Abstract
I illustrate a robust method for extracting an effective phase shift and an effective spectral weight for a coupled-channel system. These quantities are useful for describing the thermodynamics of an interacting hadron gas within the S-matrix formulation.
Highlights
The S-matrix formulation of statistical mechanics by Dashen, Ma, and Bernstein [1] expresses the grand canonical potential in terms of the scattering matrix elements
√ e−β k2+m2i is the grand potential for an uncorrelated gas of particles that do not decay under the strong interaction, such as pions, kaons, and nucleons
√ Here the sum is over all interaction channels, dg is the relevant degeneracy factor, and δIJ( s) is the scattering phase shift
Summary
The S-matrix formulation of statistical mechanics by Dashen, Ma, and Bernstein [1] expresses the grand canonical potential in terms of the scattering matrix elements. √ e−β k2+m2i is the grand potential for an uncorrelated gas of particles that do not decay under the strong interaction (i.e. ground-state particles), such as pions, kaons, and nucleons. The interacting part of the grand potential, Δ ln Z, can be written in the form
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