Spectrum-generating SU(4) in particle physics. II. Electromagnetic decays of vector mesons

The decay rates for the electromagnetic decays of vector mesons are derived within the spectrum-generating SU(4) approach. Radiative as well as leptonic decays of vector mesons can be derived from one theoretical assumption and given in terms of three reduced matrix elements. The implication of the experimental value $\Gamma (\rho \to \pi \gamma )=35\mathrm{}\pm 10$ keV for the form of the electromagnetic current operator is discussed. Two alternatives have been considered: (1) The electromagnetic current operator in SU(3) is given by the Gell-Mann-Nishijima formula; then the experimental value $\Gamma (\rho \to \pi \gamma )=35\mathrm{}\pm 10$ keV cannot be obtained. (2) The experimental value of $\Gamma (\rho \to \pi \gamma )$ is taken to determine the value of the SU(3)-scalar term in the electromagnetic current operator. The resulting ansatz for the electromagnetic current operator is compatible with the experimental values for $\frac{\Gamma (\eta \text{'}\to \rho \gamma )}{\Gamma (\eta \text{'}\to \omega \gamma )}$.