3-Point 1-Loop Integral with 1 Mass

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SUMMARY

The discussion focuses on evaluating the integral ##\int d^{d}l \frac{1}{l^2 (l+q-p)^2 ((l-p)^2-m^2)}##, which is related to a Passarino-Veltman C0 integral. The user seeks analytic results without employing mass regulators and suggests using the QCD Loop Repository for finding necessary integrals. They offer to share an analytic formula in a Mathematica notebook if needed. The integral is expected to be convergent in four dimensions.

PREREQUISITES
  • Understanding of Passarino-Veltman integrals
  • Familiarity with dimensional regularization techniques
  • Knowledge of QCD (Quantum Chromodynamics) loop calculations
  • Proficiency in using Mathematica for symbolic computation
NEXT STEPS
  • Research dimensional regularization in quantum field theory
  • Explore the QCD Loop Repository for integral lookups
  • Study the Passarino-Veltman reduction method
  • Learn how to implement integrals in Mathematica
USEFUL FOR

Physicists, particularly those working in quantum field theory, computational physicists, and anyone involved in loop calculations in QCD will benefit from this discussion.

Hepth
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I'm trying to get an analytic result, but can't seem to get it. Does anyone know of a lookup table or another way to get it? The Integral I need is of the form:

##\int d^{d}l \frac{1}{l^2 (l+q-p)^2 ((l-p)^2-m^2)}##

It should be convergent in 4 dimensions I believe, but without some regulators for the masses, which I DONT want, it might be best to work in "d" and absorb any divergences there.

This is equivalent to a passarino-veltman C0. I find results for other cases, but not this one. If I do it myself I can't find a favorable way to regulated the divergences that appear.
 
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Have you tried qcd loop repository?

There is a nice interface to find all the integrals you might need. These are d dimensions for the divergent ones.
 
Did you find what you needed? If not, pm me and I can send you the analytic formula in a mathematica nb or something.
 

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