Hadronic loop contributions to $J/\psi$ and $\psi^\prime$ radiative decays into $\gamma\eta_c$ or $\gamma\eta_c^\prime$

TL;DR

This paper investigates how hadronic loop effects influence the radiative decays of $J/$ and $$ into $\u03b7_c$ or $\u03b7_c^$, providing corrections to the dominant quark model predictions.

Contribution

It introduces a mechanism for hadronic loop contributions that interfere with M1 transitions, explaining deviations from traditional quark model predictions in these decays.

Findings

Hadronic loops provide explicit corrections to M1 transition amplitudes.

The model accounts for deviations from the Godfrey-Isgur predictions.

Predicts a small branching ratio for $ o _c^$ decays, testable experimentally.

Abstract

Intermediate hadronic meson loop contributions to $J/\psi$, $\psi^\prime \to \gamma\eta_c$ ($\gamma\eta_c^\prime$) are studied apart from the dominant M1 transitions in an effective Lagrangian approach. Due to the property of the unique antisymmetric tensor coupling in $V\to VP$, the hadronic loop transitions provide explicit corrections to the M1 transition amplitudes derived from the naive "quenched" $c\bar{c}$ transitions via the coupling form factors. This mechanism interfering with the M1 transition amplitudes naturally accounts for the deviations from the Godfrey-Isgur model predictions in $J/\psi$ and $\psi^\prime\to \gamma\eta_c$. It also predicts a small branching ratio of $\psi^\prime\to \gamma\eta_c^\prime$, which can be examined by experimental measurements at BES and CLEO-c.