On the mass and width of the Z-boson and other relativistic quasistable particles

The ambiguity in the definition for the mass and width of relativistic resonances is discussed, in particular for the case of the Z-boson. This ambiguity can be removed by requiring that a resonance's width Gamma (defined by a Breit-Wigner lineshape) and lifetime tau (defined by the exponential law) always and exactly fulfill the relation Gamma = (h) over bar/tau. To justify this, one needs relativistic Gamow vectors which in turn define the resonance's mass M-R as the real part of the square root Re root s(R) of the S-matrix pole position s(R). For the Z-boson this means that M-R approximate to M-Z - 26 MeV and Gamma(R) approximate to Gamma(Z) - 1.2 MeV where M-Z and Gamma(Z) are the values reported in the particle data tables. (C) 2000 Elsevier Science B.V. All rights reserved.