### Abstract

We discuss how massless particle reactions may be incorporated into standard S-matrix theory. The crucial element for doing so is a low-energy zero. Examples of reactions where such zeros occur are weak interaction processes involving neutrinos, chirally symmetric massless pion scattering, and two-photon exchange between neutral systems. These zeros make two-body unitarity a good approximation for sufficiently low energy despite the coalescence of multiparticle thresholds. Through two-body unitarity, these zeros produce lines of zeros in the absorptive parts and double spectral functions. These lines of zeros are the S-matrix analog of the requirement of an infrared finite field theory. Not only do they produce finite total cross sections at finite energies, but they also allow both upper and lower bounds to be derived for these cross sections at high energies. This upper bound is our main result. If a plausible smoothness assumption is made, we find σ_{tot} < s^{ε{lunate}} (where ε{lunate} is arbitrarily small). In particular, the experimentally observed linear rise of the neutrino proton cross section cannot continue indefinitely.

Original language | English (US) |
---|---|

Pages (from-to) | 214-250 |

Number of pages | 37 |

Journal | Annals of Physics |

Volume | 85 |

Issue number | 1 |

DOIs | |

State | Published - May 30 1974 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Annals of Physics*,

*85*(1), 214-250. https://doi.org/10.1016/0003-4916(74)90281-4

**Topics in the S-matrix theory of massless particles.** / Auerbach, S. P.; Rosenzweig, Carl; Pennington, M. R.

Research output: Contribution to journal › Article

*Annals of Physics*, vol. 85, no. 1, pp. 214-250. https://doi.org/10.1016/0003-4916(74)90281-4

}

TY - JOUR

T1 - Topics in the S-matrix theory of massless particles

AU - Auerbach, S. P.

AU - Rosenzweig, Carl

AU - Pennington, M. R.

PY - 1974/5/30

Y1 - 1974/5/30

N2 - We discuss how massless particle reactions may be incorporated into standard S-matrix theory. The crucial element for doing so is a low-energy zero. Examples of reactions where such zeros occur are weak interaction processes involving neutrinos, chirally symmetric massless pion scattering, and two-photon exchange between neutral systems. These zeros make two-body unitarity a good approximation for sufficiently low energy despite the coalescence of multiparticle thresholds. Through two-body unitarity, these zeros produce lines of zeros in the absorptive parts and double spectral functions. These lines of zeros are the S-matrix analog of the requirement of an infrared finite field theory. Not only do they produce finite total cross sections at finite energies, but they also allow both upper and lower bounds to be derived for these cross sections at high energies. This upper bound is our main result. If a plausible smoothness assumption is made, we find σtot < sε{lunate} (where ε{lunate} is arbitrarily small). In particular, the experimentally observed linear rise of the neutrino proton cross section cannot continue indefinitely.

AB - We discuss how massless particle reactions may be incorporated into standard S-matrix theory. The crucial element for doing so is a low-energy zero. Examples of reactions where such zeros occur are weak interaction processes involving neutrinos, chirally symmetric massless pion scattering, and two-photon exchange between neutral systems. These zeros make two-body unitarity a good approximation for sufficiently low energy despite the coalescence of multiparticle thresholds. Through two-body unitarity, these zeros produce lines of zeros in the absorptive parts and double spectral functions. These lines of zeros are the S-matrix analog of the requirement of an infrared finite field theory. Not only do they produce finite total cross sections at finite energies, but they also allow both upper and lower bounds to be derived for these cross sections at high energies. This upper bound is our main result. If a plausible smoothness assumption is made, we find σtot < sε{lunate} (where ε{lunate} is arbitrarily small). In particular, the experimentally observed linear rise of the neutrino proton cross section cannot continue indefinitely.

UR - http://www.scopus.com/inward/record.url?scp=49549158256&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=49549158256&partnerID=8YFLogxK

U2 - 10.1016/0003-4916(74)90281-4

DO - 10.1016/0003-4916(74)90281-4

M3 - Article

AN - SCOPUS:49549158256

VL - 85

SP - 214

EP - 250

JO - Annals of Physics

JF - Annals of Physics

SN - 0003-4916

IS - 1

ER -