Compact Muon Solenoid
LHC, CERN
Visit us: CMS Public Website, CMS Physics ;
Contact us: CMS Publications Committee
| CMS-SMP-16-007 ; CERN-EP-2018-126 | ||
| Measurement of the weak mixing angle using the forward-backward asymmetry of Drell-Yan events in pp collisions at 8 TeV | ||
| CMS Collaboration | ||
| 3 June 2018 | ||
| Eur. Phys. J. C 78 (2018) 701 | ||
| Abstract: A measurement is presented of the effective leptonic weak mixing angle (${\sin^2\theta^{\ell}_{\text{eff}}} $) using the forward-backward asymmetry of Drell-Yan lepton pairs ($\mu\mu$ and ee) produced in proton-proton collisions at $\sqrt{s} = $ 8 TeV at the CMS experiment of the LHC. The data correspond to integrated luminosities of 18.8 and 19.6 fb$^{-1}$ in the dimuon and dielectron channels, respectively, containing 8.2 million dimuon and 4.9 million dielectron events. With more events and new analysis techniques, including constraints obtained on the parton distribution functions from the measured forward-backward asymmetry, the statistical and systematic uncertainties are significantly reduced relative to previous CMS measurements. The extracted value of ${\sin^2\theta^{\ell}_{\text{eff}}} $ from the combined dilepton data is ${\sin^2\theta^{\ell}_{\text{eff}}} = $ 0.23101 $\pm$ 0.00036 (stat) $\pm$ 0.00018 (syst) $\pm$ 0.00016 (theo) $\pm$ 0.00031 (parton distributions in proton) $ = $ 0.23101 $\pm$ 0.00053. | ||
| Links: e-print arXiv:1806.00863 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; CADI line (restricted) ; | ||
| Figures | |
png pdf |
Figure 1:
The dependence of $ {A_\text {FB}} $ on $ {m_{\ell \ell}} $ in dimuon events generated using PYTHIA 8.212 [15] and the LO NNPDF3.0 [16] PDFs for dimuon rapidities of $ | y_{\ell \ell} | < $ 2.4. The distributions for the total production (${{\mathrm {q}} {\overline {\mathrm {q}}}}$) and the different channels are given on the left, overlaid with results based on Eq. (6), using the definition of $ {A_\text {FB}} ^\text {true}({m_{\ell \ell}})$ for the known quark direction. The middle panel gives the diluted ${A_\text {FB}}$ using instead the direction of the dilepton boost, and the right panel shows the diluted ${A_\text {FB}}$ in $ | y_{\ell \ell} | $ bins of 0.4 for all channels. |
png pdf |
Figure 1-a:
The dependence of $ {A_\text {FB}} $ on $ {m_{\ell \ell}} $ in dimuon events generated using PYTHIA 8.212 [15] and the LO NNPDF3.0 [16] PDFs for dimuon rapidities of $ | y_{\ell \ell} | < $ 2.4. This panel shows the distributions for the total production (${{\mathrm {q}} {\overline {\mathrm {q}}}}$) and the different channels, overlaid with results based on Eq. (6), using the definition of $ {A_\text {FB}} ^\text {true}({m_{\ell \ell}})$ for the known quark direction. |
png pdf |
Figure 1-b:
The dependence of $ {A_\text {FB}} $ on $ {m_{\ell \ell}} $ in dimuon events generated using PYTHIA 8.212 [15] and the LO NNPDF3.0 [16] PDFs for dimuon rapidities of $ | y_{\ell \ell} | < $ 2.4. This panel gives the diluted ${A_\text {FB}}$ using instead the direction of the dilepton boost. |
png pdf |
Figure 1-c:
The dependence of $ {A_\text {FB}} $ on $ {m_{\ell \ell}} $ in dimuon events generated using PYTHIA 8.212 [15] and the LO NNPDF3.0 [16] PDFs for dimuon rapidities of $ | y_{\ell \ell} | < $ 2.4. This panel shows the diluted ${A_\text {FB}}$ in $ | y_{\ell \ell} | $ bins of 0.4 for all channels. |
png pdf |
Figure 2:
Dimuon (left) and dielectron (right) mass distributions in three representative bins in rapidity: $ | y_{\ell \ell} | < $ 0.4 (upper), 0.8 $ < | y_{\ell \ell} | < $ 1.2 (middle), and 1.6 $ < | y_{\ell \ell} | < $ 2.0 (lower). |
png pdf |
Figure 2-a:
Dimuon mass distributions in one of the three representative bins in rapidity: $ | y_{\ell \ell} | < $ 0.4. |
png pdf |
Figure 2-b:
Dielectron mass distributions in one of the three representative bins in rapidity: $ | y_{\ell \ell} | < $ 0.4. |
png pdf |
Figure 2-c:
Dimuon mass distributions in one of the three representative bins in rapidity: 0.8 $ < | y_{\ell \ell} | < $ 1.2. |
png pdf |
Figure 2-d:
Dielectron mass distributions in one of the three representative bins in rapidity: 0.8 $ < | y_{\ell \ell} | < $ 1.2. |
png pdf |
Figure 2-e:
Dimuon mass distributions in one of the three representative bins in rapidity: 1.6 $ < | y_{\ell \ell} | < $ 2.0. |
png pdf |
Figure 2-f:
Dielectron mass distributions in one of the three representative bins in rapidity: 1.6 $ < | y_{\ell \ell} | < $ 2.0. |
png pdf |
Figure 3:
The muon (left) and electron (right) ${\cos\theta ^{*}}$ distributions in three representative bins in rapidity: $ | y_{\ell \ell} | < $ 0.4 (upper), 0.8 $ < | y_{\ell \ell} | < $ 1.2 (middle), and 1.6 $ < | y_{\ell \ell} | < $ 2.0 (lower). The small contributions from backgrounds are included in the predictions. |
png pdf |
Figure 3-a:
The muon ${\cos\theta ^{*}}$ distributions in one of three representative bins in rapidity: $ | y_{\ell \ell} | < $ 0.4. The small contributions from backgrounds are included in the predictions. |
png pdf |
Figure 3-b:
The electron ${\cos\theta ^{*}}$ distributions in one of three representative bins in rapidity: $ | y_{\ell \ell} | < $ 0.4. The small contributions from backgrounds are included in the predictions. |
png pdf |
Figure 3-c:
The muon ${\cos\theta ^{*}}$ distributions in one of three representative bins in rapidity: 0.8 $ < | y_{\ell \ell} | < $ 1.2. The small contributions from backgrounds are included in the predictions. |
png pdf |
Figure 3-d:
The electron ${\cos\theta ^{*}}$ distributions in one of three representative bins in rapidity: 0.8 $ < | y_{\ell \ell} | < $ 1.2. The small contributions from backgrounds are included in the predictions. |
png pdf |
Figure 3-e:
The muon ${\cos\theta ^{*}}$ distributions in one of three representative bins in rapidity: 1.6 $ < | y_{\ell \ell} | < $ 2.0. The small contributions from backgrounds are included in the predictions. |
png pdf |
Figure 3-f:
The electron ${\cos\theta ^{*}}$ distributions in one of three representative bins in rapidity: 1.6 $ < | y_{\ell \ell} | < $ 2.0. The small contributions from backgrounds are included in the predictions. |
png pdf |
Figure 4:
Comparison between data and best-fit ${A_\text {FB}}$ distributions in the dimuon (upper) and dielectron (lower) channels. The best-fit ${A_\text {FB}}$ value in each bin is obtained via linear interpolation between two neighboring templates. Here, the templates are based on the central prediction of the NLO NNPDF3.0 PDFs. The error bars represent the statistical uncertainties in the data. |
png pdf |
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 via linear interpolation between two neighboring templates. Here, the templates are based on the central prediction of the NLO NNPDF3.0 PDFs. The error bars represent the statistical uncertainties in the data. |
png pdf |
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 via linear interpolation between two neighboring templates. Here, the templates are based on the central prediction of the NLO NNPDF3.0 PDFs. The error bars represent the statistical uncertainties in the data. |
png pdf |
Figure 5:
Distribution in ${A_\text {FB}}$ as a function of dilepton mass, integrated over rapidity (left), and in six rapidity bins (right) for $ {\sin^2\theta ^{\ell}_{\text {eff}}} =$ 0.23120 in POWHEG. The solid lines in the bottom panel correspond to six changes at $ {\sin^2\theta ^{\ell}_{\text {eff}}} $ around the central value, corresponding to: $ \pm$ 0.00040, $ \pm $ 0.00080, and $ \pm $ 0.00120. The dashed lines refer to the ${A_\text {FB}}$ predictions for 100 NNPDF3.0 replicas. The shaded bands illustrate the standard deviation in the NNPDF3.0 replicas. |
png pdf |
Figure 5-a:
Distribution in ${A_\text {FB}}$ as a function of dilepton mass, integrated over rapidity for $ {\sin^2\theta ^{\ell}_{\text {eff}}} =$ 0.23120 in POWHEG. The solid lines in the bottom panel correspond to six changes at $ {\sin^2\theta ^{\ell}_{\text {eff}}} $ around the central value, corresponding to: $ \pm$ 0.00040, $ \pm $ 0.00080, and $ \pm $ 0.00120. The dashed lines refer to the ${A_\text {FB}}$ predictions for 100 NNPDF3.0 replicas. The shaded bands illustrate the standard deviation in the NNPDF3.0 replicas. |
png pdf |
Figure 5-b:
Distribution in ${A_\text {FB}}$ as a function of dilepton mass, in six rapidity bins for $ {\sin^2\theta ^{\ell}_{\text {eff}}} =$ 0.23120 in POWHEG. The solid lines in the bottom panel correspond to six changes at $ {\sin^2\theta ^{\ell}_{\text {eff}}} $ around the central value, corresponding to: $ \pm$ 0.00040, $ \pm $ 0.00080, and $ \pm $ 0.00120. The dashed lines refer to the ${A_\text {FB}}$ predictions for 100 NNPDF3.0 replicas. The shaded bands illustrate the standard deviation in the NNPDF3.0 replicas. |
png pdf |
Figure 6:
The upper panel in each figure shows a scatter plot in $\chi ^2_ {\text {min}} $ v.s. the best-fit ${\sin^2\theta ^{\ell}_{\text {eff}}}$ for 100 NNPDF replicas in the muon channel (upper left), electron channel (upper right), and their combination (below). The corresponding lower panels have the projected distributions in the best-fit ${\sin^2\theta ^{\ell}_{\text {eff}}}$ for the nominal (open circles) and weighted (solid circles) replicas. |
png pdf |
Figure 6-a:
The upper panel in each figure shows a scatter plot in $\chi ^2_ {\text {min}} $ v.s. the best-fit ${\sin^2\theta ^{\ell}_{\text {eff}}}$ for 100 NNPDF replicas in the muon channel. The corresponding lower panel has the projected distributions in the best-fit ${\sin^2\theta ^{\ell}_{\text {eff}}}$ for the nominal (open circles) and weighted (solid circles) replicas. |
png pdf |
Figure 6-b:
The upper panel in each figure shows a scatter plot in $\chi ^2_ {\text {min}} $ v.s. the best-fit ${\sin^2\theta ^{\ell}_{\text {eff}}}$ for 100 NNPDF replicas in the electron channel. The corresponding lower panel has the projected distributions in the best-fit ${\sin^2\theta ^{\ell}_{\text {eff}}}$ for the nominal (open circles) and weighted (solid circles) replicas. |
png pdf |
Figure 6-c:
The upper panel in each figure shows a scatter plot in $\chi ^2_ {\text {min}} $ v.s. the best-fit ${\sin^2\theta ^{\ell}_{\text {eff}}}$ for 100 NNPDF replicas in the combination of the muon and electron channels. The corresponding lower panel has the projected distributions in the best-fit ${\sin^2\theta ^{\ell}_{\text {eff}}}$ for the nominal (open circles) and weighted (solid circles) replicas. |
png pdf |
Figure 7:
The extracted values of ${\sin^2\theta ^{\ell}_{\text {eff}}}$ in the muon and electron channels, and their combination. The horizontal bars include statistical, experimental, and PDF uncertainties. The PDF uncertainties are obtained both without (left) and with (right) using the Bayesian $\chi ^2$ weighting. |
png pdf |
Figure 7-a:
The extracted values of ${\sin^2\theta ^{\ell}_{\text {eff}}}$ in the muon and electron channels, and their combination. The horizontal bars include statistical, experimental, and PDF uncertainties. The PDF uncertainties are obtained both without using the Bayesian $\chi ^2$ weighting. |
png pdf |
Figure 7-b:
The extracted values of ${\sin^2\theta ^{\ell}_{\text {eff}}}$ in the muon and electron channels, and their combination. The horizontal bars include statistical, experimental, and PDF uncertainties. The PDF uncertainties are obtained both with using the Bayesian $\chi ^2$ weighting. |
png pdf |
Figure 8:
Extracted values of $ {\sin^2\theta ^{\ell}_{\text {eff}}} $ from the dimuon data for different sets of PDFs with the nominal (left) and $\chi ^2$-reweighted (right) replicas. The horizontal error bars include contributions from statistical, experimental, and PDF uncertainties. |
png pdf |
Figure 8-a:
Extracted values of $ {\sin^2\theta ^{\ell}_{\text {eff}}} $ from the dimuon data for different sets of PDFs with the nominal replicas. The horizontal error bars include contributions from statistical, experimental, and PDF uncertainties. |
png pdf |
Figure 8-b:
Extracted values of $ {\sin^2\theta ^{\ell}_{\text {eff}}} $ from the dimuon data for different sets of PDFs with the $\chi ^2$-reweighted replicas. The horizontal error bars include contributions from statistical, experimental, and PDF uncertainties. |
png pdf |
Figure 9:
Comparison of the measured $ {\sin^2\theta ^{\ell}_{\text {eff}}} $ in the muon and electron channels and their combination, with previous LEP, SLD, Tevatron, and LHC measurements. The shaded band corresponds to the combination of the LEP and SLD measurements. |
| Tables | |
png pdf |
Table 1:
Summary of statistical uncertainties in ${\sin^2\theta ^{\ell}_{\text {eff}}}$. The statistical uncertainties in the lepton-selection efficiency and in the calibration coefficients in data are included in the estimates. |
png pdf |
Table 2:
Summary of experimental systematic uncertainties in ${\sin^2\theta ^{\ell}_{\text {eff}}}$. |
png pdf |
Table 3:
Summary of the theoretical uncertainties for the dimuon and dielectron channels, as discussed in the text. |
png pdf |
Table 4:
The central value and the PDF uncertainty in the measured ${\sin^2\theta ^{\ell}_{\text {eff}}}$ in the muon and electron channels, and their combination, obtained without and with constraining PDFs using Bayesian $\chi ^2$ reweighting. |
| Summary |
| The effective leptonic mixing angle, ${\sin^2\theta^{\ell}_{\text{eff}}} $, has been extracted from measurements of the mass and rapidity dependence of the forward-backward asymmetries ${A_\text{FB}}$ in Drell-Yan $\mu\mu$ and ee production. As a baseline model, we use the POWHEG event generator for the inclusive ${\mathrm{p}}{\mathrm{p}}\to\mathrm{Z}/\gamma\to\ell\ell$ process at leading electroweak order, where the weak mixing angle is interpreted through the improved Born approximation as the effective angle incorporating higher-order corrections. With more data and new analysis techniques, including precise lepton-momentum calibration, angular event weighting, and additional constraints on PDFs, the statistical and systematic uncertainties are significantly reduced relative to previous CMS measurements. The combined result from the dielectron and dimuon channels is ${\sin^2\theta^{\ell}_{\text{eff}}} = $ 0.23101 $\pm$ 0.00036 (stat) $\pm$ 0.00018 (syst) $\pm$ 0.00016 (theo) $\pm$ 0.00031 (PDF) or summing the uncertainties in quadrature, $ {\sin^2\theta^{\ell}_{\text{eff}}} = $ 0.23101 $\pm$ 0.00053. A comparison of the extracted $ {\sin^2\theta^{\ell}_{\text{eff}}} $ with previous results from LEP, SLC, Tevatron, and LHC, shown in Fig. 9, indicates consistency with the mean of the most precise LEP and SLD results, as well as with the other measurements. |
| References | ||||
| 1 | J. C. Collins and D. E. Soper | Angular distribution of dileptons in high-energy hadron collisions | PRD 16 (1977) 2219 | |
| 2 | D. Y. Bardin, W. F. L. Hollik, and G. Passarino | Reports of the working group on precision calculations for the z resonance | technical report, CERN | |
| 3 | D. \relax Yu. Bardin et al. | ZFITTER v.6.21: A semianalytical program for fermion pair production in $ \Pe^+\Pe^- $ annihilation | CPC 133 (2001) 229 | hep-ph/9908433 |
| 4 | The ALEPH Collaboration, the DELPHI Collaboration, the L3 Collaboration, the OPAL Collaboration, the SLD Collaboration, the LEP Electroweak Working Group, the SLD Electroweak and Heavy Flavour Groups | Precision electroweak measurements on the $ Z $ resonance | PR 427 (2006) 257 | hep-ex/0509008 |
| 5 | D0 Collaboration | Measurement of the forward-backward charge asymmetry and extraction of $ \sin^2\theta_\mathrm{W}^{\mathrm{eff}} $ in $ {\mathrm{p}}\bar{{\mathrm{p}}}\rightarrow\mathrm{Z}/\gamma^*+X \rightarrow \Pe^+\Pe^- + X $ events produced at $ \sqrt{s} = $ 1.96 TeV | PRL 101 (2008) 191801 | 0804.3220 |
| 6 | D0 Collaboration | Measurement of $ \sin^2\theta_{\rm eff}^{\ell} $ and $ Z $-light quark couplings using the forward-backward charge asymmetry in $ p\bar{p} \to Z/\gamma^{*} \to e^{+}e^{-} $ events with $ {\cal L}= $ 5.0 fb$ ^{-1} $ at $ \sqrt{s}= $ 1.96 TeV | PRD 84 (2011) 012007 | 1104.4590 |
| 7 | CMS Collaboration | Measurement of the weak mixing angle with the Drell-Yan process in proton-proton collisions at the LHC | PRD 84 (2011) 112002 | CMS-EWK-11-003 1110.2682 |
| 8 | CDF Collaboration | Indirect measurement of $ \sin^2\theta_W (M_W) $ using $ e^+e^- $ pairs in the Z-boson region with $ p\bar{p} $ collisions at a center-of-momentum energy of 1.96 TeV | PRD 88 (2013) 072002 | 1307.0770 |
| 9 | CDF Collaboration | Indirect measurement of $ \sin^2 \theta_W $ (or $ M_W $) using $ \mu^+\mu^- $ pairs from $ \gamma^*/Z $ bosons produced in $ p\bar{p} $ collisions at a center-of-momentum energy of 1.96 TeV | PRD 89 (2014) 072005 | 1402.2239 |
| 10 | D0 Collaboration | Measurement of the effective weak mixing angle in $ p\bar{p}\rightarrow Z/\gamma^{*}\rightarrow e^{+}e^{-} $ events | PRL 115 (2015) 041801 | 1408.5016 |
| 11 | ATLAS Collaboration | Measurement of the forward-backward asymmetry of electron and muon pair-production in $ pp $ collisions at $ \sqrt{s} = $ 7 TeV with the ATLAS detector | JHEP 09 (2015) 049 | 1503.03709 |
| 12 | LHCb Collaboration | Measurement of the forward-backward asymmetry in $ Z/\gamma^{\ast} \rightarrow \mu^{+}\mu^{-} $ decays and determination of the effective weak mixing angle | JHEP 11 (2015) 190 | 1509.07645 |
| 13 | CDF Collaboration | Measurement of $ \sin^2\theta^{\rm lept}_{\rm eff} $ using $ e^+e^- $ pairs from $ \gamma^*/Z $ bosons produced in $ p\bar{p} $ collisions at a center-of-momentum energy of 1.96 TeV | PRD 93 (2016) 112016 | 1605.02719 |
| 14 | CDF and D0 Collaborations | Tevatron Run II combination of the effective leptonic electroweak mixing angle | Submitted to PRD | 1801.06283 |
| 15 | T. Sjostrand et al. | An Introduction to PYTHIA 8.2 | CPC 191 (2015) 159 | 1410.3012 |
| 16 | NNPDF Collaboration | Parton distributions for the LHC Run II | JHEP 04 (2015) 040 | 1410.8849 |
| 17 | CMS Collaboration | The CMS experiment at the CERN LHC | JINST 3 (2008) S08004 | CMS-00-001 |
| 18 | CMS Collaboration | Performance of CMS muon reconstruction in $ pp $ collision events at $ \sqrt{s} = $ 7 TeV | JINST 7 (2012) P10002 | CMS-MUO-10-004 1206.4071 |
| 19 | CMS Collaboration | Performance of electron reconstruction and selection with the CMS detector in proton-proton collisions at $ \sqrt{s} = $ 8 TeV | JINST 10 (2015) P06005 | CMS-EGM-13-001 1502.02701 |
| 20 | CMS Collaboration | The CMS trigger system | JINST 12 (2017) P01020 | CMS-TRG-12-001 1609.02366 |
| 21 | CMS Collaboration | Particle-flow reconstruction and global event description with the CMS detector | JINST 12 (2017) P10003 | CMS-PRF-14-001 1706.04965 |
| 22 | D. Bourilkov | Photon-induced background for dilepton searches and measurements in pp collisions at 13 TeV | 1606.00523 | |
| 23 | S. Alioli, P. Nason, C. Oleari, and E. Re | NLO vector-boson production matched with shower in POWHEG | JHEP 07 (2008) 060 | 0805.4802 |
| 24 | P. Nason | A new method for combining NLO QCD with shower Monte Carlo algorithms | JHEP 11 (2004) 040 | hep-ph/0409146 |
| 25 | S. Frixione, P. Nason, and C. Oleari | Matching NLO QCD computations with parton shower simulations: the POWHEG method | JHEP 11 (2007) 070 | 0709.2092 |
| 26 | 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 |
| 27 | H.-L. Lai et al. | New parton distributions for collider physics | PRD 82 (2010) 074024 | 1007.2241 |
| 28 | T. Sjostrand, S. Mrenna, and P. Skands | PYTHIA 6.4 physics and manual | JHEP 05 (2006) 026 | hep-ph/0603175 |
| 29 | CMS Collaboration | Study of the underlying event at forward rapidity in pp collisions at $ \sqrt{s} = $ 0.9, 2.76, and 7 TeV | JHEP 04 (2013) 072 | CMS-FWD-11-003 1302.2394 |
| 30 | CMS Collaboration | Event generator tunes obtained from underlying event and multiparton scattering measurements | EPJC 76 (2016) 155 | CMS-GEN-14-001 1512.00815 |
| 31 | N. Davidson et al. | Universal interface of TAUOLA: Technical and physics documentation | CPC 183 (2012) 821 | 1002.0543 |
| 32 | J. Pumplin et al. | New generation of parton distributions with uncertainties from global QCD analysis | JHEP 07 (2002) 012 | hep-ph/0201195 |
| 33 | GEANT4 Collaboration | GEANT4 --- a simulation toolkit | NIMA 506 (2003) 250 | |
| 34 | CMS Collaboration | Measurement of the differential cross section and charge asymmetry for inclusive $ \mathrm {p}\mathrm {p}\rightarrow \mathrm {W}^{\pm}+X $ production at $ {\sqrt{s}} = $ 8 TeV | EPJC 76 (2016) 469 | CMS-SMP-14-022 1603.01803 |
| 35 | A. Bodek et al. | Extracting muon momentum scale corrections for hadron collider experiments | EPJC 72 (2012) 2194 | 1208.3710 |
| 36 | Y. Li and F. Petriello | Combining QCD and electroweak corrections to dilepton production in the framework of the FEWZ simulation code | PRD 86 (2012) 094034 | 1208.5967 |
| 37 | M. Czakon and A. Mitov | Top++: a program for the calculation of the top-pair cross-section at hadron colliders | CPC 185 (2014) 2930 | 1112.5675 |
| 38 | E. Mirkes and J. Ohnemus | $ W $ and $ Z $ polarization effects in hadronic collisions | PRD 50 (1994) 5692 | hep-ph/9406381 |
| 39 | A. Bodek | A simple event weighting technique for optimizing the measurement of the forward-backward asymmetry of Drell-Yan dilepton pairs at hadron colliders | EPJC 67 (2010) 321 | 0911.2850 |
| 40 | B. Efron | Bootstrap methods: Another look at the jackknife | Ann. Statist. 7 (1979) 1 | |
| 41 | U. Baur et al. | Electroweak radiative corrections to neutral current Drell-Yan processes at hadron colliders | PRD 65 (2002) 033007 | hep-ph/0108274 |
| 42 | CMS Collaboration | CMS luminosity based on pixel cluster counting --- Summer 2013 update | CMS-PAS-LUM-13-001 | CMS-PAS-LUM-13-001 |
| 43 | K. Hamilton, P. Nason, and G. Zanderighi | MINLO: multi-scale improved NLO | JHEP 10 (2012) 155 | 1206.3572 |
| 44 | P. Golonka and Z. Was | PHOTOS Monte Carlo: A precision tool for QED corrections in $ Z $ and $ W $ decays | EPJC 45 (2006) 97 | hep-ph/0506026 |
| 45 | E. Barberio and Z. W\cas | PHOTOS: A universal Monte Carlo for QED radiative corrections. Version 2.0 | CPC 79 (1994) 291 | |
| 46 | N. Davidson, T. Przedzinski, and Z. Was | PHOTOS interface in C++: Technical and Physics Documentation | CPC 199 (2016) 86 | 1011.0937 |
| 47 | W. T. Giele and S. Keller | Implications of hadron collider observables on parton distribution function uncertainties | PRD 58 (1998) 094023 | hep-ph/9803393 |
| 48 | N. Sato, J. F. Owens, and H. Prosper | Bayesian reweighting for global fits | PRD 89 (2014) 114020 | 1310.1089 |
| 49 | A. Bodek, J. Han, A. Khukhunaishvili, and W. Sakumoto | Using Drell-Yan forward-backward asymmetry to reduce PDF uncertainties in the measurement of electroweak parameters | EPJC 76 (2016) 115 | 1507.02470 |
| 50 | S. Dulat et al. | New parton distribution functions from a global analysis of quantum chromodynamics | PRD 93 (2016) 033006 | 1506.07443 |
| 51 | L. A. Harland-Lang, A. D. Martin, P. Motylinski, and R. S. Thorne | Parton distributions in the LHC era: MMHT 2014 PDFs | EPJC 75 (2015) 204 | 1412.3989 |
| 52 | S. Carrazza et al. | An unbiased Hessian representation for Monte Carlo PDFs | EPJC 75 (2015) 369 | 1505.06736 |
|
|
Compact Muon Solenoid LHC, CERN |
|
|
|
|
|
|