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 $\Gamma$ (defined by a Breit-Wigner lineshape) and lifetime $\tau$ (defined by the exponential law) always and exactly fulfill the relation $\Gamma =\hslash /\tau$. 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 $\mathrm{Re}\sqrt{{\mathrm{s}}_{\mathrm{R}}}$ of the S-matrix pole position s_R. For the Z-boson this means that $M_R\approx M_Z-26MeV$ and ${\Gamma }_R\approx {\Gamma }_Z-1.2MeV$ where M_Z and ${\Gamma }_Z$ are the values reported in the particle data tables.

Comments: 23 pages