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 $ψ(ψ') \to η_{_{c}}(η'_{_{c}})γ$, $χ_{_{J}} \to ψγ$, $ψ' \to χ_{_{J}}γ$, $h_{_{c}} \to η_{_{c}}γ$, $η'_{_{c}} \to h_{_{c}}γ$ through overlap integrals $\int ϕ^{*}_{f}(q) ϕ_{i}(q) d{\bf q}$, $\int ϕ^{*}_{f}(r)r ϕ_{i}(r) d{\bf r}$. These corrections lead to a considerable suppression of $Γ(ψ\toη_{_{c}}γ)$, 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 $χ_{_{0}} \to ψγ, χ_{_{2}} \to ψγ$ and $ψ' \to χ_{_{0}}γ, ψ' \to χ_{_{2}}γ$ transitions are extracted from experiment; the obtained results are compared with quark model predictions.