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

Abstract 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 Γ (defined by a Breit–Wigner lineshape) and lifetime τ (defined by the exponential law) always and exactly fulfill the relation Γ=ℏ/τ . 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 s R of the S -matrix pole position s R . For the Z -boson this means that M R ≈M Z −26 MeV and Γ R ≈Γ Z −1.2 MeV where M Z and Γ Z are the values reported in the particle data tables.