Why Is Momentum of One Particle Used in the Breit-Wigner Cross Section Formula?

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SUMMARY

The discussion centers on the use of momentum in the Breit-Wigner cross section formula for particle reactions. The formula is given as σ = (g π λ² Γi Γf) / ((E - E₀)² + (Γ² / 4)). Participants debate the appropriateness of using the momentum of either initial particle in the center of mass (COM) frame versus the total momentum in the lab frame. It is established that while the COM frame simplifies calculations, performing the analysis in the lab frame can yield comparable results, reinforcing the flexibility in choosing reference frames for scattering processes.

PREREQUISITES
  • Understanding of the Breit-Wigner cross section formula
  • Familiarity with center of mass (COM) and lab reference frames
  • Knowledge of particle physics and scattering processes
  • Basic concepts of momentum and energy conservation in relativistic contexts
NEXT STEPS
  • Explore the derivation of the Breit-Wigner cross section formula in detail
  • Learn about the implications of using different reference frames in particle physics
  • Study momentum conservation laws in both COM and lab frames
  • Investigate other scattering processes and their analysis methods
USEFUL FOR

Particle physicists, researchers in high-energy physics, and students studying scattering theory will benefit from this discussion, particularly those interested in the application of the Breit-Wigner formula in various reference frames.

secret2
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Is anyone familiar with Breit-Wigner Cross section? Say, for a reaction with 2 particles in the initial state, 1 intermediate and 2 final:

[tex]\sigma = \frac{g \pi \lambda^2 \Gamma_i \Gamma_f}{(E-E_0)^2 + \frac{\Gamma^2}{4}}[/tex]

I can't see why for the wavelength we should use the momentum of EITHER one particle in the initial state. Sure, I can choose either one because in the COM frame it doesn't matter which momentua of the initial particles I choose. But in the derivation of the above equation it is not obvious why the momentum cannot be, say, the TOTAL momentum in the lab frame. Afterall, isn't it true that working in the COM frame is simply a convention?
 
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Okay.Here's my advice:do the computation if the lab frame.From the very beginning till the end.No reference to COM,whatsoever.And then compare the results...

Yes,it is true.Most (if not all) scattering processes are analyzed using the COM reference frame for ease of calculations and for the fact that the COM is ALWAYS an IRS (elementary,relativistic level)...


Daniel.
 

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