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Isolation of definite naturality exchanges: The general solution

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Zeitschrift für Physik C Particles and Fields

Abstract

For an arbitrary 2→2 scattering process we show how to isolate exactly the various contributions of definite naturality from the helicity amplitudes. For a Bosonict-channel this exact separation requires knowledge of a finite number of energy-derivatives of the amplitudes. If thet-channel is Fermionic our exact separation scheme is difficult to implement; however, it can be approximated to arbitrary accuracy in terms of a finite number of energy-derivatives of the amplitudes. Taking just a single energy-derivative we obtain a single approximate isolation scheme forall 2→2 processes. We show that this approximation is likely to be good, while more conventional approximations are likely to be poor.

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References

  1. A. Yokosawa: ANL-HEP-PR-CP-47 (1977)

  2. eg. H. Becker et al.: ‘π− p→ρ0 on a polarised target’, Geneva preprint (1978)

  3. The point to be made is that the use of this approximation is almost universal. ForNN→NN most authors follow:

  4. F. Halzen, G.H. Thomas. Phys. Rev.D10, 344 (1974). For 210-2 recent papers (e.g. Ref. 2) follow:

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  5. B.R. Martin, D. Morgan, G. Shaw. Pion-pion interactions. New York: Academic Press 1976 The approximation also occurs in work on many other processes; for instance on πN→Δ, πN→ωΔ,KN→K +Δ in J.F. Owens et al.: Nucl. Phys.B94 (975). It appears again in the general treatment of naturality exchange in J.P. Ader, Ph. Salin, C. Meyers: Nucl. Phys.B82, 237 (1974) and other references by the same authors

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  6. R. Stacey: J. Phys. G. vol. 4, 1819 (1978)

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  7. Argonne data is given in Ref. [1]. We have taken our figures from: Grein and Kroll; preprint, WU-B-77-6 which incorporates other data, and obtains real parts by a dispersion analysis

  8. It is hoped that the mathematical details and proofs of our results will be published elsewhere. They are quite complicated, especially for the Fermionic case. They are available on request from the author

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Author notes

  1. Richard Stacey

    Present address: University College, WC1, London, UK

Authors and Affiliations

  1. Westfield College, Department of Physics, University of London, NW3 7S1, London, England

    Richard Stacey

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  1. Richard Stacey
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Stacey, R. Isolation of definite naturality exchanges: The general solution. Z. Phys. C - Particles and Fields 4, 207–210 (1980). https://doi.org/10.1007/BF01421798

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  • DOI: https://doi.org/10.1007/BF01421798

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