Topics in the S-matrix theory of massless particles

S. P. Auerbach, Carl Rosenzweig, M. R. Pennington

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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 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.

Original languageEnglish (US)
Pages (from-to)214-250
Number of pages37
JournalAnnals of Physics
Volume85
Issue number1
DOIs
StatePublished - May 30 1974
Externally publishedYes

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ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Auerbach, S. P., Rosenzweig, C., & Pennington, M. R. (1974). Topics in the S-matrix theory of massless particles. Annals of Physics, 85(1), 214-250. https://doi.org/10.1016/0003-4916(74)90281-4