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IBP Relations in Feynman integrals

  1. Nov 1, 2015 #1


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    I am wondering if anyone has experience in using IBP( Integration by parts) identities in the evaluation of Feynman diagrams via differential equations?

    My question is that I can't seem to understand where equation (4.8) on P.8 of this paper: http://arxiv.org/pdf/hep-ph/9912329.pdf comes from. They are relating a triangle diagram to two bubble diagrams. I can write the l.h.s of 4.8 as being of the form $$\frac{1}{k^2 (k-p_2)^2(k-q)^4}$$ which in the family of integrals associated to the box diagram is denoted as ##G(1,1,0,2)## where one of the propagators is squared and the other contracted. Then find an IBP using relation $$\int p_2^{\mu} \cdot \frac{\partial}{\partial k^{\mu}} \frac{1}{k^2(k-p_2)^2 (k-q)^2} = 0$$ which I think gives rise to the equation $$G(1,1,0,2) = \frac{1}{s+t}\left(G(0,2,0,1) - G(1,0,0,2) - G(2,0,0,1) + G(0,1,0,2\right))$$ But the problem is I now need to reduce the terms on the r.h.s down to simpler diagrams and all attempts so far have gone in the direction of introducing higher exponents.

    I don't have high hopes of getting a reply but I just thought I'd ask anyway to see if anyone is familiar with these identities and could help.

    Many thanks!
  2. jcsd
  3. Nov 6, 2015 #2
    Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
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