Why do these things take so long to find? Do they not show up in all collisions - why not, wrong matter, wrong speed? Do they regularly appear, but the "camera" has limitations? Is the "camera" all-seeing, but measurement interpretation inefficient? All/some of the above?
I think it's a matter of theory supporting observed data. They point the, "camera" at a bunch of experiments, which generates a ton of data, then it's up to theoretical physicists to explain the results. Once the results of a theory have been explained and then reproduced it stands on solid ground. I'm just speculating, of course. But that is sort of how astronomy works, at the polar opposite end of a similar field.
Your comment kind of implies that theorists analyse the data. (They don't even have access to it.) Analysis is the job of experimental physicists (like me) and can take years.
We don't wait until we have theoretical interpretations before publishing the discovery of a new particle. In fact, our results are kept confidential until the end of the collaboration's internal review process. In the absence of leaks, the first any theorist should hear of this new particle would have been the conference talk or press release.
Quantum mechanics is probabilistic. The probability of these particular particles in these particular collisions is very small. So we need to do a lot of collisions in order to have a statistically significant signal.
> but the "camera" has limitations?
Sure. While we regularly upgrade our detectors or build newer, fancier ones, there will always be some limitations.
> but measurement interpretation inefficient?
It's certainly slow. It can take months/years to infer a result from the data. The major bottleneck is people. Even the thousands-strong armies of physicists who work on the LHC experiments would take decades to fully exploit the available datasets.
Some physicists will get an idea for a new particle or decay mode. Then they will postulate various decay modes that could be captured by the detectors. The short-lived new particle arent directly detectable, but daughter particles may be. Particles leave characteristic signatures on the two large CERN detectors, each which consists of an onion of thousands of directional and intensity sensors. Then they computer search quadrillions of already recorded events at the detectors for a significant number of candidate events. This may take months for a postdoc or grad student to do.
I recall the Higgs had about 80-some possible decay modes. Only a handful of them could be measured above background noise. A couple of teams pursued two classes of them and found results.
