Line shape of the $J\psi \to \gamma {\eta }_c$ decay

Abstract

An accurate description of the photon spectrum line shape is essential for extracting resonance parameters of the ${\eta }_c$ meson through the radiative transition $J/\psi \to \gamma {\eta }_c$. However, a persistent challenge remains in the form of a divergent tail at high photon energies, arising from the $E_{\gamma }^3$ factor in theoretical calculations. Various damping functions have been proposed to mitigate this effect in practical experiments, but their empirical nature lacks a rigorous theoretical basis. In this study, we introduce two key considerations: incorporating full-order contributions of the Bessel function in the overlap integral of charmonium wave functions and the phase space factor neglected in previous experimental studies. By accounting for these factors, we demonstrate a more rational and effective damping function of the divergent tail associated with the $E_{\gamma }^3$ term. We present the implications of these findings on experimental measurements and provide further insights through toy Monte Carlo simulations.

arXiv comment5 pages, 8 figures

References in corpus (19)

• Higher Charmonia
• Properties of heavy quarkonia and B_c mesons in the relativistic quark model
• Quarkonia and their transitions
• Radiative Transitions in Charmonium from Lattice QCD
• Precision tests of the J/ψ from full lattice QCD: mass, leptonic width and radiative decay rate to η_c
• Charmonium spectrum and their electromagnetic transitions with higher multipole contributions
• Model-independent Study of Magnetic Dipole Transitions in Quarkonium
• J/psi and psi(2S) Radiative Transitions to eta_c
• Lattice QCD study of the radiative decays $J/\psi \to {\eta }_c\gamma$ and $h_c\to {\eta }_c\gamma$
• Improved determination of Heavy Quarkonium magnetic dipole transitions in pNRQCD
• Exchange Current Operators and Electromagnetic Dipole Transitions in Heavy Quarkonia
• Radiative transitions in charmonium from $N_f=2$ twisted mass lattice QCD
• Study of the pseudoscalar glueball in $J/\psi$ radiative decays
• The Confining Interaction and Radiative Decays of Heavy Quarkonia
• Precise determination of decay rates for ${\eta }_c\to \gamma \gamma$, $J/\psi \to \gamma {\eta }_c$ and $J/\psi \to {\eta }_c{e}^{+}{e}^{-}$ from lattice QCD
• Measurement of $J/\psi \to \gamma {\eta }_{\mathrm{c}}$ decay rate and ${\eta }_{\mathrm{c}}$ parameters at KEDR
• Precise determination of the eta_c mass and width in the radiative J/Psi -> eta_c gamma decay
• Study of the radiative decay $J/\psi \to {\eta }_c+\gamma$ in light cone sum rules
• Line shape and the experimental determination of the $J/\psi \to \gamma {\eta }_c$ branching fraction