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| CMS-PAS-SMP-16-007 | ||
| Measurement of the weak mixing angle with the forward-backward asymmetry of Drell-Yan events at 8 TeV | ||
| CMS Collaboration | ||
| July 2017 | ||
| Abstract: We present a measurement of the effective weak mixing angle using the forward-backward asymmetry of Drell-Yan (ee and $\mu\mu$) events in pp collisions at $\sqrt{s}= $ 8 TeV at CMS. The data sample corresponds to an integrated luminosity of 18.8 fb$^{-1}$ and 19.6 fb$^{-1}$ for muon and electron channels, respectively. The sample consists of 8.2 million dimuon and 4.9 million dielectron events. With new analysis techniques and a larger dataset, the statistical and systematic uncertainties are significantly reduced compared to our previous measurement. The extracted value of the effective weak mixing angle from the combined ee and $\mu\mu$ data samples is $ \sin^2\theta^{\text{lept}}_{\text{eff}}= $ 0.23101 $\pm$ 0.00036 (stat) $\pm$ 0.00018 (syst) $\pm$ 0.00016 (theory) $\pm$ 0.00030 (pdf) or $ \sin^2\theta^{\text{lept}}_{\text{eff}}= $ 0.23101 $\pm$ 0.00052. | ||
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Links:
CDS record (PDF) ;
inSPIRE record ;
CADI line (restricted) ;
These preliminary results are superseded in this paper, EPJC 78 (2018) 701. The superseded preliminary plots can be found here. |
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| Figures | |
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Figure 1:
$ {A_\text {FB}} (M_{ {\ell \ell }})$ distributions for dimuon events generated with PYTHIA 8 using the leading-order NNPDF3.0. The dimuon rapidity is restricted to $|Y_{ {\ell \ell }}|< $ 2.4. (Left) $ {A_\text {FB}} ^\mathrm {true}(M_{ {\ell \ell }})$ in different $\mathrm{q\bar{q}}$ production channels. The curves are made using Eq. 5. Here, the definition of $ {A_\text {FB}} ^\mathrm {true}(M_{ {\ell \ell }})$ uses the known quark direction instead of the dilepton boost direction. (Middle) The observable (diluted) $ {A_\text {FB}} $ for different $\mathrm{q\bar{q}}$ production channels. (Right) The total observable (diluted) $ {A_\text {FB}} $ for different $|Y_{ {\ell \ell }}|$ bins. |
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Figure 1-a:
$ {A_\text {FB}} (M_{ {\ell \ell }})$ distributions for dimuon events generated with PYTHIA 8 using the leading-order NNPDF3.0. The dimuon rapidity is restricted to $|Y_{ {\ell \ell }}|< $ 2.4. $ {A_\text {FB}} ^\mathrm {true}(M_{ {\ell \ell }})$ in different $\mathrm{q\bar{q}}$ production channels. The curves are made using Eq. 5. Here, the definition of $ {A_\text {FB}} ^\mathrm {true}(M_{ {\ell \ell }})$ uses the known quark direction instead of the dilepton boost direction. |
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Figure 1-b:
$ {A_\text {FB}} (M_{ {\ell \ell }})$ distributions for dimuon events generated with PYTHIA 8 using the leading-order NNPDF3.0. The dimuon rapidity is restricted to $|Y_{ {\ell \ell }}|< $ 2.4. The observable (diluted) $ {A_\text {FB}} $ for different $\mathrm{q\bar{q}}$ production channels. |
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Figure 1-c:
$ {A_\text {FB}} (M_{ {\ell \ell }})$ distributions for dimuon events generated with PYTHIA 8 using the leading-order NNPDF3.0. The dimuon rapidity is restricted to $|Y_{ {\ell \ell }}|< $ 2.4. The total observable (diluted) $ {A_\text {FB}} $ for different $|Y_{ {\ell \ell }}|$ bins. |
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Figure 2:
Dimuon (left) and dielectron (right) mass distributions in three representative rapidity bins: $|Y_{ {\ell \ell }}|< $ 0.4 (top), 0.8 $ < |Y_{ {\ell \ell }}| < $ 1.2 (center), and 1.6 $ < |Y_{ {\ell \ell }}| < $ 2.0 (bottom). |
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Figure 2-a:
Dimuon mass distribution in representative rapidity bin $|Y_{ {\ell \ell }}|< $ 0.4. |
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Figure 2-b:
Dielectron mass distribution in representative rapidity bin $|Y_{ {\ell \ell }}|< $ 0.4. |
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Figure 2-c:
Dimuon mass distribution in representative rapidity bin 0.8 $ < |Y_{ {\ell \ell }}|< $ 1.2. |
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Figure 2-d:
Dielectron mass distribution in representative rapidity bin 0.8 $ < |Y_{ {\ell \ell }}|< $ 1.2. |
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Figure 2-e:
Dimuon mass distribution in representative rapidity bin 1.6 $ < |Y_{ {\ell \ell }}| < $ 2.0. |
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Figure 2-f:
Dielectron mass distribution in representative rapidity bin 1.6 $ < |Y_{ {\ell \ell }}| < $ 2.0. |
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Figure 3:
The muon (left) and electron (right) $ {\cos\theta ^{*}} $ distributions in three representative rapidity bins: $|Y_{ {\ell \ell }}| < $ 0.4 (top), 0.8 $ < |Y_{ {\ell \ell }}| < $ 1.2 (center), and 1.6 $ < |Y_{ {\ell \ell }}| < $ 2.0 (bottom). |
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Figure 3-a:
The muon $ {\cos\theta ^{*}} $ distribution in representative rapidity bin $|Y_{ {\ell \ell }}| < $ 0.4. |
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Figure 3-b:
The electron $ {\cos\theta ^{*}} $ distribution in representative rapidity bin $|Y_{ {\ell \ell }}| < $ 0.4. |
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Figure 3-c:
The muon $ {\cos\theta ^{*}} $ distribution in representative rapidity bin 0.8 $ < |Y_{ {\ell \ell }}| < $ 1.2. |
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Figure 3-d:
The electron $ {\cos\theta ^{*}} $ distribution in representative rapidity bin 0.8 $ < |Y_{ {\ell \ell }}| < $ 1.2. |
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Figure 3-e:
The muon $ {\cos\theta ^{*}} $ distribution in representative rapidity bin 1.6 $ < |Y_{ {\ell \ell }}| < $ 2.0. |
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Figure 3-f:
The electron $ {\cos\theta ^{*}} $ distribution in representative rapidity bin 1.6 $ < |Y_{ {\ell \ell }}| < $ 2.0. |
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Figure 4:
Comparison between data and best-fit $ {A_\text {FB}} $ distributions in the dimuon (top) and dielectron (bottom) channels. The best-fit $ {A_\text {FB}} $ value in each bin is obtained by linear interpolation between the two neighboring templates. The templates are based on the central PDF of the NLO NNPDF3.0 set. |
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Figure 4-a:
Comparison between data and best-fit $ {A_\text {FB}} $ distributions in the dimuon channel. The best-fit $ {A_\text {FB}} $ value in each bin is obtained by linear interpolation between the two neighboring templates. The templates are based on the central PDF of the NLO NNPDF3.0 set. |
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Figure 4-b:
Comparison between data and best-fit $ {A_\text {FB}} $ distributions in the dielectron channel. The best-fit $ {A_\text {FB}} $ value in each bin is obtained by linear interpolation between the two neighboring templates. The templates are based on the central PDF of the NLO NNPDF3.0 set. |
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Figure 5:
Distribution of $ {A_\text {FB}} $ as a function of mass integrated over rapidity (left) and in six rapidity bins (right) for $ {\sin^2\theta ^{\text {lept}}_{\text {eff}}} = $ 0.23120. The solid lines in the bottom panel correspond to six variations of $ {\sin^2\theta ^{\text {lept}}_{\text {eff}}} $ around the central value: $\pm$ 0.00040, $\pm$ 0.00080 and $\pm$ 0.00120. The dashed lines correspond to $ {A_\text {FB}} $ predictions for 100 NNPDF3.0 replicas. The shaded band illustrates the standard deviation over the NNPDF3.0 replicas. |
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Figure 5-a:
Distribution of $ {A_\text {FB}} $ as a function of mass integrated over rapidity for $ {\sin^2\theta ^{\text {lept}}_{\text {eff}}} = $ 0.23120. The solid lines in the bottom panel correspond to six variations of $ {\sin^2\theta ^{\text {lept}}_{\text {eff}}} $ around the central value: $\pm$ 0.00040, $\pm$ 0.00080 and $\pm$ 0.00120. The dashed lines correspond to $ {A_\text {FB}} $ predictions for 100 NNPDF3.0 replicas. The shaded band illustrates the standard deviation over the NNPDF3.0 replicas. |
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Figure 5-b:
Distribution of $ {A_\text {FB}} $ as a function of mass in six rapidity bins for $ {\sin^2\theta ^{\text {lept}}_{\text {eff}}} = $ 0.23120. The solid lines in the bottom panel correspond to six variations of $ {\sin^2\theta ^{\text {lept}}_{\text {eff}}} $ around the central value: $\pm$ 0.00040, $\pm$ 0.00080 and $\pm$ 0.00120. The dashed lines correspond to $ {A_\text {FB}} $ predictions for 100 NNPDF3.0 replicas. The shaded band illustrates the standard deviation over the NNPDF3.0 replicas. |
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Figure 6:
The top panel of each figure shows the $\chi ^2_{\mathrm {min}}$ vs best-fit ${\sin^2\theta ^{\text {lept}}_{\text {eff}}} $ distribution for 100 NNPDF replicas in muon channel (top left), electron channel (top right), and their combination (bottom). The corresponding bottom panels show the best-fit ${\sin^2\theta ^{\text {lept}}_{\text {eff}}}$ distribution over the nominal (blue) and weighted (red) PDF replicas. |
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Figure 6-a:
The top panel of the figure shows the $\chi ^2_{\mathrm {min}}$ vs best-fit ${\sin^2\theta ^{\text {lept}}_{\text {eff}}} $ distribution for 100 NNPDF replicas in muon channel. The bottom panel shows the best-fit ${\sin^2\theta ^{\text {lept}}_{\text {eff}}}$ distribution over the nominal (blue) and weighted (red) PDF replicas. |
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Figure 6-b:
The top panel of the figure shows the $\chi ^2_{\mathrm {min}}$ vs best-fit ${\sin^2\theta ^{\text {lept}}_{\text {eff}}} $ distribution for 100 NNPDF replicas in electron channel.The bottom panel shows the best-fit ${\sin^2\theta ^{\text {lept}}_{\text {eff}}}$ distribution over the nominal (blue) and weighted (red) PDF replicas. |
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Figure 6-c:
The top panel of the figure shows the $\chi ^2_{\mathrm {min}}$ vs best-fit ${\sin^2\theta ^{\text {lept}}_{\text {eff}}} $ distribution for 100 NNPDF replicas in the combination of muon and electron channels. The bottom panel shows the best-fit ${\sin^2\theta ^{\text {lept}}_{\text {eff}}}$ distribution over the nominal (blue) and weighted (red) PDF replicas. |
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Figure 7:
The extracted values of ${\sin^2\theta ^{\text {lept}}_{\text {eff}}}$ in the muon and electron channels and their combination. The error bars include the statistical, experimental, and PDF uncertainties. The PDF uncertainties are derived without (left) and with using the Bayesian $\chi ^2$ weighting method (right). |
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Figure 7-a:
The extracted values of ${\sin^2\theta ^{\text {lept}}_{\text {eff}}}$ in the muon and electron channels and their combination. The error bars include the statistical, experimental, and PDF uncertainties. The PDF uncertainties are derived without using the Bayesian $\chi ^2$ weighting method. |
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Figure 7-b:
The extracted values of ${\sin^2\theta ^{\text {lept}}_{\text {eff}}}$ in the muon and electron channels and their combination. The error bars include the statistical, experimental, and PDF uncertainties. The PDF uncertainties are derived with using the Bayesian $\chi ^2$ weighting method. |
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Figure 8:
Extracted values of ${\sin^2\theta ^{\text {lept}}_{\text {eff}}}$ from the dimuon data for different PDF sets with nominal (left) and $\chi ^2$ reweighted (right) PDF replicas. The error bars include the statistical, experimental and the PDF uncertainties. |
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Figure 8-a:
Extracted values of ${\sin^2\theta ^{\text {lept}}_{\text {eff}}}$ from the dimuon data for different PDF sets with nominal PDF replicas. The error bars include the statistical, experimental and the PDF uncertainties. |
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Figure 8-b:
Extracted values of ${\sin^2\theta ^{\text {lept}}_{\text {eff}}}$ from the dimuon data for different PDF sets with $\chi ^2$ reweighted PDF replicas. The error bars include the statistical, experimental and the PDF uncertainties. |
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Figure 9:
Comparison of the measured ${\sin^2\theta ^{\text {lept}}_{\text {eff}}}$ in the muon and electron channels and their combination with the previous LEP, SLC, Tevatron and LHC measurements. The shaded band corresponds to the combination of the LEP and SLC measurements. |
| Tables | |
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Table 1:
Summary of the statistical uncertainties. The statistical uncertainties in the lepton selection efficiency and calibration coefficients in data are included. |
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Table 2:
Summary of experimental systematic uncertainties. |
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Table 3:
Theory systematic uncertainties in the dimuon (left) and dielectron (right) channels. Detailed descriptions of each systematics are given in the text. |
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Table 4:
Central value and PDF uncertainty of the measured ${\sin^2\theta ^{\text {lept}}_{\text {eff}}}$ in the muon and electron channels and their combination with and without constraining PDFs using Bayesian $\chi ^2$ reweighting. |
| Summary |
| We extract ${\sin^2\theta^{\text{lept}}_{\text{eff}}} $ from the measurements of the mass and rapidity dependence of $ {A_\text {FB}} $ in Drell-Yan ee and $\mu\mu$ events. With larger datasets and new analysis techniques, including precise lepton momentum calibration, angular event weighting, and additional PDF constraints, the statistical and systematic uncertainties are significantly reduced compared to our previous measurement. The combined result from the dielectron and dimuon channels is $ \sin^2\theta^{\text{lept}}_{\text{eff}}= $ 0.23101 $\pm$ 0.00036 (stat) $\pm$ 0.00018 (syst) $\pm$ 0.00016 (theory) $\pm$ 0.00030 (pdf) or $ \sin^2\theta^{\text{lept}}_{\text{eff}}= $ 0.23101 $\pm$ 0.00052. The results are consistent with the most precise LEP and SLD measurements. |
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