Breit-Wigner propagator Of resonance

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SUMMARY

The discussion centers on the analysis of the decay process of an excited nucleon into a nucleon and an Omega meson, utilizing the Breit-Wigner propagator. Key references include "Covariant tensor formalism for partial-wave analyses of ψ decay to mesons" by B.S. Zou and D.V. Bugg, and foundational texts such as "Field Theory in Particle Physics" by De Wit and "Lectures on Quantum Mechanics" by Weinberg. The Breit-Wigner distribution is acknowledged as a useful tool for treating resonances, though it is not universally applicable and often omits finite time corrections. The construction of a phenomenological vertex is contingent upon the specific quantum numbers of the involved particles.

PREREQUISITES
  • Understanding of particle decay processes
  • Familiarity with the Breit-Wigner propagator
  • Knowledge of quantum numbers in particle physics
  • Basic concepts of covariant tensor formalism
NEXT STEPS
  • Study the Breit-Wigner distribution and its applications in resonance analysis
  • Explore the covariant tensor formalism for partial-wave analyses
  • Read "Field Theory in Particle Physics" by De Wit for deeper insights into vertex construction
  • Investigate the role of quantum numbers in particle interactions and decay processes
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Particle physicists, researchers in quantum mechanics, and students studying decay processes and resonance phenomena will benefit from this discussion.

zhangyang
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Ｉ Want to analyze the decay from a excited nucleon to a nucleon and an Omega meson.I have seen a propagator

upload_2015-3-20_14-0-56.png


upload_2015-3-20_14-1-54.png


which descripes a process : a→b+c

(Eur. Phys. J. A16, 537–547 (2003), Covariant tensor formalism for partial-wave analyses ofψdecay to mesons ,B.S. Zou and D.V. Bugg)

But how could it be obtained? Is it general and universal?

Or ,how to construct a vertex of the process phenominologically?
 
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If you want to know exactly where the Breit-Wigner propagator comes from you can look at De Wit - Field Theory in Particle Physics, or Weinberg - Lectures on Quantim Mechanics, the chapter on resonance. The Breit-Wigner distribution (propagator), however, is not general nor universal. It is used to treat resonances and, if I remember correctly, should also contain some finite time corrections, but I'm not sure. However, they are very often ignored.

As far as the phenomenological vertex is concern, it strongly depends on your quantum numbers. What are the initial and final particles?