Computing the 1-loop Correction to the 3 Gluon Vertex with Non-Zero Quark Mass

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Discussion Overview

The discussion centers around the computation of the 1-loop correction to the 3 gluon vertex in quantum chromodynamics (QCD) involving a quark loop with non-zero quark mass. Participants explore the implications of quark loops on the amplitude and the potential vanishing of certain contributions.

Discussion Character

  • Technical explanation, Debate/contested

Main Points Raised

  • One participant inquires about references for the computation of the 3 gluon vertex correction due to a quark loop with non-zero mass.
  • Another participant suggests that the triangular quark loop at the center may lead to a vanishing amplitude, citing the trace of SU(3) generators and the QED photon 3-point function with a fermion loop.
  • This same participant elaborates that the QED three-point function vanishes due to a cancellation between two loops, while in QCD, they note a non-vanishing term proportional to the structure constants f^(a,b,c).
  • A later reply provides a reference that may be relevant to the discussion.

Areas of Agreement / Disagreement

Participants express differing views on whether the amplitude vanishes, with some arguing it does and others providing counterpoints regarding the structure constants in QCD. The discussion remains unresolved regarding the overall impact of the quark loop on the 3 gluon vertex.

Contextual Notes

There are assumptions regarding the behavior of the QED and QCD three-point functions, as well as the specific contributions of the quark loop that remain unverified within the discussion.

ParticleGrl
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Anyone know a reference in the literature that computes the correction to the 3 gluon vertex due to a quark loop with non-zero quark-mass?
 
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You mean a triangular quark loop at the center? I think this diagram vanishes. This amplitude = (trace of SU(3) generators of the gluons) * (QED photon 3-point function with a fermion loop). The latter vanishes because in QED the photon 3-point function vanishes. I may have made a mistake, so please correct me.
 
petergreat said:
You mean a triangular quark loop at the center? I think this diagram vanishes. This amplitude = (trace of SU(3) generators of the gluons) * (QED photon 3-point function with a fermion loop). The latter vanishes because in QED the photon 3-point function vanishes. I may have made a mistake, so please correct me.

The QED three point function vanishes because its a sum of two loops, one cancels against the other. In QCD, you get tr[t^a t^b t^c] - tr[t^a t^c t^b], which is proportional to f^(a,b,c), as you'd expect.
 
Maybe this can help:

arXiv:hep-ph/9806522v1[/URL]
 
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