the invariant-mass peak and bump hunting

When a single heavy particle is created and then falls apart into lighter ones, you cannot see the parent directly — it is gone almost instantly. But you can measure the energies and directions of its decay products and, using the rules of relativity, reconstruct the mass of whatever produced them. Do this for many events and a beautiful thing happens: if the decay products really came from a single kind of particle, the reconstructed mass clusters tightly around one value, forming a sharp peak. Bump hunting is the search for exactly such a peak rising above a smooth background.

The tool is the invariant mass. If a parent particle decays into, say, two photons, you take each photon's energy and momentum, add the two four-momenta together, and compute the invariant mass — a quantity that comes out the same regardless of how fast things were moving. For random background photons the invariant mass is spread out over a broad range; but for photons that genuinely came from one parent, it always equals the parent's mass. Plot the invariant mass of every pair, and a real particle reveals itself as a bump: a localized pile-up of events at its mass, perched on top of the broad, structureless background.

Bump hunting is one of the oldest and most powerful discovery techniques in the field; the J/psi, the Z, and the Higgs all announced themselves as peaks in invariant-mass plots. The width of the peak tells you about the particle's lifetime (a narrower peak means a longer-lived, more sharply defined particle), via the resonance idea. The standing caveat is that the eye is dangerously good at seeing patterns in noise: a random fluctuation can fake a bump, which is precisely why a peak must clear a stringent statistical bar (five sigma) and survive the look-elsewhere correction before anyone calls it a discovery.