Comparison of symmetry and duality constraints for radiative transitions of mesons

Abstract

Predictions for patterns of symmetry breaking in vector and tensor mesons are extracted from poledominated finite-energy sum rules. Kinematic factors relate deviations in couplings to the mass-spectrum splitting. For vector mesons, in addition to the usual problem of the small $\Gamma (p\to \pi \gamma )$, we find that $\Gamma (K^{*+}\to K^{+}\gamma )$ must almost certainly be above its present upper bound of 80 keV. Consistency arguments dictate a choice between the two possible sets of $\eta \gamma$ widths for the $\rho$ and $\omega$. In addition, we extract both $D\gamma$ and $D\pi$ widths for the charmed vector meson $D^{*}$. For the tensor mesons, predictions $\Gamma (A_2\to \pi \gamma )=490\mathrm{}\pm 60$ keV, $\Gamma (K^{**+}\to K^{+}\gamma )=125\mathrm{}\pm 60$ keV, and $\Gamma (K^{**0\mathrm{}}\to K^0\gamma )=32\mathrm{}\pm 15$ keV imply large deviations from both symmetry and naive vector-meson-dominance predictions. Additional consistency relations between $\eta$ and ${\eta }^{\prime }$ reactions lead to ${\Gamma }_{\mathrm{total}}\left({\eta }^{\prime }\right)=480\mathrm{}\pm 120$ keV.