Ok, for starters, I’m working off an OP I posted here where the jury reported that protons not only can be considered, but are spherical. (No cite.)
What is the temperature at the moment of collision? Is that a straightforward question/answer?
Have “glancing” collisions revealed interesting results? Can glancing blows even be categorized, ie, that is too Newtonian-mechanics thinking?
Again, thinking like the protons are spheres of some sort–or any shape for this question–I’m trying to keep in mind that these little suckers are as real as dirt. When you slam an object, a shock wave travels through it, which takes some amount of time. Shouldn’t this occur with a proton?
(I sort of remember a post on acoustic waves versus sonic waves (which I had conflated), and Chronos wondered aloud about acoustic waves through electrons. [Sorry Chronos if I’ve totally fucked up that memory and intellectually maligned you.] Something like that is in the back of my mind for question #3.)
Question 1 is easy enough, though it’s not entirely well-defined: The concept of temperature is really only applicable when you have large numbers of particles, with energies distributed in a particular way, while in the LHC you’re only dealing with two particles at a time (or maybe a few more, if you’re counting constituents of compound particles, but they’re still not distributed thermally). Nonetheless, if you just consider “temperature” as a measure of average energy per particle, then the energy of a particle in the LHC is roughly 1 TeV, for a temperature of roughly 10^16 K
For the second question, a “glancing collision” can be defined in some situations, but not in others, and the interesting ones are the ones where it can’t really be defined. It’s always possible to have a collision where the particles that come out are identical to the ones that went in, and in such a case, you could consider a collision where the outgoing particles have very similar momentum to the ingoing ones to be “glancing”. But the really interesting collisions are the ones where the particles that come out are different from the ones that went in, and in that case, there’s no clear way to identify which output particle corresponds to which input
On the third question, you’re basically talking about interactions between the component quarks, while the collision is taking place. You do have to take these into account to do the calculations properly, but “shock waves” would be a rather ill-suited formulation for describing them.
It’s not entirely straightforward. Properly speaking, if the molecules in a gas are at a given temperature, they’re going every which way in space with a certain average energy. On the other hand, the particles at CERN are not going every which way; they’re basically colliding head-on. However, you can ask, “for what temperature would the particles in a gas have the same energy that they do in the collider at CERN?” The answer there would be on the order of 10[sup]17[/sup] Kelvin.
I’m not quite sure what you mean by “glancing” collisions. If you mean collisions where the protons just “graze” each other as they fly by, then I don’t think they have a way of telling this. They’re colliding beams, each containing many protons; imagine two crowds of people standing on opposite sides of a busy street waiting for the signal to change, and when the signal changes the two crowds walk towards each other. If the people do nothing to avoid one another, there will be some will be head-on and some will be more glancing. But I don’t think that the minimum separation of the protons is something that can be easily measured for a given collision event.
I’ll have to think about this one a little more carefully. It might be possible for the quarks inside a proton to interact with one another in some kind of shock-wave analog, but I’m not sure whether it would be useful to think about it this way.
Just to add, the LHC operates in another mode where heavy ions (nuclei, up to lead) are accelerated instead of protons. In that case, you’ve got many more particles involved, to where it’s more reasonable to say it has a temperature. There’s less total energy, spread among many more particles, so the temperature they claim is only a paltry 5.5 trillion Kelvin.
At these energies, a proton-proton collision is more like a “bunch of independent quarks and gluons”-“bunch of independent quarks and gluons” collision. For linguistic convenience, the quarks and gluons are individually called “partons”, and one talks about the collision of partons.
If the LHC is operating at, say, 14 TeV, that’ll be the energy of each proton, but the constituent partons will be sharing that energy in a random way. The probability distribution for how the energy is divided between the partons has been measured to a reasonable degree in past experiments and is typically an input to LHC analyses. Calculating the distributions outright is challenging, but certain scaling laws and constraints can be obtained from first principles and are applied when interpretation the measurements. Note that the constituent partons include the familiar three quarks in the proton (up, up, down) and gluons and “sea” quarks (virtual quark/antiquark pairs).
In the most interesting collisions, the primary partons smack into each other with a good fraction of the total energy while the remaining “spectator” partons hadronize, producing jets of colorless hadrons that stream generally forward/backward along the beam direction (as opposed to streaming out transversely, which requires a good smack, which by definition hasn’t happened to these guys). Such collisions are called “hard” collisions. In “soft” collisions, the two partons that hit one another don’t have all that much energy and don’t do anything very interesting, but this results in a shredded proton nontheless. Hadronization still happens due to color confinement, and you get a relatively boring set of hadron jets as a result. This latter category is what you might call a “glancing” blow if you wanted to find a place to apply that term.
An important point is that the energy available in the parton-parton collisions (for instance, the energy to make new particles) is not 14 TeV since the proton energy is shared among the partons. The two actual colliding partons will have some smaller center-of-mass energy. Take a look at this figure (PDF)[sup]1[/sup]. It shows the luminosity (think “relative probability”) of quark-quark collisions versus the center-of-mass energy in their collision (horizontal axis, sqrt(s)) for different LHC beam energies (different colored curves). The 14 TeV case is in gray. One thing to notice is that the curve plummets well before reaching 14 TeV. Indeed, there are many more partons available for low energy collisions than there are for high. (This is why, for instance, proton-proton machines has very different specs than electron-positron machines. In the latter, the beam’s center-of-mass energy is the center-of-mass energy.)
[sup]1[/sup][0908.3660] LHC Physics Potential vs. Energy
Why does the luminosity increase seemingly without bound for low center-of-mass energy? I would expect it to have a peak at some value related to the beam energy. Maybe not at fully 1/3rd the energy, but something on the order of 1 TeV for the 14 TeV curve, and peaks at progressively lower energy for the other curves.
It’s not really a luminosity despite the labeling and in fact has units of cross section. A factor of 1/s is folded in, as that’s how the relevant cross sections scale. So, the feature you correctly expect to see is just the elbow at, say, a fifth or so of the proton-proton center-of-mass energy.
iirc, the detectors at the LHC (and most other particle colliders) actually discard most of the data they receive as ‘uninteresting’ (i.e. we’ve seen it before, we expect it here).
If that’s true, they may not notice ‘glancing’ blows as a glancing blow wouldn’t produce any ‘interesting’ data (same stuff coming out that went in, only change is the direction).
