Mean $p_T$ values of the $\Upsilon(1$S$)$, $\Upsilon(2$S$)$, and $\Upsilon(3$S$)$ states with $p_T\,>\,0\,GeV$ and $|y|\,<\,1.2$ as a function of track multiplicity $N_{track}$

Ratio $\Upsilon(2$S$)\,/\,\Upsilon(1$S$)$ with $|y|\,<\,1.2$ as a function of track multiplicity $N_{track}$ in $0<p_T<5\,$GeV range

Ratio $\Upsilon(2$S$)\,/\,\Upsilon(1$S$)$ with $|y|\,<\,1.2$ as a function of track multiplicity $N_{track}$ in $5<p_T<7\,$GeV range

Ratio $\Upsilon(2$S$)\,/\,\Upsilon(1$S$)$ with $|y|\,<\,1.2$ as a function of track multiplicity $N_{track}$ in $7<p_T<9\,$GeV range

Ratio $\Upsilon(2$S$)\,/\,\Upsilon(1$S$)$ with $|y|\,<\,1.2$ as a function of track multiplicity $N_{track}$ in $9<p_T<11\,$GeV range

Ratio $\Upsilon(2$S$)\,/\,\Upsilon(1$S$)$ with $|y|\,<\,1.2$ as a function of track multiplicity $N_{track}$ in $11<p_T<15\,$GeV range

Ratio $\Upsilon(2$S$)\,/\,\Upsilon(1$S$)$ with $|y|\,<\,1.2$ as a function of track multiplicity $N_{track}$ in $15<p_T<20\,$GeV range

Ratio $\Upsilon(2$S$)\,/\,\Upsilon(1$S$)$ with $|y|\,<\,1.2$ as a function of track multiplicity $N_{track}$ in $20<p_T<50\,$GeV range

Ratio $\Upsilon(3$S$)\,/\,\Upsilon(1$S$)$ with $|y|\,<\,1.2$ as a function of track multiplicity $N_{track}$ in $0<p_T<5\,$GeV range

Ratio $\Upsilon(3$S$)\,/\,\Upsilon(1$S$)$ with $|y|\,<\,1.2$ as a function of track multiplicity $N_{track}$ in $5<p_T<7\,$GeV range

Ratio $\Upsilon(3$S$)\,/\,\Upsilon(1$S$)$ with $|y|\,<\,1.2$ as a function of track multiplicity $N_{track}$ in $7<p_T<9\,$GeV range

Ratio $\Upsilon(3$S$)\,/\,\Upsilon(1$S$)$ with $|y|\,<\,1.2$ as a function of track multiplicity $N_{track}$ in $9<p_T<11\,$GeV range

Ratio $\Upsilon(3$S$)\,/\,\Upsilon(1$S$)$ with $|y|\,<\,1.2$ as a function of track multiplicity $N_{track}$ in $11<p_T<15\,$GeV range

Ratio $\Upsilon(3$S$)\,/\,\Upsilon(1$S$)$ with $|y|\,<\,1.2$ as a function of track multiplicity $N_{track}$ in $15<p_T<20\,$GeV range

Ratio $\Upsilon(3$S$)\,/\,\Upsilon(1$S$)$ with $|y|\,<\,1.2$ as a function of track multiplicity $N_{track}$ in $20<p_T<50\,$GeV range

Ratios $\Upsilon(2$S$)\,/\,\Upsilon(1$S$)$ and $\Upsilon(3$S$)\,/\,\Upsilon(1$S$)$ as functions of "forward" track multiplicity $N_{track}^{\Delta\phi}$ for $\Upsilon(n$S$)$ states with $p_T\,>\,7\,GeV$ and $|y|\,<\,1.2$. Forward tracks are those with momentum direction in $\Delta\phi\,<\,\pi/3$ w.r.t. the $\Upsilon(n$S$)$ momentum direction.

Ratios $\Upsilon(2$S$)\,/\,\Upsilon(1$S$)$ and $\Upsilon(3$S$)\,/\,\Upsilon(1$S$)$ as functions of "transverse" track multiplicity $N_{track}^{\Delta\phi}$ for $\Upsilon(n$S$)$ states with $p_T\,>\,7\,GeV$ and $|y|\,<\,1.2$. Transverse tracks are those with momentum direction in $\pi/3\,<\,\Delta\phi\,<\,2\pi/3$ w.r.t. the $\Upsilon(n$S$)$ momentum direction.

Ratios $\Upsilon(2$S$)\,/\,\Upsilon(1$S$)$ and $\Upsilon(3$S$)\,/\,\Upsilon(1$S$)$ as functions of "backward" track multiplicity $N_{track}^{\Delta\phi}$ for $\Upsilon(n$S$)$ states with $p_T\,>\,7\,GeV$ and $|y|\,<\,1.2$. Backward tracks are those with momentum direction in $\Delta\phi\,>\,2\pi/3$ w.r.t. the $\Upsilon(n$S$)$ momentum direction.

Ratios $\Upsilon(2$S$)\,/\,\Upsilon(1$S$)$ and $\Upsilon(3$S$)\,/\,\Upsilon(1$S$)$ as functions of track multiplicity $N_{track}$ for $\Upsilon(n$S$)$ states with $p_T\,>\,7\,GeV$ and $|y|\,<\,1.2$ and $N^{\Delta R}_{track}\,=\,0$ charged particles produced in $\Delta R\,<\,0.5$ cone around $\Upsilon(n$S$)$ momentum direction.

Ratios $\Upsilon(2$S$)\,/\,\Upsilon(1$S$)$ and $\Upsilon(3$S$)\,/\,\Upsilon(1$S$)$ as functions of track multiplicity $N_{track}$ for $\Upsilon(n$S$)$ states with $p_T\,>\,7\,GeV$ and $|y|\,<\,1.2$ and $N^{\Delta R}_{track}\,=\,1$ charged particles produced in $\Delta R\,<\,0.5$ cone around $\Upsilon(n$S$)$ momentum direction.

Ratios $\Upsilon(2$S$)\,/\,\Upsilon(1$S$)$ and $\Upsilon(3$S$)\,/\,\Upsilon(1$S$)$ as functions of track multiplicity $N_{track}$ for $\Upsilon(n$S$)$ states with $p_T\,>\,7\,GeV$ and $|y|\,<\,1.2$ and $N^{\Delta R}_{track}\,=\,2$ charged particles produced in $\Delta R\,<\,0.5$ cone around $\Upsilon(n$S$)$ momentum direction.

Ratios $\Upsilon(2$S$)\,/\,\Upsilon(1$S$)$ and $\Upsilon(3$S$)\,/\,\Upsilon(1$S$)$ as functions of track multiplicity $N_{track}$ for $\Upsilon(n$S$)$ states with $p_T\,>\,7\,GeV$ and $|y|\,<\,1.2$ and $N^{\Delta R}_{track}\,>\,2$ charged particles produced in $\Delta R\,<\,0.5$ cone around $\Upsilon(n$S$)$ momentum direction.

Ratios $\Upsilon(2$S$)\,/\,\Upsilon(1$S$)$ and $\Upsilon(3$S$)\,/\,\Upsilon(1$S$)$ as functions of track multiplicity $N_{track}$ in transverse sphericity bin $0.00\,<\,S_T\,<\,0.55$ for $\Upsilon(n$S$)$ states with $p_T\,>\,7\,GeV$ and $|y|\,<\,1.2$.

Ratios $\Upsilon(2$S$)\,/\,\Upsilon(1$S$)$ and $\Upsilon(3$S$)\,/\,\Upsilon(1$S$)$ as functions of track multiplicity $N_{track}$ in transverse sphericity bin $0.55\,<\,S_T\,<\,0.70$ for $\Upsilon(n$S$)$ states with $p_T\,>\,7\,GeV$ and $|y|\,<\,1.2$.

Ratios $\Upsilon(2$S$)\,/\,\Upsilon(1$S$)$ and $\Upsilon(3$S$)\,/\,\Upsilon(1$S$)$ as functions of track multiplicity $N_{track}$ in transverse sphericity bin $0.70\,<\,S_T\,<\,0.85$ for $\Upsilon(n$S$)$ states with $p_T\,>\,7\,GeV$ and $|y|\,<\,1.2$.

Ratios $\Upsilon(2$S$)\,/\,\Upsilon(1$S$)$ and $\Upsilon(3$S$)\,/\,\Upsilon(1$S$)$ as functions of track multiplicity $N_{track}$ in transverse sphericity bin $0.85\,<\,S_T\,<\,1.00$ for $\Upsilon(n$S$)$ states with $p_T\,>\,7\,GeV$ and $|y|\,<\,1.2$.

Efficiency-corrected multiplicity bins used in the $\Upsilon(n$S$)$ ratio analysis and the corresponding mean number of charged particle tracks.

Measured DPS effective cross section

pp -> J/psi J/psi J/psi X cross section

$pp \rightarrow J/\psi J/\psi J/\psi X~$ fiducial cross section

The $m_{jj}$ distributions for the CRs and the BDT classifier response distribution for the SR after the fit in all regions. The dashed line shows the total background distribution before the fit. The vertical error bars on the data points correspond to the data's statistical uncertainty. Overflows are included in the last bin. The uncertainty band corresponds to the combination of the MC statistical uncertainty and systematic uncertainties obtained in the fit.

The $m_{jj}$ distributions for the CRs and the BDT classifier response distribution for the SR after the fit in all regions. The dashed line shows the total background distribution before the fit. The vertical error bars on the data points correspond to the data's statistical uncertainty. Overflows are included in the last bin. The uncertainty band corresponds to the combination of the MC statistical uncertainty and systematic uncertainties obtained in the fit.

The $m_{jj}$ distributions for the CRs and the BDT classifier response distribution for the SR after the fit in all regions. The dashed line shows the total background distribution before the fit. The vertical error bars on the data points correspond to the data's statistical uncertainty. Overflows are included in the last bin. The uncertainty band corresponds to the combination of the MC statistical uncertainty and systematic uncertainties obtained in the fit.

Observed and expected event yields for the signal and all of the background processes considered in this analysis after the fit to the data in all of the regions. The uncertainty on the expected yield is the combination of statistical and systematic uncertainties obtained in the fit. The individual uncertainties can be correlated and do not necessarily add in quadrature to equal the total background uncertainty.

Summary of the event yield for processes in all regions, after the fit over all regions. The dashed line shows the total background distribution before the fit. The vertical error bars on the data points correspond to the data's statistical uncertainty. The uncertainty band corresponds to the combination of the MC statistical uncertainty and systematic uncertainties obtained in the fit.

Impact of different components of systematic uncertainty on the measured cross section, without taking into account the correlations. The impact is calculated by fixing the value of the corresponding nuisance parameters to the values obtained in the fit used to measure the cross section, performing the fit, estimating the signal strength uncertainty and subtracting it from the nominal uncertainty in quadrature.

Fitted POI values for this analysis, the previous ATLAS analysis, and their combination. The first and second columns present the values obtained in the individual analyses. The third column presents the values obtained in the combination.

Observed and expected one-dimensional limits on dimension 8 aQGC parameters. Limits are obtained by setting all aQGCs parameters except one to zero. Unitarity is not preserved.

Observed and expected one-dimensional limits on dimension 8 aQGC parameters in the region, where unitarity is preserved. Cutoff scales in MC, $E_{c}$, are given for each parameter. Limits are obtained by setting all aQGCs parameters except one to zero.

The $E_{T}^{\gamma}$ distribution in the SR after the fit in the control regions. The red (green) line shows the expected number of events in the case of non-zero EFT coefficient $f_{T0}/\Lambda^4$ ($f_{M0}/\Lambda^4$) with the value shown in the legend. The vertical error bars on the data points correspond to the data statistical uncertainty. Overflows are included in the last bin. The uncertainty band corresponds to the combination of the MC statistical uncertainty and systematic uncertainties obtained in the fit.

Evolution of the expected (red line) and observed (blue line) limits versus $E_{c}$ values for $f_{T0}/\Lambda^4$. The unitarity bound is shown by the black line. The $E_{c}<4$ TeV regime was obtained with $E_{T}^{\gamma} > 600$ GeV. The $E_{c} \geq 4$ TeV regime was obtained with $E_{T}^{\gamma} > 900$ GeV.

Evolution of the expected (red line) and observed (blue line) limits versus $E_{c}$ values for $f_{T5}/\Lambda^4$. The unitarity bound is shown by the black line. The $E_{c}<4$ TeV regime was obtained with $E_{T}^{\gamma} > 600$ GeV. The $E_{c} \geq 4$ TeV regime was obtained with $E_{T}^{\gamma} > 900$ GeV.

Evolution of the expected (red line) and observed (blue line) limits versus $E_{c}$ values for $f_{T8}/\Lambda^4$. The unitarity bound is shown by the black line. The $E_{c}<4$ TeV regime was obtained with $E_{T}^{\gamma} > 600$ GeV. The $E_{c} \geq 4$ TeV regime was obtained with $E_{T}^{\gamma} > 900$ GeV.

Evolution of the expected (red line) and observed (blue line) limits versus $E_{c}$ values for $f_{T9}/\Lambda^4$. The unitarity bound is shown by the black line. The $E_{c}<4$ TeV regime was obtained with $E_{T}^{\gamma} > 600$ GeV. The $E_{c} \geq 4$ TeV regime was obtained with $E_{T}^{\gamma} > 900$ GeV.

Evolution of the expected (red line) and observed (blue line) limits versus $E_{c}$ values for $f_{M0}/\Lambda^4$. The unitarity bound is shown by the black line. The $E_{c}<4$ TeV regime was obtained with $E_{T}^{\gamma} > 400$ GeV. The $E_{c} \geq 4$ TeV regime was obtained with $E_{T}^{\gamma} > 900$ GeV.

Evolution of the expected (red line) and observed (blue line) limits versus $E_{c}$ values for $f_{M1}/\Lambda^4$. The unitarity bound is shown by the black line. The $E_{c}<4$ TeV regime was obtained with $E_{T}^{\gamma} > 400$ GeV. The $E_{c} \geq 4$ TeV regime was obtained with $E_{T}^{\gamma} > 900$ GeV.

Evolution of the expected (red line) and observed (blue line) limits versus $E_{c}$ values for $f_{M2}/\Lambda^4$. The unitarity bound is shown by the black line. The $E_{c}<4$ TeV regime was obtained with $E_{T}^{\gamma} > 400$ GeV. The $E_{c} \geq 4$ TeV regime was obtained with $E_{T}^{\gamma} > 900$ GeV.

Correlation matrix of the parameters for the fit in all regions. Only parameters with absolute value of the correlation coefficient larger than 10 are shown.

Leading tau Pt distributions obtained before the fit to data (Pre-Fit) showing the expected background and tuH signals after applying fake factors in the $t_{h}\tau_{lep}\tau_{had}$-2j region. Other MC includes single top, V+jets, and other small backgrounds. The tuH signals with nominal branching ratio of 0.1% are scaled using normalization factors of 2 to 50. Statistical and systematic uncertainties are included in the "Total background".

Leading tau Pt distributions obtained before the fit to data (Pre-Fit) showing the expected background and tuH signals after applying fake factors in the $t_{h}\tau_{lep}\tau_{had}$-3j region. Other MC includes single top, V+jets, and other small backgrounds. The tuH signals with nominal branching ratio of 0.1% are scaled using normalization factors of 2 to 50. Statistical and systematic uncertainties are included in the "Total background".

Leading tau Pt distributions obtained before the fit to data (Pre-Fit) showing the expected background and tuH signals after applying fake factors in the $t_{\ell}\tau_{had}\tau_{had}$SS region. Other MC includes single top, V+jets, and other small backgrounds. The tuH signals with nominal branching ratio of 0.1% are scaled using normalization factors of 2 to 50. Statistical and systematic uncertainties are included in the "Total background".

Leading tau Pt distributions obtained before the fit to data (Pre-Fit) showing the expected background and tuH signals after applying fake factors in the $t_{h}\tau_{had}\tau_{had}$-2j region. Rare includes single top, V+jets, and other small backgrounds. $\tau_{sub}$ real includes the contribution of fakes for which the sub-leading tau is real. The tuH signals with nominal branching ratio of 0.1% are scaled using normalization factors of 2 to 50. Statistical and systematic uncertainties are included in the "Total background".

Leading tau Pt distributions obtained before the fit to data (Pre-Fit) showing the expected background and tuH signals after applying fake factors in the $t_{h}\tau_{had}\tau_{had}$-3j region. Rare includes single top, V+jets, and other small backgrounds. $\tau_{sub}$ real includes the contribution of fakes for which the sub-leading tau is real. The tuH signals with nominal branching ratio of 0.1% are scaled using normalization factors of 2 to 50. Statistical and systematic uncertainties are included in the "Total background".

Leading tau Pt distributions obtained before the fit to data (Pre-Fit) showing the expected background and tuH signals after applying fake factors in the $t_{h}\tau_{had}\tau_{had}$-3jSS region. Rare includes single top, V+jets, and other small backgrounds. $\tau_{sub}$ real includes the contribution of fakes for which the sub-leading tau is real. The tuH signals with nominal branching ratio of 0.1% are scaled using normalization factors of 2 to 50. Statistical and systematic uncertainties are included in the "Total background".

Di-tau mass distributions obtained before the fit to data (Pre-Fit) showing the expected background and tuH signals after applying fake factors in the $t_{\ell}\tau_{had}\tau_{had}$ region. Other MC includes single top, V+jets, and other small backgrounds. The tuH signals with nominal branching ratio of 0.1% are scaled using normalization factors of 2 to 50. Statistical and systematic uncertainties are included in the "Total background".

Di-tau mass distributions obtained before the fit to data (Pre-Fit) showing the expected background and tuH signals after applying fake factors in the $t_{\ell}\tau_{had}$-1j region. Other MC includes single top, V+jets, and other small backgrounds. The tuH signals with nominal branching ratio of 0.1% are scaled using normalization factors of 2 to 50. Statistical and systematic uncertainties are included in the "Total background".

Di-tau mass distributions obtained before the fit to data (Pre-Fit) showing the expected background and tuH signals after applying fake factors in the $t_{\ell}\tau_{had}$-2j region. Other MC includes single top, V+jets, and other small backgrounds. The tuH signals with nominal branching ratio of 0.1% are scaled using normalization factors of 2 to 50. Statistical and systematic uncertainties are included in the "Total background".

Di-tau mass distributions obtained before the fit to data (Pre-Fit) showing the expected background and tuH signals after applying fake factors in the $t_{h}\tau_{lep}\tau_{had}$-2j region. Other MC includes single top, V+jets, and other small backgrounds. The tuH signals with nominal branching ratio of 0.1% are scaled using normalization factors of 2 to 50. Statistical and systematic uncertainties are included in the "Total background".

Di-tau mass distributions obtained before the fit to data (Pre-Fit) showing the expected background and tuH signals after applying fake factors in the $t_{h}\tau_{lep}\tau_{had}$-3j region. Other MC includes single top, V+jets, and other small backgrounds. The tuH signals with nominal branching ratio of 0.1% are scaled using normalization factors of 2 to 50. Statistical and systematic uncertainties are included in the "Total background".

Di-tau mass distributions obtained before the fit to data (Pre-Fit) showing the expected background and tuH signals after applying fake factors in the $t_{\ell}\tau_{had}\tau_{had}$SS region. Other MC includes single top, V+jets, and other small backgrounds. The tuH signals with nominal branching ratio of 0.1% are scaled using normalization factors of 2 to 50. Statistical and systematic uncertainties are included in the "Total background".

Di-tau mass distributions obtained before the fit to data (Pre-Fit) showing the expected background and tuH signals after applying fake factors in the $t_{h}\tau_{had}\tau_{had}$-2j region. Rare includes single top, V+jets, and other small backgrounds. $\tau_{sub}$ real includes the contribution of fakes for which the sub-leading tau is real. The tuH signals with nominal branching ratio of 0.1% are scaled using normalization factors of 2 to 50. Statistical and systematic uncertainties are included in the "Total background".

Di-tau mass distributions obtained before the fit to data (Pre-Fit) showing the expected background and tuH signals after applying fake factors in the $t_{h}\tau_{had}\tau_{had}$-3j region. Rare includes single top, V+jets, and other small backgrounds. $\tau_{sub}$ real includes the contribution of fakes for which the sub-leading tau is real. The tuH signals with nominal branching ratio of 0.1% are scaled using normalization factors of 2 to 50. Statistical and systematic uncertainties are included in the "Total background".

Di-tau mass distributions obtained before the fit to data (Pre-Fit) showing the expected background and tuH signals after applying fake factors in the $t_{h}\tau_{had}\tau_{had}$-3jSS region. Rare includes single top, V+jets, and other small backgrounds. $\tau_{sub}$ real includes the contribution of fakes for which the sub-leading tau is real. The tuH signals with nominal branching ratio of 0.1% are scaled using normalization factors of 2 to 50. Statistical and systematic uncertainties are included in the "Total background".

BDT output distributions obtained from a signal+background fit to the data for the tuH search in the $t_{\ell}\tau_{had}\tau_{had}$ region, Other MC includes single top, V+jets, and other small backgrounds. Statistical and systematic uncertainties are included in the "Total background". The signal shapes of tt(uH), tH, and their sum are also shown using a normalisation of 2 x $\mathcal{B}(\mathrm{t}\to\mathrm{uH})$ of 0.1%.

BDT output distributions obtained from a signal+background fit to the data for the tuH search in the $t_{\ell}\tau_{had}$-1j region, Other MC includes single top, V+jets, and other small backgrounds. Statistical and systematic uncertainties are included in the "Total background". The signal shapes of tt(uH), tH, and their sum are also shown using a normalisation of 2 x $\mathcal{B}(\mathrm{t}\to\mathrm{uH})$ of 0.1%.

BDT output distributions obtained from a signal+background fit to the data for the tuH search in the $t_{\ell}\tau_{had}$-2j region, Other MC includes single top, V+jets, and other small backgrounds. Statistical and systematic uncertainties are included in the "Total background". The signal shapes of tt(uH), tH, and their sum are also shown using a normalisation of 2 x $\mathcal{B}(\mathrm{t}\to\mathrm{uH})$ of 0.1%.

BDT output distributions obtained from a signal+background fit to the data for the tuH search in the $t_{h}\tau_{lep}\tau_{had}$-2j region, Other MC includes single top, V+jets, and other small backgrounds. Statistical and systematic uncertainties are included in the "Total background". The signal shapes of tt(uH), tH, and their sum are also shown using a normalisation of 2 x $\mathcal{B}(\mathrm{t}\to\mathrm{uH})$ of 0.1%.

BDT output distributions obtained from a signal+background fit to the data for the tuH search in the $t_{h}\tau_{lep}\tau_{had}$-3j region, Other MC includes single top, V+jets, and other small backgrounds. Statistical and systematic uncertainties are included in the "Total background". The signal shapes of tt(uH), tH, and their sum are also shown using a normalisation of 2 x $\mathcal{B}(\mathrm{t}\to\mathrm{uH})$ of 0.1%.

BDT output distributions obtained from a signal+background fit to the data for the tuH search in the $t_{\ell}\tau_{had}\tau_{had}$SS region, Other MC includes single top, V+jets, and other small backgrounds. Statistical and systematic uncertainties are included in the "Total background". The signal shapes of tt(uH), tH, and their sum are also shown using a normalisation of 2 x $\mathcal{B}(\mathrm{t}\to\mathrm{uH})$ of 0.1%.

BDT output distributions obtained from a signal+background fit to the data for the tuH search in the $t_{h}\tau_{had}\tau_{had}$-2j region, Rare includes single top, V+jets, and other small backgrounds. $\tau_{sub}$ real includes the contribution of fakes for which the sub-leading tau is real. Statistical and systematic uncertainties are included in the "Total background". The signal shapes of tt(uH), tH, and their sum are also shown using a normalisation of 2 x $\mathcal{B}(\mathrm{t}\to\mathrm{uH})$ of 0.1%.

BDT output distributions obtained from a signal+background fit to the data for the tuH search in the $t_{h}\tau_{had}\tau_{had}$-3j region, Rare includes single top, V+jets, and other small backgrounds. $\tau_{sub}$ real includes the contribution of fakes for which the sub-leading tau is real. Statistical and systematic uncertainties are included in the "Total background". The signal shapes of tt(uH), tH, and their sum are also shown using a normalisation of 2 x $\mathcal{B}(\mathrm{t}\to\mathrm{uH})$ of 0.1%.

BDT output distributions obtained from a signal+background fit to the data for the tuH search in the $t_{h}\tau_{had}\tau_{had}$-3jSS region, Rare includes single top, V+jets, and other small backgrounds. $\tau_{sub}$ real includes the contribution of fakes for which the sub-leading tau is real. Statistical and systematic uncertainties are included in the "Total background". The signal shapes of tt(uH), tH, and their sum are also shown using a normalisation of 2 x $\mathcal{B}(\mathrm{t}\to\mathrm{uH})$ of 0.1%.

BDT output distributions obtained from a signal+background fit to the data for the tcH search in the $t_{\ell}\tau_{had}\tau_{had}$ region, Other MC includes single top, V+jets, and other small backgrounds. Statistical and systematic uncertainties are included in the "Total background". The signal shapes of tt(cH), tH, and their sum are also shown using a normalisation of 2 x $\mathcal{B}(\mathrm{t}\to\mathrm{cH})$ of 0.1%.

BDT output distributions obtained from a signal+background fit to the data for the tcH search in the $t_{\ell}\tau_{had}$-1j region, Other MC includes single top, V+jets, and other small backgrounds. Statistical and systematic uncertainties are included in the "Total background". The signal shapes of tt(cH), tH, and their sum are also shown using a normalisation of 2 x $\mathcal{B}(\mathrm{t}\to\mathrm{cH})$ of 0.1%.

BDT output distributions obtained from a signal+background fit to the data for the tcH search in the $t_{\ell}\tau_{had}$-2j region, Other MC includes single top, V+jets, and other small backgrounds. Statistical and systematic uncertainties are included in the "Total background". The signal shapes of tt(cH), tH, and their sum are also shown using a normalisation of 2 x $\mathcal{B}(\mathrm{t}\to\mathrm{cH})$ of 0.1%.

BDT output distributions obtained from a signal+background fit to the data for the tcH search in the $t_{h}\tau_{lep}\tau_{had}$-2j region, Other MC includes single top, V+jets, and other small backgrounds. Statistical and systematic uncertainties are included in the "Total background". The signal shapes of tt(cH), tH, and their sum are also shown using a normalisation of 2 x $\mathcal{B}(\mathrm{t}\to\mathrm{cH})$ of 0.1%.

BDT output distributions obtained from a signal+background fit to the data for the tcH search in the $t_{h}\tau_{lep}\tau_{had}$-3j region,Other MC includes single top, V+jets, and other small backgrounds. Statistical and systematic uncertainties are included in the "Total background". The signal shapes of tt(cH), tH, and their sum are also shown using a normalisation of 2 x $\mathcal{B}(\mathrm{t}\to\mathrm{cH})$ of 0.1%.

BDT output distributions obtained from a signal+background fit to the data for the tcH search in the $t_{\ell}\tau_{had}\tau_{had}$SS region, Other MC includes single top, V+jets, and other small backgrounds. Statistical and systematic uncertainties are included in the "Total background". The signal shapes of tt(cH), tH, and their sum are also shown using a normalisation of 2 x $\mathcal{B}(\mathrm{t}\to\mathrm{cH})$ of 0.1%.

BDT output distributions obtained from a signal+background fit to the data for the tcH search in the $t_{h}\tau_{had}\tau_{had}$-2j region, Rare includes single top, V+jets, and other small backgrounds. $\tau_{sub}$ real includes the contribution of fakes for which the sub-leading tau is real. Statistical and systematic uncertainties are included in the "Total background". The signal shapes of tt(cH), tH, and their sum are also shown using a normalisation of 2 x $\mathcal{B}(\mathrm{t}\to\mathrm{cH})$ of 0.1%.

BDT output distributions obtained from a signal+background fit to the data for the tcH search in the $t_{h}\tau_{had}\tau_{had}$-3j region, Rare includes single top, V+jets, and other small backgrounds. $\tau_{sub}$ real includes the contribution of fakes for which the sub-leading tau is real. Statistical and systematic uncertainties are included in the "Total background". The signal shapes of tt(cH), tH, and their sum are also shown using a normalisation of 2 x $\mathcal{B}(\mathrm{t}\to\mathrm{cH})$ of 0.1%.

BDT output distributions obtained from a signal+background fit to the data for the tcH search in the $t_{h}\tau_{had}\tau_{had}$-3jSS region, Rare includes single top, V+jets, and other small backgrounds. $\tau_{sub}$ real includes the contribution of fakes for which the sub-leading tau is real. Statistical and systematic uncertainties are included in the "Total background". The signal shapes of tt(cH), tH, and their sum are also shown using a normalisation of 2 x $\mathcal{B}(\mathrm{t}\to\mathrm{cH})$ of 0.1%.

95% CL upper limits on $\mathcal{B}(\mathrm{t}\to\mathrm{cH})$ for the individual searches as well as their combination, assuming $\mathcal{B}(\mathrm{t}\to\mathrm{uH}) = 0$. The observed limits are compared with the expected (median) limits under the background-only hypothesis. The surrounding shaded bands correspond to the 68% and 95% CL intervals around the expected limits, denoted by $\pm 1\sigma$ and $\pm 2\sigma$, respectively.

95% CL upper limits on $\mathcal{B}(\mathrm{t}\to\mathrm{uH})$ for the individual searches as well as their combination, assuming $\mathcal{B}(\mathrm{t}\to\mathrm{cH}) = 0$. The observed limits are compared with the expected (median) limits under the background-only hypothesis. The surrounding shaded bands correspond to the 68% and 95% CL intervals around the expected limits, denoted by $\pm 1\sigma$ and $\pm 2\sigma$, respectively.

Observed upper limits at 95% CL on the branching fractions in the plane of $\mathcal{B}(\mathrm{t}\to\mathrm{uH})$ and $\mathcal{B}(\mathrm{t}\to\mathrm{cH})$.

Expected upper limits at 95% CL on the branching fractions in the plane of $\mathcal{B}(\mathrm{t}\to\mathrm{uH})$ and $\mathcal{B}(\mathrm{t}\to\mathrm{cH})$.

Expected $+2\sigma$ upper limits at 95% CL on the branching fractions in the plane of $\mathcal{B}(\mathrm{t}\to\mathrm{uH})$ and $\mathcal{B}(\mathrm{t}\to\mathrm{cH})$.

Expected $+1\sigma$ upper limits at 95% CL on the branching fractions in the plane of $\mathcal{B}(\mathrm{t}\to\mathrm{uH})$ and $\mathcal{B}(\mathrm{t}\to\mathrm{cH})$.

Expected $-1\sigma$ upper limits at 95% CL on the branching fractions in the plane of $\mathcal{B}(\mathrm{t}\to\mathrm{uH})$ and $\mathcal{B}(\mathrm{t}\to\mathrm{cH})$.

Expected $-2\sigma$ upper limits at 95% CL on the branching fractions in the plane of $\mathcal{B}(\mathrm{t}\to\mathrm{uH})$ and $\mathcal{B}(\mathrm{t}\to\mathrm{cH})$.

Observed upper limits at 95% CL on the anomalous couplings in the plane of $C_{\mathrm{c\phi}}$ and $C_{\mathrm{u\phi}}$.

Expected upper limits at 95% CL on the anomalous couplings in the plane of $C_{\mathrm{c\phi}}$ and $C_{\mathrm{u\phi}}$.

Expected $+2\sigma$ upper limits at 95% CL on the anomalous couplings in the plane of $C_{\mathrm{c\phi}}$ and $C_{\mathrm{u\phi}}$.

Expected $+1\sigma$ upper limits at 95% CL on the anomalous couplings in the plane of $C_{\mathrm{c\phi}}$ and $C_{\mathrm{u\phi}}$.

Expected $-1\sigma$ upper limits at 95% CL on the anomalous couplings in the plane of $C_{\mathrm{c\phi}}$ and $C_{\mathrm{u\phi}}$.

Expected $-2\sigma$ upper limits at 95% CL on the anomalous couplings in the plane of $C_{\mathrm{c\phi}}$ and $C_{\mathrm{u\phi}}$.

Predicted and observed yields in each of the analysis regions considered in leptonic channel.

Predicted and observed yields in each of the analysis regions considered in hadronic channel.

Absolute uncertainties on $\mathcal{B}(\mathrm{t}\to\mathrm{qH})$ obtained from the combined fit to the data.

Summary of 95% CL upper limits on $\mathcal{B}(\mathrm{t}\to\mathrm{qH})$, significance and best-fit branching ratio in the signal regions. The values in the tables are in the form of observed(expected).

Results of applying the BH algorithm to the mass spectra in the leading photon category, using the fitted background estimations from the initial step

Results of applying the BH algorithm to the mass spectra in the leading electron category, using the fitted background estimations from the initial step

Results of applying the BH algorithm to the mass spectra in the leading muon category, using the fitted background estimations from the initial step

Results of applying the BH algorithm to the mass spectra in the leading small-R jet category, using the fitted background estimations from the initial step

Results of applying the BH algorithm to the mass spectra in the leading bjet category, using the fitted background estimations from the initial step

Results of applying the BH algorithm to the mass spectra in the leading large-R jet category, using the fitted background estimations from the initial step

Results of applying the BH algorithm to the mass spectra in the leading photon category, using the fitted background estimations from the initial step

Results of applying the BH algorithm to the mass spectra in the leading electron category, using the fitted background estimations from the initial step

Results of applying the BH algorithm to the mass spectra in the leading muon category, using the fitted background estimations from the initial step

Results of applying the BH algorithm to the mass spectra in the inclusive category, using the fitted background estimations from the initial step

Results of applying the BH algorithm to the mass spectra in the inclusive category, using the fitted background estimations from the initial step

Upper limits at 95% CL on the cross section times branching fraction times acceptance for a Gaussian-shaped signal with a relative width value of 3% as a function of mass in the leading small-R jet category

Upper limits at 95% CL on the cross section times branching fraction times acceptance for a Gaussian-shaped signal with a relative width value of 3% as a function of mass in the leading bjet category

Upper limits at 95% CL on the cross section times branching fraction times acceptance for a Gaussian-shaped signal with a relative width value of 3% as a function of mass in the leading large-R jet category

Upper limits at 95% CL on the cross section times branching fraction times acceptance for a Gaussian-shaped signal with a relative width value of 3% as a function of mass in the leading photon category

Upper limits at 95% CL on the cross section times branching fraction times acceptance for a Gaussian-shaped signal with a relative width value of 3% as a function of mass in the leading electron category

Upper limits at 95% CL on the cross section times branching fraction times acceptance for a Gaussian-shaped signal with a relative width value of 3% as a function of mass in the leading muon category

Upper limits at 95% CL on the cross section times branching fraction times acceptance for a Gaussian-shaped signal with a relative width value of 3% as a function of mass in the leading small-R jet category

Upper limits at 95% CL on the cross section times branching fraction times acceptance for a Gaussian-shaped signal with a relative width value of 3% as a function of mass in the leading bjet category

Upper limits at 95% CL on the cross section times branching fraction times acceptance for a Gaussian-shaped signal with a relative width value of 3% as a function of mass in the leading large-R jet category

Upper limits at 95% CL on the cross section times branching fraction times acceptance for a Gaussian-shaped signal with a relative width value of 3% as a function of mass in the leading photon category

Upper limits at 95% CL on the cross section times branching fraction times acceptance for a Gaussian-shaped signal with a relative width value of 3% as a function of mass in the leading electron category

Upper limits at 95% CL on the cross section times branching fraction times acceptance for a Gaussian-shaped signal with a relative width value of 3% as a function of mass in the leading muon category

Upper limits at 95% CL on the cross section times branching fraction times acceptance for a Gaussian-shaped signal with a relative width value of 3% as a function of mass in the inclusive category

Upper limits at 95% CL on the cross section times branching fraction times acceptance for a Gaussian-shaped signal with a relative width value of 3% as a function of mass in the inclusive category

Comparison of observed upper limits at 95% CL on the cross section times branching fraction times acceptance for a Gaussian-shaped signals with relative width values as a function of mass in the leading small-R jet category

Comparison of observed upper limits at 95% CL on the cross section times branching fraction times acceptance for a Gaussian-shaped signals with relative width values as a function of mass in the leading bjet category

Comparison of observed upper limits at 95% CL on the cross section times branching fraction times acceptance for a Gaussian-shaped signals with relative width values as a function of mass in the leading large-R jet category

Comparison of observed upper limits at 95% CL on the cross section times branching fraction times acceptance for a Gaussian-shaped signals with relative width values as a function of mass in the leading photon category

Comparison of observed upper limits at 95% CL on the cross section times branching fraction times acceptance for a Gaussian-shaped signals with relative width values as a function of mass in the leading electron category

Comparison of observed upper limits at 95% CL on the cross section times branching fraction times acceptance for a Gaussian-shaped signals with relative width values as a function of mass in the leading muon category

Comparison of observed upper limits at 95% CL on the cross section times branching fraction times acceptance for a Gaussian-shaped signals with relative width values as a function of mass in the leading small-R jet category

Comparison of observed upper limits at 95% CL on the cross section times branching fraction times acceptance for a Gaussian-shaped signals with relative width values as a function of mass in the leading bjet category

Comparison of observed upper limits at 95% CL on the cross section times branching fraction times acceptance for a Gaussian-shaped signals with relative width values as a function of mass in the leading large-R jet category

Comparison of observed upper limits at 95% CL on the cross section times branching fraction times acceptance for a Gaussian-shaped signals with relative width values as a function of mass in the leading photon category

Comparison of observed upper limits at 95% CL on the cross section times branching fraction times acceptance for a Gaussian-shaped signals with relative width values as a function of mass in the leading electron category

Comparison of observed upper limits at 95% CL on the cross section times branching fraction times acceptance for a Gaussian-shaped signals with relative width values as a function of mass in the leading muon category

Comparison of observed upper limits at 95% CL on the cross section times branching fraction times acceptance for a Gaussian-shaped signals with relative width values as a function of mass in the inclusive category

Comparison of observed upper limits at 95% CL on the cross section times branching fraction times acceptance for a Gaussian-shaped signals with relative width values as a function of mass in the inclusive category

Acceptance times efficiency in an HVT model as a function of mass in the leading large-R jet category

Upper limits at 95% CL on the cross section times the branching fraction($W^{\prime} \to ZW$) for the HVT signal as functions of mass($m_{ZX}$) in the leading large-R jet category.The full(dashed) red curves correspond to the theoretical predictions of HVT model A(B)

Comparison of the identification efficiencies using standard and merged-ee reconstruction as a function of true PT(Z)

Background rejection factor as a function of signal efficiency. The red curve shows the BDT performance whereas the blue curve corresponds to that of a cut-based analysis relying only on the jet energyfraction deposited in the EM calorimeter

BH p-values of the 100 pseudo-experiments as a function of in the leading small-R jet category for an injected Gaussian-shaped signal with a relative width value of 3%. The fractions of the pseudo-experiments that have the correctly identified interval and BH p-values below the threshold of 0.01 are indicated. The background is derived by the background-only fit in the full fitting range.

BH p-values of the 100 pseudo-experiments as a function of in the leading small-R jet category for an injected Gaussian-shaped signal with a relative width value of 3%. The fractions of the pseudo-experiments that have the correctly identified interval and BH p-values below the threshold of 0.01 are indicated. The background is derived by the background-only fit in the range excluding the BH interval.

Fractions of pseudo-experiments in which the detected BH interval agrees with the injected mass point and the BH p-value is below 0.01 as a function of mass in the leading small-R jet category for Gaussian-shaped signal with a relative width of 3%.

Fractions of pseudo-experiments in which the detected BH interval agrees with the injected mass point and the BH p-value is below 0.01 as a function of mass in the leading small-R jet category for Gaussian-shaped signal with a relative width of 3%.

Distribution of exclusion upper limits on signal event yields at 95% CL from 1000 pseudo-experiments for Gaussian-shaped signals with relative width values of 3% at the low boundary of the limit-sensitive mass range for the ZX spectrum of the leading small-R jet category. The vertical line corresponds to the expected nominal exclusion limit at 95% CL.

Distribution of exclusion upper limits on signal event yields at 95% CL from 1000 pseudo-experiments for Gaussian-shaped signals with relative width values of 3% at the high boundary of the limit-sensitive mass range for the ZX spectrum of the leading small-R jet category. The vertical line corresponds to the expected nominal exclusion limit at 95% CL.

Distribution of exclusion upper limits on signal event yields at 95% CL from 1000 pseudo-experiments for Gaussian-shaped signals with relative width values of 5% at the low boundary of the limit-sensitive mass range for the ZX spectrum of the leading small-R jet category. The vertical line corresponds to the expected nominal exclusion limit at 95% CL.

Distribution of exclusion upper limits on signal event yields at 95% CL from 1000 pseudo-experiments for Gaussian-shaped signals with relative width values of 5% at the high boundary of the limit-sensitive mass range for the ZX spectrum of the leading small-R jet category. The vertical line corresponds to the expected nominal exclusion limit at 95% CL.

Distribution of exclusion upper limits on signal event yields at 95% CL from 1000 pseudo-experiments for Gaussian-shaped signals with relative width values of 10% at the low boundary of the limit-sensitive mass range for the ZX spectrum of the leading small-R jet category. The vertical line corresponds to the expected nominal exclusion limit at 95% CL.

Distribution of exclusion upper limits on signal event yields at 95% CL from 1000 pseudo-experiments for Gaussian-shaped signals with relative width values of 10% at the high boundary of the limit-sensitive mass range for the ZX spectrum of the leading small-R jet category. The vertical line corresponds to the expected nominal exclusion limit at 95% CL.

Data yields of the six event categories in the $Z\to e^+e^-$ and $\mu^+\mu^-$ decay channels. The merged-$e^+e^-$ events are included in the $e^+e^-$ channel, increasing the event yield, mainly in the leading large-$R$-jet category, by 0.6 %.

A list of mass spectra, event categories and their corresponding fit ranges, functional forms, numbers of free parameters and global $\chi^2$ $p$-values from background-only fits. The fit range values are rounded to the nearest 5 GeV. Here $f_1(x)=p_0\left(\mathrm{e}^{-p_1x}+p_2\mathrm{e}^{-(p_1+p_3)x}+p_4\mathrm{e}^{-(p_1+p_3+p_5)x}+\cdots\right)$ and $f_2(x)=p_0(1-x)^{p_1}x^{p_2+p_3\ln\!x+p_4\ln^2\!x+\cdots}$

A list of mass spectra, event categories and their corresponding signal-sensitive mass ranges. The initial BH $p$-value is obtained by using the background derived from the background-only fit in the full fit range, whereas the new BH $p$-value uses the background derived from the background-only fit in the range excluding the initial BH interval.

A list of mass spectra, event categories, relative width values of Gaussian-shaped signals and limit-sensitive mass ranges and fractions, corresponding to the mass values in the previous column, of pseudo-experiments having exclusion upper limits higher than the nominal exclusion limit at 95% CL

Cutflow of HVT model $A$ signals ($W^\prime \to ZW \to \ell\ell qq$) with $m_{W^\prime} = 1$ TeV and $m_{W^\prime} = 4$ TeV based on MC simulations.

Acceptance times efficiency ($\mathcal{A} \times \epsilon$) values in % in the dominant event category for $p^Z_{\mathrm{T}} > 100$ GeV in the $Z \to \ell^{+}\ell^{-}$ decay channel.

Ratio of $p_{\mathrm{T,ch\ jet}}$-differential cross section of charm jets tagged with $\mathrm{D^{0}}$ mesons for different $R$: $\sigma(R=0.2)/\sigma(R=0.4)$ and $\sigma(R=0.2)/\sigma(R=0.6)$ in pp collisions at $\sqrt{s}=13$ TeV.

Ratio of $p_{\mathrm{T,ch\ jet}}$-differential cross section of charm jets tagged with $\mathrm{D^{0}}$ mesons for different $R$: $\sigma(R=0.2)/\sigma(R=0.4)$ and $\sigma(R=0.2)/\sigma(R=0.6)$ in pp collisions at $\sqrt{s}=5.02$ TeV.

The fraction of $\mathrm{D^{0}}$ jets over inclusive charged-particle jets in pp collisions at $\sqrt{s}=5.02$ TeV for $R=0.2$, $0.4$, and $0.6$.

Distributions of $z^{\mathrm{ch}}_{||}$-differential yield of charm jets tagged with $\mathrm{D^{0}}$ mesons normalised by the number of $\mathrm{D^{0}}$ jets within each distribution in pp collisions at $\sqrt{s}=13$ TeV in four jet-$p_{\mathrm{T}}$ intervals $5<p_{\mathrm{T,ch\ jet}}<7$ GeV/$c$, $7<p_{\mathrm{T,ch\ jet}}<10$ GeV/$c$, $10<p_{\mathrm{T,ch\ jet}}<15$ GeV/$c$, and $15<p_{\mathrm{T,ch\ jet}}<50$ GeV/$c$ for jet radii $R=0.2$, $0.4$, and $0.6$.

Distributions of $z^{\mathrm{ch}}_{||}$-differential yield of charm jets tagged with $\mathrm{D^{0}}$ mesons normalised by the number of $\mathrm{D^{0}}$ jets within each distribution in pp collisions at $\sqrt{s}=5.02$ TeV in four jet-$p_{\mathrm{T}}$ intervals $5<p_{\mathrm{T,ch\ jet}}<7$ GeV/$c$, $7<p_{\mathrm{T,ch\ jet}}<10$ GeV/$c$, $10<p_{\mathrm{T,ch\ jet}}<15$ GeV/$c$, and $15<p_{\mathrm{T,ch\ jet}}<50$ GeV/$c$ for jet radii $R=0.2$, $0.4$, and $0.6$.

$p_{\mathrm{T,ch\ jet}}$-differential cross section of charm jets tagged with $\mathrm{D^{0}}$ mesons for $R=0.3$ in pp collisions at $\sqrt{s}=5.02$ TeV.

The fraction of $\mathrm{D^{0}}$ jets over inclusive charged-particle jets in pp collisions at $\sqrt{s}=5.02$ TeV for $R=0.3$.

Distributions of $z^{\mathrm{ch}}_{||}$-differential yield of charm jets tagged with $\mathrm{D^{0}}$ mesons normalised by the number of $\mathrm{D^{0}}$ jets within each distribution in pp collisions at $\sqrt{s}=5.02$ TeV in four jet-$p_{\mathrm{T}}$ intervals $5<p_{\mathrm{T,ch\ jet}}<7$ GeV/$c$, $7<p_{\mathrm{T,ch\ jet}}<10$ GeV/$c$, $10<p_{\mathrm{T,ch\ jet}}<15$ GeV/$c$, and $15<p_{\mathrm{T,ch\ jet}}<50$ GeV/$c$ for jet radius $R=0.3$.

Observed and expected 95% CL upper limits on the product of the production cross section ($\sigma$) and the branching fraction, obtained after combining all categories with 138 $\mathrm{fb}^{−1}$ of data at $\sqrt{s}$ = 13 TeV for $\mathrm{V'}$ to $VV$ + $VH$ signal in HVT model C.

Total signal efficiency including all event categories as a function of the resonance mass $M_X$ for all DY/ggF signal models under consideration. The estimates from MC simulation (markers) are interpolated with a functional form (lines).

Total signal efficiency including all event categories as a function of the resonance mass $M_X$ for all VBF signal models under consideration. The estimates from MC simulation (markers) are interpolated with a functional form (lines).

J/$\psi$ coherent photoproduction cross section as a function of $\langle N_{\rm part}\rangle$ at forward rapidity in Pb–Pb collisions at $\sqrt{s_{\rm NN}}$ = 5.02 TeV. The centrality correlated uncertainty of 6.5% is not included. The uncertainty on the most central value corresponds to a 95% confidence interval.

J/$\psi$ coherent photoproduction cross section ratio for two different energies ($\sqrt{s_{\rm NN}}$ = 5.02 TeV over $\sqrt{s_{\rm NN}}$ = 2.76 TeV) as a function of centrality.