Theory and Practice of Complex Regge Poles

  • F. Zachariasen
Conference paper
Part of the Few-Body Systems book series (FEWBODY, volume 8/1971)


In the form in which it was originally put forward, Regge phenomenology contained a wealth of predictions. If Regge poles alone dominated scattering amplitudes at high energies, then the simple form taken by a single Regge pole term, together with factorization of Regge residues, permitted one to parametrize scattering amplitudes with only very few unknowns, and also dictated very specific relations between scattering amplitudes describing different processes.


Branch Point Regge Pole Complex Pole Partial Wave Amplitude Complex Conjugate Pair 
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References and Footnotes

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    S. Mandelstam, Nuovo Cimento 30, 1127 (1963).CrossRefGoogle Scholar
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    R. Eden et al., “The Analytic S-matrix” ( Cambridge Univ. Press, 1966 ).Google Scholar
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    R. Carlitz and M. Kislinger, Phys. Rev. Letters 24, 186 (1970). It should be emphasized that the cut occurring in this model may well be the same as that suggested by Mandelstam (ref. 1). For example, if a(t)=1, then the first Mandelstam cut is also flat and crosses the pole at t=o. Or, the identification may be more subtle. It might be that the C-K cut coincides with the ultimate Mandelstam cut which is, perhaps, flat. Or it might be that the C-K cut is not really flat, but only appears so in the simple model in which they first obtained it. In any case it is highly unattractive to believe that the C-K and Mandelstam cuts really represent different phenomena.Google Scholar
  4. 4.
    In fact, we shall show that the specific values for the cut discontinuities assumed in these models are unlikely ever to be correct. Thus all cut models in use so far are, in fact, wrong. The predictions of such models may be specific; they are also wrong.Google Scholar
  5. 5.
    The partial wave amplitude is of a given signature. It should be emphasized that we presume there to be a cut, of the same quantum numbers and the same signature, associated with each Regge pole of a given signature. Generally, however, the signature is merely a notational complication; we shall therefore normally ignore it, and mention it only where its inclusion is not entirely obvious or where it makes some important difference.Google Scholar
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    Evidently, Dc is not uniquely defined by Eq. (2.1). The following examples illustrate what is meant by it.Google Scholar
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    In order to keep N real on the right-hand cut, αin must be a polynomial in t, which we take to be linear. In order to assure that αout is a zero of D, and not a pole of N, N and D are both multiplied by (j-αin);this, of course, does not alter their analyticity properties.Google Scholar
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    G. Chew and D. Snider, Phys. Letters 31B, 71 (1970). It should be noted that the model which these authors base their discussion on has a logarithmic cut; the complex poles are therefore always on unphysical sheets. Hence oscillating terms, the total cross-sections cannot occur.Google Scholar
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    See Ref. 11.Google Scholar
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    See G. F. Chew and D. R. Snider (Ref. 10). They interpret the physical sheet pole in a logarithmic cut model as the Pomeron, and the nearest unphysical sheet complex pair as the P’.Google Scholar
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    The suggestion that the Pomeron is a complex pair was made first by Freund and Oehme, Phys. Rev. Letters 10, 459 (1963). They suggest, in addition, that αp=1, a constant, for the Pomeron, in an attempt to have (nearly) non shrinking diffraction peaks without violating t-channel unitarity.Google Scholar
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    D. P. Roy, J. Kwiecinski, B. R. Desai and F. Zachariasen, to be published.Google Scholar
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Copyright information

© Springer-Verlag 1971

Authors and Affiliations

  • F. Zachariasen
    • 1
  1. 1.CERNGenevaSwitzerland

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