Feynman Diagrams & Scattering

resonance

Push a child on a swing at just the right rhythm and the swing soars; push at the wrong rhythm and almost nothing happens. That special, matched response is resonance, and it is everywhere in nature — from tuning a radio to shattering a glass with a singer's note. In particle physics, the same idea appears in a striking way: when you collide particles at just the right energy, the chance of a reaction can suddenly spike, because that energy happens to match a fleeting particle that wants to be created.

Here is what is really going on. If the collision energy equals the mass-energy of some unstable particle, the incoming particles can briefly merge into that particle before it decays. At that magic energy the reaction rate shoots up to a peak; tune away from it and the rate falls off again. A resonance, then, is both a phenomenon (a bump in the rate versus energy) and, more profoundly, the signature of a short-lived particle. Its peak position tells you the particle's mass, and the width of the peak tells you how fast it decays — a wider bump means a shorter-lived particle, through the uncertainty principle.

Resonances are how a huge number of particles were discovered. Many of the short-lived hadrons and the famous Z boson first showed up not as tracks in a detector but as peaks in graphs of reaction rate against collision energy. Honestly, calling a resonance a particle is a matter of degree: the shortest-lived resonances exist for so little time that they are really better thought of as enhancements in a scattering process than as objects with a definite, lasting identity. But the line between a long-lived particle and a fleeting resonance is one of lifetime, not of kind.

When electrons and positrons were collided at sliding energies, the production rate stayed modest until the energy reached about 91 GeV, where it suddenly spiked enormously: that towering peak was the Z boson being made resonantly. Its height, position, and width pinned down the Z's mass and lifetime with great precision.

A towering peak at 91 GeV: the Z boson made to order.

A resonance and a particle are the same thing viewed differently; the shortest-lived resonances last so briefly that whether to call them 'particles' is partly a question of convention, set by lifetime rather than by any sharp boundary.

Also called
resonant stateshort-lived particle共振态共振態