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| CMS-PAS-SMP-22-010 | ||
| Measurement of the Drell-Yan forward-backward asymmetry and of the effective leptonic weak mixing angle using proton-proton collisions at $ \sqrt{s}= $ 13 TeV | ||
| CMS Collaboration | ||
| 27 March 2024 | ||
| Abstract: The forward-backward asymmetry in Drell-Yan production and the effective leptonic electroweak mixing angle are measured using a sample of proton-proton collisions at $ \sqrt{s}= $ 13 TeV collected by the CMS experiment and corresponding to an integrated luminosity of 137 fb$ ^{-1} $. The measurement uses both dimuon and dielectron events, and is performed as a function of the dilepton's mass and rapidity. Using the CT18Z set of parton distribution functions (PDF), we obtain $ \sin^2\theta^\ell_{\mathrm{eff}} = $ 0.23157 $\pm$ 0.00010 (stat) $\pm$ 0.00015 (syst) $\pm$ 0.00009 (theo) $\pm$ 0.00027(PDF), the total uncertainty being 0.00031. The measured value agrees with the standard model prediction. The total uncertainty varies between 0.00024 and 0.00035, depending on the PDF set. This is the most precise $ \sin^2\theta^\ell_{\mathrm{eff}} $ measurement at a hadron collider, with a precision comparable to the results obtained at LEP and SLD. | ||
| Links: CDS record (PDF) ; Physics Briefing ; CADI line (restricted) ; | ||
| Figures | |
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Figure 1:
Misidentification rates measured in the 2018 samples, for electrons in the 2.0 $ < |\eta| < $ 2.5 bin that pass the single-lepton trigger. The several misidentification rates are: (1) majority (circles) and selective (squares) charge ID; (2) misidentification of electrons as positrons $ (+|-) $ (solid markers) or positrons as electrons $ (-|+) $ (open markers); (3) true (red), simulation (blue), and data (black). The true charge misidentification rate is measured by counting electrons with wrong reconstructed charge using the generated electron information, while simulation mis-identification rate is measured with the same method as in data, as described in the text. |
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Figure 2:
Dilepton mass distributions in the same-sign dimuon samples (left) and single-muon triggered $ \mu\mathrm{e} $ events (right). The electroweak and top-quark backgrounds are normalized to the measured luminosity using the NNLO cross sections. The multijet background is evaluated by applying the transfer factors to the multijet-enriched sample of the same-sign leptons. The error bars include the statistical and background systematic uncertainties described in Section 5. |
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Figure 2-a:
Dilepton mass distributions in the same-sign dimuon samples (left) and single-muon triggered $ \mu\mathrm{e} $ events (right). The electroweak and top-quark backgrounds are normalized to the measured luminosity using the NNLO cross sections. The multijet background is evaluated by applying the transfer factors to the multijet-enriched sample of the same-sign leptons. The error bars include the statistical and background systematic uncertainties described in Section 5. |
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Figure 2-b:
Dilepton mass distributions in the same-sign dimuon samples (left) and single-muon triggered $ \mu\mathrm{e} $ events (right). The electroweak and top-quark backgrounds are normalized to the measured luminosity using the NNLO cross sections. The multijet background is evaluated by applying the transfer factors to the multijet-enriched sample of the same-sign leptons. The error bars include the statistical and background systematic uncertainties described in Section 5. |
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Figure 3:
Lepton $ \cos\theta_\mathrm{CS} $ distribution in $ \mu\mathrm{h} $ events. The multijet and W+jets backgrounds are scaled to the data as described in the text. The error bars include the statistical and background systematic uncertainties described in Section 5. |
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Figure 3-a:
Lepton $ \cos\theta_\mathrm{CS} $ distribution in $ \mu\mathrm{h} $ events. The multijet and W+jets backgrounds are scaled to the data as described in the text. The error bars include the statistical and background systematic uncertainties described in Section 5. |
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Figure 3-b:
Lepton $ \cos\theta_\mathrm{CS} $ distribution in $ \mu\mathrm{h} $ events. The multijet and W+jets backgrounds are scaled to the data as described in the text. The error bars include the statistical and background systematic uncertainties described in Section 5. |
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Figure 4:
Dilepton mass (top), rapidity (middle), and $ \cos\theta_\mathrm{CS} $ (bottom) distributions, for the $ \mu\mu $ (left) and $ \mathrm{e}\mathrm{h} $ (right) channels in the 2018 data, after applying all the corrections. |
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Figure 4-a:
Dilepton mass (top), rapidity (middle), and $ \cos\theta_\mathrm{CS} $ (bottom) distributions, for the $ \mu\mu $ (left) and $ \mathrm{e}\mathrm{h} $ (right) channels in the 2018 data, after applying all the corrections. |
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Figure 4-b:
Dilepton mass (top), rapidity (middle), and $ \cos\theta_\mathrm{CS} $ (bottom) distributions, for the $ \mu\mu $ (left) and $ \mathrm{e}\mathrm{h} $ (right) channels in the 2018 data, after applying all the corrections. |
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Figure 4-c:
Dilepton mass (top), rapidity (middle), and $ \cos\theta_\mathrm{CS} $ (bottom) distributions, for the $ \mu\mu $ (left) and $ \mathrm{e}\mathrm{h} $ (right) channels in the 2018 data, after applying all the corrections. |
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Figure 4-d:
Dilepton mass (top), rapidity (middle), and $ \cos\theta_\mathrm{CS} $ (bottom) distributions, for the $ \mu\mu $ (left) and $ \mathrm{e}\mathrm{h} $ (right) channels in the 2018 data, after applying all the corrections. |
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Figure 4-e:
Dilepton mass (top), rapidity (middle), and $ \cos\theta_\mathrm{CS} $ (bottom) distributions, for the $ \mu\mu $ (left) and $ \mathrm{e}\mathrm{h} $ (right) channels in the 2018 data, after applying all the corrections. |
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Figure 4-f:
Dilepton mass (top), rapidity (middle), and $ \cos\theta_\mathrm{CS} $ (bottom) distributions, for the $ \mu\mu $ (left) and $ \mathrm{e}\mathrm{h} $ (right) channels in the 2018 data, after applying all the corrections. |
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Figure 5:
Left: Effect of different POWHEG -EW variations in $ A_4(m) $. Right: Comparison of $ A_4(y,m) $ values for the central predictions of several PDF sets The $ y-m $ on the $ x $-axis corresponds to the serialized rapidity-mass bin. No lepton kinematic cuts are applied in these figures. |
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Figure 5-a:
Left: Effect of different POWHEG -EW variations in $ A_4(m) $. Right: Comparison of $ A_4(y,m) $ values for the central predictions of several PDF sets The $ y-m $ on the $ x $-axis corresponds to the serialized rapidity-mass bin. No lepton kinematic cuts are applied in these figures. |
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Figure 5-b:
Left: Effect of different POWHEG -EW variations in $ A_4(m) $. Right: Comparison of $ A_4(y,m) $ values for the central predictions of several PDF sets The $ y-m $ on the $ x $-axis corresponds to the serialized rapidity-mass bin. No lepton kinematic cuts are applied in these figures. |
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Figure 6:
Measured and best-fit angular weighted $ A_\mathrm{FB}^w(y,m) $ distributions for the 2018 period and in the $ \mu\mu $, $ \mathrm{e}\mathrm{e} $, $ \mathrm{e}\mathrm{g} $, and $ \mathrm{e}\mathrm{h} $ channels. The error bars represent the statistical uncertainties of the measured and simulated samples. |
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Figure 6-a:
Measured and best-fit angular weighted $ A_\mathrm{FB}^w(y,m) $ distributions for the 2018 period and in the $ \mu\mu $, $ \mathrm{e}\mathrm{e} $, $ \mathrm{e}\mathrm{g} $, and $ \mathrm{e}\mathrm{h} $ channels. The error bars represent the statistical uncertainties of the measured and simulated samples. |
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Figure 6-b:
Measured and best-fit angular weighted $ A_\mathrm{FB}^w(y,m) $ distributions for the 2018 period and in the $ \mu\mu $, $ \mathrm{e}\mathrm{e} $, $ \mathrm{e}\mathrm{g} $, and $ \mathrm{e}\mathrm{h} $ channels. The error bars represent the statistical uncertainties of the measured and simulated samples. |
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Figure 6-c:
Measured and best-fit angular weighted $ A_\mathrm{FB}^w(y,m) $ distributions for the 2018 period and in the $ \mu\mu $, $ \mathrm{e}\mathrm{e} $, $ \mathrm{e}\mathrm{g} $, and $ \mathrm{e}\mathrm{h} $ channels. The error bars represent the statistical uncertainties of the measured and simulated samples. |
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Figure 6-d:
Measured and best-fit angular weighted $ A_\mathrm{FB}^w(y,m) $ distributions for the 2018 period and in the $ \mu\mu $, $ \mathrm{e}\mathrm{e} $, $ \mathrm{e}\mathrm{g} $, and $ \mathrm{e}\mathrm{h} $ channels. The error bars represent the statistical uncertainties of the measured and simulated samples. |
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Figure 7:
Measured and best-fit $ \cos\theta_\mathrm{CS} $ distributions in the $ \mu\mu $ (left) and $ \mathrm{e}\mathrm{h} $ (right) channels of the 2018 samples, for the dilepton mass peak and relevant rapidity bins for each channel. The error bars represent the statistical uncertainties. |
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Figure 7-a:
Measured and best-fit $ \cos\theta_\mathrm{CS} $ distributions in the $ \mu\mu $ (left) and $ \mathrm{e}\mathrm{h} $ (right) channels of the 2018 samples, for the dilepton mass peak and relevant rapidity bins for each channel. The error bars represent the statistical uncertainties. |
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Figure 7-b:
Measured and best-fit $ \cos\theta_\mathrm{CS} $ distributions in the $ \mu\mu $ (left) and $ \mathrm{e}\mathrm{h} $ (right) channels of the 2018 samples, for the dilepton mass peak and relevant rapidity bins for each channel. The error bars represent the statistical uncertainties. |
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Figure 8:
Measured and best-fit $ A_4(y,m) $ distributions in the combined Run 2 fit for the CT18Z PDF set. The shaded band represents the post-fit PDF uncertainty. |
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Figure 9:
Values of $ \sin^2\theta_\mathrm{eff}^\ell $ measured in each of the four channels using the full Run 2 data sample (upper) and in each of the four data-taking periods combining the four channels (lower), using the CT18Z PDF set. The results obtained with the $ A_\mathrm{FB} $, $ A_4 $, and $ \cos\theta_\mathrm{CS} $ fits are shown using different markers and colors. The orange line and the yellow band correspond to the result obtained with all channels and runs combined. For the $ A_\mathrm{FB} $-based result, the violet error bands show the combined statistical and experimental systematic uncertainties, while the black error bars represent the total uncertainties. |
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Figure 9-a:
Values of $ \sin^2\theta_\mathrm{eff}^\ell $ measured in each of the four channels using the full Run 2 data sample (upper) and in each of the four data-taking periods combining the four channels (lower), using the CT18Z PDF set. The results obtained with the $ A_\mathrm{FB} $, $ A_4 $, and $ \cos\theta_\mathrm{CS} $ fits are shown using different markers and colors. The orange line and the yellow band correspond to the result obtained with all channels and runs combined. For the $ A_\mathrm{FB} $-based result, the violet error bands show the combined statistical and experimental systematic uncertainties, while the black error bars represent the total uncertainties. |
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Figure 9-b:
Values of $ \sin^2\theta_\mathrm{eff}^\ell $ measured in each of the four channels using the full Run 2 data sample (upper) and in each of the four data-taking periods combining the four channels (lower), using the CT18Z PDF set. The results obtained with the $ A_\mathrm{FB} $, $ A_4 $, and $ \cos\theta_\mathrm{CS} $ fits are shown using different markers and colors. The orange line and the yellow band correspond to the result obtained with all channels and runs combined. For the $ A_\mathrm{FB} $-based result, the violet error bands show the combined statistical and experimental systematic uncertainties, while the black error bars represent the total uncertainties. |
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Figure 10:
Values of $ \sin^2\theta_\mathrm{eff}^\ell $ measured with the $ A_\mathrm{FB} $ and $ A_4 $ fits, for seven alternative PDF sets, combining the four detection channels and using the full Run 2 data sample. The orange line and the yellow band correspond to the default result, obtained with the CT18Z PDFs. The green open squares show the results obtained without profiling the corresponding PDF uncertainties. For the $ A_\mathrm{FB} $-based result, the violet error band represents the PDF uncertainty while the black error bar represents the total uncertainty. |
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Figure 10-a:
Values of $ \sin^2\theta_\mathrm{eff}^\ell $ measured with the $ A_\mathrm{FB} $ and $ A_4 $ fits, for seven alternative PDF sets, combining the four detection channels and using the full Run 2 data sample. The orange line and the yellow band correspond to the default result, obtained with the CT18Z PDFs. The green open squares show the results obtained without profiling the corresponding PDF uncertainties. For the $ A_\mathrm{FB} $-based result, the violet error band represents the PDF uncertainty while the black error bar represents the total uncertainty. |
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Figure 10-b:
Values of $ \sin^2\theta_\mathrm{eff}^\ell $ measured with the $ A_\mathrm{FB} $ and $ A_4 $ fits, for seven alternative PDF sets, combining the four detection channels and using the full Run 2 data sample. The orange line and the yellow band correspond to the default result, obtained with the CT18Z PDFs. The green open squares show the results obtained without profiling the corresponding PDF uncertainties. For the $ A_\mathrm{FB} $-based result, the violet error band represents the PDF uncertainty while the black error bar represents the total uncertainty. |
| Tables | |
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Table 1:
The lepton $ \eta $ and $ p_{\mathrm{T}} $ acceptance windows applied in the four measurement channels. The 1.44-1.57 $ |\eta| $ range between the barrel and endcap ECAL is excluded for central electrons. |
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Table 2:
Free parameters in the $ A_\mathrm{FB}^w(y, m) $ fit. The ``Var." column indicates the number of variations for each type. For $ p_{\mathrm{T}} $ modeling, multijet, and W+jets background, ``Var." indicates the number of rapidity bins where these uncertainties are considered uncorrelated. Some of the ``Total" values reflect the four data-taking periods and/or the four final-state channels, when the corresponding uncertainties are uncorrelated. |
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Table 3:
Fit results (in units of 10$^{-5} $) for the four final-state channels and for all ($ {\ell\ell} $) channels, using the full Run 2 event sample. The experimental systematic uncertainties (``exp") include all the uncertainties listed in the last four columns, which correspond to the statistical uncertainties of the MC samples and to the categories listed in Table 2. |
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Table 4:
Number of bins and free parameters in the unfolding. |
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Table 5:
Measured $ \sin^2\theta_\mathrm{eff}^\ell $ values when using the $ A_4(y,m) $ distributions for the four final-state channels and for all ($ {\ell\ell} $) channels. |
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Table 6:
Values of $ \sin^2\theta_\mathrm{eff}^\ell $ measured with the $ A_\mathrm{FB} $ and $ A_4 $ fits, for seven alternative PDF sets, combining the four detection channels and using the full Run 2 data sample. The $ \sin^2\theta_\mathrm{eff}^\ell $ values are presented in units of $ 10^{-5} $. |
| Summary |
| A precise measurement of the effective leptonic electroweak mixing angle has been performed, using event samples of proton-proton collisions at $ \sqrt{s} = $ 13 TeV collected in 2016-2018 by the CMS experiment and corresponding to a total integrated luminosity of 137 fb$ ^{-1} $. The measurement, based on the study of Drell-Yan dimuon and dielectron events, has a significantly smaller uncertainty than that of previous CMS results, thanks to the increase in the size of the data samples, the improved analysis techniques, and the inclusion of central-forward dielectrons. Using the CT18Z set of parton densities, the result is $ \sin^2\theta_\mathrm{eff}^\ell = $ 0.23157 $\pm$ 0.00010 (stat) $\pm$ 0.00015 (syst) $\pm$ 0.00009 (theo) $\pm$ 0.00027(PDF). The total uncertainty, dominated by the PDF term, is 0.00031, accounting for correlated uncertainties; it varies between 0.00024 and 0.00035, depending on the PDF set used. For the central values of the CT18Z set, the combined statistical and experimental systematic uncertainty is 0.00014. The measured $ \sin^2\theta_\mathrm{eff}^\ell $ value is in good agreement with the standard model prediction, 0.23155 $ \pm $ 0.00004, and is the most precise among the hadron-collider measurements. The precision is comparable to that of the two most precise measurements performed in $ \mathrm{e}^+ \mathrm{e}^- $ collisions at LEP and SLD, with respective uncertainties of 0.00026 and 0.00029. We have also measured the $ A_4 $ coefficient differentially, as a function of the dilepton's mass and rapidity, a result that can be used in combination with other LHC measurements and in improvements of the $ \sin^2\theta_\mathrm{eff}^\ell $ measurement with future PDF sets. |
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Compact Muon Solenoid LHC, CERN |
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