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The most fundamental cornerstone of the PDG tables is the uniqueness of
S-matrix pole positions of unstable particles, as a consequence of
quantum-field-theory principles. Therefore, the unitarity property of
the S-matrix should ideally be respected in whatever description of
hadronic resonances in experiment, on the lattice, and in quark models.
Unfortunately, simple Breit-Wigner (BW) parametrisations continue to be
widely used in data analyses of hadronic processes, while lattice and
model calculations are often still done by ignoring strong decay and
its dynamical effects. All such approaches manifestly violate
unitarity.
In the present talk I shall show how a BW description of a resonance
produces a wrong pole position, even in the elastic case, while for
inelastic decays the error can become huge, in excess of 100 MeV.
Its consequences for meson spectroscopy and possible remedies will be
discussed. As for the lattice, some recent calculations of meson
resonances will be presented that do satisfy unitarity, by using
Luescher's method to compute scattering phase shifts in a Euclidean
framework. These calculations lend strong support to earlier model
descriptions of enigmatic resonances like the light scalar mesons, as
well as the puzzling states Ds0(2317), Ds1(2460), and X(3872). Finally,
a case is made for considering non-resonant, threshold-related
enhancements, which are a consequence of extended unitarity in
production processes. Typical examples of such enhancements will be
discussed, as e.g. X(4260), X(4660), and Upsilon(10580).