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| CMS-SMP-14-022 ; CERN-EP-2016-043 | ||
| Measurement of the differential cross section and charge asymmetry for inclusive pp $ \to \mathrm{ W }^{\pm}+X$ production at $ \sqrt{s} = $ 8 TeV | ||
| CMS Collaboration | ||
| 5 March 2016 | ||
| Eur. Phys. J. C 76 (2016) 469 | ||
| Abstract: The differential cross section and charge asymmetry for inclusive pp $ \to \mathrm{ W }^{\pm}+X \to \mu^{\pm}\nu+X$ production at $ \sqrt{s} = $ 8 TeV are measured as a function of muon pseudorapidity. The data sample corresponds to an integrated luminosity of 18.8 fb$^{-1}$ recorded with the CMS detector at the LHC. These results provide important constraints on the parton distribution functions of the proton in the range of the Bjorken scaling variable $x$ from 10$^{-3}$ to 10$^{-1}$. | ||
| Links: e-print arXiv:1603.01803 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; CADI line (restricted) ; | ||
| Figures | |
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Figure 1:
Examples of fits in three $ { {| \eta | }} $ ranges: 0.0 $ < { {| \eta | }} < $ 0.2 (top), 1.0 $ < { {| \eta | }} < $ 1.2 (center), and 2.1 $ < { {| \eta | }} < $ 2.4 (bottom). For each $\eta $ range, results for $\mathrm{ W^{+} } $ (left) and $\mathrm{ W^{-} } $ (right) are shown. The ratios between the data points and the final fits are shown at the bottom of each panel. |
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Figure 1-a:
Example of fit for $\mathrm{ W^{+} } $ in $ | \eta | $ range 0.0 $ < { {| \eta | }} < $ 0.2. The ratios between the data points and the final fits are shown at the bottom of each panel. |
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Figure 1-b:
Example of fit for $\mathrm{ W^{-} } $ in $ | \eta | $ range 0.0 $ < { {| \eta | }} < $ 0.2. The ratios between the data points and the final fits are shown at the bottom of each panel. |
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Figure 1-c:
Example of fit for $\mathrm{ W^{+} } $ in 1.0 $ < { {| \eta | }} < $ 1.2. The ratios between the data points and the final fits are shown at the bottom of each panel. |
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Figure 1-d:
Example of fit for $\mathrm{ W^{-} } $ in 1.0 $ < { {| \eta | }} < $ 1.2. The ratios between the data points and the final fits are shown at the bottom of each panel. |
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Figure 1-e:
Example of fit for $\mathrm{ W^{+} } $ in 2.1 $ < { {| \eta | }} < $ 2.4. The ratios between the data points and the final fits are shown at the bottom of each panel. |
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Figure 1-f:
Example of fit for $\mathrm{ W^{-} } $ in 2.1 $ < { {| \eta | }} < $ 2.4. The ratios between the data points and the final fits are shown at the bottom of each panel. |
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Figure 2:
Distribution of ${R_{\pm }^{\mathrm {QCD}}}$ in QCD control region for data (solid circles), QCD control region for simulation (solid squares), and signal region for simulation (open squares). Open circles show the ${R_{\pm }^{\mathrm {QCD}}}$distribution when QCD contributions in $ {\mathrm {W^+}}$ and $ {\mathrm {W^-}}$ events are not constrained. Shaded area indicates assigned systematic uncertainty. |
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Figure 3:
Comparison of the measured cross sections (upper plot for $ {\sigma _\eta } ^+$ and middle for $ {\sigma _\eta } ^-$) and asymmetries (lower plot) to NNLO predictions calculated using the FEWZ3.1 MC tool interfaced with different PDF sets. The right column shows the ratios (differences) between the theoretical predictions and the measured cross sections (asymmetries). The smaller vertical error bars on the data points represent the statistical and systematic uncertainties. The full error bars include the integrated luminosity uncertainty. The PDF uncertainty of each PDF set is shown by a shaded (or hatched) band and corresponds to 68% CL . |
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Figure 3-a:
Comparison of the measured cross sections for $ {\sigma _\eta } ^+$ to NNLO predictions calculated using the FEWZ3.1 MC tool interfaced with different PDF sets. The smaller vertical error bars on the data points represent the statistical and systematic uncertainties. The full error bars include the integrated luminosity uncertainty. The PDF uncertainty of each PDF set is shown by a shaded (or hatched) band and corresponds to 68% CL . |
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Figure 3-b:
Ratios between the theoretical predictions and the measured cross sections plot for $ {\sigma _\eta } ^+$. The smaller vertical error bars on the data points represent the statistical and systematic uncertainties. The full error bars include the integrated luminosity uncertainty. The PDF uncertainty of each PDF set is shown by a shaded (or hatched) band and corresponds to 68% CL . |
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Figure 3-c:
Comparison of the measured cross sections for $ {\sigma _\eta } ^-$ to NNLO predictions calculated using the FEWZ3.1 MC tool interfaced with different PDF sets. The smaller vertical error bars on the data points represent the statistical and systematic uncertainties. The full error bars include the integrated luminosity uncertainty. The PDF uncertainty of each PDF set is shown by a shaded (or hatched) band and corresponds to 68% CL . |
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Figure 3-d:
Ratios between the theoretical predictions and the measured cross sections for $ {\sigma _\eta } ^-$. The smaller vertical error bars on the data points represent the statistical and systematic uncertainties. The full error bars include the integrated luminosity uncertainty. The PDF uncertainty of each PDF set is shown by a shaded (or hatched) band and corresponds to 68% CL . |
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Figure 3-e:
Comparison of asymmetries to NNLO predictions calculated using the FEWZ3.1 MC tool interfaced with different PDF sets. The smaller vertical error bars on the data points represent the statistical and systematic uncertainties. The full error bars include the integrated luminosity uncertainty. The PDF uncertainty of each PDF set is shown by a shaded (or hatched) band and corresponds to 68% CL . |
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Figure 3-f:
Differences between the theoretical predictions and the measured asymmetries. The smaller vertical error bars on the data points represent the statistical and systematic uncertainties. The full error bars include the integrated luminosity uncertainty. The PDF uncertainty of each PDF set is shown by a shaded (or hatched) band and corresponds to 68% CL . |
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Figure 4:
Distributions of u valence (left) and d valence (right) quarks as functions of $x$ at the scale $Q^2=m^2_{\mathrm{ W } }$. The results of the fit to the HERA data and muon asymmetry measurements (light shaded band), and to HERA data only (hatched band) are compared. The total PDF uncertainties are shown. In the bottom panels the distributions are normalized to 1 for a direct comparison of the uncertainties. The change of the PDFs with respect to the HERA-only fit is represented by a solid line. |
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Figure 4-a:
Distribution of u valence quarks as a function of $x$ at the scale $Q^2=m^2_{\mathrm{ W } }$. The results of the fit to the HERA data and muon asymmetry measurements (light shaded band), and to HERA data only (hatched band) are compared. The total PDF uncertainties are shown. In the bottom panel the distribution is normalized to 1 for a direct comparison of the uncertainties. The change of the PDFs with respect to the HERA-only fit is represented by a solid line. |
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Figure 4-b:
Distributions of d valence quarks as a function of $x$ at the scale $Q^2=m^2_{\mathrm{ W } }$. The results of the fit to the HERA data and muon asymmetry measurements (light shaded band), and to HERA data only (hatched band) are compared. The total PDF uncertainties are shown. In the bottom panel the distribution is normalized to 1 for a direct comparison of the uncertainties. The change of the PDFs with respect to the HERA-only fit is represented by a solid line. |
| Tables | |
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Table 1:
Summary of the fitted $N^{+}$, $N^{-}$, the correlation ($\rho _{+,-}$) between the uncertainties in $N^{+}$ and $N^{-}$, and the $\chi ^{2}$ of the fit for each $ {| \eta | }$ bin. The number of degrees of freedom($n_{\text {dof}}$) in each fit is 197. The quoted uncertainties are statistical and include statistical uncertainties in the templates. The correlation coefficients are expressed as percentages. |
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Table 2:
Systematic uncertainties in cross sections ($\delta {\sigma _\eta } ^\pm $) and charge asymmetry ($\delta \mathcal {A}$) for each $ {| \eta | }$ bin. The statistical and integrated luminosity uncertainties are also shown for comparison. A detailed description of each systematic uncertainty is given in the text. |
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Table 3:
Correlation matrices of systematic uncertainties for $ {\sigma _\eta } ^\pm $ and $\mathcal {A}$. The statistical and integrated luminosity uncertainties are not included. The full 22$\times $22 correlation matrix for $ {\sigma _\eta } ^\pm $ is presented as four blocks of 11$\times $11 matrices. The $C_{++}$ and $C_{-}$ blocks on the diagonal represent the bin-to-bin correlations of $\delta {\sigma _\eta } ^+$ and $\delta {\sigma _\eta } ^-$, respectively. The off-diagonal $C_{+-}$ and $C_{+-}^T$ blocks describe the correlations between the two charges. The values are expressed as percentages. |
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Table 4:
Summary of the measured differential cross sections $ {\sigma _\eta } ^\pm $ (pb) and charge asymmetry $\mathcal {A}$. The first uncertainty is statistical, the second uncertainty is systematic, and the third is the integrated luminosity uncertainty. The theoretical predictions are obtained using the fewz3.1 [37] NNLO MC tool interfaced with five different PDF sets. |
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Table 5:
Partial $\chi ^2$ per number of data points, $n_{\text {dp}}$, and the global $\chi ^2$ per degrees of freedom, $n_{\text {dof}}$, as obtained in the QCD analysis of HERA DIS and the CMS muon charge asymmetry data. For HERA measurements, the energy of the proton beam is listed for each data set, with electron energy being $E_{ {\mathrm {e}}}=$ 27.5 GeV. |
| Summary |
| In summary, we have measured the differential cross section and charge asymmetry of the $\mathrm{W}^{\pm} \to \mu^{\pm}\nu$ production in pp collisions at $ \sqrt{s} = $ 8 TeV using a data sample corresponding to an integrated luminosity of 18.8 fb$^{-1}$ collected with the CMS detector at the LHC. The measurements were performed in 11 bins of absolute muon pseudorapidity $| \eta |$ for muons with $p_{\mathrm{T}}>$ 25 GeV. The results have been incorporated into a QCD analysis at next-to-next-to-leading-order together with the inclusive deep inelastic scattering data from HERA. A significant improvement in the accuracy of the valence quark distributions is observed in the range $10^{-3} < x <10^{-1}$, demonstrating the power of these muon charge asymmetry measurements to improve the main constraints on the valence distributions imposed by the HERA data, in the kinematics range probed. This strongly suggests the use of these measurements in future PDF determinations. |
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Compact Muon Solenoid LHC, CERN |
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