“I often feel a discomfort, a kind of embarrassment, when I explain elementary-particle physics to laypeople. It all seems so arbitrary – the ridiculous collection of fundamental particles, the lack of pattern to their masses.” -Leonard Susskind
When it comes to physics, there are a tremendous number of unsolved problems that seem to mandate the existence of a new particle. These include the dark matter problem, the matter-antimatter asymmetry problem, the massive neutrino problem and the strong-CP problem. Moreover, these particles required cannot be part of the Standard Model: they must lie beyond it.
Yet not only have detectors and colliders failed to turn up anything new despite 50 years of searches, but most models that would solve these problems are theoretically doomed from the start. Constraints on what new physics could do from big bang nucleosynthesis and the lack of observed flavor-changing neutral currents forbid almost all of the theoretical models we can build.