2
$\begingroup$

I'm studying a very particular conformal field theory where unusual Feynman integrals appear when I'm trying to evaluate a two-loop correlator (in position space). These integrals are on the form $\int_0^1du\frac{\text{Log}(b^2 + (a^2 - b^2)u)}{\sqrt{b^2 + (a^2 - b^2)u}} \ , \ \int_0^1du\frac{\text{Log}[u(1 - u)]}{\sqrt{b^2 + (a^2 - b^2)u}}$ and $\int_\mathbb{R^3}\frac{dzdw}{(x - z)^2(y - w)^2(z - w)^{2n}} \ ,$ where I need to solve the last of these for three different cases: $n\in\{1,2,3\} \ .$ Any help on solving these integrals would be appreciated. Alternatively if you know a good reference where similar integrals are studied.

$\endgroup$
0
$\begingroup$
  1. I assume log(x) = ln(x). The first integral: enter image description here

  2. Unfortunately the second integral is divergent.

enter image description here

$\endgroup$
  • $\begingroup$ Thanks for your answer! I appreciate it. Do you know whether it's possible to regularize the second integral. If I'm able to isolate the divergence I can add a counterterm that removes it. $\endgroup$ – A.Dunder Apr 19 '18 at 10:33
  • $\begingroup$ @A.Dunder You're welcome. I edited my post above. $\endgroup$ – Székely Balázs Apr 19 '18 at 11:42
  • $\begingroup$ How did you find this? Did you use a program or did you do a couple of suitable variables changes? Edit: Nevermind I managed to do it with Mathematica. $\endgroup$ – A.Dunder Apr 19 '18 at 11:56
  • $\begingroup$ I did a few integration by parts. Please note: I don't use any program for calculation, it would kill all the fun, but feel free to check the results if you like. $\endgroup$ – Székely Balázs Apr 19 '18 at 12:07

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.