Doubt on sign of the propagator on Peskin

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SUMMARY

The discussion centers on the sign of the propagator in Quantum Chromodynamics (QCD) corrections to the low energy electroweak Lagrangian as outlined in Peskin's "An Introduction to Quantum Field Theory," specifically section 18.2 and equation 18.35. The extra minus sign in the numerator of the second fermion propagator arises due to the conservation of momentum, where one quark momentum is represented as -k when the gluon momentum is k. This clarification is essential for accurately reproducing the calculations involved in QCD corrections.

PREREQUISITES
  • Understanding of Quantum Chromodynamics (QCD)
  • Familiarity with Peskin's "An Introduction to Quantum Field Theory"
  • Knowledge of fermion propagators in quantum field theory
  • Basic concepts of momentum conservation in particle physics
NEXT STEPS
  • Review Peskin section 18.2 for detailed explanations of propagators
  • Study the derivation of equation 18.35 in Peskin's text
  • Explore the implications of momentum conservation in QCD calculations
  • Learn about the role of external momenta in loop integrals
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This discussion is beneficial for theoretical physicists, graduate students in particle physics, and anyone studying quantum field theory, particularly those focusing on QCD and electroweak interactions.

Einj
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Hi everyone. I was trying to reproduce the calculation needed to include the QCD correction to the low energy electroweak Lagrangian. In particular I am looking at Peskin section 18.2. In equation 18.35 an extra minus sign appears on the numerator of the second fermion propagator.

Can anyone explain me why?

Thanks
 
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As stated in the text, all external momenta have been set to zero. Thus the only momentum is the loop momentum k. If we take the gluon momentum to be k, by conservation of momentum one of the quark momenta must be -k.
 
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Oops... stupid question! Thanks a lot
 
Einj said:
Oops... stupid question! Thanks a lot

Most definitely NOT a stupid question!
 

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