  The definition of mass and width of relativistic resonances and in particular
of the $Z$-boson is discussed. For this we use the theory based on time
asymmetric boundary conditions given by Hardy class spaces ${\mathbf \Phi}_-$
and ${\mathbf \Phi}_+$ for prepared in-states and detected out-states
respectively, rather than time symmetric Hilbert space theory. This Hardy class
boundary condition is a mathematically rigorous form of the singular
Lippmann-Schwinger equation. In addition to the rigorous definition of the
Lippmann-Schwinger kets $|[j,{\mathsf s}]^{\pm}>$ as functionals on the spaces
${\mathbf \Phi}_{\mp}$, one obtains Gamow kets $|[j,{\mathsf s}_R]^- >$ with
complex centre-of-mass energy value ${\mathsf s}_R=(M_R-i\Gamma_R/2)^2$. The
Gamow kets have an exponential time evolution given by
$\exp{(-iM_Rt-\Gamma_Rt/2)}$ which suggests that $(M_R,\Gamma_R)$ is the right
definition of the mass and width of a resonance. This is different from the two
definitions of the $Z$-boson mass and width used in the Particle Data Table and
leads to a numerical value of $M_R=(91.1626\pm 0.0031) {\rm GeV}$ from the
$Z$-boson lineshape data.
