POLES AND SHADOW POLES IN THE MANY-CHANNEL S MATRIX

Journal Article · Mon Mar 23 04:00:00 EST 1964 · Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D

DOI:https://doi.org/10.1103/PhysRev.133.B1575· OSTI ID:4070453

Eden, R J; Taylor, J R

The connection between the partial-wave S matrix on different Riemann sheets is obtained from unitarity and analyticity. Under the assumption that coupling between channels can be varied analytically, it is shown that a resonance pole or bound-state pole may lead also to shadow poles'' on other Riemann sheets. The existence of shadow poles is illustrated by a unltary resonance model based on a sum of Feynman diagrams. In general, the number of shadow poles that can be deduced from an observed resonance depends on the number of channels that still have a particular resonance pole in the absence of coupling between channels. If the pole still appears in all channels, then shadow poles occur on every Riemann sheet; if it appears in only one channel, then shadow poles appear on half the sheets. If the resonance disappears in the absence of channel coupling, the method leads to no conclusions. In connection with the unitary symmetry scheme it is noted that the existence of shadow poles would permit a simple changeover from the separated poles of a resonance multiplet with broken symmetry to the coincident poles of the multiplet that must occur when the symmetry breaking interaction is switched off. (auth)

• Research Organization: Cambridge Univ., Eng.
• NSA Number: NSA-18-014877
• OSTI ID: 4070453
• Journal Information: Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D, Journal Name: Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D Vol. Vol: 133; ISSN PHRVA
• Country of Publication: Country unknown/Code not available
• Language: English

Related Subjects

BINDING ENERGY
ELEMENTARY PARTICLES
FEYNMAN DIAGRAM
FIELD THEORY
INTERACTIONS
MATHEMATICS
MATRICES
P-WAVE
PHYSICS
POLOLOGY
QUANTUM MECHANICS
RESONANCE
RIEMANN SHEET
S-MATRIX
UNITARITY