Gluons turning into quarks and antiquarks

[PotatoMan]

When looking into how particles decay, it seems that it will happen if there exists an interaction between the initial and final state, and if the final state has lower potential energy than the initial. (i.e. turning mass into kinetic energy) If this is true, how does a gluon turn into a quark and antiquark pair if the final state here has more mass than the initial? What interaction is even happening here?

 

[Nugatory]

how does a gluon turn into a quark and antiquark pair if the final state here has more mass than the initial

It's not the mass that matters, it's the total energy of which the mass is one component. For a more prosaic example, consider how a massless photon can produce an electron-positron pair if sufficiently energetic.

 

[PeroK]

Also, the purpose of things like the LHC is to produce heavier particles from lighter particles colliding at high energy.

 

[PotatoMan]

It's not the mass that matters, it's the total energy of which the mass is one component. For a more prosaic example, consider how a massless photon can produce an electron-positron pair if sufficiently energetic.

Thanks for the clarification. So the total energy of the system goes down? Or are you referring to just the total potential energy of it?

 

[Vanadium 50]

consider how a massless photon can produce an electron-positron pair if sufficiently energetic.

Note that this does not happen in free space. You need a particle to recoil to conserve energy and momentum. Gluons are the same way.

 

[Nugatory]

Note that this does not happen in free space. You need a particle to recoil to conserve energy and momentum. Gluons are the same way.

Yes, thought about mentioning that, decided that it went beyond the scope of the B-level question. Of course I could have avoided the issue completely by considering the two-photon case, but it felt wrong to use the way less probable interaction as the example.

A quibble: the heavy particle recoil is needed to conserve momentum - if we were to only consider energy the single-photon process would appear possible in vacuum?

 

[Vanadium 50]

I was also trying not to get lost in the weeds and said "energy and momentum" instead of "4-momentum".

 

[PeterDonis]

if we were to only consider energy

You can't; in relativity the split between "energy" and "momentum" is frame-dependent.

 

[Nugatory]

You can't; in relativity the split between "energy" and "momentum" is frame-dependent.

Of course, but that doesn’t stop me from working in the lab frame in which if the (frame-dependent) energy of a photon is greater than 1.022 MeV pair production appears to be energetically permitted but cannot be reconciled with momentum conservation.