Abstract
We demonstrate the construction of a density of states from the S-matrix describing a coupled-channel (S-wave pi pi , K {bar{K}}) system, and examine the influences from various structures of particle dynamics: poles, roots, and Riemann sheets.
Highlights
This effective spectral function defines the thermodynamics of an interacting system [1,2,3,4]
The trace operation implies that this quantity is basis independent, i.e., two S-matrices related by unitary rotations will give the same density of state
Q generalizes the notion of a 2-body phase shift in Eq (1) for describing dynamical processes
Summary
The S-matrix theory provides a natural language to describe resonances and multi-channel dynamics. While each S-matrix element represents a specific physical process, inelastic processes, expressed by offdiagonal terms, are included but only via the determinant This poses strong theoretical constraints in model studies: when an inelastic process α → β is considered, it is necessary to consider the processes: β → α and β → β, on top of the elastic channel α → α. The trace operation implies that this quantity is basis independent, i.e., two S-matrices related by unitary rotations will give the same density of state This suggests that B(E) does not depend explicitly on the inelasticity parameters. Q generalizes the notion of a 2-body phase shift in Eq (1) for describing dynamical processes It is defined even for a 3 → 3 scattering [3]:
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