When does a proton break? I have read that most proton-proton collision are elastic, and that rarely a proton is smashed, and that happens only at large angles: can you expand on this situation?
What does a large angle mean? I suppose it's the scattering angle, so, does that imply that a proton is more fragile when the impact is off CoM? why so?
Can you link or add some details on when exacly a break takes place, is there a critical relative velocity/momentum governing the process, or is in any way that related to the angle? Is the number of fragments related to the force of the impact and/or the angle? and what are the actual values of the breaking points?
 A: Suppose we take the proton to be a bound state of (on average three) quarks. This is a gross oversimplification because a proton is a seething mass of energy that isn't simply three distinct quarks, but let's gloss over this and carry on regardless.
When we talk about a collision of two protons what we actually mean is that a quark in one proton and a quark in the other proton pass close enough to each other to scatter each other i.e. to exchange momentum. (At this point someone is going to point out that most scattering is actually quark-gluon, but again let's try and keep things simple.)
So the two quarks have to transfer enough momentum to each other to knock themselves out of the proton. Depending on how closely they approach their interaction will look something like one of these possibilities:

The collision in (a) is a glancing collision. The two particles scatter only weakly so not much energy and momentum is exchanged. This won't cause the quarks to be knocked out of the nucleus.
The collision in (c) is head on and is the maximum exchange of energy and momentum possible. This will definitely knock the quarks out of the nucleus. But the probability of this collision is exceedingly low because for a head on collision the trajectories of the two particles have to be exactly aligned. So this happens only rarely.
The collision in (b) is a happy medium. The quarks scatter strongly enough to knock each other out of the protons, and since their trajectories don't have to be exactly aligned there is a reasonably high probability that the collision will occur.
So most of the proton-breaking collisions we observe are going to look like (b) i.e. the scattering is large in the sense of being at angles to the trajectories comparable to $\pi/2$. This is because of a trade-off of the two effects:


*

*as the angle increases the momentum and energy exchange increases

*as the angle increases the scattering probability decreases
