Fermi's Golden Rule (Decay Amplitude)

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SUMMARY

The discussion centers on Fermi's Golden Rule as it applies to the decay amplitude of a neutral pion into two photons, as detailed in Griffiths' "Introduction to Elementary Particles," specifically on page 196. The amplitude for this decay process is represented as M(p_2, p_3), where p_2 and p_3 are the momentum three-vectors of the resulting massless photons. The conservation of momentum leads to the conclusion that p_2 = -p_3. Furthermore, it is established that the squared amplitude |M|^2 is solely a function of |p_2|, indicating that there is no angular dependency in this decay process due to the spin-zero nature of the neutral pion.

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  • Familiarity with Fermi's Golden Rule and its applications in particle physics.
  • Knowledge of momentum conservation in particle interactions.
  • Basic concepts of angular momentum and spin in quantum mechanics.
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  • Study the derivation of Fermi's Golden Rule in detail.
  • Explore the implications of spin-zero particles in decay processes.
  • Investigate the role of momentum conservation in particle physics.
  • Learn about the properties of massless particles, particularly photons, in quantum field theory.
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Students and researchers in particle physics, particularly those studying decay processes and the implications of spin in quantum mechanics, will benefit from this discussion.

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This question relates to Griffiths: Introduction to Elementary Particles, p. 196

The process in question is a neutral pion decay into two photons. It is stated that because the secondary particles are massless, the amplitude for this process is:

<br /> M(p_2,p_3)<br />

where p_2 and p_3 are the momentum three-vectors of the secondary photons. Conservation of momentum further implies that p_2=-p_3. So far, so good.

However, Griffiths then states that
<br /> |M|^2<br />
is a function of |p_2| only, meaning that |M|^2 has no angular dependency. Why is this?
 
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The pi zero has spin zero, so its decay cannot have any angular dependence.
 

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