Quark-antiquark states and their radiative transitions in terms of the spectral integral equation: Charmonia
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ELEMENTARY PARTICLES AND FIELDS Theory
Quark–Antiquark States and Their Radiative Transitions in Terms of the Spectral Integral Equation: Charmonia* V. V. Anisovich, L. G. Dakhno, M. A. Matveev, V. A. Nikonov, and A. V. Sarantsev Petersburg Nuclear Physics Institute, Russian Academy of Sciences, Gatchina, 188350 Russia Received November 15, 2005; in final form, March 1, 2006
Abstract—Earlier by the authors (Yad. Fiz. 70, 68 (2007)), the b¯b states were treated in the framework of the spectral integral equation, together with simultaneous calculations of radiative decays of the considered bottomonia. In the present paper, such a study is carried out for the charmonium (c¯ c) states. We reconstruct the interaction in the c¯ c sector on the basis of the data for the charmonium levels with J P C = 0−+ , 1−− , 0++ , 1++ , 2++ , 1+− and radiative transitions ψ(2S) → γχc0 (1P ), γχc1 (1P ), γχc2 (1P ), γηc (1S) c levels and their wave functions are calculated for the and χc0 (1P ), χc1 (1P ), χc2 (1P ) → γJ/ψ. The c¯ radial excitations with n ≤ 6. Also, we determine the c¯ c component of the photon wave function using the e+ e− -annihilation data: e+ e− → J/ψ(3097), ψ(3686), ψ(3770), ψ(4040), ψ(4160), ψ(4415) and perform the calculations of the partial widths of the two-photon decays for the n = 1 states ηc0 (1S), χc0 (1P ), χc2 (1P ) → γγ and n = 2 states ηc0 (2S) → γγ, χc0 (2P ), χc2 (2P ) → γγ. We discuss the status of the recently observed c¯ c states X(3872) and Y (3941): according to our results, the X(3872) can be either χc1 (2P ) or ηc2 (1D), while Y (3941) is χc2 (2P ). PACS numbers : 1440.-n, 12.38.-t, 12.39.-Mk DOI: 10.1134/S1063778807020184
1. INTRODUCTION In this paper, we continue the study initiated in [1] for the b¯b states in the framework of the spectral integral equation. Here, the results for the c¯ c states are presented. In [2], the program has been formulated for the reconstruction of the quark–antiquark interaction based on our knowledge of meson levels and their radiative decays. Within this program, as a first step, we have considered the bottomonia [1]. Now we present analogous results for the charmonia. In the subsequent publication, we plan to give the corresponding results for the light-quark–antiquark systems. Our study is carried out in terms of the spectral integral technique. The application of this technique to the composite quark–antiquark systems and its relation to the dispersion N/D method have been discussed in [1, 2], where one may find the necessary details. Still, let us point once again to particular properties of our approach. The quark–antiquark interaction given, the spectral integral equations provide us unambiguously with both levels and wave functions of composite systems. But if the interaction is unknown, to reconstruct it one needs to know the levels as well as their wave functions. Our knowledge ∗
The text was submitted by the authors in English.
of the interaction of constituent quarks (in particular, long-range interaction) is rather fragmentary, so actually the desc
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