### Abstract

The consequences of the existence of complex poles in scattering amplitudes, corresponding to resonances or unstable particles, are investigated. Specific examples show that corresponding to such poles are normal threshold cuts lying near the physical region and which cause "wooly cusps" in scattering cross sections. The discontinuity across such a cut is expressed by a unitarity-like relation in terms of unphysical amplitudes with unstable external particles defined by the residues of the complex poles. More generally, it is shown that the Landau equations for the singularities must be extended to include all unstable as well as stable particles. The Cutkosky formulas specify the corresponding discontinuities in terms of the physical and unphysical amplitudes.

Original language | English (US) |
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Pages (from-to) | 888-898 |

Number of pages | 11 |

Journal | Physical Review |

Volume | 131 |

Issue number | 2 |

DOIs | |

State | Published - 1963 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Physical Review*,

*131*(2), 888-898. https://doi.org/10.1103/PhysRev.131.888

**Unstable particles in s-matrix theory.** / Zwanziger, Daniel.

Research output: Contribution to journal › Article

*Physical Review*, vol. 131, no. 2, pp. 888-898. https://doi.org/10.1103/PhysRev.131.888

}

TY - JOUR

T1 - Unstable particles in s-matrix theory

AU - Zwanziger, Daniel

PY - 1963

Y1 - 1963

N2 - The consequences of the existence of complex poles in scattering amplitudes, corresponding to resonances or unstable particles, are investigated. Specific examples show that corresponding to such poles are normal threshold cuts lying near the physical region and which cause "wooly cusps" in scattering cross sections. The discontinuity across such a cut is expressed by a unitarity-like relation in terms of unphysical amplitudes with unstable external particles defined by the residues of the complex poles. More generally, it is shown that the Landau equations for the singularities must be extended to include all unstable as well as stable particles. The Cutkosky formulas specify the corresponding discontinuities in terms of the physical and unphysical amplitudes.

AB - The consequences of the existence of complex poles in scattering amplitudes, corresponding to resonances or unstable particles, are investigated. Specific examples show that corresponding to such poles are normal threshold cuts lying near the physical region and which cause "wooly cusps" in scattering cross sections. The discontinuity across such a cut is expressed by a unitarity-like relation in terms of unphysical amplitudes with unstable external particles defined by the residues of the complex poles. More generally, it is shown that the Landau equations for the singularities must be extended to include all unstable as well as stable particles. The Cutkosky formulas specify the corresponding discontinuities in terms of the physical and unphysical amplitudes.

UR - http://www.scopus.com/inward/record.url?scp=36149012136&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=36149012136&partnerID=8YFLogxK

U2 - 10.1103/PhysRev.131.888

DO - 10.1103/PhysRev.131.888

M3 - Article

VL - 131

SP - 888

EP - 898

JO - Physical Review

JF - Physical Review

SN - 0031-899X

IS - 2

ER -