Is there an experiment which can detect the virtual particles in-directly or maybe directly? so I am currently participating in the CERN Beamline for schools contest and wanted to know if this sort of experiment is even possible and then if it is feasible to do at the facilities that CERN or DESY particle accelerators have. also If you have any other seed ideas please let me know I am willing to do more research on it.
 A: It depends on what you mean by "detect" and "virtual".
Quantum Electrodynamic (QED) – the quantum theory of electromagnetism – depends on virtual particles, so one can argue that every experiment testing QED shows the existance of virtual particles. For example, the best measurements of the muon magnetic moment are somewhat inconsistent with theory; if true, it could be that this experiment is detecting new virtual particles.
Another example is the virtual quarks and gluons inside protons, so every CERN or DESY experiment observing quark and gluon jets is "detecting" virtual particles.
It is possible, however, to take the view that virtual particles are just theoretical/mathematical constructs, and that any agreement between theory and experiment just shows that the theory works, not that we've "detected" these constructs.
This certainly has some validity and different physicists may have different criteria for what counts as "detection", but I would be surprised if many physicists would claim that we have not "detected" the virtual quark and gluon sea within the proton.
