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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
(defined by a Breit-Wigner lineshape) and lifetime (defined by the
exponential law) always and exactly fulfill the relation .
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 of
the S-matrix pole position s_R. For the Z-boson this means that and where M_Z and
are the values reported in the particle data tables.Comment: 23 page