An interesting effect of this is that you can only find in a particle collider what you expect to see.
i.e. you can confirm or deny that this effect or particle exists. But if something entirely new that no one expects is occurring you would never notice because you would never look - there is simply too much output.
At best you scan an energy range and look for bumps (indicating something interesting is happening), but you still have to decide what kind of collision to scan.
Basically run "energy balance" calculations - calculate the expected result of a certain experiment, run it a huge number of time, then check the totals and see if they match what you expect.
You also look for symmetry - if this thing is found, and there appears to be "room" for something like it, check for it.
So despite the limitations we found all sorts of things. But it's important to understand the limitations so you know what to imagine, and then look for.
There are different types of colliders, leptonic and hadronic colliders. Hadrons, usually protons, are composite particles so when you smash them together a wide range of output is produced. You can absolutely see unexpected things, and a lot of effort goes into analyzing and collecting data to explore many avenues for new physics. Leptonic colliders (usually electrons) involve point-like particles, so here you scan the energy and indeed it is much easier to find things when you know where to look.
Could you elaborate?
I thought the difference between leptonic and hadronic colliders was only in the beam & resulting signal purity?
Smashing an electron and a positron together produces pure energy to be converted into matter. It could generate photons or it could generate Hadrons just as likely could it not (as long as all quantum numbers are conserved)?
Protons are not fundamental particles, they are made up of quarks and gluons. The exact composition is determined by the nuclear PDF's, it is not nearly as simple as "protons are made of two Up quarks and a Down quark". As a result, the actual energy of each collision varies widely since the amount of energy 'given' to each parton (quark or gluon) is randomly distributed. So even though the beam energy is set to a specific value the energy of each collision is not given and must be measured in each case. Different collision energies lead to different interactions taking place. Contrast this to a lepton collider where electrons and positrons are being collided. They are both fundamental particles so they collide with the full beam energy each time, making it possible to conduct very precise measurements at a specific energy.
At the end the author mentions a number theory (analytic geometry) correlation that not only suggests an optimization, but a correction. The current theory used to compute the more complex scenarios is not only computationally intensive, it also includes simulations that never occur in a lab.
I'm a bit confused about that part too. I first thought loops are just repeated collisions, but "Loops represent all the intermediate collisions that could take place between the initial and final states" seems to describe something slightly different.
Later edit:
this https://en.wikipedia.org/wiki/One-loop_Feynman_diagram ?
When a single electron collides with another single electron, quantum field theory predicts the scattering probability distribution as a sum of Feynman diagrams. All of them must have two incoming and two outgoing legs, so the only difference between them is the number of internal loops. The basic ones, having no internal loops, is called the "tree level diagrams" (there may be one or more of these). The rest, having internal loops, can be thought of as higher order corrections to the results you get from just the tree-level diagrams.
Now, these internal loops are best thought of as vacuum fluctuations that pop out and interact with the two scattering particles. Say two electrons scatter: the tree-level diagram is two electrons approaching, interacting via a virtual photon (the force carrier for electromagnetism) and then going away from each other again. (There is also another tree-level diagram for this.) And then there are higher-order contributions, e.g. from the case where the virtual photon fluctuates into an electron-positron pair, which then decays back into a photon, in between the two electrons.
i.e. you can confirm or deny that this effect or particle exists. But if something entirely new that no one expects is occurring you would never notice because you would never look - there is simply too much output.
At best you scan an energy range and look for bumps (indicating something interesting is happening), but you still have to decide what kind of collision to scan.
Basically run "energy balance" calculations - calculate the expected result of a certain experiment, run it a huge number of time, then check the totals and see if they match what you expect.
You also look for symmetry - if this thing is found, and there appears to be "room" for something like it, check for it.
So despite the limitations we found all sorts of things. But it's important to understand the limitations so you know what to imagine, and then look for.