Particle momenta and cross section

In summary, the conversation is about massless particles and their behavior in electron muon scattering. The topic is approached with the assumption that the particles have high enough momenta/energy to be considered massless. The concept of a CM frame is mentioned, but it is clarified that it has no relevance to the discussion. The approximation of setting E/c = p is explained and it is noted that this is an approximation for massless particles. The equation E = p + \mathcal{O}\big(\frac{m^2}{2p}\big) is also mentioned as a way to approximate the energy of a massless particle.
  • #1
Schwarzschild90
113
1
Will someone explain this step to me?
 

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  • #2
Some more background would be helpful. I suppose this is for massless particles where p^2=0?
 
  • #3
Yes. It's for electron muon scattering
 
  • #4
But neither electrons nor myons are massless. Or is this some approximation?
 
  • #5
The event is viewed in a CM frame.
 
  • #6
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)
 
  • #7
They neglect the particle masses, right.
 
  • #8
I was in a rush. CM has nothing to do with it.

Indeed, the particles considered are massless.

I figured it out.
 
Last edited:
  • #9
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)
 

FAQ: Particle momenta and cross section

1. What is particle momentum?

Particle momentum is a measure of the motion of a particle. It is defined as the product of the particle's mass and velocity. In other words, it is the quantity of motion an object has based on its mass and speed.

2. How is particle momentum related to cross section?

Particle momentum is directly related to cross section, as cross section is a measure of the effective area that a particle interacts with when it collides with another particle. As momentum increases, the cross section also increases, indicating a higher likelihood of interaction.

3. What factors affect particle momenta and cross section?

Particle momenta and cross section can be affected by a variety of factors, including the mass and velocity of the particles involved, the angle of collision, and the type of interaction (e.g. elastic or inelastic).

4. How is particle momenta and cross section measured?

Particle momenta and cross section are typically measured using particle accelerators, which use strong electric and magnetic fields to accelerate particles to high speeds and then collide them with a target. The resulting data is then analyzed to determine the momenta and cross section of the particles involved.

5. What is the importance of understanding particle momenta and cross section?

Understanding particle momenta and cross section is crucial in fields such as particle physics and nuclear physics. It allows scientists to study the fundamental building blocks of matter and the interactions between them, leading to a deeper understanding of the universe and its origins.

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