !

  1. Jan 20, 2014 #1
    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..
  2. jcsd
  3. Jan 20, 2014 #2


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    Science Advisor

    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).
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