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Fits to the di-$J/\psi$ and $J/\psi+\psi$(2S) mass spectra in the SRs for model $A$ (top panel) and $B$ (bottom panel). For each model, the di-$J/\psi$ spectrum (left) and the $J/\psi+\psi$(2S) spectra in the $4\mu$ (middle) and $4\mu+2\pi$ (right) channels are shown. The purple dash-dotted lines represent the components of individual resonances, and the green short dashed ones represent the interferences. Note that no interference is present in the $J/\psi+\psi$(2S) channels with model $B$ since $X$(6900) is standalone.

Fits to the di-$J/\psi$ and $J/\psi+\psi$(2S) mass spectra in the SRs for model $A$ (top panel) and $B$ (bottom panel). For each model, the di-$J/\psi$ spectrum (left) and the $J/\psi+\psi$(2S) spectra in the $4\mu$ (middle) and $4\mu+2\pi$ (right) channels are shown. The purple dash-dotted lines represent the components of individual resonances, and the green short dashed ones represent the interferences. Note that no interference is present in the $J/\psi+\psi$(2S) channels with model $B$ since $X$(6900) is standalone.

Fits to the di-$J/\psi$ and $J/\psi+\psi$(2S) mass spectra in the SRs for model $A$ (top panel) and $B$ (bottom panel). For each model, the di-$J/\psi$ spectrum (left) and the $J/\psi+\psi$(2S) spectra in the $4\mu$ (middle) and $4\mu+2\pi$ (right) channels are shown. The purple dash-dotted lines represent the components of individual resonances, and the green short dashed ones represent the interferences. Note that no interference is present in the $J/\psi+\psi$(2S) channels with model $B$ since $X$(6900) is standalone.

Fits to the di-$J/\psi$ and $J/\psi+\psi$(2S) mass spectra in the SRs for model $A$ (top panel) and $B$ (bottom panel). For each model, the di-$J/\psi$ spectrum (left) and the $J/\psi+\psi$(2S) spectra in the $4\mu$ (middle) and $4\mu+2\pi$ (right) channels are shown. The purple dash-dotted lines represent the components of individual resonances, and the green short dashed ones represent the interferences. Note that no interference is present in the $J/\psi+\psi$(2S) channels with model $B$ since $X$(6900) is standalone.

Fits to the di-$J/\psi$ and $J/\psi+\psi$(2S) mass spectra in the SRs for model $A$ (top panel) and $B$ (bottom panel). For each model, the di-$J/\psi$ spectrum (left) and the $J/\psi+\psi$(2S) spectra in the $4\mu$ (middle) and $4\mu+2\pi$ (right) channels are shown. The purple dash-dotted lines represent the components of individual resonances, and the green short dashed ones represent the interferences. Note that no interference is present in the $J/\psi+\psi$(2S) channels with model $B$ since $X$(6900) is standalone.

Fits to the di-$J/\psi$ and $J/\psi+\psi$(2S) mass spectra in the SRs for model $A$ (top panel) and $B$ (bottom panel). For each model, the di-$J/\psi$ spectrum (left) and the $J/\psi+\psi$(2S) spectra in the $4\mu$ (middle) and $4\mu+2\pi$ (right) channels are shown. The purple dash-dotted lines represent the components of individual resonances, and the green short dashed ones represent the interferences. Note that no interference is present in the $J/\psi+\psi$(2S) channels with model $B$ since $X$(6900) is standalone.

Fits to the $J/\psi$+$\psi$(2S) mass spectra with model $C$ in the SRs of the $4\mu$ (left) and $4\mu+2\pi$ (right) channels. The purple dash-dotted lines represent the signal resonances.

Fits to the $J/\psi$+$\psi$(2S) mass spectra with model $C$ in the SRs of the $4\mu$ (left) and $4\mu+2\pi$ (right) channels. The purple dash-dotted lines represent the signal resonances.

The $J/\psi$+$\psi$(2S) mass spectra in the total background CR (top), analysis CR (middle) and SR (bottom) of the $4\mu$ (left) and $4\mu+2\pi$ (right) channels before the fit (excess in SR is due to the signal). $b\bar{b}\to \text{charmonia}+X$ represents the non-prompt background. The bars (shaded areas) represent uncertainties of data (background predictions) in each bin. The arrows in the lower panel indicate that the ratio of data to background prediction is out of range in that bin.

The $J/\psi$+$\psi$(2S) mass spectra in the total background CR (top), analysis CR (middle) and SR (bottom) of the $4\mu$ (left) and $4\mu+2\pi$ (right) channels before the fit (excess in SR is due to the signal). $b\bar{b}\to \text{charmonia}+X$ represents the non-prompt background. The bars (shaded areas) represent uncertainties of data (background predictions) in each bin. The arrows in the lower panel indicate that the ratio of data to background prediction is out of range in that bin.

The $J/\psi$+$\psi$(2S) mass spectra in the total background CR (top), analysis CR (middle) and SR (bottom) of the $4\mu$ (left) and $4\mu+2\pi$ (right) channels before the fit (excess in SR is due to the signal). $b\bar{b}\to \text{charmonia}+X$ represents the non-prompt background. The bars (shaded areas) represent uncertainties of data (background predictions) in each bin. The arrows in the lower panel indicate that the ratio of data to background prediction is out of range in that bin.

The $J/\psi$+$\psi$(2S) mass spectra in the total background CR (top), analysis CR (middle) and SR (bottom) of the $4\mu$ (left) and $4\mu+2\pi$ (right) channels before the fit (excess in SR is due to the signal). $b\bar{b}\to \text{charmonia}+X$ represents the non-prompt background. The bars (shaded areas) represent uncertainties of data (background predictions) in each bin. The arrows in the lower panel indicate that the ratio of data to background prediction is out of range in that bin.

The $J/\psi$+$\psi$(2S) mass spectra in the total background CR (top), analysis CR (middle) and SR (bottom) of the $4\mu$ (left) and $4\mu+2\pi$ (right) channels before the fit (excess in SR is due to the signal). $b\bar{b}\to \text{charmonia}+X$ represents the non-prompt background. The bars (shaded areas) represent uncertainties of data (background predictions) in each bin. The arrows in the lower panel indicate that the ratio of data to background prediction is out of range in that bin.

The $J/\psi$+$\psi$(2S) mass spectra in the total background CR (top), analysis CR (middle) and SR (bottom) of the $4\mu$ (left) and $4\mu+2\pi$ (right) channels before the fit (excess in SR is due to the signal). $b\bar{b}\to \text{charmonia}+X$ represents the non-prompt background. The bars (shaded areas) represent uncertainties of data (background predictions) in each bin. The arrows in the lower panel indicate that the ratio of data to background prediction is out of range in that bin.

The distributions of input variables (top and middle) and the BDT scores for SS (bottom left) and OS (bottom right) events in the total background CR of the $4\mu+2\pi$ channel. $b\bar{b}\to \text{charmonia}+X$ represents the non-prompt background. The bars (shaded areas) represent uncertainties of data (background predictions) in each bin. The arrows in the lower panel indicate that the ratio of data to background prediction is out of range in that bin.

The distributions of input variables (top and middle) and the BDT scores for SS (bottom left) and OS (bottom right) events in the total background CR of the $4\mu+2\pi$ channel. $b\bar{b}\to \text{charmonia}+X$ represents the non-prompt background. The bars (shaded areas) represent uncertainties of data (background predictions) in each bin. The arrows in the lower panel indicate that the ratio of data to background prediction is out of range in that bin.

The distributions of input variables (top and middle) and the BDT scores for SS (bottom left) and OS (bottom right) events in the total background CR of the $4\mu+2\pi$ channel. $b\bar{b}\to \text{charmonia}+X$ represents the non-prompt background. The bars (shaded areas) represent uncertainties of data (background predictions) in each bin. The arrows in the lower panel indicate that the ratio of data to background prediction is out of range in that bin.

The distributions of input variables (top and middle) and the BDT scores for SS (bottom left) and OS (bottom right) events in the total background CR of the $4\mu+2\pi$ channel. $b\bar{b}\to \text{charmonia}+X$ represents the non-prompt background. The bars (shaded areas) represent uncertainties of data (background predictions) in each bin. The arrows in the lower panel indicate that the ratio of data to background prediction is out of range in that bin.

The distributions of input variables (top and middle) and the BDT scores for SS (bottom left) and OS (bottom right) events in the total background CR of the $4\mu+2\pi$ channel. $b\bar{b}\to \text{charmonia}+X$ represents the non-prompt background. The bars (shaded areas) represent uncertainties of data (background predictions) in each bin. The arrows in the lower panel indicate that the ratio of data to background prediction is out of range in that bin.

The distributions of input variables (top and middle) and the BDT scores for SS (bottom left) and OS (bottom right) events in the total background CR of the $4\mu+2\pi$ channel. $b\bar{b}\to \text{charmonia}+X$ represents the non-prompt background. The bars (shaded areas) represent uncertainties of data (background predictions) in each bin. The arrows in the lower panel indicate that the ratio of data to background prediction is out of range in that bin.

The $J/\psi+\psi$(2S) mass spectrum (left) and the simultaneous fit result with model $C$ (right) in the SS SR-like of the $4\mu+2\pi$ channel. In the left figure, the excess in data over the total background is due to feed-up.

The $J/\psi+\psi$(2S) mass spectrum (left) and the simultaneous fit result with model $C$ (right) in the SS SR-like of the $4\mu+2\pi$ channel. In the left figure, the excess in data over the total background is due to feed-up.