Quark--antiquark states and their radiative transitions in terms of the spectral integral equation. {\Huge II.} Charmonia

Abstract

In the precedent paper of the authors (hep-ph/0510410), the $b\bar b$ 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 $(c\bar c)$ states. We reconstruct the interaction in the $c\bar c$-sector on the basis of data for the charmonium levels with $J^{PC}=0^{-+}$, $1^{--}$, $0^{++}$, $1^{++}$, $2^{++}$, $1^{+-}$ and radiative transitions $ψ(2S)\toγχ_{c0}(1P)$, $γχ_{c1}(1P)$, $γχ_{c2}(1P)$, $γη_{c}(1S)$ and $χ_{c0}(1P)$, $χ_{c1}(1P)$, $χ_{c2}(1P)\toγJ/ψ$. The $c\bar c$ levels and their wave functions are calculated for the radial excitations with $n\le 6$. Also, we determine the $c\bar c$ component of the photon wave function using the $e^+e^-$ annihilation data: $e^+e^- \to J/ψ(3097)$, $ψ(3686)$, $ψ(3770)$, $ψ(4040)$, $ ψ(4160)$, $ψ(4415)$ and perform the calculations of the partial widths of the two-photon decays for the $n=1$ states: $η_{c0}(1S)$, $χ_{c0}(1P)$, $χ_{c2}(1P)\toγγ$, and $n=2$ states: $η_{c0}(2S)\toγγ$, $χ_{c0}(2P)$, $χ_{c2}(2P)\to γγ$. We discuss the status of the recently observed $c\bar c$ states X(3872) and Y(3941): according to our results, the X(3872) can be either $χ_{c1}(2P)$ or $η_{c2}(1D)$, while Y(3941) is $χ_{c2}(2P)$.