Particle Decay Width and Lifetime Calculator

The decay width Γ is a measure of how quickly an unstable particle or resonance decays, expressed in energy units (eV, MeV, GeV). It is directly related to the particle's mean lifetime τ by τ=ħ/Γ, the energy-time uncertainty relation.

τ = ħ/Γ, where ħ is the reduced Planck constant (≈6.582×10⁻¹⁶ eV·s), Γ is the decay width in energy units, and τ is the mean lifetime in seconds. Equivalently, Γ=ħ/τ.

This follows directly from the energy-time uncertainty principle: a state that only exists for a short time τ cannot have a perfectly sharp energy (mass), it necessarily has an energy spread (width) Γ≈ħ/τ. Longer-lived states can have much more sharply defined masses.

The Z boson has a measured decay width of Γ_Z≈2.4952 GeV, corresponding to a mean lifetime of only about 2.64×10⁻²⁵ seconds, far too short to measure directly. Instead, physicists measure the width of the resonance peak in collision data and use τ=ħ/Γ to infer the lifetime.

The muon has a mean lifetime of about 2.197 microseconds (2.197×10⁻⁶ s), corresponding to an extremely narrow decay width of roughly 3×10⁻¹⁹ GeV, far too narrow to ever measure as a mass-peak width; the muon's lifetime is instead measured directly by timing its decay in detectors.

No, this calculator relates a quantum resonance's energy width to its lifetime via the uncertainty principle. Classical radioactive decay (N(t)=N₀e^(−λt), with half-life t½=ln(2)/λ) describes population decay over time for a large ensemble of unstable nuclei, a related but distinct concept.

For very short-lived particles and resonances, physicists measure the width of the peak in a plot of collision cross-section (or event count) versus invariant mass, directly reading off Γ as the peak's full width at half maximum, then converting to lifetime via τ=ħ/Γ if desired.

eV, keV, MeV, and GeV, the standard energy units used across particle physics for decay widths ranging from the extraordinarily narrow (long-lived particles) to hundreds of MeV or GeV wide (very short-lived resonances).

Yes, a wider decay width directly corresponds to a shorter mean lifetime (they are inversely proportional via τ=ħ/Γ), so a particle or resonance with a large measured width decays away correspondingly faster.

For an exponentially decaying quantum state (the standard Breit-Wigner resonance lineshape), τ=ħ/Γ is exact, not an approximation, it follows directly from the Fourier-transform relationship between a state's time evolution and its energy spectrum.