Moment-operator expansion for the two-meson, two-photon and fermion-antifermion states.pdf

Moment-operator expansion for the two-meson, two-photon and fermion-antifermion states.pdf

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Moment-operator expansion for the two-meson, two-photon and fermion-antifermion states

a r X i v : h e p - p h / 0 1 0 5 3 3 0 v 2 1 1 S e p 2 0 0 1 Moment–operator expansion for the two-meson, two-photon and fermion-antifermion states A.V. Anisovich, V.V. Anisovich, V.N. Markov, M.A. Matveev and A.V. Sarantsev St. Petersburg Nuclear Physics Institute, 188300, Gatchina, Russia Abstract A complete set of formulae in terms of the moment–operator expansion is pre- sented for the two-meson, two-photon and fermion-antifermion states that can be used in the analysis of scalar (S) and pseudoscalar (P ) meson production in pp? and γγ collisions: pp? → SS,PP, SP and γγ → SS,PP, SP . Method of a generalization of the formulae for amplitudes of multi-meson production in the two-stage processes of the type (spin-j) resonance + meson → three mesons is also discussed. 1 Introduction The moment–operator expansion is a powerful tool for the study of the analytical structure of amplitudes, in particular, for the determination of the resonance amplitudes. In this paper we present a full set of formulae which are necessary for the analysis of reactions pp? → ππ, pp? → ηη, pp? → ηη′, pp? → πf0 in flight, and we explain the way of generalization of the formulae for the analysis of reactions with the production of resonances with non-zero spin, such as πρ, πf2, ππ2, and so on. The data obtained by Crystal Barrel Collaboration provide us with rich possibilities to study resonances in the mass region 1900-2400 MeV [1, 2]. The reconstruction of analytical meson amplitudes and definition of pole singularities are forced by the problem of classification of meson states, exotics included (glueballs, hybrids). The establishing of a complete set of meson states is a necessary step in understanding of Strong QCD, see e.g. [3, 4, 5, 6]. We give formulae for γγ-states; our interest in these processes is stimulated by rich experimental information on γγ → hadrons obtained at LEP (e.g. see [7, 8]). Starting from early 1960s, the operator expansion was exploited for the amplitude a

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