Observation of the decay $η_c\toγγ$ at BESIII

TL;DR

This work addresses the charmonium QCD puzzle by measuring the product branching fraction $\mathcal{B}(J/\psi \to \gamma \eta_c)\times\mathcal{B}(\eta_c \to \gamma\gamma)$ in the decay chain $\psi(3686)\to \pi^+\pi^- J/\psi$, $J/\psi\to \gamma \eta_c$, $\eta_c\to \gamma\gamma$ using BESIII data of $(2712.4 \pm 14.3)\times 10^{6}$ $\psi(3686)$ events. An unbinned extended maximum likelihood fit to the $M_{12}$ distribution after a 4C kinematic fit yields $N_{\rm sig} = 677.7 \pm 33.5$, leading to $\mathcal{B}(J/\psi \to \gamma \eta_c)\times\mathcal{B}(\eta_c \to \gamma\gamma) = (5.23 \pm 0.26_{\rm stat.} \pm 0.30_{\rm syst.}) \times 10^{-6}$. With external inputs from PDG, the corresponding $\Gamma(\eta_c \to \gamma\gamma)$ is determined to be $(11.30 \pm 0.56_{\rm stat.} \pm 0.66_{\rm syst.} \pm 1.14_{\rm ref.})$ keV, in agreement with recent lattice QCD predictions and providing important input toward resolving the charmonium QCD puzzle, though it cannot independently determine the two branching fractions. Future measurements that determine either $\mathcal{B}(\eta_c \to \gamma\gamma)$ or $\mathcal{B}(J/\psi \to \gamma \eta_c)$ separately are needed.

Abstract

In the decays of $η_c\toγγ$ and $J/ψ\toγη_c$, there are discrepancies between the theoretical calculations and the PDG experimental values, referred to as the charmonium QCD puzzle. We observe the decay $η_c\toγγ$ in $J/ψ\toγη_c$ using $(2712.4\pm14.3)\times10^{6}$ $ψ(3686)$ events collected with the BESIII detector, and determine the product branching fraction $\mathcal{B}(J/ψ\toγη_c)\times\mathcal{B}(η_c\toγγ)=(5.23\pm0.26_{\rm{stat.}}\pm0.30_{\rm{syst.}})\times10^{-6}$. This measurement is consistent with the two most recent lattice QCD calculations, providing significant input toward resolving the charmonium QCD puzzle.

Figures (5)

• Figure 1: (a) Comparison of the decay width $\Gamma(\eta_c \to \gamma\gamma)$ between LQCD calculations (top) and experimental measurements (bottom). (b) Comparison of $V(0)$ between LQCD calculations (colored points) and experimental values (black point) Meng:2024axn, where $|V(0)|^2 \propto \Gamma(J/\psi \to \gamma\eta_c)$.
• Figure 2: (a) Distribution of $\chi^2_{4C}$. All selection criteria have been applied except for the $\chi^2_{4C}$ requirement. (b) Distribution of $M_{13} - M_{23}$ for the data samples. (c) Distribution of $M_{12}$ before applying the $M_{13} - M_{23}$ veto. (d) Distribution of $M_{12}$ after applying the $M_{13} - M_{23}$ veto. In (a), (c), and (d), the black points with error bars represent the observed data, while the colored histograms correspond to different background components as modeled by the MC simulation.
• Figure 3: Three signal candidates from real data in the event displays Li:2024poxHuang:2022wuoSong:2025pnt, collected on March 7, 2009 (a), December 31, 2011 (b), and June 28, 2021 (c), respectively. In these displays, the blue barrel represents the electromagnetic calorimeter (EMC) sub-detector, the red hits within the EMC correspond to showers from photons or charged tracks, and the internal hits denote charged tracks in the multilayer drift chamber (MDC).
• Figure 4: (a) Mass-dependent efficiency derived from the signal MC simulation. (b) Fit to the $M_{12}$ distribution. The black points with error bars represent the data, the red line denotes the fit result, the green line corresponds to the signal, and the lines in other colors illustrate various background contributions.
• Figure 5: (a) Comparison of $\mathcal{B}(\eta_c \to \gamma\gamma)$ versus $\mathcal{B}(J/\psi \to \gamma\eta_c)$ at the $1\sigma$ confidence level. The red-filled region represents our measurement, the yellow-filled and green-filled regions correspond to the LQCD calculations Colquhoun:2023zbcMeng:2021ecsMeng:2024axn. Other colored lines or filled regions indicate results from previous experimental measurements or PDG. (b) Comparison of $\Gamma(\eta_c \to \gamma\gamma)$. In the plot labeled "This work", the black solid line represents the total uncertainty, including the reference uncertainties of $J/\psi \to \gamma\eta_c$ and $\Gamma_{\eta_c}$pdg:2024. The dark, dark-to-light, and light red-filled regions correspond to the $1\sigma$, $2\sigma$, and $3\sigma$ confidence levels, respectively.