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

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 resonanceʹs 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 resonanceʹs mass MR as the real part of the square root ResR of the S-matrix pole position sR. For the Z-boson this means that MR≈MZ−26 MeV and ΓR≈ΓZ−1.2 MeV where MZ and ΓZ are the values reported in the particle data tables.