What is the difference between parton, detector and particle level in high energy physics?
I found a similar question but I couldn't understand the explanation for detector and particle level given there which seem really tricky. So, any other explanations/analogies are welcome, maybe in simpler words if possible.
The LHC collides proton--proton beams, but at the high energies at which the collisions occur, you can consider collisions to occur between the partons (i.e. quarks and gluons) in each colliding proton, instead. A "parton-level" cross section is the cross section of some process involving partons in the initial state, and this is where you start when you want to do some theory calculation.
"Particle level" refers to the stable particles that are produced as a result of a collision. If you have a process producing a parton(s), these are unstable products and will hadronise quickly (due to confinement). A particle-level final state would refer to the collimated shower of stable particles produced in the hadronisation ("particle jets") (along with any other stable products, e.g. leptons, etc.). You might also sometimes hear people referring to this as "truth level".
Finally, each particle level object interacts in some way with the detector system$^*$, and how we infer these signals to reconstruct the corresponding particle is what "detector level" refers to. If our detectors were perfect and 100% efficient, the detector level would be identical to the particle level, but the inefficiencies associated with a physical detector (e.g. gaps between detector material, finite resolution/limited granularity, etc.) means that what we observe coming out of a collision may not necessarily be what "actually" was produced. For example, resolution effects will smear the 4-momentum of reconstructed objects w.r.t. the particle-level 4-momentum, or maybe the particle-level object falls outside of the detector acceptance in which case it isn't reconstructed at all at the detector level, and so on.
For a one-line summary, you could think of it in this way: parton-level = theory, particle = phenomenology, and detector = experiment.
$^*$including not interacting at all, e.g. neutrinos
The link you give explains the three terms clearly.
The parton model was a model for the nucleons imagined before the discovery of quarks , anti quarks and gluons which are the constituents of the nucleon in our present theory.
In the parton theory one calculated how generic partons would interact in proton proton scattering and calculate distributions. That is the parton level.
Since now we know of the existence of specific particles, quark and gluons, and specific interactions, the strong force, the parton calculations can be used at the level of specifying the partons as quarks and gluons, and that is the particle level.
The detector level is where data are registered, the interaction of the partons with the detectors to measure the parton properties. This level also can be modified to model the distributions of the particles coming from the interaction to the detectors .
