What happens to the non-interacting part of protons in LHC collisions?

[Malamala]

Hello! I am sorry if this questions is dumb, but in a pp interaction at LHC, as far as I understand, we have one quark or gluon from one proton, interacting with another quark or gluon from the other. This is the main interaction and most of the resulting particles are produced perpendicular to the beam axis, at least for interesting interactions (hence the use of $p_T$ variable). I am not sure I understand what happens to the rest of the 2 protons (the 2 remaining valence quarks and the rest of the sea quarks and gluons). Now they shouldn't be colorless anymore, so they can't stay like that for long. Do they form jets that travel forward, along the beam line? Do they keep going around the beam line for a while (I am not even sure what charge they have). What actually happens to the non-interacting part of the 2 interacting protons? Thank you!

 

[mfb]

They hadronize and form two jets close to the beam directions, yes. They have a lower energy (but cannot have a lower but non-zero electric charge), so even particles that are nicely aligned with the beam axis won't travel farther than the beginning of the next dipole section. Most of them hit the beam pipe, the shielding, or other elements somewhere downstream. There are some smaller experiments in these regions, LHCf near ATLAS and TOTEM near CMS, to look for particles in the extreme forward direction.

For a while people were concerned about lead-lead operation. If two lead nuclei pass each other closely (without colliding) the electric field is so strong that you can produce electron/positron pairs and one of the electrons can stick to a nucleus. You would produce a set of Pb⁸¹⁺, all with the same momentum as the fully ionized Pb⁸²⁺, so these lead ions could all hit the accelerator wall in the same spot, potentially damaging it. As operation showed this is not a big deal.