Fixed Target & CoM Energy of colliding protons

In summary, the conversation discusses the calculation of the energy in the lab frame and the center of mass frame for a cosmic ray proton collision. The formula used for the lab frame is E_lab^2/c^2 - p^2 = 2Em_p + m_p^2c^2 = m^2c^2, where E is the energy of the proton. The centre of mass frame has E_CoM^2/c^2 = m^2c^2. The speaker clarifies that there is no new particle produced and the invariant mass is equal to the mass of the protons. They also mention using 7TeV as the center of mass energy and finding E_lab, which was approximately 2.
  • #1
Sekonda
207
0
Hey,

My question is with part (c) of the below:

tmst3.png


I wanted to check that I had done this write as I struggle to determine the correct invariants for each frame... despite their invariance. So for the lab frame I had

[tex]\frac{\ E_{lab}^{2}}{c^{2}}-p^{2}=(\frac{E}{c}+m_{p}c)^{2}-p^{2}=2Em_{p}+m_{p}^{2}c^{2}=m^{2}c^{2}[/tex]

(Where E is the energy of the cosmic ray proton)

Where the last step is done by using the relativistic energy-momentum relation and the very last term is the invariant mass. The Centre of mass frame has:

[tex]\frac{E_{CoM}^{2}}{c^{2}}=m^{2}c^{2}[/tex]

Finally we attain:

[tex]2Em_{p}+m_{p}^{2}c^{2}=\frac{E_{CoM}^{2}}{c^{2}}\: ,\: E=\frac{\frac{E_{CoM}^{2}}{c^{2}}-m_{p}^{2}c^{2}}{2m_{p}}[/tex]

I think this is correct but I used 7TeV for the centre of mass energy, should I use 14TeV? It says the 7TeV is the centre of mass energy per collision, so I'm guessing I use E(CoM)=7TeV and find E(lab) which was about 2.5*10^4 TeV.

Thanks if anyone can tell me if this is correct!
sk
 
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  • #2
Sekonda said:
[tex]\frac{\ E_{lab}^{2}}{c^{2}}-p^{2}=(\frac{E}{c}+m_{p}c)^{2}-p^{2}=2Em_{p}+m_{p}^{2}c^{2}=m^{2}c^{2}[/tex]

(Where E is the energy of the cosmic ray proton)
Where is the difference between E and E_lab?
What happened to E^2-p^2 at the second "="? It should give an additional mc^2.
Why should this be equal to the total energy in the center of mass frame?
There is no new particle produced, you don't have an invariant mass (apart from the masses of the protons).

I wonder how you used momentum conservation here.

I think this is correct but I used 7TeV for the centre of mass energy, should I use 14TeV? It says the 7TeV is the centre of mass energy per collision, so I'm guessing I use E(CoM)=7TeV and find E(lab) which was about 2.5*10^4 TeV.
Use 7 TeV as center of mass energy.

E(lab) = 2.5*10^4 TeV has the right order of magnitude.
 
  • #3
Thanks

Yeah I forgot the mc^2 term - there should be one in that second =, thanks! I thought the invariant for the lab frame has to be the same in any frame and for the CoM frame there's no momentum term due to equal and opposite momenta's of the particles. I guess I mean the mass of the protons then instead of invariant mass!

Thanks,
SK
 

1. What is a fixed target experiment?

A fixed target experiment involves colliding particles, such as protons, with a stationary or fixed target. This allows for the study of the properties and interactions of the colliding particles.

2. How is the center-of-mass energy determined in a fixed target experiment?

In a fixed target experiment, the center-of-mass (CoM) energy is determined by the energy of the incoming particles and the mass of the target. The CoM energy is the total energy available for the collision and is an important factor in determining the types of particles that can be produced in a collision.

3. What is the significance of the CoM energy in colliding protons?

The CoM energy of colliding protons is important because it determines the maximum energy at which new particles can be created. This energy is directly related to the mass of the particles produced and can provide insight into the fundamental forces and interactions in nature.

4. How is the CoM energy of colliding protons increased in experiments?

The CoM energy of colliding protons can be increased by accelerating the particles using particle accelerators. Higher energy collisions allow for the production of more massive particles and can provide a deeper understanding of the fundamental building blocks of matter.

5. What are some current experiments studying the CoM energy of colliding protons?

Some current experiments studying the CoM energy of colliding protons include the Large Hadron Collider (LHC) at CERN and the Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory. These experiments are aimed at understanding the fundamental properties of matter and the early universe through high energy collisions.

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