the Breit-Wigner shape
/ BRITE-VIG-ner /
When a resonance shows up as a bump in a graph of reaction rate versus energy, the bump is not just any blob — it has a very specific, recognizable shape, like a bell that is tall and narrow in the middle and tapers off on both sides. This characteristic curve is called the Breit-Wigner shape, after the two physicists who derived it. If you have ever seen the response curve of a tuned radio circuit, you have already seen its sibling; the same mathematics describes both.
The shape is fully described by just two numbers. The first is where the peak sits — the central energy, which equals the mass-energy of the short-lived particle producing the resonance. The second is how wide the peak is at half its height, called the width and written Gamma; this width is directly tied to the particle's lifetime, since a particle that decays quickly has a fuzzy, spread-out energy and so a broad peak, while a long-lived particle gives a razor-thin spike. So by fitting a measured bump to the Breit-Wigner formula, an experimenter reads off both the mass (from the peak) and the lifetime (from the width) of a particle they may never see directly.
The Breit-Wigner shape is one of the most practical tools in the field. Almost every short-lived particle, from hadron resonances to the Z and the Higgs, announces itself as a Breit-Wigner bump in the right plot, and fitting that shape is the standard way to measure masses and decay widths. A useful caveat: real experimental peaks are also smeared by the detector's finite resolution, so the observed width is the true Breit-Wigner width broadened by measurement effects, and physicists must carefully unfold the two to get the genuine lifetime.
The Z boson's Breit-Wigner peak has a width of about 2.5 GeV. Reading that width off the curve gives the Z a lifetime of roughly a tenth of a trillionth of a trillionth of a second — far too short to see any track, yet precisely measured straight from the shape of the bump.
Peak position gives the mass; peak width gives the lifetime.
The observed peak width is the true Breit-Wigner width broadened by detector resolution; the two must be carefully separated, or the lifetime read off the raw plot will be too short.