Figure 1b, lower panel, subevent

Figure 2a, full-event

Figure 2b, subevent

Figure 3b

Figure 3c

Figure 3e

Figure 3f

Figure 4a

Figure 4b

Figure 5a, full-event

Figure 5b, subevent

Figure 5c, full-event

Figure 5d, subevent

Figure 6a

Figure 6b

Figure 7a, full-event

Figure 7b, subevent

Figure 7c, full-event

Figure 7d, subevent

Figure 8a, full-event

Figure 8b, subevent

Figure 9a, full-event

Figure 9b, subevent

Figure 10a, full-event

Figure 10b, subevent

Figure 11a, full-event

Figure 11b, full-event

Figure 11c, full-event

Figure 11d, subevent

Figure 11e, subevent

Figure 11f, subevent

Figure 12a, full-event

Figure 12b, subevent

Figure 13

Figure 14a

Figure 14b

Invariant mass distributions of $^3\hbox{He}+\pi^-$ (A), $^3\overline{\hbox{He}}+\pi^+$ (B), $^4\hbox{He}+\pi^-$ (C) and $^4\overline{\hbox{He}}+\pi^+$ (D). The solid bands mark the signal invariant mass regions. The obtained signal count ($N_{\rm Sig}$), background count ($N_{\rm Bg}$), and signal significance are listed in each panel.

(A) (anti)hypernuclei yields versus $L/\beta\gamma$. The vertical error bars represent the statistical error only.

(A) (anti)hypernuclei yields versus $L/\beta\gamma$. The vertical error bars represent the statistical error only.

Our measured (anti)hypernuclei lifetimes compared with world data and theoretical predictions (solid triangles). Error bars and boxes represent statistical and systematic uncertainties, respectively. Vertical solid lines with shaded regions show the average lifetime of (anti)hypernuclei and their corresponding uncertainties. The vertical gray line shows the lifetime of the free $\Lambda$.

Production yield ratios of various particles with the same baryon number. Results combining all collision systems in this work are shown by filled stars. Open stars show results with only U+U and Au+Au collisions, while quadrangular stars show results with only Zr+Zr and Ru+Ru collisions. Statistical uncertainties and systematic uncertainties are shown by vertical bars and boxes, respectively. Previous measurement results and thermal model predictions are also shown for comparison. Ratio Typle Index, 0:$\frac{{}^{3}\bar{He}}{{}^{3}He}$ 1:$\frac{{}^{3}\bar{He}}{{}^{3}He}\times\frac{\bar{p}}{p}$ 2:$\frac{{}^{4}\bar{He}}{{}^{4}He}$ 3:$\frac{{}^{3}_{\bar{\Lambda}}\bar{H}}{{}^{3}_{\Lambda}H}$ 4:$\frac{{}^{3}_{\bar{\Lambda}}\bar{H}}{{}^{3}_{\Lambda}H}\times\frac{\bar{p}}{p}$ 5:$\frac{{}^{4}_{\bar{\Lambda}}\bar{H}}{{}^{4}_{\Lambda}H}$ 6:$\frac{{}^{3}_{\Lambda}H}{{}^{3}He}$ 7:$\frac{{}^{4}_{\Lambda}H}{{}^{4}He}$ 8:$\frac{{}^{3}_{\bar{\Lambda}}\bar{H}}{^{3}\bar{He}}$ 9:$\frac{{}^{4}_{\bar{\Lambda}}\bar{H}}{^{4}\bar{He}}$

Production yield ratios of various particles with the same baryon number. Results combining all collision systems in this work are shown by filled stars. Open stars show results with only U+U and Au+Au collisions, while quadrangular stars show results with only Zr+Zr and Ru+Ru collisions. Statistical uncertainties and systematic uncertainties are shown by vertical bars and boxes, respectively. Previous measurement results and thermal model predictions are also shown for comparison. Ratio Typle Index, 0:$\frac{{}^{3}\bar{He}}{{}^{3}He}$ 1:$\frac{{}^{3}\bar{He}}{{}^{3}He}\times\frac{\bar{p}}{p}$ 2:$\frac{{}^{4}\bar{He}}{{}^{4}He}$ 3:$\frac{{}^{3}_{\bar{\Lambda}}\bar{H}}{{}^{3}_{\Lambda}H}$ 4:$\frac{{}^{3}_{\bar{\Lambda}}\bar{H}}{{}^{3}_{\Lambda}H}\times\frac{\bar{p}}{p}$ 5:$\frac{{}^{4}_{\bar{\Lambda}}\bar{H}}{{}^{4}_{\Lambda}H}$ 6:$\frac{{}^{3}_{\Lambda}H}{{}^{3}He}$ 7:$\frac{{}^{4}_{\Lambda}H}{{}^{4}He}$ 8:$\frac{{}^{3}_{\bar{\Lambda}}\bar{H}}{^{3}\bar{He}}$ 9:$\frac{{}^{4}_{\bar{\Lambda}}\bar{H}}{^{4}\bar{He}}$

Production yield ratios of various particles with the same baryon number. Results combining all collision systems in this work are shown by filled stars. Open stars show results with only U+U and Au+Au collisions, while quadrangular stars show results with only Zr+Zr and Ru+Ru collisions. Statistical uncertainties and systematic uncertainties are shown by vertical bars and boxes, respectively. Previous measurement results and thermal model predictions are also shown for comparison. Ratio Typle Index, 0:$\frac{{}^{3}\bar{He}}{{}^{3}He}$ 1:$\frac{{}^{3}\bar{He}}{{}^{3}He}\times\frac{\bar{p}}{p}$ 2:$\frac{{}^{4}\bar{He}}{{}^{4}He}$ 3:$\frac{{}^{3}_{\bar{\Lambda}}\bar{H}}{{}^{3}_{\Lambda}H}$ 4:$\frac{{}^{3}_{\bar{\Lambda}}\bar{H}}{{}^{3}_{\Lambda}H}\times\frac{\bar{p}}{p}$ 5:$\frac{{}^{4}_{\bar{\Lambda}}\bar{H}}{{}^{4}_{\Lambda}H}$ 6:$\frac{{}^{3}_{\Lambda}H}{{}^{3}He}$ 7:$\frac{{}^{4}_{\Lambda}H}{{}^{4}He}$ 8:$\frac{{}^{3}_{\bar{\Lambda}}\bar{H}}{^{3}\bar{He}}$ 9:$\frac{{}^{4}_{\bar{\Lambda}}\bar{H}}{^{4}\bar{He}}$

Production yield ratios of various particles with the same baryon number. Results combining all collision systems in this work are shown by filled stars. Open stars show results with only U+U and Au+Au collisions, while quadrangular stars show results with only Zr+Zr and Ru+Ru collisions. Statistical uncertainties and systematic uncertainties are shown by vertical bars and boxes, respectively. Previous measurement results and thermal model predictions are also shown for comparison. Ratio Typle Index, 0:$\frac{{}^{3}\bar{He}}{{}^{3}He}$ 1:$\frac{{}^{3}\bar{He}}{{}^{3}He}\times\frac{\bar{p}}{p}$ 2:$\frac{{}^{4}\bar{He}}{{}^{4}He}$ 3:$\frac{{}^{3}_{\bar{\Lambda}}\bar{H}}{{}^{3}_{\Lambda}H}$ 4:$\frac{{}^{3}_{\bar{\Lambda}}\bar{H}}{{}^{3}_{\Lambda}H}\times\frac{\bar{p}}{p}$ 5:$\frac{{}^{4}_{\bar{\Lambda}}\bar{H}}{{}^{4}_{\Lambda}H}$ 6:$\frac{{}^{3}_{\Lambda}H}{{}^{3}He}$ 7:$\frac{{}^{4}_{\Lambda}H}{{}^{4}He}$ 8:$\frac{{}^{3}_{\bar{\Lambda}}\bar{H}}{^{3}\bar{He}}$ 9:$\frac{{}^{4}_{\bar{\Lambda}}\bar{H}}{^{4}\bar{He}}$

Reconstruction efficiency as a function of $L/(\beta\gamma)$ obtained from the embedding Monte Carlo technique. Hypernuclei have stricter topological cuts than antihypernuclei to suppress knock-out $^3\hbox{He}$ and $^4\hbox{He}$, resulting in lower efficiencies.

Reconstruction efficiency as a function of $L/(\beta\gamma)$ obtained from the embedding Monte Carlo technique. Hypernuclei have stricter topological cuts than antihypernuclei to suppress knock-out $^3\hbox{He}$ and $^4\hbox{He}$, resulting in lower efficiencies.

H3L, antiH3L, H4L and antiH4L candidate invariant-mass distributions in different $L/\beta\gamma$ intervals.

H3L, antiH3L, H4L and antiH4L candidate invariant-mass distributions in different $L/\beta\gamma$ intervals.

H3L, antiH3L, H4L and antiH4L candidate invariant-mass distributions in different $L/\beta\gamma$ intervals.

H3L, antiH3L, H4L and antiH4L candidate invariant-mass distributions in different $L/\beta\gamma$ intervals.

$dN/d(L/\beta\gamma)$ as a function of $L/\beta\gamma$ for $\Lambda$ and $\bar{\Lambda}$, and exponential fits to obtain their lifetimes.

Efficiency corrected $p_{T}$ spectra for $^3\hbox{He}$, $^3\overline{\hbox{He}}$, \htl, and \ahtl. The spectra are in the phase space of $|y|<0.7$ with only MB-triggered events. The spectra are not normalized by the number of events. The lines represent the BW-function fits.

Efficiency corrected $p_{T}$ spectra for $^3\hbox{He}$, $^3\overline{\hbox{He}}$, \htl, and \ahtl. The spectra are in the phase space of $|y|<0.7$ with only MB-triggered events. The spectra are not normalized by the number of events. The lines represent the BW-function fits.

Transverse dilepton-$p_{T}^{miss}$ mass pre-fit distribution for selected events in SR2 of the di-leptonic channel for the full dataset. The error bars on the data points represent the statistical uncertainty of the data, and the error bars on the predicted yields represent the combined systematic and statistical uncertainty in each bin. The signal prediction represents the mass point: $m_s = 160 GeV, m_{\chi} = 100 GeV, m_{Z'} = 500 GeV$. The last bin includes the overflow.

Dilepton mass pre-fit distribution for selected events in SR3 of the di-leptonic channel for the full dataset. The error bars on the data points represent the statistical uncertainty of the data, and the error bars on the predicted yields represent the combined systematic and statistical uncertainty in each bin. The signal prediction represents the mass point: $m_s = 160 GeV, m_{\chi} = 100 GeV, m_{Z'} = 500 GeV$. The last bin includes the overflow.

Dilepton $p_T$ pre-fit distribution for selected events in SR3 of the di-leptonic channel for the full dataset. The error bars on the data points represent the statistical uncertainty of the data, and the error bars on the predicted yields represent the combined systematic and statistical uncertainty in each bin. The signal prediction represents the mass point: $m_s = 160 GeV, m_{\chi} = 100 GeV, m_{Z'} = 500 GeV$. The last bin includes the overflow.

Dijet $p_T$ pre-fit distribution for selected events in the semi-leptonic channel for the full dataset. The error bars on the data points represent the statistical uncertainty of the data, and the error bars on the predicted yields represent the combined systematic and statistical uncertainty in each bin. The signal prediction represents the mass point: $m_s = 160 GeV, m_{\chi} = 100 GeV, m_{Z'} = 500 GeV$. The last bin includes the overflow.

Lepton-dijet $p_T$ pre-fit distribution for selected events in the semi-leptonic channel for the full dataset. The error bars on the data points represent the statistical uncertainty of the data, and the error bars on the predicted yields represent the combined systematic and statistical uncertainty in each bin. The signal prediction represents the mass point: $m_s = 160 GeV, m_{\chi} = 100 GeV, m_{Z'} = 500 GeV$. The last bin includes the overflow.

Maximum $p_T$ of the visible particles divided by the missing $p_T$, for selected events in the semi-leptonic channel for the full dataset. The error bars on the data points represent the statistical uncertainty of the data, and the error bars on the predicted yields represent the combined systematic and statistical uncertainty in each bin. The signal prediction represents the mass point: $m_s = 160 GeV, m_{\chi} = 100 GeV, m_{Z'} = 500 GeV$. The last bin includes the overflow.

Pre-fit distribution of the $\Delta \phi$ angle between jets, for selected events in the semi-leptonic channel for the full dataset. The error bars on the data points represent the statistical uncertainty of the data, and the error bars on the predicted yields represent the combined systematic and statistical uncertainty in each bin. The signal prediction represents the mass point: $m_s = 160 GeV, m_{\chi} = 100 GeV, m_{Z'} = 500 GeV$. The last bin includes the overflow.

Pre-fit distribution of the $\Delta \phi$ angle between the lepton and missing $p_T$, for selected events in the semi-leptonic channel for the full dataset. The error bars on the data points represent the statistical uncertainty of the data, and the error bars on the predicted yields represent the combined systematic and statistical uncertainty in each bin. The signal prediction represents the mass point: $m_s = 160 GeV, m_{\chi} = 100 GeV, m_{Z'} = 500 GeV$. The last bin includes the overflow.

Pre-fit distribution of the $\Delta \phi$ angle between the lepton and the dijet system, for selected events in the semi-leptonic channel for the full dataset. The error bars on the data points represent the statistical uncertainty of the data, and the error bars on the predicted yields represent the combined systematic and statistical uncertainty in each bin. The signal prediction represents the mass point: $m_s = 160 GeV, m_{\chi} = 100 GeV, m_{Z'} = 500 GeV$. The last bin includes the overflow.

Pre-fit distribution of the $\Delta R$ distance between the leptons, for selected events in the non-prompt validation region of the di-leptonic channel for the full dataset. The error bars on the data points represent the statistical uncertainty of the data, and the error bars on the predicted yields represent the combined systematic and statistical uncertainty in each bin. The signal prediction represents the mass point: $m_s = 160 GeV, m_{\chi} = 100 GeV, m_{Z'} = 500 GeV$. The last bin includes the overflow.

Pre-fit distribution of the $\Delta \phi$ angle between the di-lepton system and the missing $p_T$, for selected events in the non-prompt validation region of the di-leptonic channel for the full dataset. The error bars on the data points represent the statistical uncertainty of the data, and the error bars on the predicted yields represent the combined systematic and statistical uncertainty in each bin. The signal prediction represents the mass point: $m_s = 160 GeV, m_{\chi} = 100 GeV, m_{Z'} = 500 GeV$. The last bin includes the overflow.

Pre-fit distribution of the $\Delta \phi$ angle between the lepton and the di-jet system, for selected events in the non-prompt validation region of the semi-leptonic channel for the full dataset. The error bars on the data points represent the statistical uncertainty of the data, and the error bars on the predicted yields represent the combined systematic and statistical uncertainty in each bin. The signal prediction represents the mass point: $m_s = 160 GeV, m_{\chi} = 100 GeV, m_{Z'} = 500 GeV$. The last bin includes the overflow.

Pre-fit distribution of the $\Delta \phi$ angle between the lepton-dijet system and the missing $p_T$, for selected events in the non-prompt validation region of the semi-leptonic channel for the full dataset. The error bars on the data points represent the statistical uncertainty of the data, and the error bars on the predicted yields represent the combined systematic and statistical uncertainty in each bin. The signal prediction represents the mass point: $m_s = 160 GeV, m_{\chi} = 100 GeV, m_{Z'} = 500 GeV$. The last bin includes the overflow.

Leading lepton $p_T$ pre-fit distribution for selected events in the top control region of the di-leptonic channel for the full dataset. The error bars on the data points represent the statistical uncertainty of the data, and the error bars on the predicted yields represent the combined systematic and statistical uncertainty in each bin. The signal prediction represents the mass point: $m_s = 160 GeV, m_{\chi} = 100 GeV, m_{Z'} = 500 GeV$. The last bin includes the overflow.

Trailing lepton $p_T$ pre-fit distribution for selected events in the top control region of the di-leptonic channel for the full dataset. The error bars on the data points represent the statistical uncertainty of the data, and the error bars on the predicted yields represent the combined systematic and statistical uncertainty in each bin. The signal prediction represents the mass point: $m_s = 160 GeV, m_{\chi} = 100 GeV, m_{Z'} = 500 GeV$. The last bin includes the overflow.

Dilepton mass pre-fit distribution for selected events in the Drell-Yan control region of the di-leptonic channel for the full dataset. The error bars on the data points represent the statistical uncertainty of the data, and the error bars on the predicted yields represent the combined systematic and statistical uncertainty in each bin. The signal prediction represents the mass point: $m_s = 160 GeV, m_{\chi} = 100 GeV, m_{Z'} = 500 GeV$. The last bin includes the overflow.

Missing $p_T$ pre-fit distribution for selected events in the Drell-Yan control region of the di-leptonic channel for the full dataset. The error bars on the data points represent the statistical uncertainty of the data, and the error bars on the predicted yields represent the combined systematic and statistical uncertainty in each bin. The signal prediction represents the mass point: $m_s = 160 GeV, m_{\chi} = 100 GeV, m_{Z'} = 500 GeV$. The last bin includes the overflow.

Missing $p_T$ pre-fit distribution for selected events in the $WW$ control region of the di-leptonic channel for the full dataset. The error bars on the data points represent the statistical uncertainty of the data, and the error bars on the predicted yields represent the combined systematic and statistical uncertainty in each bin. The signal prediction represents the mass point: $m_s = 160 GeV, m_{\chi} = 100 GeV, m_{Z'} = 500 GeV$. The last bin includes the overflow.

Dilepton $p_T$ pre-fit distribution for selected events in the $WW$ control region of the di-leptonic channel for the full dataset. The error bars on the data points represent the statistical uncertainty of the data, and the error bars on the predicted yields represent the combined systematic and statistical uncertainty in each bin. The signal prediction represents the mass point: $m_s = 160 GeV, m_{\chi} = 100 GeV, m_{Z'} = 500 GeV$. The last bin includes the overflow.

Minimum $p_T$ of the visible particles divided by the missing $p_T$, for selected events in the top control region of the semi-leptonic channel for the full dataset. The error bars on the data points represent the statistical uncertainty of the data, and the error bars on the predicted yields represent the combined systematic and statistical uncertainty in each bin. The signal prediction represents the mass point: $m_s = 160 GeV, m_{\chi} = 100 GeV, m_{Z'} = 500 GeV$. The last bin includes the overflow.

Pre-fit distribution of the $\Delta \phi$ angle between jets, for selected events in the top control region of the semi-leptonic channel for the full dataset. The error bars on the data points represent the statistical uncertainty of the data, and the error bars on the predicted yields represent the combined systematic and statistical uncertainty in each bin. The signal prediction represents the mass point: $m_s = 160 GeV, m_{\chi} = 100 GeV, m_{Z'} = 500 GeV$. The last bin includes the overflow.

Pre-fit distribution of the $\Delta \phi$ angle between the lepton and missing $p_T$, for selected events in the $W$+jets control region of the semi-leptonic channel for the full dataset. The error bars on the data points represent the statistical uncertainty of the data, and the error bars on the predicted yields represent the combined systematic and statistical uncertainty in each bin. The signal prediction represents the mass point: $m_s = 160 GeV, m_{\chi} = 100 GeV, m_{Z'} = 500 GeV$. The last bin includes the overflow.

Pre-fit distribution of the $\Delta \phi$ angle between the lepton and the dijet system, for selected events in the $W$+jets control region of the semi-leptonic channel for the full dataset. The error bars on the data points represent the statistical uncertainty of the data, and the error bars on the predicted yields represent the combined systematic and statistical uncertainty in each bin. The signal prediction represents the mass point: $m_s = 160 GeV, m_{\chi} = 100 GeV, m_{Z'} = 500 GeV$. The last bin includes the overflow.

Unrolled $m_{ll}-m_{T}^{l min, p_{T}^{miss}}$ post-fit distributions in the di-leptonic channel in SR1 for the full data set. The histogram bins are spaced uniformly. Each group of five bins (from left to right) corresponds to $m_{T}^{l min, p_{T}^{miss}}$ distribution in a $m_{ll}$ region, placed in ascending order. The signal prediction represents the mass point: $m_s = 160 GeV, m_{\chi} = 100 GeV, m_{Z'} = 500 GeV$.

Unrolled $m_{ll}-m_{T}^{l min, p_{T}^{miss}}$ post-fit distributions in the di-leptonic channel in SR2 for the full data set. The histogram bins are spaced uniformly. Each group of five bins (from left to right) corresponds to $m_{T}^{l min, p_{T}^{miss}}$ distribution in a $m_{ll}$ region, placed in ascending order. The signal prediction represents the mass point: $m_s = 160 GeV, m_{\chi} = 100 GeV, m_{Z'} = 500 GeV$.

Unrolled $m_{ll}-m_{T}^{l min, p_{T}^{miss}}$ post-fit distributions in the di-leptonic channel in SR3 for the full data set. The histogram bins are spaced uniformly. Each group of five bins (from left to right) corresponds to $m_{T}^{l min, p_{T}^{miss}}$ distribution in a $m_{ll}$ region, placed in ascending order. The signal prediction represents the mass point: $m_s = 160 GeV, m_{\chi} = 100 GeV, m_{Z'} = 500 GeV$.

Post-fit BDT distributions in the semi-leptonic channel for the full data set in the top control region. The signal prediction represents the mass point: $m_{s} = 160$ GeV, $m_{\chi} = 100$ GeV, $m_{Z'} = 500$ GeV

Post-fit BDT distributions in the semi-leptonic channel for the full data set in the $W$+jets control region. The signal prediction represents the mass point: $m_{s} = 160$ GeV, $m_{\chi} = 100$ GeV, $m_{Z'} = 500$ GeV

Post-fit BDT distributions in the semi-leptonic channel in the 2016 signal region. The signal prediction represents the mass point: $m_{s} = 160$ GeV, $m_{\chi} = 100$ GeV, $m_{Z'} = 500$ GeV

Post-fit BDT distributions in the semi-leptonic channel in the 2017+2018 signal region. The signal prediction represents the mass point: $m_{s} = 160$ GeV, $m_{\chi} = 100$ GeV, $m_{Z'} = 500$ GeV

Contour of the 95% CL observed upper limits representing $\sigma / \sigma_{theory} = 1$ for the dark Higgs model in the ($m_{s}$, $m_{Z'}$) plane for $m_{\chi} = 100 GeV$.

Contour of the 95% CL expected + 2 std. upper limits representing $\sigma / \sigma_{theory} = 1$ for the dark Higgs model in the ($m_{s}$, $m_{Z'}$) plane for $m_{\chi} = 100 GeV$.

Contour of the 95% CL expected + 1 std. upper limits representing $\sigma / \sigma_{theory} = 1$ for the dark Higgs model in the ($m_{s}$, $m_{Z'}$) plane for $m_{\chi} = 100 GeV$.

Contour of the 95% CL expected upper limits representing $\sigma / \sigma_{theory} = 1$ for the dark Higgs model in the ($m_{s}$, $m_{Z'}$) plane for $m_{\chi} = 100 GeV$.

Contour of the 95% CL expected - 1 std. upper limits representing $\sigma / \sigma_{theory} = 1$ for the dark Higgs model in the ($m_{s}$, $m_{Z'}$) plane for $m_{\chi} = 100 GeV$.

Contour of the 95% CL expected - 2 std. upper limits representing $\sigma / \sigma_{theory} = 1$ for the dark Higgs model in the ($m_{s}$, $m_{Z'}$) plane for $m_{\chi} = 100 GeV$.

Contour of the 95% CL observed upper limits representing $\sigma / \sigma_{theory} = 1$ for the dark Higgs model in the ($m_{s}$, $m_{Z'}$) plane for $m_{\chi} = 150 GeV$.

Contour of the 95% CL expected + 2 std. upper limits representing $\sigma / \sigma_{theory} = 1$ for the dark Higgs model in the ($m_{s}$, $m_{Z'}$) plane for $m_{\chi} = 150 GeV$.

Contour of the 95% CL expected + 1 std. upper limits representing $\sigma / \sigma_{theory} = 1$ for the dark Higgs model in the ($m_{s}$, $m_{Z'}$) plane for $m_{\chi} = 150 GeV$.

Contour of the 95% CL expected upper limits representing $\sigma / \sigma_{theory} = 1$ for the dark Higgs model in the ($m_{s}$, $m_{Z'}$) plane for $m_{\chi} = 150 GeV$.

Contour of the 95% CL expected - 1 std. upper limits representing $\sigma / \sigma_{theory} = 1$ for the dark Higgs model in the ($m_{s}$, $m_{Z'}$) plane for $m_{\chi} = 150 GeV$.

Contour of the 95% CL expected - 2 std. upper limits representing $\sigma / \sigma_{theory} = 1$ for the dark Higgs model in the ($m_{s}$, $m_{Z'}$) plane for $m_{\chi} = 150 GeV$.

Contour of the 95% CL observed upper limits representing $\sigma / \sigma_{theory} = 1$ for the dark Higgs model in the ($m_{s}$, $m_{Z'}$) plane for $m_{\chi} = 200 GeV$.

Contour of the 95% CL expected + 2 std. upper limits representing $\sigma / \sigma_{theory} = 1$ for the dark Higgs model in the ($m_{s}$, $m_{Z'}$) plane for $m_{\chi} = 200 GeV$.

Contour of the 95% CL expected + 1 std. upper limits representing $\sigma / \sigma_{theory} = 1$ for the dark Higgs model in the ($m_{s}$, $m_{Z'}$) plane for $m_{\chi} = 200 GeV$.

Contour of the 95% CL expected upper limits representing $\sigma / \sigma_{theory} = 1$ for the dark Higgs model in the ($m_{s}$, $m_{Z'}$) plane for $m_{\chi} = 200 GeV$.

Contour of the 95% CL expected - 1 std. upper limits representing $\sigma / \sigma_{theory} = 1$ for the dark Higgs model in the ($m_{s}$, $m_{Z'}$) plane for $m_{\chi} = 200 GeV$.

Contour of the 95% CL expected - 2 std. upper limits representing $\sigma / \sigma_{theory} = 1$ for the dark Higgs model in the ($m_{s}$, $m_{Z'}$) plane for $m_{\chi} = 200 GeV$.

Contour of the 95% CL observed upper limits representing $\sigma / \sigma_{theory} = 1$ for the dark Higgs model in the ($m_{s}$, $m_{Z'}$) plane for $m_{\chi} = 300 GeV$.

Contour of the 95% CL expected + 2 std. upper limits representing $\sigma / \sigma_{theory} = 1$ for the dark Higgs model in the ($m_{s}$, $m_{Z'}$) plane for $m_{\chi} = 300 GeV$.

Contour of the 95% CL expected + 1 std. upper limits representing $\sigma / \sigma_{theory} = 1$ for the dark Higgs model in the ($m_{s}$, $m_{Z'}$) plane for $m_{\chi} = 300 GeV$.

Contour of the 95% CL expected upper limits representing $\sigma / \sigma_{theory} = 1$ for the dark Higgs model in the ($m_{s}$, $m_{Z'}$) plane for $m_{\chi} = 300 GeV$.

Contour of the 95% CL expected - 1 std. upper limits representing $\sigma / \sigma_{theory} = 1$ for the dark Higgs model in the ($m_{s}$, $m_{Z'}$) plane for $m_{\chi} = 300 GeV$.

Contour of the 95% CL expected - 2 std. upper limits representing $\sigma / \sigma_{theory} = 1$ for the dark Higgs model in the ($m_{s}$, $m_{Z'}$) plane for $m_{\chi} = 300 GeV$.

The $\sigma / \sigma_{theory}$ 95% CL upper limit values for the dark Higgs model in the ($m_{s}$, $m_{Z'}$) plane for $m_{\chi} = 100 GeV$.

The $\sigma / \sigma_{theory}$ 95% CL upper limit values for the dark Higgs model in the ($m_{s}$, $m_{Z'}$) plane for $m_{\chi} = 150 GeV$.

The $\sigma / \sigma_{theory}$ 95% CL upper limit values for the dark Higgs model in the ($m_{s}$, $m_{Z'}$) plane for $m_{\chi} = 200 GeV$.

The $\sigma / \sigma_{theory}$ 95% CL upper limit values for the dark Higgs model in the ($m_{s}$, $m_{Z'}$) plane for $m_{\chi} = 300 GeV$.

Expected (dashed line) value of $-2\ln\Lambda$ as a function of $\kappa_{2V}$, when all other coupling modifiers are fixed to their SM predictions.

Likelihood observed contours at 68% CL (solid line) and 95% CL (dashed line) in the $\kappa_{\lambda}$, $\kappa_{2V}$ parameter space, when all other coupling modifiers are fixed to their SM predictions. The best-fit value, denoted by a cross in the plot, corresponds to the very first entry in the table.

Likelihood expected contours at 68% CL (teal shaded region) and 95% CL (yellow shaded region) in the $\kappa_{\lambda}$, $\kappa_{2V}$ parameter space, when all other coupling modifiers are fixed to their SM predictions.In the plot, the SM prediction is indicated by the star.

Likelihood observed contours at 68% CL (solid line) and 95% CL (dashed line) in the $c_{gghh}$ versus $c_{hhh}$ HEFT parameter space, with the remaining coefficient fixed to its SM value. The best-fit value, denoted by a cross in the plot, corresponds to the very first entry in the table.

Likelihood expected contours at 68% CL (teal shaded region) 95% CL (yellow shaded region) in the $c_{gghh}$ versus $c_{hhh}$ HEFT parameter space, with the remaining coefficient fixed to its SM value. In the plot, the SM prediction is indicated by the star.

Likelihood observed contours at 68% CL (solid line) and 95% CL (dashed line) in the $c_{tthh}$ versus $c_{hhh}$ HEFT parameter space, with the remaining coefficient fixed to its SM value. The best-fit value, denoted by a cross in the plot, corresponds to the very first entry in the table.

Likelihood exptected contours at 68% CL (teal shaded region) and 95% CL (yellow shaded region) in the $c_{tthh}$ versus $c_{hhh}$ HEFT parameter space, with the remaining coefficient fixed to its SM value. In the plot, the SM prediction is indicated by the star.

The observed (filled circles) and expected (hollow circles) 95% CL upper limits on the $HH$ ggF production cross-section in the Standard Model and for seven HEFT benchmark points. The teal and yellow colored bands indicate the $\pm 1\sigma$ and $\pm 2\sigma$ variations on the expected limit due to statistical and systematic uncertainties. The predicted cross-sections of each of the models under consideration are shown by the red crosses. The contribution from VBF production to the total $HH$ production cross-section is neglected.

Likelihood observed contours at 68% CL (solid line) and 95% CL (dashed line) in the $c_{{H}\boxed{}}$ versus $c_{H}$ SMEFT parameter space, with the remaining coefficient fixed to its SM value. The best-fit value, denoted by a cross in the plot, corresponds to the very first entry in the table.

Likelihood expected contours at 68% CL (teal shaded region) 95% CL (yellow shaded region) in the $c_{{H}\boxed{}}$ versus $c_{H}$ SMEFT parameter space, with the remaining coefficient fixed to its SM value. In the plot, the SM prediction is indicated by the star.

The acceptance times efficiency for the signal ggF $HH$ process as a function of the coupling modifier $\kappa_{\lambda}$ in each analysis category. The other coupling modifiers affecting ggF $HH$ production are fixed to their SM predictions. The bands indicate the simulation statistical uncertainty.

The acceptance times efficiency for the signal VBF $HH$ process as a function of the coupling modifier $\kappa_{\lambda}$ in each analysis category. When varying $\kappa_{\lambda}$, the other coupling modifiers affecting the VBF $HH$ production mode are set to their SM predictions. The bands indicate the simulation statistical uncertainty.

The acceptance times efficiency for the signal VBF $HH$ process as a function of the coupling modifier $\kappa_{2V}$ in each analysis category. When varying $\kappa_{2V}$, the other coupling modifiers affecting the VBF $HH$ production mode are set to their SM predictions. The bands indicate the simulation statistical uncertainty.

Expected yields of the signal $HH$ process as a function of the coupling modifier $\kappa_{\lambda}$ after applying the analysis preselection and in each analysis category after the final selection. The $HH$ yield is obtained considering both the $ggF$ and $VBF$ contributions. The other coupling modifiers affecting $HH$ production are fixed to their SM predictions. The bands indicate the simulation statistical uncertainty.

The acceptance times efficiency for the signal ggF $HH$ process in each analysis category as a function of the $c_{hhh}$ HEFT coefficients. The dashed lines denote values that are excluded at 95% CL. The bottom panels show the efficiency of the sum of all analysis categories.

The acceptance times efficiency for the signal ggF $HH$ process in each analysis category as a function of the $c_{tthh}$ HEFT coefficients. The dashed lines denote values that are excluded at 95% CL. The bottom panels show the efficiency of the sum of all analysis categories.

The acceptance times efficiency for the signal ggF $HH$ process in each analysis category as a function of the $c_{gghh}$ HEFT coefficients. The dashed lines denote values that are excluded at 95% CL. The bottom panels show the efficiency of the sum of all analysis categories.

The acceptance times efficiency for the signal ggF $HH$ process in each analysis category as a function of the $c_{H}$ SMEFT coefficients. The dashed lines denote values that are excluded at 95% CL. The bottom panels show the efficiency of the sum of all analysis categories.

The acceptance times efficiency for the signal ggF $HH$ process in each analysis category as a function of the $c_{{H}\boxed{}}$ SMEFT coefficients. The dashed lines denote values that are excluded at 95% CL. The bottom panels show the efficiency of the sum of all analysis categories.

The yield of the signal ggF $HH$ process in each analysis category as a function of the $c_{hhh}$ HEFT coefficients. The dashed lines denote values that are excluded at 95% CL. The bottom panels show the efficiency of the sum of all analysis categories.

The yield of the signal ggF $HH$ process in each analysis category as a function of the $c_{tthh}$ HEFT coefficients. The dashed lines denote values that are excluded at 95% CL. The bottom panels show the efficiency of the sum of all analysis categories.

The yield of the signal ggF $HH$ process in each analysis category as a function of the $c_{gghh}$ HEFT coefficients. The dashed lines denote values that are excluded at 95% CL. The bottom panels show the efficiency of the sum of all analysis categories.

The yield of the signal ggF $HH$ process in each analysis category as a function of the $c_{H}$ SMEFT coefficients. The dashed lines denote values that are excluded at 95% CL. The bottom panels show the efficiency of the sum of all analysis categories.

The yield of the signal ggF $HH$ process in each analysis category as a function of the $c_{{H}\boxed{}}$ SMEFT coefficients. The dashed lines denote values that are excluded at 95% CL. The bottom panels show the efficiency of the sum of all analysis categories.

Distributions of the diphoton invariant mass for events in data (black dots with error bars) compared to the sum of the expected signal and backgrounds (histograms) in the low mass 1 region.

Distributions of the diphoton invariant mass for events in data (black dots with error bars) compared to the sum of the expected signal and backgrounds (histograms) in the low mass 2 region.

Distributions of the diphoton invariant mass for events in data (black dots with error bars) compared to the sum of the expected signal and backgrounds (histograms) in the low mass 3 region.

Distributions of the diphoton invariant mass for events in data (black dots with error bars) compared to the sum of the expected signal and backgrounds (histograms) in the low mass 4 region.

Distributions of the diphoton invariant mass for events in data (black dots with error bars) compared to the sum of the expected signal and backgrounds (histograms) in the high mass 1 region.

Distributions of the diphoton invariant mass for events in data (black dots with error bars) compared to the sum of the expected signal and backgrounds (histograms) in the high mass 2 region.

Distributions of the diphoton invariant mass for events in data (black dots with error bars) compared to the sum of the expected signal and backgrounds (histograms) in the high mass 3 region.

Observed (solid line) value of $-2\ln\Lambda$ as a function of the $c_{hhh}$ HEFT coefficients when all other coupling modifiers are fixed to the SM value

Expected (dashed line) value of $-2\ln\Lambda$ as a function of the $c_{hhh}$ HEFT coefficients when all other coupling modifiers are fixed to the SM value

Observed (solid line) value of $-2\ln\Lambda$ as a function of the $c_{gghh}$ HEFT coefficients when all other coupling modifiers are fixed to the SM value

Expected (dashed line) value of $-2\ln\Lambda$ as a function of the $c_{gghh}$ HEFT coefficients when all other coupling modifiers are fixed to the SM value

Observed (solid line) value of $-2\ln\Lambda$ as a function of the $c_{tthh}$ HEFT coefficients when all other coupling modifiers are fixed to the SM value

Expected (dashed line) value of $-2\ln\Lambda$ as a function of the $c_{tthh}$ HEFT coefficients when all other coupling modifiers are fixed to the SM value

Observed (solid line) value of $-2\ln\Lambda$ as a function of the $c_{H}$ SMEFT coefficients when all other coupling modifiers are fixed to the SM value.

Expected (dashed line) value of $-2\ln\Lambda$ as a function of the $c_{H}$ SMEFT coefficients when all other coupling modifiers are fixed to the SM value.

Observed (solid line) value of $-2\ln\Lambda$ as a function of the $c_{{H}\boxed{}}$ SMEFT coefficients when all other coupling modifiers are fixed to the SM value.

Expected (dashed line) value of $-2\ln\Lambda$ as a function of the $c_{{H}\boxed{}}$ SMEFT coefficients when all other coupling modifiers are fixed to the SM value.

Summary of the expected (blue) and observed (orange) one-dimensional constraints at 68% (solid error bars) and 95% (dashed error bars) CL on the coefficients of selected HEFT (top) and SMEFT (bottom) operators describing Higgs boson interactions affecting $HH$ production through gluon--gluon fusion. The results are obtained from one dimensional scans of the profile log-likelihood assuming that all other Wilson coefficients are fixed to their SM values. The contribution from VBF $HH$ production is neglected.

Unfolded $M(l^{-}\gamma)$ distribution for $Z \to \mu\mu\gamma$ process with dressed leptons and bkg subtraction. $M_{ll}>20$ GeV. Nexp.un f. = 64822.9 $\pm$ 254.6, NPowHeg truth =634276.

Unfolded dR distribution for $Z \to ee\gamma$ process with dressed leptons and bkg subtraction. $M_{ll}>20$ GeV. Nexp.un f. = 64273.2 $\pm$ 253.5, NPowHeg truth =338671.

Unfolded dR distribution for $Z \to \mu\mu\gamma$ process with dressed leptons and bkg subtraction. $M_{ll}>20$ GeV. Nexp.un f. = 65362.4 $\pm$ 255.7 , NPowHeg truth =634214.

Unfolded $P_{T}^{\gamma}$ distribution for $Z \to ee\gamma$ process with dressed leptons and bkg subtraction. $M_{ll}>20$ GeV. Nexp.un f. = 63486.8 $\pm$ 252.0, NPowHeg truth =333348.

Unfolded $P_{T}^{\gamma}$ distribution for $Z \to \mu\mu\gamma$ process with dressed leptons and bkg subtraction. $M_{ll}>20$ GeV. Nexp.un f. = 64432.6 $\pm$ 253.8, NPowHeg truth =624059.

Unfolded $M(l^{+}\gamma)$ distribution for $Z \to ee\gamma$ process with dressed leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 57095.9 $\pm$ 254 , NPowHeg truth =301666, N Sherpa truth =76327.

Unfolded $M(l^{-}\gamma)$ distribution for $Z \to ee\gamma$ process with dressed leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 57130 $\pm$ 254 , NPowHeg truth =301666, N Sherpa truth =763273.

Unfolded $M(l^{+}\gamma)$ distribution for $Z \to \mu\mu\gamma$ process with dressed leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 58310.9 $\pm$ 245, NPowHeg truth =564672, N Sherpa truth =814016.

Unfolded $M(l^{-}\gamma)$ distribution for $Z \to \mu\mu\gamma$ process with dressed leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 58320.9 $\pm$ 245, NPowHeg truth =564672, N Sherpa truth =814016.

Unfolded dR distribution for $Z \to ee\gamma$ process with dressed leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 57705.4 $\pm$ 254 , NPowHeg truth =301655, N Sherpa truth =763259.

Unfolded dR distribution for $Z \to \mu\mu\gamma$ process with dressed leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 58869.2 $\pm$ 256, NPowHeg truth =564660, NS herpa truth =813995.

Unfolded $P_{T}^{\gamma}$ distribution for $Z \to ee\gamma$ process with dressed leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 57358.6 $\pm$ 254 , NPowHeg truth =298662, N Sherpa truth =756609.

Unfolded $P_{T}^{\gamma}$ distribution for $Z \to \mu\mu\gamma$ process with dressed leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 58226.4 $\pm$ 254, NPowHeg truth =558949, N Sherpa truth =806988.

Unfolded $M(l^{+}\gamma)$ distribution for $Z \to ee\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>20$ GeV. Nexp.un f. = 63717.4 $\pm$ 252.4, NPowHeg truth =338714.

Unfolded $M(l^{-}\gamma)$ distribution for $Z \to ee\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>20$ GeV. Nexp.un f. = 63855.8 $\pm$ 252.7 , NPowHeg truth =338708.

Unfolded $M(l^{+}\gamma)$ distribution for $Z \to \mu\mu\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>20$ GeV. Nexp.un f. = 64809.8 $\pm$ 254.6, NPowHeg truth =634285.

Unfolded $M(l^{-}\gamma)$ distribution for $Z \to \mu\mu\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>20$ GeV. Nexp.un f. = 64822.9 $\pm$ 254.6, NPowHeg truth =634276.

Unfolded dR distribution for $Z \to ee\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>20$ GeV. Nexp.un f. = 64273.2 $\pm$ 253.5, NPowHeg truth =338671.

Unfolded dR distribution for $Z \to \mu\mu\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>20$ GeV. Nexp.un f. = 65362.4 $\pm$ 255.7 , NPowHeg truth =634214.

Unfolded $P_{T}^{\gamma}$ distribution for $Z \to ee\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>20$ GeV. Nexp.un f. = 63486.8 $\pm$ 252.0, NPowHeg truth =333348.

Unfolded $P_{T}^{\gamma}$ distribution for $Z \to \mu\mu\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>20$ GeV. Nexp.un f. = 64432.6 $\pm$ 253.8, NPowHeg truth =624059.

Unfolded $M(l^{+}\gamma)$ distribution for $Z \to ee\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 57095.9 $\pm$ 254 , NPowHeg truth =301666, N Sherpa truth =76327.

Unfolded $M(l^{-}\gamma)$ distribution for $Z \to ee\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 57130 $\pm$ 254 , NPowHeg truth =301666, N Sherpa truth =763273.

Unfolded $M(l^{+}\gamma)$ distribution for $Z \to \mu\mu\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 58310.9 $\pm$ 245, NPowHeg truth =564672, N Sherpa truth =814016.

Unfolded $M(l^{-}\gamma)$ distribution for $Z \to \mu\mu\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 58320.9 $\pm$ 245, NPowHeg truth =564672, N Sherpa truth =814016.

Unfolded dR distribution for $Z \to ee\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 57705.4 $\pm$ 254 , NPowHeg truth =301655, N Sherpa truth =763259.

Unfolded dR distribution for $Z \to \mu\mu\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 58869.2 $\pm$ 256, NPowHeg truth =564660, NS herpa truth =813995.

Unfolded $P_{T}^{\gamma}$ distribution for $Z \to ee\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 57358.6 $\pm$ 254 , NPowHeg truth =298662, N Sherpa truth =756609.

Unfolded $P_{T}^{\gamma}$ distribution for $Z \to \mu\mu\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 58226.4 $\pm$ 254, NPowHeg truth =558949, N Sherpa truth =806988.

Truth $P_{T}^{Z}$ distribution after reweghting to data.

Combined Covariance Matrix for Unfolded $M(l^{+}\gamma)$ distribution for $Z \to ee\gamma$ process with dressed leptons and bkg subtraction. $M_{ll}>20$ GeV. Nexp.un f. = 63717.4 $\pm$ 252.4, NPowHeg truth =338714.

Combined Covariance Matrix for Unfolded $M(l^{-}\gamma)$ distribution for $Z \to ee\gamma$ process with dressed leptons and bkg subtraction. $M_{ll}>20$ GeV. Nexp.un f. = 63855.8 $\pm$ 252.7 , NPowHeg truth =338708.

Combined Covariance Matrix for Unfolded $M(l^{+}\gamma)$ distribution for $Z \to \mu\mu\gamma$ process with dressed leptons and bkg subtraction. $M_{ll}>20$ GeV. Nexp.un f. = 64809.8 $\pm$ 254.6, NPowHeg truth =634285.

Combined Covariance Matrix for Unfolded $M(l^{-}\gamma)$ distribution for $Z \to \mu\mu\gamma$ process with dressed leptons and bkg subtraction. $M_{ll}>20$ GeV. Nexp.un f. = 64822.9 $\pm$ 254.6, NPowHeg truth =634276.

Combined Covariance Matrix for Unfolded dR distribution for $Z \to ee\gamma$ process with dressed leptons and bkg subtraction. $M_{ll}>20$ GeV. Nexp.un f. = 64273.2 $\pm$ 253.5, NPowHeg truth =338671.

Combined Covariance Matrix for Unfolded dR distribution for $Z \to \mu\mu\gamma$ process with dressed leptons and bkg subtraction. $M_{ll}>20$ GeV. Nexp.un f. = 65362.4 $\pm$ 255.7 , NPowHeg truth =634214.

Combined Covariance Matrix for Unfolded $P_{T}^{\gamma}$ distribution for $Z \to ee\gamma$ process with dressed leptons and bkg subtraction. $M_{ll}>20$ GeV. Nexp.un f. = 63486.8 $\pm$ 252.0, NPowHeg truth =333348.

Combined Covariance Matrix for Unfolded $P_{T}^{\gamma}$ distribution for $Z \to \mu\mu\gamma$ process with dressed leptons and bkg subtraction. $M_{ll}>20$ GeV. Nexp.un f. = 64432.6 $\pm$ 253.8, NPowHeg truth =624059.

Combined Covariance Matrix for Unfolded $M(l^{+}\gamma)$ distribution for $Z \to ee\gamma$ process with dressed leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 57095.9 $\pm$ 254 , NPowHeg truth =301666, N Sherpa truth =76327.

Combined Covariance Matrix for Unfolded $M(l^{-}\gamma)$ distribution for $Z \to ee\gamma$ process with dressed leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 57130 $\pm$ 254 , NPowHeg truth =301666, N Sherpa truth =763273.

Combined Covariance Matrix for Unfolded $M(l^{+}\gamma)$ distribution for $Z \to \mu\mu\gamma$ process with dressed leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 58310.9 $\pm$ 245, NPowHeg truth =564672, N Sherpa truth =814016.

Combined Covariance Matrix for Unfolded $M(l^{-}\gamma)$ distribution for $Z \to \mu\mu\gamma$ process with dressed leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 58320.9 $\pm$ 245, NPowHeg truth =564672, N Sherpa truth =814016.

Combined Covariance Matrix for Unfolded dR distribution for $Z \to ee\gamma$ process with dressed leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 57705.4 $\pm$ 254 , NPowHeg truth =301655, N Sherpa truth =763259.

Combined Covariance Matrix for Unfolded dR distribution for $Z \to \mu\mu\gamma$ process with dressed leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 58869.2 $\pm$ 256, NPowHeg truth =564660, NS herpa truth =813995.

Combined Covariance Matrix for Unfolded $P_{T}^{\gamma}$ distribution for $Z \to ee\gamma$ process with dressed leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 57358.6 $\pm$ 254 , NPowHeg truth =298662, N Sherpa truth =756609.

Combined Covariance Matrix for Unfolded $P_{T}^{\gamma}$ distribution for $Z \to \mu\mu\gamma$ process with dressed leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 58226.4 $\pm$ 254, NPowHeg truth =558949, N Sherpa truth =806988.

Combined Covariance Matrix for Unfolded $M(l^{+}\gamma)$ distribution for $Z \to ee\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>20$ GeV. Nexp.un f. = 63717.4 $\pm$ 252.4, NPowHeg truth =338714.

Combined Covariance Matrix for Unfolded $M(l^{-}\gamma)$ distribution for $Z \to ee\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>20$ GeV. Nexp.un f. = 63855.8 $\pm$ 252.7 , NPowHeg truth =338708.

Combined Covariance Matrix for Unfolded $M(l^{+}\gamma)$ distribution for $Z \to \mu\mu\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>20$ GeV. Nexp.un f. = 64809.8 $\pm$ 254.6, NPowHeg truth =634285.

Combined Covariance Matrix for Unfolded $M(l^{-}\gamma)$ distribution for $Z \to \mu\mu\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>20$ GeV. Nexp.un f. = 64822.9 $\pm$ 254.6, NPowHeg truth =634276.

Combined Covariance Matrix for Unfolded dR distribution for $Z \to ee\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>20$ GeV. Nexp.un f. = 64273.2 $\pm$ 253.5, NPowHeg truth =338671.

Combined Covariance Matrix for Unfolded dR distribution for $Z \to \mu\mu\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>20$ GeV. Nexp.un f. = 65362.4 $\pm$ 255.7 , NPowHeg truth =634214.

Combined Covariance Matrix for Unfolded $P_{T}^{\gamma}$ distribution for $Z \to ee\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>20$ GeV. Nexp.un f. = 63486.8 $\pm$ 252.0, NPowHeg truth =333348.

Combined Covariance Matrix for Unfolded $P_{T}^{\gamma}$ distribution for $Z \to \mu\mu\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>20$ GeV. Nexp.un f. = 64432.6 $\pm$ 253.8, NPowHeg truth =624059.

Combined Covariance Matrix for Unfolded $M(l^{+}\gamma)$ distribution for $Z \to ee\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 57095.9 $\pm$ 254 , NPowHeg truth =301666, N Sherpa truth =76327.

Combined Covariance Matrix for Unfolded $M(l^{-}\gamma)$ distribution for $Z \to ee\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 57130 $\pm$ 254 , NPowHeg truth =301666, N Sherpa truth =763273.

Combined Covariance Matrix for Unfolded $M(l^{+}\gamma)$ distribution for $Z \to \mu\mu\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 58310.9 $\pm$ 245, NPowHeg truth =564672, N Sherpa truth =814016.

Combined Covariance Matrix for Unfolded $M(l^{-}\gamma)$ distribution for $Z \to \mu\mu\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 58320.9 $\pm$ 245, NPowHeg truth =564672, N Sherpa truth =814016.

Combined Covariance Matrix for Unfolded dR distribution for $Z \to ee\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 57705.4 $\pm$ 254 , NPowHeg truth =301655, N Sherpa truth =763259.

Combined Covariance Matrix for Unfolded dR distribution for $Z \to \mu\mu\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 58869.2 $\pm$ 256, NPowHeg truth =564660, NS herpa truth =813995.

Combined Covariance Matrix for Unfolded $P_{T}^{\gamma}$ distribution for $Z \to ee\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 57358.6 $\pm$ 254 , NPowHeg truth =298662, N Sherpa truth =756609.

Combined Covariance Matrix for Unfolded $P_{T}^{\gamma}$ distribution for $Z \to \mu\mu\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 58226.4 $\pm$ 254, NPowHeg truth =558949, N Sherpa truth =806988.

Unfolded $M(l^{+}\gamma\gamma)$ distribution for $Z \to ll\gamma\gamma$ process with dressed leptons.

Unfolded $M(l^{+}\gamma\gamma)$ distribution for $Z \to ll\gamma\gamma$ process with bare leptons.

Unfolded dR distribution for $Z \to ll\gamma\gamma$ process with dressed leptons for leading photon.

Unfolded dR distribution for $Z \to ll\gamma\gamma$ process with bare leptons for leading photon.

Unfolded dR distribution for $Z \to ll\gamma\gamma$ process with dressed leptons for second photon.

Unfolded dR distribution for $Z \to ll\gamma\gamma$ process with bare leptons for second photon.

Unfolded dRgg distribution for $Z \to ll\gamma\gamma$ process with dressed leptons.

Unfolded dRgg distribution for $Z \to ll\gamma\gamma$ process with bare leptons.

Unfolded $P_{T}^{\gamma 1}$ distribution for $Z \to ll\gamma\gamma$ process with dressed leptons for leading photon.

Unfolded $P_{T}^{\gamma 1}$ distribution for $Z \to ll\gamma\gamma$ process with bare leptons for leading photon.

Unfolded $P_{T}^{\gamma 2}$ distribution for $Z \to ll\gamma\gamma$ process with dressed leptons for second photon.

Unfolded $P_{T}^{\gamma 2}$ distribution for $Z \to ll\gamma\gamma$ process with bare leptons for second photon.

Likelihood profiles of the $\kappa_\lambda$ parameter.

Likelihood profiles of the $\kappa_{2V}$ parameter.

The 95% CL upper limits on the $HH$ cross-section for different values of $\kappa_\lambda$. The expected limits assume no $HH$ production. The red line shows the theory prediction for the combined ggF $HH$ and VBF $HH$ cross-section as a function of $\kappa_\lambda$ where all parameters and couplings are set to their SM values except $\kappa_\lambda$. The bands surrounding the red cross-section line indicate the theoretical uncertainty on the predicted cross-section. The $\kappa_\lambda$ values in the interval $[-6.7, 15.3]$ cannot be excluded by this analysis.

The 95% CL upper limits on the VBF $HH$ cross section for different values of $\kappa_{2V}$. The expected limits assume no VBF $HH$ production. SM ggF $HH$ production is considered as background. The red line shows the theory prediction for the VBF $HH$ cross-section as a function of $\kappa_{2V}$ where all parameters and couplings are set to their SM values except $\kappa_{2V}$. The uncertainty band is smaller than the width of the plotted line. The $\kappa_{2V}$ values in the interval $[-0.3, 2.4]$ cannot be excluded by this analysis.

The distributions of the invariant mass of the dilepton-photon system after the signal region selection before the fit to data.The shaded band represents the Monte Carlo statistical unc

The distributions of the invariant mass of the transverse mass of the WW system after the signal region selection before the fit to data.The shaded band represents the Monte Carlo statistical unc

The unrolled two-dimensional mTWW-mll$\gamma$ distributions with category 0 jet after the fit to data. The data are compared to the sum of the signal and expected background. The black points with error bars represent the data and their statistical uncertainties, whereas the hatched bands represent the total uncertainties in the predictions.

The unrolled two-dimensional mTWW-mll$\gamma$ distributions with category 1more jets after the fit to data. The data are compared to the sum of the signal and expected background. The black points with error bars represent the data and their statistical uncertainties, whereas the hatched bands represent the total uncertainties in the predictions.