Reggeon quantum mechanics: A critical discussion |
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Authors: | M Ciafaloni M Le Bellac GC Rossi |
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Institution: | Scuola Normale Superiore, Pisa, and INFN, Sezione di Pisa, Italy;CERN, Geneva, Switzerland |
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Abstract: | The quantum-mechanical problem of reggeon field theory in zero transverse dimensions is re-examined in order to set up a precise mathematical framework for the case μ = α(0) ? 1 > 0. We establish a Hamiltonian formulation in a Hilbert space for (ifμ > 0) and we prove the equivalence of the related eigenvalue problem with a “radial” Schrödinger-type equation in an L2(0, ∞) space. We prove that the S-matrix and the pomeron Green functions, at fixed rapidity Y and triple-pomeron coupling λ ≠ 0, have a spectral decomposition and are analytic in μ for ?∞ < μ < + ∞. For μ > 0, we confirm most of the qualitative results found by previous authors, and in particular the tunnelling shift ~ exp(?μ2/2λ2)] setting the scale for the asymptotic behaviour in Y.In the classical limit of λ/μ small we find that the action, for μ > 0, develops a singularity in Y at some value Yc. We give arguments to show that for Y ? Yc the perturbative result is reached, while for perturbation theory breaks down. Most of these results are shown to be stable against the addition of a small quartic coupling of the simplest type ] up to the “magic” vvalue λ′ = λ2/μ. The existence of a level crossing at this value is confirmed by an analytic continuation in λ′. |
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