Quark-antiquark states and their radiative transitions in terms of the spectral integral equation: Charmonia

Earlier by the authors (Yad. Fiz. 70, 68 (2007)), the bƃ 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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$(c\bar c)$$ \end{document} states. We reconstruct the interaction in the c-c sector on the basis of the data for the charmonium levels with JPC = 0−+, 1−−, 0++, 1++, 2++, 1+− and radiative transitions ψ(2S) → γχc0(1P), γχc1(1P), γχc2(1P), γχc(1S) and χc0(1P), χc1(1P), χc2(1P) → γJ/ψ. The c-c levels and their wave functions are calculated for the 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) → 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).