103 research outputs found
Chiral Breit-Wigner
Chiral symmetry and unitarization are combined into generalized Breit-Wigner
expressions describing scalar resonances, which contain free parameters and
allow flexible descriptions of masses, widths and pole positions. This
theoretical tool is especially designed to be used in analyses of low-energy
data.Comment: Talk given at the XI International Conference on Hadron Spectroscopy,
Rio de Janeiro, Brazil, August 200
Chiral symmetry: An analytic unitary matrix
The unitary matrix employed in hadronic low-energy processes has
both exponential and analytic representations, related by . One extends this result to
the unitary matrix by deriving an analytic expression which, for
Gell-Mann matrices , reads , with , , and factors written in terms of
elementary functions depending on and . This result does not depend on the
particular meaning attached to the variable and the analytic
expression is used to calculate explicitly the associated left and right forms.
When represents pseudoscalar meson fields, the classical limit
corresponds to and
yields the cyclic structure , which gives rise to a tilted
circumference with radius in the space defined by ,
, and . The axial transformations of the analytic matrix are also
evaluated explicitly
Scalar resonances: scattering and production amplitudes
Scattering and production amplitudes involving scalar resonances are known,
according to Watson's theorem, to share the same phase . We show
that, at low energies, the production amplitude is fully determined by the
combination of with another phase , which describes
intermediate two-meson propagation and is theoretically unambiguous. Our main
result is a simple and almost model independent expression, which generalizes
the usual -matrix unitarization procedure and is suited to be used in
analyses of production data involving scalar resonances.Comment: 10 pages, 4 figures. Minor changes, references added, version to
appear in Phys. Rev.
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