How higher charmonia shape the puzzling data of the $e^{+}{e}^{-}\to \eta J/\psi$ cross section

Abstract

Recently, the BESIII collaboration performed a precise measurement of the $e^{+}{e}^{-}\to \eta J/\psi$ cross section. It is puzzling that the resonance parameters of the reported $Y(4230)$ show a substantial divergence from the previously measured results in both the open-charmed and hidden-charmed decay channels, and the line shape asymmetry of the data approaching 4.2 GeV also suggests that it might be difficult to characterize the details of the structure around 4.2 GeV by a single resonance. This has motivated our great curiosity about how the charmonium states are distributed in the measured energy range and how they shape the puzzling data of the $e^{+}{e}^{-}\to \eta J/\psi$ cross section. In this work, we use five theoretically constructed charmonia in the range of $4.0-4.5$ $\text{GeV}$, i.e., $\psi (4040)$, $\psi (4160)$, $\psi (4220)$, $\psi (4380)$, and $\psi (4415)$, to apply a combined fit to the data, in which their calculated decay ratios into $\eta J/\psi$ via hadronic loop mechanism are taken as input. The fit results can reproduce the measured cross section data well, especially for the subtle line shape around 4.2 GeV, showing that the structure around 4.2 GeV is possible from the contribution of both $\psi (4160)$ and $\psi (4220)$.

arXiv comment11 pages, 4 figures and 4 tables. Accepted by Phys. Rev. D. More discussions were added

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• Global coupled-channel analysis of $e^{+}{e}^{-}\to c\bar{c}$ processes in $\sqrt{s}=3.75-4.7$ GeV
• Role of $4S$-$3D$ mixing in explaining the $\omega$-like $Y(2119)$ observed in $e^{+}{e}^{-}\to \rho \pi$ and $\rho (1450)\pi$
• Reevaluating the $\psi (4160)$ Resonance Parameter Using $B^{+}\to K^{+}{\mu }^{+}{\mu }^{-}$ Data in the Context of Unquenched Charmonium Spectroscopy
• Coupled-channel study of $4S$-$3D$ mixing dynamics in $\psi (4220)$ and $\psi (4380)$
• Non-$D\bar{D}$ Decays into Light Meson Pairs of the $D$-Wave Charmonium ${\psi }_3(3842)$
• Decoding the role of $\rho$ mesonic states for elucidating the $e^{+}{e}^{-}\to a_2(1320)\pi$ data and other reactions
• Prospects for observing the missing $2D$ and $1F$ charmonium states around 4 GeV
• Proposed mixing between $2P$ and $1F$ wave charmonia