Proton-proton collision threshold for proton-antiproton pair production

[Olibaba]

Hi, just registered to Physics Forums after doing a lot of lurking...

Anyway, the semester is restarting and my brain is rusty. Please help!

Here is my question:

I am asked to show that a proton colliding with a proton at rest must have energy greater than 5.6 GeV in order to produce a proton antiproton pair, and to do this using relativistic energy/momentum conservation.

Here is where I am at in my thinking.. Please let me know if I am making this too hard for myself, or if I am missing some big obvious detail!

1. In order to produce the proton-antiproton pair, the moving proton must overcome the coulomb barrier of the 'at rest' proton. (This seems trivial.. and I don't think I should include any math to take this into account).

2. Since it is suggested 5.6 GeV is the minimum energy, both proton and antiproton will be at rest after the collision.

So now I wonder where to go. I know the equations

E = K + m_p (setting c=1)
E = sqrt(p^2 + m_p^2)

I take it they both have m_p = 938 MeV (rest energy).

I am confused.. After the collision, the proton-antiproton will have a total energy of 2*938 MeV. Where does that 5.6 GeV go to?

 

[Vanadium 50]

What frame do you want to work the problem in?

 

[Olibaba]

I would start in the lab frame.

 

[Olibaba]

I solved the problem! (Thanks to physicsforums) For reference, see this comment:

https://www.physicsforums.com/showthread.php?t=402121&highlight=proton+proton+collision

Thanks to you all!

Guess next time I will search a little harder before posting.. Sorry for the inconvenience!

 

[Vanadium 50]

I would start in the lab frame.

Almost never the right thing to do.

 

[Olibaba]

Is the flaw of using the lab frame that we aren't seeing the system from the particle's viewpoint?

In such a case, that would mean that using the lab frame in this case would only work as we specify that one of the particles is at rest (and thus its frame coincides with the lab frame)?

Thanks!