CMSSMP22010 ; CERNEP2024208  
Measurement of the DrellYan forwardbackward asymmetry and of the effective leptonic weak mixing angle in protonproton collisions at $ \sqrt{s} = $ 13 TeV  
CMS Collaboration  
14 August 2024  
Submitted to Phys. Lett. B  
Abstract: The forwardbackward asymmetry in DrellYan production and the effective leptonic electroweak mixing angle are measured in protonproton collisions at $ \sqrt{s} = $ 13 TeV, collected by the CMS experiment and corresponding to an integrated luminosity of 138 fb$ ^{1} $. The measurement uses both dimuon and dielectron events, and is performed as a function of the dilepton mass and rapidity. The unfolded angular coefficient $ A_4 $ is also extracted, as a function of the dilepton mass and rapidity. Using the CT18Z set of parton distribution functions, we obtain $ \sin^2\theta_\text{eff}^{\ell} = $ 0.23157 $ \pm $ 0.00031, where the uncertainty includes the experimental and theoretical contributions. The measured value agrees with the standard model fit result to global experimental data. This is the most precise $ \sin^2\theta_\text{eff}^{\ell} $ measurement at a hadron collider, with a precision comparable to the results obtained at LEP and SLD.  
Links: eprint arXiv:2408.07622 [hepex] (PDF) ; CDS record ; inSPIRE record ; CADI line (restricted) ; 
Figures & Tables  Summary  Additional Figures  References  CMS Publications 

Figures  
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Figure 1:
Misidentification rates in the 2018 samples, for electrons in the 2.0 $ < \eta < $ 2.5 bin that pass the singlelepton trigger (SLT): (1) majority (circles) and selective (squares) charge identification; (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 evaluated by counting electrons with wrong reconstructed charge using generationlevel information; the simulated misidentification rate is evaluated with the method used in data. 
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Figure 2:
Samesign dimuon mass distribution for the 2018 sample. The EW and top quark backgrounds are normalized to the integrated luminosity using NNLO cross sections. The multijet background is evaluated by applying weights to the corresponding multijetenriched samples. The error bars in the lower panel include 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 in 2018. The multijet and $ \mathrm{W}\!+\!\text{jets} $ backgrounds are scaled to the data as described in the text. The error bars include statistical and background systematic uncertainties (described in Section 5). 
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Figure 4:
Dilepton mass (left), rapidity (middle), and $ \cos\theta_\mathrm{CS} $ (right) distributions, for the $ \mu\mu $ (upper) and $ \mathrm{e}\mathrm{h} $ (lower) channels in the 2018 sample, after applying all the corrections. The signal is scaled to match the total number of events in the data. 
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Figure 5:
The $ A_4 $ coefficient in the nominal configuration (upper panels) and its variations (lower panels) when changing the inputs mentioned in the legends: different POWHEG Z_ew options (left) and different PDF sets (right). No lepton kinematic selection criteria are applied. 
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Figure 5a:
The $ A_4 $ coefficient in the nominal configuration (upper panels) and its variations (lower panels) when changing the inputs mentioned in the legends: different POWHEG Z_ew options (left) and different PDF sets (right). No lepton kinematic selection criteria are applied. 
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Figure 5b:
The $ A_4 $ coefficient in the nominal configuration (upper panels) and its variations (lower panels) when changing the inputs mentioned in the legends: different POWHEG Z_ew options (left) and different PDF sets (right). No lepton kinematic selection criteria are applied. 
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Figure 6:
Measured and best fit $ \mu\mu $ (left) and $ \mathrm{e}\mathrm{h} $ (right) $ A_\mathrm{FB}^\mathrm{w}(y,m) $ distributions for the 2018 data. The error bars represent the statistical uncertainties in the measured and simulated samples. The rapidity bins are given in Table 2. 
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Figure 6a:
Measured and best fit $ \mu\mu $ (left) and $ \mathrm{e}\mathrm{h} $ (right) $ A_\mathrm{FB}^\mathrm{w}(y,m) $ distributions for the 2018 data. The error bars represent the statistical uncertainties in the measured and simulated samples. The rapidity bins are given in Table 2. 
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Figure 6b:
Measured and best fit $ \mu\mu $ (left) and $ \mathrm{e}\mathrm{h} $ (right) $ A_\mathrm{FB}^\mathrm{w}(y,m) $ distributions for the 2018 data. The error bars represent the statistical uncertainties in the measured and simulated samples. The rapidity bins are given in Table 2. 
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Figure 7:
Measured and best fit $ \mu\mu $ (left) and $ \mathrm{e}\mathrm{h} $ (right) $ \cos\theta_\mathrm{CS} $ distributions for 2018, for the Z boson peak and two rapidity bins. The error bars represent the statistical uncertainties. 
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Figure 7a:
Measured and best fit $ \mu\mu $ (left) and $ \mathrm{e}\mathrm{h} $ (right) $ \cos\theta_\mathrm{CS} $ distributions for 2018, for the Z boson peak and two rapidity bins. The error bars represent the statistical uncertainties. 
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Figure 7b:
Measured and best fit $ \mu\mu $ (left) and $ \mathrm{e}\mathrm{h} $ (right) $ \cos\theta_\mathrm{CS} $ distributions for 2018, for the Z boson peak and two rapidity bins. The error bars represent the statistical uncertainties. 
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Figure 8:
Measured and best fit $ A_4(Y, M) $ distributions for the combined 20162018 fit with the CT18Z PDF set. The shaded band represents the postfit PDF uncertainty. 
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Figure 9:
Values of $ \sin^2\theta_\text{eff}^{\ell} $ measured with the $ A_\mathrm{FB}^\mathrm{w} $, $ A_4 $, and $ \cos\theta_\mathrm{CS} $ fits, in each of the four channels using the full 20162018 sample (upper) and in each of the four datataking periods combining the four channels (lower), always with the CT18Z PDF set. The ``comb" band shows the result for all channels and runs combined. For the $ A_\mathrm{FB}^\mathrm{w} $ results, the magenta bands show the combined statistical and experimental systematic uncertainties, and the black bars represent the total uncertainties. 
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Figure 10:
Values of $ \sin^2\theta_\text{eff}^{\ell} $ measured with the $ A_\mathrm{FB}^\mathrm{w} $ and $ A_4 $ fits, for seven PDF sets, combining the four channels and using the full 20162018 sample. The orange line and yellow band correspond to the result obtained with the CT18Z PDFs. The red open squares are the results obtained without profiling the corresponding PDF uncertainties. For the $ A_\mathrm{FB}^\mathrm{w} $ results, the cyan bands show the PDF uncertainties and the black bars represent the total uncertainties. 
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Figure 11:
Comparison of the $ \sin^2\theta_\text{eff}^{\ell} $ values measured in this analysis with previous measurements [1,11,12,9,10,14] and the result of a SM global fit [2]. 
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Figure 12:
The $ A_4 $ coefficient obtained with the latest POWHEG Z_ew version [55] for the nominal configuration (upper panel) and its variations when changing input options (lower panel). No lepton kinematic selection criteria are applied. 
Tables  
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Table 1:
The lepton $ \eta $ and $ p_{\mathrm{T}} $ acceptance windows applied in the four measurement channels. The 1.441.57 $ \eta $ range, between the barrel and endcap ECAL, is excluded for central electrons. 
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Table 2:
Dilepton rapidity and mass binning used in the fits; $ n_{y} $, $ n_m $, and $ n_M $ are the numbers of bins in each category. 
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Table 3:
Free parameters in the $ A_\mathrm{FB}^\mathrm{w}(y,m) $ fit, indicating the number of independent variations (e.g., number of rapidity bins where the uncertainties are considered uncorrelated). Some of the total values reflect the four datataking periods and/or the four finalstate channels. 
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Table 4:
Fitted $ \sin^2\theta_\text{eff}^{\ell} $ (in units of 10$^{5} $) for the four channels and their sum ($ \ell\ell $), using the full data sample. The fit quality is good, as indicated by the $ \chi^2 $ probabilities ($ p $). The experimental systematic uncertainties (``exp") are the sum of the values in the five rightmost columns, corresponding to the statistical uncertainties of the MC samples and the categories listed in Table 3. 
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Table 5:
Numbers of bins and free parameters used in the unfolding. 
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Table 6:
Measured $ \sin^2\theta_\text{eff}^{\ell} $ values (in units of 10$^{5} $) when using the $ A_4(Y, M) $ distributions for the four finalstate channels and their sum. 
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Table 7:
Values of $ \sin^2\theta_\text{eff}^{\ell} $ (in units of 10$^{5} $) obtained by fitting the measured $ A_\mathrm{FB}^\mathrm{w} $ or unfolded $ A_4 $, for seven PDF sets, combining the four channels and using the full 20162018 sample. 
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Table 8:
Values of $ \sin^2\theta_\text{eff}^{\ell} $ (in units of 10$^{5} $) extracted by profiling the $ A_4 $ distribution (with 63 data points) using XFITTER, for several PDF sets. The reported uncertainties are the total ones, including contributions from the statistical, experimental systematic, theoretical, and PDF sources. 
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Table 9:
Values of $ \sin^2\theta_\text{eff}^{\ell} $ (in units of 10$^{5} $) extracted by profiling the $ A_4 $ distribution (with 63 data points) using XFITTER, for several PDF sets. The reported uncertainties are the total ones, including contributions from the statistical, experimental systematic, theoretical, and PDF sources. 
Summary 
A precise measurement of the forwardbackward asymmetry has been performed, using protonproton collisions at $ \sqrt{s} = $ 13 TeV collected in 20162018 by the CMS experiment and corresponding to a total integrated luminosity of 138 fb$ ^{1} $. The measurement is based on the study of DrellYan dimuon and dielectron events. The effective leptonic electroweak mixing angle $ \sin^2\theta_\text{eff}^{\ell} $ is extracted very precisely by fitting the detectorlevel angularweighted $ A_\mathrm{FB}^\mathrm{w}(y,m) $ and the unfolded $ A_4(Y, M) $ angular coefficient of the preFSR dilepton, obtaining compatible results. Given that the angularweighted asymmetry method [17] benefits from the cancelation of systematic uncertainties in the detection acceptance and efficiencies, we use this method for our baseline result. This measurement has a significantly smaller uncertainty than the previous CMS result [14] because of the larger data sample, an improved analysis technique, and the inclusion of centralforward dielectron configurations. Using the CT18Z set of parton distribution functions we obtain $ \sin^2\theta_\text{eff}^{\ell} = $ 0.23157 $\pm$ 0.00010 (stat) $\pm$ 0.00015 (exp) $\pm$ 0.00009 (theo) $\pm$ 0.00027 (PDF), where ``stat", ``exp", ``theo", and ``PDF" denote, respectively, the statistical uncertainty and the systematic uncertainties reflecting experimental effects, the theory modeling, and the PDFs. Accounting for the correlations between the various contributions, the total uncertainty, dominated by the PDF term, is 0.00031. It varies between 0.00024 and 0.00035 depending on the PDF set. From the unfolded $ A_4(Y, M) $ angular coefficient, and using the CT18Z PDF set, the extracted $ \sin^2\theta_\text{eff}^{\ell} $ value is 0.23155 $ \pm $ 0.00032 or 0.23153 $ \pm $ 0.00032, depending on the analysis framework, the latter value being obtained with the latest POWHEG Z_ew program version. Our result agrees with the standard model expectation, 0.23155 $ \pm $ 0.00004, and is the most precise hadroncollider measurement. 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 0.00029 and 0.00026. The $ A_4 $ coefficient, measured as a function of the dilepton mass and rapidity, can be used in combination with other LHC measurements or to improve the $ \sin^2\theta_\text{eff}^{\ell} $ measurement using future PDF sets. 
Additional Figures  
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Additional Figure 1:
Dilepton mass resolution in four channels as a function of dilepton rapidity in 2018 simulated samples. 
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Additional Figure 2:
Electron $ \eta $ distribution in 2018 for $ \mathrm{e^e^} $ majority (left) and selective (right) ID dielectron samples. The correction factors have been applied to the charge misID rates. The shaded bands include statistical uncertainties in the misID corrections, as well as the full size of the correction used as a conservative estimate of its systematic uncertainty. 
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Additional Figure 2a:
Electron $ \eta $ distribution in 2018 for $ \mathrm{e^e^} $ majority (left) and selective (right) ID dielectron samples. The correction factors have been applied to the charge misID rates. The shaded bands include statistical uncertainties in the misID corrections, as well as the full size of the correction used as a conservative estimate of its systematic uncertainty. 
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Additional Figure 2b:
Electron $ \eta $ distribution in 2018 for $ \mathrm{e^e^} $ majority (left) and selective (right) ID dielectron samples. The correction factors have been applied to the charge misID rates. The shaded bands include statistical uncertainties in the misID corrections, as well as the full size of the correction used as a conservative estimate of its systematic uncertainty. 
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Additional Figure 3:
Dilepton mass distribution in the samesign dielectrons (left) and $ \mu\mathrm{e} $ (right) samples. The electroweak and topquark events are normalized to the NNLO cross sections and include corrections described in the text. The multijet background is estimated by applying the transfer factors to the corresponding multijetenriched sample. To reduce large signal contamination in the samesign $ \mathrm{e}\mathrm{e} $ sample due to the electron chargemisidentification, the Z boson peak region of 76 GeV $ < m_{\mathrm{e}\mathrm{e}} < $ 106 GeV is removed and the selective charge ID is required for both electrons. 
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Additional Figure 3a:
Dilepton mass distribution in the samesign dielectrons (left) and $ \mu\mathrm{e} $ (right) samples. The electroweak and topquark events are normalized to the NNLO cross sections and include corrections described in the text. The multijet background is estimated by applying the transfer factors to the corresponding multijetenriched sample. To reduce large signal contamination in the samesign $ \mathrm{e}\mathrm{e} $ sample due to the electron chargemisidentification, the Z boson peak region of 76 GeV $ < m_{\mathrm{e}\mathrm{e}} < $ 106 GeV is removed and the selective charge ID is required for both electrons. 
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Additional Figure 3b:
Dilepton mass distribution in the samesign dielectrons (left) and $ \mu\mathrm{e} $ (right) samples. The electroweak and topquark events are normalized to the NNLO cross sections and include corrections described in the text. The multijet background is estimated by applying the transfer factors to the corresponding multijetenriched sample. To reduce large signal contamination in the samesign $ \mathrm{e}\mathrm{e} $ sample due to the electron chargemisidentification, the Z boson peak region of 76 GeV $ < m_{\mathrm{e}\mathrm{e}} < $ 106 GeV is removed and the selective charge ID is required for both electrons. 
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Additional Figure 4:
Dilepton $ p_{\mathrm{T}} $ in $ \mu\mathrm{g} $ and $ \mu\mathrm{h} $ events (upper), and $ \cos\theta_\mathrm{CS} $ in $ \mu\mathrm{g} $ events (lower). The multijet and W$+$jets backgrounds are scaled to the data as described in the text. The error bars include the statistical and systematic uncertainties. 
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Additional Figure 4a:
Dilepton $ p_{\mathrm{T}} $ in $ \mu\mathrm{g} $ and $ \mu\mathrm{h} $ events (upper), and $ \cos\theta_\mathrm{CS} $ in $ \mu\mathrm{g} $ events (lower). The multijet and W$+$jets backgrounds are scaled to the data as described in the text. The error bars include the statistical and systematic uncertainties. 
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Additional Figure 4b:
Dilepton $ p_{\mathrm{T}} $ in $ \mu\mathrm{g} $ and $ \mu\mathrm{h} $ events (upper), and $ \cos\theta_\mathrm{CS} $ in $ \mu\mathrm{g} $ events (lower). The multijet and W$+$jets backgrounds are scaled to the data as described in the text. The error bars include the statistical and systematic uncertainties. 
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Additional Figure 4c:
Dilepton $ p_{\mathrm{T}} $ in $ \mu\mathrm{g} $ and $ \mu\mathrm{h} $ events (upper), and $ \cos\theta_\mathrm{CS} $ in $ \mu\mathrm{g} $ events (lower). The multijet and W$+$jets backgrounds are scaled to the data as described in the text. The error bars include the statistical and systematic uncertainties. 
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Additional Figure 5:
Dilepton mass (upper), rapidity (middle), and $ \cos\theta_\mathrm{CS} $ (lower) distributions, for the $ \mathrm{e}\mathrm{e} $ (left) and $\mathrm{e}\mathrm{g}$ (right) channels in the 2018 samples, after applying all the corrections described in the text. 
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Additional Figure 5a:
Dilepton mass (upper), rapidity (middle), and $ \cos\theta_\mathrm{CS} $ (lower) distributions, for the $ \mathrm{e}\mathrm{e} $ (left) and $\mathrm{e}\mathrm{g}$ (right) channels in the 2018 samples, after applying all the corrections described in the text. 
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Additional Figure 5b:
Dilepton mass (upper), rapidity (middle), and $ \cos\theta_\mathrm{CS} $ (lower) distributions, for the $ \mathrm{e}\mathrm{e} $ (left) and $\mathrm{e}\mathrm{g}$ (right) channels in the 2018 samples, after applying all the corrections described in the text. 
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Additional Figure 5c:
Dilepton mass (upper), rapidity (middle), and $ \cos\theta_\mathrm{CS} $ (lower) distributions, for the $ \mathrm{e}\mathrm{e} $ (left) and $\mathrm{e}\mathrm{g}$ (right) channels in the 2018 samples, after applying all the corrections described in the text. 
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Additional Figure 5d:
Dilepton mass (upper), rapidity (middle), and $ \cos\theta_\mathrm{CS} $ (lower) distributions, for the $ \mathrm{e}\mathrm{e} $ (left) and $\mathrm{e}\mathrm{g}$ (right) channels in the 2018 samples, after applying all the corrections described in the text. 
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Additional Figure 5e:
Dilepton mass (upper), rapidity (middle), and $ \cos\theta_\mathrm{CS} $ (lower) distributions, for the $ \mathrm{e}\mathrm{e} $ (left) and $\mathrm{e}\mathrm{g}$ (right) channels in the 2018 samples, after applying all the corrections described in the text. 
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Additional Figure 5f:
Dilepton mass (upper), rapidity (middle), and $ \cos\theta_\mathrm{CS} $ (lower) distributions, for the $ \mathrm{e}\mathrm{e} $ (left) and $\mathrm{e}\mathrm{g}$ (right) channels in the 2018 samples, after applying all the corrections described in the text. 
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Additional Figure 6:
The data and bestfit angular weighted $ A_\mathrm{FB}^\mathrm{w}(y,m) $ distributions for the 2018 period and in the $ \mathrm{e}\mathrm{e} $ (left) and $\mathrm{e}\mathrm{g}$ (right) channels. The error bars represent the statistical uncertainties of the measured and simulated samples. 
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Additional Figure 6a:
The data and bestfit angular weighted $ A_\mathrm{FB}^\mathrm{w}(y,m) $ distributions for the 2018 period and in the $ \mathrm{e}\mathrm{e} $ (left) and $\mathrm{e}\mathrm{g}$ (right) channels. The error bars represent the statistical uncertainties of the measured and simulated samples. 
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Additional Figure 6b:
The data and bestfit angular weighted $ A_\mathrm{FB}^\mathrm{w}(y,m) $ distributions for the 2018 period and in the $ \mathrm{e}\mathrm{e} $ (left) and $\mathrm{e}\mathrm{g}$ (right) channels. The error bars represent the statistical uncertainties of the measured and simulated samples. 
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Additional Figure 7:
The data and bestfit $ \cos\theta_\mathrm{CS} $ distributions in the $ \mathrm{e}\mathrm{e} $ (left) and $\mathrm{e}\mathrm{g}$ (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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Additional Figure 7a:
The data and bestfit $ \cos\theta_\mathrm{CS} $ distributions in the $ \mathrm{e}\mathrm{e} $ (left) and $\mathrm{e}\mathrm{g}$ (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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Additional Figure 7b:
The data and bestfit $ \cos\theta_\mathrm{CS} $ distributions in the $ \mathrm{e}\mathrm{e} $ (left) and $\mathrm{e}\mathrm{g}$ (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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Additional Figure 8:
The data vs. prefit (left) and postfit (right) $ A_4(Y, M) $ distributions in the combined Run2 fit for NNPDF40 (upper), MSHT20 (middle), and CT18 (lower) PDF sets. The shaded bands correspond to the PDF uncertainty. 
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Additional Figure 8a:
The data vs. prefit (left) and postfit (right) $ A_4(Y, M) $ distributions in the combined Run2 fit for NNPDF40 (upper), MSHT20 (middle), and CT18 (lower) PDF sets. The shaded bands correspond to the PDF uncertainty. 
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Additional Figure 8b:
The data vs. prefit (left) and postfit (right) $ A_4(Y, M) $ distributions in the combined Run2 fit for NNPDF40 (upper), MSHT20 (middle), and CT18 (lower) PDF sets. The shaded bands correspond to the PDF uncertainty. 
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Additional Figure 8c:
The data vs. prefit (left) and postfit (right) $ A_4(Y, M) $ distributions in the combined Run2 fit for NNPDF40 (upper), MSHT20 (middle), and CT18 (lower) PDF sets. The shaded bands correspond to the PDF uncertainty. 
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Additional Figure 8d:
The data vs. prefit (left) and postfit (right) $ A_4(Y, M) $ distributions in the combined Run2 fit for NNPDF40 (upper), MSHT20 (middle), and CT18 (lower) PDF sets. The shaded bands correspond to the PDF uncertainty. 
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Additional Figure 8e:
The data vs. prefit (left) and postfit (right) $ A_4(Y, M) $ distributions in the combined Run2 fit for NNPDF40 (upper), MSHT20 (middle), and CT18 (lower) PDF sets. The shaded bands correspond to the PDF uncertainty. 
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Additional Figure 8f:
The data vs. prefit (left) and postfit (right) $ A_4(Y, M) $ distributions in the combined Run2 fit for NNPDF40 (upper), MSHT20 (middle), and CT18 (lower) PDF sets. The shaded bands correspond to the PDF uncertainty. 
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Additional Figure 9:
The measured vs. predicted combined Run2 $ A_4(Y, M) $ distributions for CT18Z PDF set. The shaded bands correspond to the PDF uncertainty. 
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Additional Figure 10:
Values of $ \sin^2\theta_\mathrm{eff}^\ell $ measured in the four channels and four datataking periods. The results obtained with the $ A_\mathrm{FB}^\mathrm{w} $, $ 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}^\mathrm{w} $based result, the violet error bands show the combined statistical and experimental systematic uncertainties, while the black error bars represent the total uncertainties. 
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Additional Figure 11:
Comparison of pre and post$ A_4 $fit valence quark distributions and their combinations for different PDFs. The error bars are only shown for the postfit distributions. 
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Additional Figure 11a:
Comparison of pre and post$ A_4 $fit valence quark distributions and their combinations for different PDFs. The error bars are only shown for the postfit distributions. 
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Additional Figure 11b:
Comparison of pre and post$ A_4 $fit valence quark distributions and their combinations for different PDFs. The error bars are only shown for the postfit distributions. 
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Additional Figure 11c:
Comparison of pre and post$ A_4 $fit valence quark distributions and their combinations for different PDFs. The error bars are only shown for the postfit distributions. 
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Additional Figure 11d:
Comparison of pre and post$ A_4 $fit valence quark distributions and their combinations for different PDFs. The error bars are only shown for the postfit distributions. 
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Additional Figure 11e:
Comparison of pre and post$ A_4 $fit valence quark distributions and their combinations for different PDFs. The error bars are only shown for the postfit distributions. 
References  
1  ALEPH, DELPHI, L3, OPAL, SLD, LEP Electroweak Working Group, SLD Electroweak Group, SLD Heavy Flavour Group Collaboration  Precision electroweak measurements on the Z resonance  Phys. Rept. 427 (2006) 257  hepex/0509008 
2  Particle Data Group Collaboration  Review of Particle Physics  PTEP 2022 (2022) 083C01  
3  D0 Collaboration  Measurement of the forwardbackward charge asymmetry and extraction of $ \sin^2\theta_W^{\text{eff}} $ in $ \mathrm{p}\overline{\mathrm{p}} \rightarrow \mathrm{Z}/\gamma^{\ast}+\mathrm{X} \rightarrow \mathrm{e}^+\mathrm{e}^ + \mathrm{X} $ events produced at $ \sqrt{s}= $ 1.96 TeV  PRL 101 (2008) 191801  0804.3220 
4  D0 Collaboration  Measurement of $ \sin^2\theta_\text{eff}^{\ell} $ and Zlight quark couplings using the forwardbackward charge asymmetry in $ \mathrm{p}\overline{\mathrm{p}} \to \mathrm{Z}/\gamma^{\ast} \to \mathrm{e}^+\mathrm{e}^ $ events with $ {\cal L}= $ 5.0 fb$ ^{1} $ at $ \sqrt{s}= $ 1.96 TeV  PRD 84 (2011) 012007  1104.4590 
5  CMS Collaboration  Measurement of the weak mixing angle with the DrellYan process in protonproton collisions at the LHC  PRD 84 (2011) 112002  CMSEWK11003 1110.2682 
6  CDF Collaboration  Indirect measurement of $ \sin^2\theta_W (M_\mathrm{W}) $ using $ \mathrm{e}^+\mathrm{e}^ $ pairs in the Zboson region with $ \mathrm{p}\overline{\mathrm{p}} $ collisions at a centerofmomentum energy of 1.96 TeV  PRD 88 (2013) 072002  1307.0770 
7  CDF Collaboration  Indirect measurement of $ \sin^2 \theta_W $ (or $ M_\mathrm{W} $) using $ \mu^{+}\mu^{} $ pairs from $ \gamma^{\ast}/\mathrm{Z} $ bosons produced in $ \mathrm{p}\overline{\mathrm{p}} $ collisions at a centerofmomentum energy of 1.96 TeV  PRD 89 (2014) 072005  1402.2239 
8  D0 Collaboration  Measurement of the effective weak mixing angle in $ \mathrm{p}\overline{\mathrm{p}} \rightarrow \mathrm{Z}/\gamma^{\ast}\rightarrow \mathrm{e}^+\mathrm{e}^ $ events  PRL 115 (2015) 041801  1408.5016 
9  ATLAS Collaboration  Measurement of the forwardbackward asymmetry of electron and muon pairproduction in pp collisions at $ \sqrt{s} = $ 7 TeV with the ATLAS detector  JHEP 09 (2015) 049  1503.03709 
10  LHCb Collaboration  Measurement of the forwardbackward asymmetry in $ \mathrm{Z}/\gamma^{\ast} \rightarrow \mu^{+}\mu^{} $ decays and determination of the effective weak mixing angle  JHEP 11 (2015) 190  1509.07645 
11  CDF Collaboration  Measurement of $ \sin^2\theta^\text{lept}_\text{eff} $ using $ \mathrm{e}^+\mathrm{e}^ $ pairs from $ \gamma^{\ast}/\mathrm{Z} $ bosons produced in $ \mathrm{p}\overline{\mathrm{p}} $ collisions at a centerofmomentum energy of 1.96 TeV  PRD 93 (2016) 112016  1605.02719 
12  D0 Collaboration  Measurement of the effective weak mixing angle in $ \mathrm{p}\overline{\mathrm{p}} \rightarrow \mathrm{Z}/\gamma^{\ast} \rightarrow \ell^+\ell^ $ events  PRL 120 (2018) 241802  1710.03951 
13  CDF and D0 collaborations  Tevatron Run II combinations of the effective leptonic electroweak mixing angle  PRD 97 (2018) 112007  1801.06283 
14  CMS Collaboration  Measurement of the weak mixing angle using the forwardbackward asymmetry of DrellYan events in pp collisions at 8 TeV  EPJC 78 (2018) 701  CMSSMP16007 1806.00863 
15  J. C. Collins and D. E. Soper  Angular distribution of dileptons in highenergy hadron collisions  PRD 16 (1977) 2219  
16  P. Faccioli and C. Lourenço  Particle polarization in high energy physics: an introduction and case studies on vector particle production at the LHC  Lecture Notes in Physics. Springer, 2022 link 

17  A. Bodek  A simple event weighting technique for optimizing the measurement of the forwardbackward asymmetry of DrellYan dilepton pairs at hadron colliders  EPJC 67 (2010) 321  0911.2850 
18  CMS Collaboration  The CMS experiment at the CERN LHC  JINST 3 (2008) S08004  
19  CMS Collaboration  Development of the CMS detector for the CERN LHC Run 3  JINST 19 (2024) P05064  CMSPRF21001 2309.05466 
20  CMS Collaboration  Performance of the CMS Level1 trigger in protonproton collisions at $ \sqrt{s} = $ 13 TeV  JINST 15 (2020) P10017  CMSTRG17001 2006.10165 
21  CMS Collaboration  The CMS trigger system  JINST 12 (2017) P01020  CMSTRG12001 1609.02366 
22  CMS Collaboration  Electron and photon reconstruction and identification with the CMS experiment at the CERN LHC  JINST 16 (2021) P05014  CMSEGM17001 2012.06888 
23  CMS Collaboration  Performance of the CMS muon detector and muon reconstruction with protonproton collisions at $ \sqrt{s} = $ 13 TeV  JINST 13 (2018) P06015  CMSMUO16001 1804.04528 
24  CMS Collaboration  Description and performance of track and primaryvertex reconstruction with the CMS tracker  JINST 9 (2014) P10009  CMSTRK11001 1405.6569 
25  CMS Collaboration  Particleflow reconstruction and global event description with the CMS detector  JINST 12 (2017) P10003  CMSPRF14001 1706.04965 
26  CMS HCAL Collaboration  Design, performance and calibration of the CMS forward calorimeter wedges  EPJC 53 (2008) 139  
27  CMS Collaboration  Performance of reconstruction and identification of $ \tau $ leptons decaying to hadrons and $ \nu_\tau $ in pp collisions at $ \sqrt{s}= $ 13 TeV  JINST 13 (2018) P10005  CMSTAU16003 1809.02816 
28  CMS Collaboration  Jet energy scale and resolution in the CMS experiment in pp collisions at 8 TeV  JINST 12 (2017) P02014  CMSJME13004 1607.03663 
29  CMS Collaboration  Performance of missing transverse momentum reconstruction in protonproton collisions at $ \sqrt{s} = $ 13 TeV using the CMS detector  JINST 14 (2019) P07004  CMSJME17001 1903.06078 
30  CMS Collaboration  Strategies and performance of the CMS silicon tracker alignment during LHC Run 2  NIM A 1037 (2022) 166795  CMSTRK20001 2111.08757 
31  CMS Collaboration  Precision luminosity measurement in protonproton collisions at $ \sqrt{s} = $ 13 TeV in 2015 and 2016 at CMS  EPJC 81 (2021) 800  CMSLUM17003 2104.01927 
32  CMS Collaboration  CMS luminosity measurement for the 2017 datataking period at $ \sqrt{s} = $ 13 TeV  CMS Physics Analysis Summary, 2018 link 
CMSPASLUM17004 
33  CMS Collaboration  CMS luminosity measurement for the 2018 datataking period at $ \sqrt{s} = $ 13 TeV  CMS Physics Analysis Summary, 2019 link 
CMSPASLUM18002 
34  CMS Collaboration  Performance of the CMS muon trigger system in protonproton collisions at $ \sqrt{s} = $ 13 TeV  JINST 16 (2021) P07001  CMSMUO19001 2102.04790 
35  TMVA Collaboration  TMVA: Toolkit for multivariate data analysis  AIP Conf. Proc. 1504 (2012) 1013  
36  M. Cacciari, G. P. Salam, and G. Soyez  The anti$ k_{\mathrm{T}} $ jet clustering algorithm  JHEP 04 (2008) 063  0802.1189 
37  M. Abadi et al.  TensorFlow: largescale machine learning on heterogeneous distributed systems  link  1603.04467 
38  S. Frixione, P. Nason, and C. Oleari  Matching NLO QCD computations with parton shower simulations: the POWHEG method  JHEP 11 (2007) 070  0709.2092 
39  S. Alioli, P. Nason, C. Oleari, and E. Re  A general framework for implementing NLO calculations in shower Monte Carlo programs: the POWHEG BOX  JHEP 06 (2010) 043  1002.2581 
40  P. F. Monni et al.  MiNNLO$ _\mathrm{PS} $: a new method to match NNLO QCD to parton showers  JHEP 05 (2020) 143  1908.06987 
41  P. F. Monni, E. Re, and M. Wiesemann  MiNNLO$ _{\mathrm{PS}} $: optimizing 2 $ \rightarrow $ 1 hadronic processes  EPJC 80 (2020) 1075  2006.04133 
42  T. Sjöstrand et al.  An introduction to PYTHIA8.2  Comput. Phys. Commun. 191 (2015) 159  1410.3012 
43  E. Barberio and Z. Was  PHOTOS: A universal Monte Carlo for QED radiative corrections. Version 2.0  Comput. Phys. Commun. 79 (1994) 291  
44  P. Golonka and Z. Was  PHOTOS Monte Carlo: A precision tool for QED corrections in Z and W decays  EPJC 45 (2006) 97  hepph/0506026 
45  NNPDF Collaboration  Parton distributions from highprecision collider data  EPJC 77 (2017) 663  1706.00428 
46  NNPDF Collaboration  The path to proton structure at 1\% accuracy  EPJC 82 (2022) 428  2109.02653 
47  T.J. Hou et al.  New CTEQ global analysis of quantum chromodynamics with highprecision data from the LHC  PRD 103 (2021) 014013  1912.10053 
48  S. Bailey et al.  Parton distributions from LHC, HERA, Tevatron and fixed target data: MSHT20 PDFs  EPJC 81 (2021) 341  2012.04684 
49  J. Butterworth et al.  PDF4LHC recommendations for LHC Run II  JPG 43 (2016) 023001  1510.03865 
50  J. Alwall et al.  The automated computation of treelevel and nexttoleading order differential cross sections, and their matching to parton shower simulations  JHEP 07 (2014) 079  1405.0301 
51  GEANT 4 Collaboration  GEANT 4a simulation toolkit  NIM A 506 (2003) 250  
52  CMS Collaboration  Measurement of the inelastic protonproton cross section at $ \sqrt{s}= $ 13 TeV  JHEP 07 (2018) 161  CMSFSQ15005 1802.02613 
53  L. Barzè et al.  Neutral current DrellYan with combined QCD and electroweak corrections in the POWHEG BOX  EPJC 73 (2013) 2474  1302.4606 
54  M. Chiesa, F. Piccinini, and A. Vicini  Direct determination of $ \sin^2 \theta^\ell_\text{eff} $ at hadron colliders  PRD 100 (2019) 071302  1906.11569 
55  M. Chiesa, C. L. Del Pio, and F. Piccinini  On electroweak corrections to neutral current DrellYan with the POWHEG BOX  EPJC 84 (2024) 539  2402.14659 
56  CMS Collaboration  Measurement of the inclusive W and Z production cross sections in pp collisions at $ \sqrt{s}= $ 7 TeV  JHEP 10 (2011) 132  CMSEWK10005 1107.4789 
57  A. Bodek et al.  Extracting muon momentum scale corrections for hadron collider experiments  EPJC 72 (2012) 2194  1208.3710 
58  B. Efron  Bootstrap methods: another look at the jackknife  Annals Statist. 7 (1979) 1  
59  A. Bodek, J. Han, A. Khukhunaishvili, and W. Sakumoto  Using DrellYan forwardbackward asymmetry to reduce PDF uncertainties in the measurement of electroweak parameters  EPJC 76 (2016) 115  1507.02470 
60  CMS Collaboration  Measurement of associated production of a W boson and a charm quark in protonproton collisions at $ \sqrt{s} = $ 13 TeV  EPJC 79 (2019) 269  CMSSMP17014 1811.10021 
61  CMS Collaboration  Measurement of the muon charge asymmetry in inclusive $ \mathrm{p}\mathrm{p} \to \mathrm{W} + \mathrm{X} $ production at $ \sqrt{s} = $ 7 TeV and an improved determination of light parton distribution functions  PRD 90 (2014) 032004  CMSSMP12021 1312.6283 
62  D. C. Liu and J. Nocedal  On the limited memory BFGS method for large scale optimization  Math. Programming 45 (1989) 503  
63  NNPDF Collaboration  The path to N$^3$LO parton distributions  EPJC 84 (2024) 659  2402.18635 
64  T. Cridge, L. A. HarlandLang, and R. S. Thorne  Combining QED and approximate N$ ^3 $LO QCD corrections in a global PDF fit: MSHT20qed_an3lo PDFs  2312.07665  
65  S. Alekhin et al.  HERAFitter  EPJC 75 (2015) 304  1410.4412 
66  HERAFitter developers' Team Collaboration  QCD analysis of W and Zboson production at Tevatron  EPJC 75 (2015) 458  1503.05221 
67  C. Schwan  PineAPPL: NLO EW corrections for PDF processes  SciPost Phys. Proc. 8 (2022) 079  2108.05816 
68  S. Carrazza, E. R. Nocera, C. Schwan, and M. Zaro  PineAPPL: combining EW and QCD corrections for fast evaluation of LHC processes  JHEP 12 (2020) 108  2008.12789 
69  NNPDF Collaboration  Determination of the theory uncertainties from missing higher orders on NNLO parton distributions with percent accuracy  EPJC 84 (2024) 517  2401.10319 
70  S. Alekhin, J. Blümlein, S. Moch, and R. Placakyte  Parton distribution functions, $ \alpha_s $, and heavyquark masses for LHC Run II  PRD 96 (2017) 014011  1701.05838 
71  PDF4LHC Working Group Collaboration  The PDF4LHC21 combination of global PDF fits for the LHC Run III  JPG 49 (2022) 080501  2203.05506 
72  T.J. Hou, H.W. Lin, M. Yan, and C. P. Yuan  Impact of lattice strangeness asymmetry data in the CTEQTEA global analysis  PRD 107 (2023) 076018  2211.11064 
73  H1 and ZEUS Collaborations  Combination of measurements of inclusive deep inelastic $ {\mathrm{e}^{\pm }\mathrm{p}} $ scattering cross sections and QCD analysis of HERA data  EPJC 75 (2015) 580  1506.06042 
74  CMS Collaboration  HEPData record for this analysis  link 
Compact Muon Solenoid LHC, CERN 