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CMS-FSQ-12-028 ; CERN-PH-EP-2013-224
Study of double parton scattering using W + 2-jet events in proton-proton collisions at $\sqrt{s} = $ 7 TeV
J. High Energy Phys. 03 (2014) 032
Abstract: Double parton scattering is investigated in proton-proton collisions at $\sqrt{s} = $ 7 TeV where the final state includes a W boson, which decays into a muon and a neutrino, and two jets. The data sample corresponds to an integrated luminosity of 5 fb$^{-1}$, collected with the CMS detector at the LHC. Observables sensitive to double parton scattering are investigated after being corrected for detector effects and selection efficiencies. The fraction of W + 2-jet events due to double parton scattering is measured to be 0.055 $\pm$ 0.002 (stat) $\pm$ 0.014 (syst). The effective cross section, $\sigma_\text{eff}$, characterizing the effective transverse area of hard partonic interactions in collisions between protons is measured to be 20.7 $\pm$ 0.8 (stat) $\pm$ 6.6 (syst) mb.
Figures & Tables Summary References CMS Publications
Figures

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Figure 1:
Feynman diagrams for W + 2-jet production from (left) double parton scattering and (right) single parton scattering.

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Figure 1-a:
Feynman diagrams for W + 2-jet production from (left) double parton scattering and (right) single parton scattering.

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Figure 1-b:
Feynman diagrams for W + 2-jet production from (left) double parton scattering and (right) single parton scattering.

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Figure 2:
Detector-level comparison of data with MC simulations for the multiplicity (top left) of jets (N$_{ {\mathrm {j}} }$) with ${ {p_{\mathrm {T}}} } > $ 20 GeV/$c$ and $ {| \eta | } < $ 2.0. Data and simulations for the sample with exactly two jets are plotted as a function of the $ {p_{\mathrm {T}}} $ of the leading (top right) and subleading (lower left) jets, as well as of the magnitude of the vector sum of the muon $ {p_{\mathrm {T}}} $ and ${E_{\mathrm {T}}}$ (lower right). The background distribution represents the sum of the contributions of Drell-Yan, $\mathrm{ W } \rightarrow \tau \nu $, diboson, multijet, $\mathrm{ t \bar{t} } $, and single-top-quark processes. The bottom panels show the ratio of the data and simulated distributions. The band shows the total uncertainty, with the contributions of the jet energy scale uncertainty and the statistical uncertainties of the MC samples added in quadrature. The error bars on the ratio histogram represent the statistical uncertainty of the data and the simulated samples added in quadrature.

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Figure 2-a:
Detector-level comparison of data with MC simulations for the multiplicity (top left) of jets (N$_{ {\mathrm {j}} }$) with ${ {p_{\mathrm {T}}} } > $ 20 GeV/$c$ and $ {| \eta | } < $ 2.0. Data and simulations for the sample with exactly two jets are plotted as a function of the $ {p_{\mathrm {T}}} $ of the leading (top right) and subleading (lower left) jets, as well as of the magnitude of the vector sum of the muon $ {p_{\mathrm {T}}} $ and ${E_{\mathrm {T}}}$ (lower right). The background distribution represents the sum of the contributions of Drell-Yan, $\mathrm{ W } \rightarrow \tau \nu $, diboson, multijet, $\mathrm{ t \bar{t} } $, and single-top-quark processes. The bottom panels show the ratio of the data and simulated distributions. The band shows the total uncertainty, with the contributions of the jet energy scale uncertainty and the statistical uncertainties of the MC samples added in quadrature. The error bars on the ratio histogram represent the statistical uncertainty of the data and the simulated samples added in quadrature.

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Figure 2-b:
Detector-level comparison of data with MC simulations for the multiplicity (top left) of jets (N$_{ {\mathrm {j}} }$) with ${ {p_{\mathrm {T}}} } > $ 20 GeV/$c$ and $ {| \eta | } < $ 2.0. Data and simulations for the sample with exactly two jets are plotted as a function of the $ {p_{\mathrm {T}}} $ of the leading (top right) and subleading (lower left) jets, as well as of the magnitude of the vector sum of the muon $ {p_{\mathrm {T}}} $ and ${E_{\mathrm {T}}}$ (lower right). The background distribution represents the sum of the contributions of Drell-Yan, $\mathrm{ W } \rightarrow \tau \nu $, diboson, multijet, $\mathrm{ t \bar{t} } $, and single-top-quark processes. The bottom panels show the ratio of the data and simulated distributions. The band shows the total uncertainty, with the contributions of the jet energy scale uncertainty and the statistical uncertainties of the MC samples added in quadrature. The error bars on the ratio histogram represent the statistical uncertainty of the data and the simulated samples added in quadrature.

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Figure 2-c:
Detector-level comparison of data with MC simulations for the multiplicity (top left) of jets (N$_{ {\mathrm {j}} }$) with ${ {p_{\mathrm {T}}} } > $ 20 GeV/$c$ and $ {| \eta | } < $ 2.0. Data and simulations for the sample with exactly two jets are plotted as a function of the $ {p_{\mathrm {T}}} $ of the leading (top right) and subleading (lower left) jets, as well as of the magnitude of the vector sum of the muon $ {p_{\mathrm {T}}} $ and ${E_{\mathrm {T}}}$ (lower right). The background distribution represents the sum of the contributions of Drell-Yan, $\mathrm{ W } \rightarrow \tau \nu $, diboson, multijet, $\mathrm{ t \bar{t} } $, and single-top-quark processes. The bottom panels show the ratio of the data and simulated distributions. The band shows the total uncertainty, with the contributions of the jet energy scale uncertainty and the statistical uncertainties of the MC samples added in quadrature. The error bars on the ratio histogram represent the statistical uncertainty of the data and the simulated samples added in quadrature.

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Figure 2-d:
Detector-level comparison of data with MC simulations for the multiplicity (top left) of jets (N$_{ {\mathrm {j}} }$) with ${ {p_{\mathrm {T}}} } > $ 20 GeV/$c$ and $ {| \eta | } < $ 2.0. Data and simulations for the sample with exactly two jets are plotted as a function of the $ {p_{\mathrm {T}}} $ of the leading (top right) and subleading (lower left) jets, as well as of the magnitude of the vector sum of the muon $ {p_{\mathrm {T}}} $ and ${E_{\mathrm {T}}}$ (lower right). The background distribution represents the sum of the contributions of Drell-Yan, $\mathrm{ W } \rightarrow \tau \nu $, diboson, multijet, $\mathrm{ t \bar{t} } $, and single-top-quark processes. The bottom panels show the ratio of the data and simulated distributions. The band shows the total uncertainty, with the contributions of the jet energy scale uncertainty and the statistical uncertainties of the MC samples added in quadrature. The error bars on the ratio histogram represent the statistical uncertainty of the data and the simulated samples added in quadrature.

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Figure 3:
Comparison of data with MC simulations at detector level for the DPS-sensitive observables $\Delta ^\text {rel} {p_{\mathrm {T}}} $ (left), and $ {\Delta \mathrm {S}} $ (right). The background distribution represents the sum of the contributions of Drell-Yan, W $\rightarrow \tau \nu $, diboson, multijet, $\mathrm{ t \bar{t} } $, and single-top-quark processes. The bottom panels show the ratio of the data and simulated distributions. The band shows the total uncertainty, with the contributions of the jet energy scale uncertainty and the statistical uncertainties of the MC samples added in quadrature. The error bars on the ratio histogram represent the statistical uncertainty of the data and the simulated samples added in quadrature.

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Figure 3-a:
Comparison of data with MC simulations at detector level for the DPS-sensitive observables $\Delta ^\text {rel} {p_{\mathrm {T}}} $ (left), and $ {\Delta \mathrm {S}} $ (right). The background distribution represents the sum of the contributions of Drell-Yan, W $\rightarrow \tau \nu $, diboson, multijet, $\mathrm{ t \bar{t} } $, and single-top-quark processes. The bottom panels show the ratio of the data and simulated distributions. The band shows the total uncertainty, with the contributions of the jet energy scale uncertainty and the statistical uncertainties of the MC samples added in quadrature. The error bars on the ratio histogram represent the statistical uncertainty of the data and the simulated samples added in quadrature.

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Figure 3-b:
Comparison of data with MC simulations at detector level for the DPS-sensitive observables $\Delta ^\text {rel} {p_{\mathrm {T}}} $ (left), and $ {\Delta \mathrm {S}} $ (right). The background distribution represents the sum of the contributions of Drell-Yan, W $\rightarrow \tau \nu $, diboson, multijet, $\mathrm{ t \bar{t} } $, and single-top-quark processes. The bottom panels show the ratio of the data and simulated distributions. The band shows the total uncertainty, with the contributions of the jet energy scale uncertainty and the statistical uncertainties of the MC samples added in quadrature. The error bars on the ratio histogram represent the statistical uncertainty of the data and the simulated samples added in quadrature.

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Figure 4:
Fully corrected data distributions, normalized to unity, for the DPS-sensitive observables $\Delta ^\text {rel} {p_{\mathrm {T}}} $ (left) and $ {\Delta \mathrm {S}} $ (right). The second panel in both plots shows the ratio of data over MadGraph 5 + PYTHIA 8 with and without MPI, whereas in the third panel the ratio with POWHEG 2 + PYTHIA 6 is shown. The ratio of the data and PYTHIA 8 is shown in the fourth panel of both plots. The band represents the total uncertainty of the data (cf. Table 5).

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Figure 4-a:
Fully corrected data distributions, normalized to unity, for the DPS-sensitive observables $\Delta ^\text {rel} {p_{\mathrm {T}}} $ (left) and $ {\Delta \mathrm {S}} $ (right). The second panel in both plots shows the ratio of data over MadGraph 5 + PYTHIA 8 with and without MPI, whereas in the third panel the ratio with POWHEG 2 + PYTHIA 6 is shown. The ratio of the data and PYTHIA 8 is shown in the fourth panel of both plots. The band represents the total uncertainty of the data (cf. Table 5).

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Figure 4-b:
Fully corrected data distributions, normalized to unity, for the DPS-sensitive observables $\Delta ^\text {rel} {p_{\mathrm {T}}} $ (left) and $ {\Delta \mathrm {S}} $ (right). The second panel in both plots shows the ratio of data over MadGraph 5 + PYTHIA 8 with and without MPI, whereas in the third panel the ratio with POWHEG 2 + PYTHIA 6 is shown. The ratio of the data and PYTHIA 8 is shown in the fourth panel of both plots. The band represents the total uncertainty of the data (cf. Table 5).

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Figure 5:
The extracted value of the DPS fraction in W + jets events, simulated with MadGraph 5 + PYTHIA 8, using different background templates obtained by varying the transverse momentum cutoff (${ {p_{\mathrm {T}}} ^\text {cut}}$) for the second hard interaction. The DPS fractions obtained by performing both simultaneous and individual fits to the $\Delta ^\text {rel}{ {p_{\mathrm {T}}} }$ and $ {\Delta \mathrm {S}} $ observables are shown. The DPS fraction, ${f_\mathrm {DPS}^\text {evt}}$, for the simulated W + jets events is shown by a dashed black line. The error bars/bands represent the statistical uncertainty added in quadrature to the systematic uncertainty of the DPS template (as discussed in the text).

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Figure 6:
Fit results for the DPS-sensitive observables $\Delta ^\text {rel}{ {p_{\mathrm {T}}} }$ (left) and $ {\Delta \mathrm {S}} $ (right) using signal and background templates. The distributions of the simulated W + 2-jet events are fitted with signal and background templates. The bottom panels show the ratio of the distributions to the fit results. Here, the term ``inclusive'' means the simulation also includes the DPS contribution.

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Figure 6-a:
Fit results for the DPS-sensitive observables $\Delta ^\text {rel}{ {p_{\mathrm {T}}} }$ (left) and $ {\Delta \mathrm {S}} $ (right) using signal and background templates. The distributions of the simulated W + 2-jet events are fitted with signal and background templates. The bottom panels show the ratio of the distributions to the fit results. Here, the term ``inclusive'' means the simulation also includes the DPS contribution.

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Figure 6-b:
Fit results for the DPS-sensitive observables $\Delta ^\text {rel}{ {p_{\mathrm {T}}} }$ (left) and $ {\Delta \mathrm {S}} $ (right) using signal and background templates. The distributions of the simulated W + 2-jet events are fitted with signal and background templates. The bottom panels show the ratio of the distributions to the fit results. Here, the term ``inclusive'' means the simulation also includes the DPS contribution.

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Figure 7:
Fit results for the DPS-sensitive observables $\Delta ^\text {rel}{ {p_{\mathrm {T}}} }$ (left) and $ {\Delta \mathrm {S}} $ (right). Corrected data distributions are fitted with signal and background templates (as discussed in the text).

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Figure 7-a:
Fit results for the DPS-sensitive observables $\Delta ^\text {rel}{ {p_{\mathrm {T}}} }$ (left) and $ {\Delta \mathrm {S}} $ (right). Corrected data distributions are fitted with signal and background templates (as discussed in the text).

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Figure 7-b:
Fit results for the DPS-sensitive observables $\Delta ^\text {rel}{ {p_{\mathrm {T}}} }$ (left) and $ {\Delta \mathrm {S}} $ (right). Corrected data distributions are fitted with signal and background templates (as discussed in the text).

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Figure 8:
Centre-of-mass energy dependence of $\sigma _\text {eff}$ measured by different experiments using different processes [8,9,10,11,12,21]. These measurements used different approaches for extraction of the DPS fraction and $\sigma _\text {eff}$. The ``Corrected CDF'' data point indicates the $\sigma _\text {eff}$ value corrected for the exclusive event selection [23].
Tables

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Table 1:
Cross sections of the various processes and their uncertainties.

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Table 2:
Summary of the W + 2-jet event selection and reconstruction criteria at the detector level.

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Table 3:
Expected yields for various processes for 5 fb$^{-1}$ and observed number of events in the data. The top production background is the sum of the single-top-quark and $\mathrm{ t \bar{t} } $ processes. The estimated event yields from the simulated samples include uncertainties in the respective cross sections.

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Table 4:
Phase space definition for the visible cross section at the particle level.

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Table 5:
Summary of the systematic uncertainties (in %) for different observables. Uncertainties in integrated luminosity, muon identification (ID), and trigger efficiency only affect the W + 2-jet cross section measurement.

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Table 6:
Systematic uncertainties in the DPS fraction determination.

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Table 7:
Systematic uncertainties in the measurement of $R$.

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Table 8:
Uncertainties in the measured value of the dijet cross section.

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Table 9:
Measured value of ${f_\mathrm {DPS}}$, R, $\sigma '_{2 {\mathrm {j}} }$, and the effective cross section.
Summary
A study of double parton scattering in W + 2-jet events in pp collisions is presented. The data correspond to an integrated luminosity of 5 fb$^{-1}$ collected in pp collisions at a centre-of-mass energy of 7 TeV. Events with a W boson, reconstructed from the muon and $E_\mathrm{T}^{\text{miss}}$ information, are required to have exactly two jets with ${p_{\mathrm{T}}} > $ 20 GeV/$c$ and $ | {\eta} | < $ 2.0. The DPS-sensitive observables $\Delta ^\text{rel} {p_{\mathrm{T}}}$ and $\Delta S$ are corrected for detector effects and selection efficiencies. Simulations of W + jets events with MadGraph5 + PYTHIA8 (or PYTHIA6) and NLO predictions of POWHEG2 + PYTHIA6 (or HERWIG6) provide a good description of the observables and describe the data only if multiple parton interactions are included. The fraction of DPS in W + 2-jet events is extracted with a DPS + SPS template fit to the distribution of the $\Delta ^\text{rel} {p_{\mathrm{T}}}$ and ${\Delta\mathrm{S}} $ observables.
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Compact Muon Solenoid
LHC, CERN