Relativistic effects in radiative transitions of charmonia

Abstract

In the framework of a relativistic quark model constructed in an infinite momentum frame, corrections of the order of $v^{2}/c^{2}$ are obtained in the formulas which express amplitudes of the transitions $\psi(\psi') \to \eta_{_{c}}(\eta'_{_{c}})\gamma$, $\chi_{_{J}} \to \psi\gamma$, $\psi' \to \chi_{_{J}}\gamma$, $h_{_{c}} \to \eta_{_{c}}\gamma$, $\eta'_{_{c}} \to h_{_{c}}\gamma$ through overlap integrals $\int \phi^{*}_{f}(q) \phi_{i}(q) d{\bf q}$, $\int \phi^{*}_{f}(r)r \phi_{i}(r) d{\bf r}$. These corrections lead to a considerable suppression of $\Gamma(\psi\to\eta_{_{c}}\gamma)$, however, they are insufficient to remove the existing disagreement of quark model predictions with experiment. Taking into account the relativistic corrections, the ratios of overlap integrals for $\chi_{_{0}} \to \psi\gamma, \chi_{_{2}} \to \psi\gamma$ and $\psi' \to \chi_{_{0}}\gamma, \psi' \to \chi_{_{2}}\gamma$ transitions are extracted from experiment; the obtained results are compared with quark model predictions.