Proton creation and annihilation

[DiracPool]

1. Can a proton be created in a particle accelerator that doesn't use protons? For instance, an "electron-positron" collider? I understand baryon number needs to be conserved, so this would necessitate the accompanying creation of an anti-proton, but I'm wondering if these colliders have enough energy to accomplish this and if it's routinely done, etc. If so, does the created proton and anti-proton just annihilate each other immediately, or can it happen that the created proton goes on to live a happy life for eternity whilst the created anti-proton annihilates with some other unlucky proton?

2. At the LHC, protons are smashed into each other which creats pure energy that reforms into "other" particles, such as the Higgs and a number of others. Are these protons lost forever? Again, since the baryon number must be conserved, how does the balance add up? What are we left with?

 

[Orodruin]

Can a proton be created in a particle accelerator that doesn't use protons? For instance, an "electron-positron" collider?

Yes, this is perfectly possible as long as you (as you say) also create an anti-proton. Generally, they will fly off into different directions and the anti-proton can very well annihilate with some other proton.

At the LHC, protons are smashed into each other which creats pure energy that reforms into "other" particles, such as the Higgs and a number of others.

Well to start with, there is nothing such as "pure energy". Energy is conserved and that is about it, the kinetic and mass energy carried by the protons will be transformed into kinetic and mass energy of the produced final state. There is no intermediate state which is some sort of pure energy.

Second, there is nothing "pure" about a proton-proton collision. The LHC energies are so high that you can essentially consider the collisions as being collisions of the proton constituents (i.e, quarks and gluons) and not of the protons themselves. This typically results in a big mess of particles. The remains of the proton once the quark/gluon has collided will hadronise and a hadron jet is typically formed from this. The same goes for quarks flying off from the reaction itself. Hadron colliders are quite messy in that sense, unlike lepton colliders, which are colliding elementary particles.

Are these protons lost forever?

What do you mean by being "lost forever"? There is actually no way of checking this as you cannot mark the protons - all protons are the same.

Again, since the baryon number must be conserved, how does the balance add up? What are we left with?

Since baryon number is conserved, you must end up with a final state with a baryon number of two. This will typically be taken care of by the hadron jets.