Particle momenta and cross section

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Discussion Overview

The discussion revolves around the treatment of particle momenta and cross sections, specifically in the context of electron-muon scattering. Participants explore the implications of massless particle approximations and the relevance of different reference frames in the analysis.

Discussion Character

  • Technical explanation, Conceptual clarification, Debate/contested

Main Points Raised

  • Some participants seek clarification on specific steps in the derivation related to particle momenta.
  • Others suggest that the discussion pertains to massless particles, questioning whether this is an approximation for the electrons and muons involved.
  • One participant asserts that the event is analyzed in the center of mass (CM) frame, while another challenges the relevance of this frame to the massless approximation.
  • There is a proposal that the approximation of massless particles is valid when considering high momentum/energy conditions, leading to the suggestion that certain equalities should be treated as approximations.
  • Participants discuss the relationship between energy and momentum, with one noting that the approximation arises from Taylor expanding the energy equation for low mass compared to momentum.

Areas of Agreement / Disagreement

Participants express differing views on the relevance of the CM frame and the treatment of particle masses, indicating that multiple competing perspectives remain without a clear consensus.

Contextual Notes

There are unresolved assumptions regarding the conditions under which particles can be treated as massless, and the implications of different reference frames on the analysis.

Schwarzschild90
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Will someone explain this step to me?
 

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Some more background would be helpful. I suppose this is for massless particles where p^2=0?
 
Yes. It's for electron muon scattering
 
But neither electrons nor myons are massless. Or is this some approximation?
 
The event is viewed in a CM frame.
 
it has nothing to do with CM frame ([itex]p^2= m^2[/itex] in any frame -frame independent minkowski product).
Probably they consider electron/muon with high enough momenta/Energy so that they can be considered massless (i.e. the last [itex]=[/itex] in 2nd line should be [itex]\approx[/itex] instead)
 
They neglect the particle masses, right.
 
I was in a rush. CM has nothing to do with it.

Indeed, the particles considered are massless.

I figured it out.
 
Last edited:
Why can we set E/c = p?
 
  • #10
It is the same approximation of massless particles.
 
  • #11
[itex]E = \sqrt{p^2 + m^2} \Rightarrow E = p + \mathcal{O}\big(\frac{m^2}{2p}\big)[/itex]
(taylor expanding the square root for m<<p)
 

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