decay width

Strike a long-ringing bell and you hear a clear, pure note; strike a dead one that thuds and stops, and the sound is a muddy smear of pitches. The same trade-off shows up for unstable particles: the shorter a particle lives, the fuzzier its mass appears to be. Physicists capture that fuzziness with a number called the decay width, often written with the Greek letter Gamma.

The decay width is the spread in energy (in mass) that an unstable particle shows, and it is simply the inverse of the particle's lifetime: a wide width means a short life, a narrow width means a long one. This is a direct consequence of the uncertainty principle, which ties how long something lasts to how precisely its energy can be defined. Because mass is energy in particle physics, a short-lived particle does not have one sharp mass value but a small range of masses; measure it many times and you get a bump with a characteristic width rather than a spike. Width is quoted in energy units (often MeV or GeV), and dividing a constant by the width immediately gives the lifetime in seconds.

Decay width matters because it is what experiments actually measure for very short-lived particles. You cannot time the decay of something that lives a trillionth of a trillionth of a second, but you can measure the width of the bump it makes in a mass plot, and from that infer the lifetime. The total width also adds up contributions from every way a particle can decay, so it secretly contains the branching ratios. A point worth keeping straight: width and lifetime are two descriptions of the very same fact — one in the language of energy, the other in the language of time.