The psion family: Relativistic charmonium

The authors have reported earlier that the spectrum of the psion family suggests a treatment based on an O(4) harmonic-oscillator family with O(4) quantum number $M=0\mathrm{}$ (equally spaced, mass-squared linear Regge trajectories). This results in the new $J^{\mathrm{PC}}$ quantum numbers: $0^{++}$ for 2.8 GeV/${\mathit{c}}^2$; $2^{++}$, $1^{-+}$, $0^{++}$ for the 3.4-GeV/${\mathit{c}}^2$ mass region. All radiative decays are related through a single O(4) coupling $S_{\mu \nu }{F}_{\mu \nu }$, where $S_{\mu \nu }$ is the internal-space angular-momentum operator. In this article the details of the calculations of radiative transition widths and of the $\gamma \gamma$ angular correlation functions are given. Experimental signatures are discussed and compared with the nonrelativistic charmonium scheme; among others $J\to O\left(2.8\right)+\gamma$ and ${\psi }^{\prime }\to O\left(2.8\right)+\gamma$ are small, being forbidden in the strict O(4) limit. $O\left(2.8\right)\mathrm{}$ is expected to be narrow like all other psions below the 4.0-GeV/${\mathit{c}}^2$ region. ${\chi }_0\mathrm{}\left(3.41\right)\mathrm{}$ and ${\chi }_1\mathrm{}\left(3.49\right)\mathrm{}$ total widths are expected to be around 630 keV and 185 keV, respectively. The missing decays of ${\psi }^{\prime }$ could be due to ${\psi }^{\prime }\to O+\omega (\sim 32\%)$.