The definition of mass and width of relativistic resonances

For relativistic resonances, the lineshape alone does not uniquely determine the resonance parameters, namely the mass (M) and width ( Gamma ). A unique definition of the resonance parameters is given if one uses a broader theory of quasistable particles, i.e. which unifies resonances and decaying states. The theory of quasistable particles is developed in analogy to that of stable particles: Wigner's Unitary Irreducible representations of the Poincare group characterize stable particles by mass (M) and spin (j), whereas quasistable particles will be characterized by mass squared sdR = (MdR - ii Gamma dR/2) and spin (j). It follows that the resonance width Gamma dR is related to the lifetime of the state by Gamma dR = 1/ tau . The Z-boson is used as an example.