Measurement of $t$-channel production of single top quarks and antiquarks in $pp$ collisions at 13 TeV using the full ATLAS Run 2 data sample

The ATLAS collaboration Aad, Georges ; Abbott, Braden Keim ; Abeling, Kira ; et al.
CERN-EP-2023-289, 2024.
Inspire Record 2764820 DOI 10.17182/hepdata.150693

The production of single top quarks and top antiquarks via the $t$-channel exchange of a virtual $W$ boson is measured in proton-proton collisions at a centre-of-mass energy of 13 TeV at the LHC using $140\,\mathrm{fb^{-1}}$ of ATLAS data. The total cross-sections are determined to be $\sigma(tq)=137^{+8}_{-8}\,\mathrm{pb}$ and $\sigma(\bar{t}q)=84^{+6}_{-5}\,\mathrm{pb}$ for top-quark and top-antiquark production, respectively. The combined cross-section is found to be $\sigma(tq+\bar{t}q)=221^{+13}_{-13}\,\mathrm{pb}$ and the cross-section ratio is $R_{t}=\sigma(tq)/\sigma(\bar{t}q)=1.636^{+0.036}_{-0.034}$. The predictions at next-to-next-to-leading-order in quantum chromodynamics are in good agreement with these measurements. The predicted value of $R_{t}$ using different sets of parton distribution functions is compared with the measured value, demonstrating the potential to further constrain the functions when using this result in global fits. The measured cross-sections are interpreted in an effective field theory approach, setting limits at the 95% confidence level on the strength of a four-quark operator and an operator coupling the third quark generation to the Higgs boson doublet: $-0.37 < C_{Qq}^{3,1}/\Lambda^2 < 0.06$ and $-0.87 < C_{\phi Q}^{3}/\Lambda^2 < 1.42$. The constraint $|V_{tb}|>0.95$ at the 95% confidence level is derived from the measured value of $\sigma(tq+\bar{t}q)$. In a more general approach, pairs of CKM matrix elements involving top quarks are simultaneously constrained, leading to confidence contours in the corresponding two-dimensional parameter spaces.

21 data tables

The 17 variables used for the training of the NN ordered by their discriminating power. The jet that is not \(b\)-tagged is referred to as the untagged jet. The charged lepton is denoted \(\ell\). The sphericity tensor \(S^{\alpha\beta}\) used to define the sphericity \(S\) is formed with the three-momenta \(\vec{p}_i\) of the reconstructed objects, namely the jets, the charged lepton and the reconstructed neutrino. The tensor is given by \(S^{\alpha\beta}=\frac{\sum_i p_i^\alpha p_i^\beta}{\sum_i |\vec{p}_i|^2}\) where \(\alpha\) and \(\beta\) correspond to the spatial components $x$, $y$ and $z$.

The impact of different groups of systematic uncertainties on the \(\sigma(tq)\) , \(\sigma(\bar t q)\), \(\sigma(tq + \bar t q)\) and \(R_t\), given in %.

The impact of the eight most important systematic uncertainties on the \(\sigma(tq)\) , \(\sigma(\bar t q)\) and \(\sigma(tq + \bar t q)\), given in %. The sequence of the uncertainties is given by the impact on \(\sigma(tq + \bar t q)\)

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Version 2
Comprehensive measurements of $t$-channel single top-quark production cross sections at $\sqrt{s} = 7$ TeV with the ATLAS detector

The ATLAS collaboration Aad, Georges ; Abbott, Brad ; Abdallah, Jalal ; et al.
Phys.Rev.D 90 (2014) 112006, 2014.
Inspire Record 1303905 DOI 10.17182/hepdata.64385

This article presents measurements of the $t$-channel single top-quark ($t$) and top-antiquark ($\bar{t}$) total production cross sections $\sigma(tq)$ and $\sigma(\bar{t}q)$, their ratio $R_{t}=\sigma(tq)/\sigma(\bar{t}q)$, and a measurement of the inclusive production cross section $\sigma(tq + \bar{t}q)$ in proton--proton collisions at $\sqrt{s} = 7$ TeV at the LHC. Differential cross sections for the $tq$ and $\bar{t}q$ processes are measured as a function of the transverse momentum and the absolute value of the rapidity of $t$ and $\bar{t}$, respectively. The analyzed data set was recorded with the ATLAS detector and corresponds to an integrated luminosity of 4.59 fb$^{-1}$. Selected events contain one charged lepton, large missing transverse momentum, and two or three jets. The cross sections are measured by performing a binned maximum-likelihood fit to the output distributions of neural networks. The resulting measurements are $\sigma(tq)= 46\pm 6\; \mathrm{pb}$, $\sigma(\bar{t}q)= 23 \pm 4\; \mathrm{pb}$, $R_{t}=2.04\pm 0.18$, and $\sigma(tq + \bar{t}q)= 68 \pm 8\; \mathrm{pb}$, consistent with the Standard Model expectation. The uncertainty on the measured cross sections is dominated by systematic uncertainties, while the uncertainty on $R_{t}$ is mainly statistical. Using the ratio of $\sigma(tq + \bar{t}q)$ to its theoretical prediction, and assuming that the top-quark-related CKM matrix elements obey the relation $|V_{tb}|\gg |V_{ts}|, |V_{td}|$, we determine $|V_{tb}|=1.02 \pm 0.07$.

40 data tables

Differential t-channel top-quark production cross sections and normalized differential t-channel top-quark production cross sections as functions of PT(TOP).

Predicted and observed events yields for the 2-jet and 3-jet channels considered in this measurement. The multijet background is estimated using data-driven techniques (see Sec. VB); an uncertainty of $50\%$ is applied. All the other expectations are derived using theoretical cross sections and their uncertainties (see Secs. VA and VC in the paper).

Differential t-channel top-quark production cross sections and normalized differential t-channel top-quark production cross sections as functions of PT(TOPBAR).

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Measurement of associated Z + charm production in proton-proton collisions at $\sqrt{s} = $ 8 TeV

The CMS collaboration Sirunyan, A.M. ; Tumasyan, Armen ; Adam, Wolfgang ; et al.
Eur.Phys.J.C 78 (2018) 287, 2018.
Inspire Record 1634835 DOI 10.17182/hepdata.85868

A study of the associated production of a Z boson and a charm quark jet (Z + c), and a comparison to production with a b quark jet (Z + b), in pp collisions at a centre-of-mass energy of 8 TeV are presented. The analysis uses a data sample corresponding to an integrated luminosity of 19.7 fb$^{-1}$, collected with the CMS detector at the CERN LHC. The Z boson candidates are identified through their decays into pairs of electrons or muons. Jets originating from heavy flavour quarks are identified using semileptonic decays of c or b flavoured hadrons and hadronic decays of charm hadrons. The measurements are performed in the kinematic region with two leptons with $p_{\rm T}^{\ell} > $ 20 GeV, ${|\eta^{\ell}|} < $ 2.1, 71 $ < m_{\ell\ell} < $ 111 GeV, and heavy flavour jets with $p_{\rm T}^{{\rm jet}} > $ 25 GeV and ${|\eta^{{\rm jet}}|} < $ 2.5. The Z + c production cross section is measured to be $\sigma({\mathrm{p}}{\mathrm{p}} \rightarrow \mathrm{Z} + \mathrm{c} + \mathrm{X}) {\cal B}(\mathrm{Z} \rightarrow \ell^+\ell^-) = $ 8.8 $ \pm $ 0.5 (stat) $ \pm $ 0.6 (syst) pb. The ratio of the Z + c and Z + b production cross sections is measured to be $\sigma({\mathrm{p}}{\mathrm{p}} \rightarrow \mathrm{Z} + \mathrm{c} + \mathrm{X}) / \sigma({\mathrm{p}}{\mathrm{p}} \rightarrow \mathrm{Z} + \mathrm{b} + \mathrm{X}) = $ 2.0 $ \pm $ 0.2 (stat) $ \pm $ 0.2 (syst). The Z + c production cross section and the cross section ratio are also measured as a function of the transverse momentum of the Z boson and of the heavy flavour jet. The measurements are compared with theoretical predictions.

28 data tables

Signal yields N(Z+c) and N(Z+b), efficiency*acceptance correction factors C(Z+c) and C(Z+b), cross section sigma(Z+c)B and cross section ratios sigma(Z+c)/sigma(Z+b) in the three categories (semileptonic, D+-, D*) and in the two Z boson decay channels (e+e-, mu+mu-). The factors that correct the acceptance and selection inefficiencies are also given. They include the relevant branching fraction for the corresponding channel. All uncertainties quoted in the table are statistical, except for those of the measured cross sections and cross section ratios where the first uncertainty is statistical and the second is the estimated systematic uncertainty

Z+c and Z+b signal yields, differential cross section dsigma(Z+c)/dpTZ times branching ratio and differential cross sections ratio dsigma(Z+c)/dpTZ / dsigma(Z+b)/dpTZ for three ranges of the transverse momentum of the Z boson in the semileptonic mode

Z+c and Z+b signal yields, differential cross section dsigma(Z+c)/dpTZ times branching ratio and differential cross sections ratio dsigma(Z+c)/dpTZ / dsigma(Z+b)/dpTZ for three ranges of the transverse momentum of the jet in the semileptonic mode

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Combination of searches for Higgs boson pair production in proton-proton collisions at $\sqrt{s} =$ 13 TeV

The CMS collaboration Sirunyan, Albert M ; Tumasyan, Armen ; Adam, Wolfgang ; et al.
Phys.Rev.Lett. 122 (2019) 121803, 2019.
Inspire Record 1704939 DOI 10.17182/hepdata.89935

This Letter describes a search for Higgs boson pair production using the combined results from four final states: bb$\gamma\gamma$, bb$\tau\tau$, bbbb, and bbVV, where V represents a W or Z boson. The search is performed using data collected in 2016 by the CMS experiment from LHC proton-proton collisions at $\sqrt{s} =$ 13 TeV, corresponding to an integrated luminosity of 35.9 fb$^{-1}$. Limits are set on the Higgs boson pair production cross section. A 95% confidence level observed (expected) upper limit on the nonresonant production cross section is set at 22.2 (12.8) times the standard model value. A search for narrow resonances decaying to Higgs boson pairs is also performed in the mass range 250-3000 GeV. No evidence for a signal is observed, and upper limits are set on the resonance production cross section.

10 data tables

Expected and observed 95\% \CL exclusion limits on the HH production signal strength for the different channels and their combination.

Expected and observed 95\% \CL exclusion limits on the HH production cross section as a function of the k_lambda parameter.

Expected and observed 95\% \CL exclusion limits on the production of a narrow, spin zero resonance (X) decaying into a pair of Higgs bosons.

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Constraints on anomalous $HVV$ couplings from the production of Higgs bosons decaying to $\tau$ lepton pairs

The CMS collaboration Sirunyan, Albert M ; Tumasyan, Armen ; Adam, Wolfgang ; et al.
Phys.Rev.D 100 (2019) 112002, 2019.
Inspire Record 1725474 DOI 10.17182/hepdata.87255

A study is presented of anomalous HVV interactions of the Higgs boson, including its $CP$ properties. The study uses Higgs boson candidates produced mainly in vector boson fusion and gluon fusion that subsequently decay to a pair of $\tau$ leptons. The data were recorded by the CMS experiment at the LHC in 2016 at a center-of-mass energy of 13 TeV and correspond to an integrated luminosity of 35.9 fb$^{-1}$. A matrix element technique is employed for the analysis of anomalous interactions. The results are combined with those from the H $\to 4\ell$ decay channel presented earlier, yielding the most stringent constraints on anomalous Higgs boson couplings to electroweak vector bosons expressed as effective cross section fractions and phases: the $CP$-violating parameter $f_{a3}\cos(\phi_{a3})$ $=$ $(0.00 \pm 0.27) \times 10^{-3}$ and the $CP$-conserving parameters $f_{a2}\cos(\phi_{a2})$ $=$ $(0.08 ^{+1.04}_{-0.21}) \times 10^{-3}$, $f_{\Lambda1}\cos(\phi_{\Lambda1})$ $=$ $(0.00 ^{+0.53}_{-0.09}) \times 10^{-3}$, and $f_{\Lambda1}^{\mathrm{Z}\gamma}\cos(\phi_{\Lambda1}^{\mathrm{Z}\gamma})$ $=$ $(0.0 ^{+1.1}_{-1.3}) \times 10^{-3}$. The current dataset does not allow for precise constraints on $CP$ properties in the gluon fusion process. The results are consistent with standard model expectations.

4 data tables

Observed and expected likelihood scans of $f_{a3}\cos\phi_{a3}$. See Section 4 of the paper for more details.

Observed and expected likelihood scans of $f_{a2}\cos\phi_{a2}$. See Section 4 of the paper for more details.

Observed and expected likelihood scans of $f_{\Lambda1}\cos\phi_{\Lambda1}$. See Section 4 of the paper for more details.

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Measurements of the Higgs boson production and decay rates and constraints on its couplings from a combined ATLAS and CMS analysis of the LHC $pp$ collision data at $\sqrt{s}=$ 7 and 8 TeV

The ATLAS & CMS collaborations Aad, Georges ; Abbott, Brad ; Abdallah, Jalal ; et al.
JHEP 08 (2016) 045, 2016.
Inspire Record 1468068 DOI 10.17182/hepdata.78403

Combined ATLAS and CMS measurements of the Higgs boson production and decay rates, as well as constraints on its couplings to vector bosons and fermions, are presented. The combination is based on the analysis of five production processes, namely gluon fusion, vector boson fusion, and associated production with a $W$ or a $Z$ boson or a pair of top quarks, and of the six decay modes $H \to ZZ, WW$, $\gamma\gamma, \tau\tau, bb$, and $\mu\mu$. All results are reported assuming a value of 125.09 GeV for the Higgs boson mass, the result of the combined measurement by the ATLAS and CMS experiments. The analysis uses the CERN LHC proton--proton collision data recorded by the ATLAS and CMS experiments in 2011 and 2012, corresponding to integrated luminosities per experiment of approximately 5 fb$^{-1}$ at $\sqrt{s}=7$ TeV and 20 fb$^{-1}$ at $\sqrt{s} = 8$ TeV. The Higgs boson production and decay rates measured by the two experiments are combined within the context of three generic parameterisations: two based on cross sections and branching fractions, and one on ratios of coupling modifiers. Several interpretations of the measurements with more model-dependent parameterisations are also given. The combined signal yield relative to the Standard Model prediction is measured to be 1.09 $\pm$ 0.11. The combined measurements lead to observed significances for the vector boson fusion production process and for the $H \to \tau\tau$ decay of $5.4$ and $5.5$ standard deviations, respectively. The data are consistent with the Standard Model predictions for all parameterisations considered.

44 data tables

Best fit values of $\sigma_i \cdot \mathrm{B}^f$ for each specific channel $i \to H\to f$, as obtained from the generic parameterisation with 23 parameters for the combination of the ATLAS and CMS measurements, using the $\sqrt{s}$=7 and 8 TeV data. The cross sections are given for $\sqrt{s}$=8 TeV, assuming the SM values for $\sigma_i(7 \mathrm{TeV})/\sigma_i(8 \mathrm{TeV})$. The results are shown together with their total uncertainties and their breakdown into statistical and systematic components. The missing values are either not measured with a meaningful precision and therefore not quoted, in the case of the $H\to ZZ$ decay channel for the $WH$, $ZH$, and $ttH$ production processes, or not measured at all and therefore fixed to their corresponding SM predictions, in the case of the $H\to bb$ decay mode for the $gg\mathrm{F}$ and VBF production processes.

Best fit values of $\sigma_i \cdot \mathrm{B}^f$ relative to their SM prediction for each specific channel $i \to H\to f$, as obtained from the generic parameterisation with 23 parameters for the combination of the ATLAS and CMS measurements, using the $\sqrt{s}$=7 and 8 TeV data. The results are shown together with their total uncertainties and their breakdown into statistical and systematic components. The missing values are either not measured with a meaningful precision and therefore not quoted, in the case of the $H\to ZZ$ decay channel for the $WH$, $ZH$, and $ttH$ production processes, or not measured at all and therefore fixed to their corresponding SM predictions, in the case of the $H\to bb$ decay mode for the $gg\mathrm{F}$ and VBF production processes.

Best fit values of $\sigma(gg\to H\to ZZ)$, $\sigma_i/\sigma_{gg\mathrm{F}}$, and $\mathrm{B}^f/\mathrm{B}^{ZZ}$ from the combined analysis of the $\sqrt{s}$=7 and 8 TeV data. The values involving cross sections are given for $\sqrt{s}$=8 TeV, assuming the SM values for $\sigma_i(7 \mathrm{TeV})/\sigma_i(8 \mathrm{TeV})$. The results are shown for the combination of ATLAS and CMS, and also separately for each experiment, together with their total uncertainties and their breakdown into the four components described in the text. The expected uncertainties in the measurements are also shown.

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Constraints on anomalous Higgs boson couplings using production and decay information in the four-lepton final state

The CMS collaboration Sirunyan, Albert M ; Tumasyan, Armen ; Adam, Wolfgang ; et al.
Phys.Lett.B 775 (2017) 1-24, 2017.
Inspire Record 1608386 DOI 10.17182/hepdata.80811

A search is performed for anomalous interactions of the recently discovered Higgs boson using matrix element techniques with the information from its decay to four leptons and from associated Higgs boson production with two quark jets in either vector boson fusion or associated production with a vector boson. The data were recorded by the CMS experiment at the LHC at a center-of-mass energy of 13 TeV and correspond to an integrated luminosity of 38.6 inverse femtobarns. These data are combined with the data collected at center-of-mass energies of 7 and 8 TeV, corresponding to integrated luminosities of 5.1 and 19.7 inverse femtobarns, respectively. All observations are consistent with the expectations for the standard model Higgs boson.

4 data tables

Observed and expected likelihood scans $f_{a3}\cos\phi_{a3}$. See Section 2 of the paper for more details.

Observed and expected likelihood scans $f_{a2}\cos\phi_{a2}$. See Section 2 of the paper for more details.

Observed and expected likelihood scans $f_{\Lambda1}\cos\phi_{\Lambda1}$. See Section 2 of the paper for more details.

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Measurement of the ZZ production cross section and Z to l+l-l'+l'- branching fraction in pp collisions at sqrt(s) = 13 TeV

The CMS collaboration Khachatryan, Vardan ; Sirunyan, Albert M ; Tumasyan, Armen ; et al.
Phys.Lett.B 763 (2016) 280-303, 2016.
Inspire Record 1478600 DOI 10.17182/hepdata.75368

Four-lepton production in proton-proton collisions, pp to (Z/gamma*)(Z/gamma*) to l+l-l'+l'-, where l, l' = e or mu, is studied at a center-of-mass energy of 13 TeV with the CMS detector at the LHC. The data sample corresponds to an integrated luminosity of 2.6 inverse femtobarns. The ZZ production cross section, sigma(pp to ZZ) = 14.6 +1.9/-1.8 (stat) +0.5/-0.3 (syst) +/- 0.2 (theo) +/- 0.4 (lumi) pb, is measured for events with two opposite-sign, same-flavor lepton pairs produced in the mass region 60 < m[l+l-], m[l'+l'-] < 120 GeV. The Z boson branching fraction to four leptons is measured to be B(Z to l+l-l'+l'-) = 4.9 +0.8/-0.7 (stat) +0.3/-0.2 (syst) +0.2/-0.1 (theo) +/- 0.1 (lumi) x E-6 for the four-lepton invariant mass in the range 80 < m[l+l-l'+l'-] < 100 GeV and dilepton mass m[l+l-] > 4 GeV for all opposite-sign, same-flavor lepton pairs. The results are in agreement with standard model predictions.

5 data tables

The (P P to Z Z to l+l-l'+l'-) fiducial cross section. The first systematic uncertainty is detector systematics, the second is luminosity uncertainty. The theoretical prediction is POWHEG generated at NLO plus the gluon-gluon initial state contribution from MCFM, using NNPDF3.0 PDFs and scales mu_F = mu_R = 0.5m[l+l-l'+l'-].

The (P P to Z to l+l-l'+l'-) fiducial cross section. The first systematic uncertainty is detector systematics, the second is luminosity uncertainty. The theoretical prediction is POWHEG generated at NLO using NNPDF3.0 PDFs and scales mu_F = mu_R = m[l+l-l'+l'-].

The total (P P to Z) cross section times the (Z to l+l-l'+l'-) branching ratio. The first systematic uncertainty is detector systematics, the second is theoretical uncertainty, and the third is luminosity uncertainty.

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Search for a Higgs boson decaying into gamma* gamma to ll gamma with low dilepton mass in pp collisions at sqrt(s) = 8 TeV

The CMS collaboration Khachatryan, Vardan ; Sirunyan, Albert M ; Tumasyan, Armen ; et al.
Phys.Lett.B 753 (2016) 341-362, 2016.
Inspire Record 1382587 DOI 10.17182/hepdata.73712

A search is described for a Higgs boson decaying into two photons, one of which has an internal conversion to a muon or an electron pair (ll gamma). The analysis is performed using proton-proton collision data recorded with the CMS detector at the LHC at a centre-of-mass energy of 8 TeV, corresponding to an integrated luminosity of 19.7 inverse femtobarns. The events selected have an opposite-sign muon or electron pair and a high transverse momentum photon. No excess above background has been found in the three-body invariant mass range 120 < m[ll gamma] < 150 GeV, and limits have been derived for the Higgs boson production cross section times branching fraction for the decay H to gamma* gamma to ll gamma, where the dilepton invariant mass is less than 20 GeV. For a Higgs boson with m[H] = 125 GeV, a 95% confidence level (CL) exclusion observed (expected) limit is 6.7 (5.9 +2.8/-1.8) times the standard model prediction. Additionally, an upper limit at 95% CL on the branching fraction of H to J/Psi gamma for the 125 GeV Higgs boson is set at 1.5E-3.

4 data tables

The 95% CL exclusion limit, as a function of the mass hypothesis, $m_H$ , on $\sigma/\sigma_{SM}$, the cross section times the branching fraction of a Higgs boson decaying into a photon and a lepton pair with $m_{\ell\ell}$ < 20 GeV, divided by the SM value.

The 95% CL exclusion limit, as a function of the mass hypothesis, $m_H$ , on $\sigma/\sigma_{SM}$, the cross section times the branching fraction of a Higgs boson decaying into a photon and a lepton pair with $m_{\ell\ell}$ < 20 GeV, divided by the SM value.

The 95% CL exclusion limit, as a function of the mass hypothesis, $m_H$ , on $\sigma/\sigma_{SM}$, the cross section times the branching fraction of a Higgs boson decaying into a photon and a lepton pair with $m_{\ell\ell}$ < 20 GeV, divided by the SM value.

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Observation and measurements of the production of prompt and non-prompt $J/\psi$ mesons in association with a $Z$ boson in $pp$ collisions at $\sqrt{s}= 8$ TeV with the ATLAS detector

The ATLAS collaboration Aad, Georges ; Abbott, Brad ; Abdallah, Jalal ; et al.
Eur.Phys.J.C 75 (2015) 229, 2015.
Inspire Record 1335136 DOI 10.17182/hepdata.73284

The production of a $Z$ boson in association with a $J/\psi$ meson in proton-proton collisions probes the production mechanisms of quarkonium and heavy flavour in association with vector bosons, and allows studies of multiple parton scattering. Using $20.3\, \mathrm{fb^{-1}}$ of data collected with the ATLAS experiment at the LHC in $pp$ collisions at $\sqrt{s}=8\, \mathrm{TeV}$, the first measurement of associated $Z + J/\psi$ production is presented for both prompt and non-prompt $J/\psi$ production, with both signatures having a significance in excess of $5\sigma$. The inclusive production cross-sections for $Z$ boson production (analysed in $\mu^+\mu^-$ or $e^+e^-$ decay modes) in association with prompt and non-prompt $J/\psi(\to\mu^+\mu^-)$ are measured relative to the inclusive production rate of $Z$ bosons in the same fiducial volume to be $(36.8\pm 6.7\pm 2.5) \times 10^{-7}$ and $(65.8\pm 9.2\pm 4.2) \times 10^{-7}$ respectively. Normalised differential production cross-section ratios are also determined as a function of the $J/\psi$ transverse momentum. The fraction of signal events arising from single and double parton scattering is estimated, and a lower limit of $5.3\ (3.7)\, \mathrm{mb}$ at $68\ (95)$% confidence level is placed on the effective cross-section regulating double parton interactions.

6 data tables

The fiducial, inclusive (SPS+DPS) and DPS-subtracted differential cross-section ratio $R_{Z+J/\psi}$ for prompt $J/\psi$.

The fiducial, inclusive (SPS+DPS) and DPS-subtracted differential cross-section ratio $R_{Z+J/\psi}$ for non-prompt $J/\psi$.

The fiducial, inclusive (SPS+DPS) and DPS-subtracted differential cross-section ratio $\mathrm{d}R_{Z+J/\psi}/\mathrm{d}y$ as a function of $y_{J/\psi}$ for prompt $J/\psi$.

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