ABSTRACT
The lifetime of an elementary particle is the average amount of time it takes for the particle to decay into something else. Unstable particles are observed as resonances. These are local maxima in the cross-section as a function of energy, or as a maximum in the invariant mass distribution of the particles in the final state of a reaction. The search for unstable particles in particle physics is analogous to the search for unstable atomic states of an atom. The shape of the peak will be given by the Breit-Wigner shape function. Hence an experimentalist can measure the differential cross section by counting the number of particles scattered into a given solid angle per unit time and dividing by the luminosity, which is controlled by the apparatus. Quantum-mechanically, the probability for scattering is given by the square of the magnitude of the amplitude.
