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CMS-SMP-20-006 ; CERN-EP-2020-168

Measurements of production cross sections of polarized same-sign W boson pairs in association with two jets in proton-proton collisions at $\sqrt{s} = $ 13 TeV

CMS Collaboration

20 September 2020

Phys. Lett. B 812 (2020) 136018

Abstract: The first measurements of production cross sections of polarized same-sign ${\mathrm{W}^\pm\mathrm{W}^\pm} $ boson pairs in proton-proton collisions are reported. The measurements are based on a data sample collected with the CMS detector at the LHC at a center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 137 fb$^{-1}$. Events are selected by requiring exactly two same-sign leptons, electrons or muons, moderate missing transverse momentum, and two jets with a large rapidity separation and a large dijet mass to enhance the contribution of same-sign $ {\mathrm{W}^\pm\mathrm{W}^\pm} $ scattering events. An observed (expected) 95% confidence level upper limit of 1.17 (0.88) fb is set on the production cross section for longitudinally polarized same-sign ${\mathrm{W}^\pm\mathrm{W}^\pm} $ boson pairs. The electroweak production of same-sign ${\mathrm{W}^\pm\mathrm{W}^\pm} $ boson pairs with at least one of the W bosons longitudinally polarized is measured with an observed (expected) significance of 2.3 (3.1) standard deviations.

Links: e-print arXiv:2009.09429 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; CADI line (restricted) ;

Figures
png pdf	Figure 1: Illustrative Feynman diagrams of VBS processes, where W bosons are radiated from incoming quarks (q), contributing to the EW-induced production of events containing two forward jets and $ {\mathrm{W} ^\pm \mathrm{W} ^\pm} $ boson pairs decaying to leptons. Diagrams with the triple gauge coupling vertex (left), the quartic gauge coupling vertex (center), and the $t$-channel Higgs boson exchange (right) are shown.
png pdf	Figure 1-a: Illustrative Feynman diagram of VBS process, where W bosons are radiated from incoming quarks (q), contributing to the EW-induced production of events containing two forward jets and $ {\mathrm{W} ^\pm \mathrm{W} ^\pm} $ boson pairs decaying to leptons, with triple gauge coupling vertex.
png pdf	Figure 1-b: Illustrative Feynman diagram of VBS process, where W bosons are radiated from incoming quarks (q), contributing to the EW-induced production of events containing two forward jets and $ {\mathrm{W} ^\pm \mathrm{W} ^\pm} $ boson pairs decaying to leptons, with quartic gauge coupling vertex.
png pdf	Figure 1-c: Illustrative Feynman diagram of VBS process, where W bosons are radiated from incoming quarks (q), contributing to the EW-induced production of events containing two forward jets and $ {\mathrm{W} ^\pm \mathrm{W} ^\pm} $ boson pairs decaying to leptons, with $t$-channel Higgs boson exchange.
png pdf	Figure 2: Generator level distributions of $ {\Delta \phi _{{\mathrm {j}} {\mathrm {j}}}} $ (upper), $\Delta \phi _{\ell \ell}$ (center), and $ {m_{\ell \ell}} $ (lower) in the fiducial region for the $ {\mathrm{W} ^\pm _{\mathrm {L}}\mathrm{W} ^\pm _{\mathrm {L}}} $, $ {\mathrm{W} ^\pm _{\mathrm {L}}\mathrm{W} ^\pm _{\mathrm {T}}} $, and $ {\mathrm{W} ^\pm _{\mathrm {T}}\mathrm{W} ^\pm _{\mathrm {T}}} $ processes with the helicity eigenstates defined in the parton-parton (left) and $ {\mathrm{W} ^\pm \mathrm{W} ^\pm} $ (right) center-of-mass reference frames. The error bars represent the uncertainties associated with the limited numbers of simulated events.
png pdf	Figure 2-a: Generator level distributions of $ {\Delta \phi _{{\mathrm {j}} {\mathrm {j}}}} $ in the fiducial region for the $ {\mathrm{W} ^\pm _{\mathrm {L}}\mathrm{W} ^\pm _{\mathrm {L}}} $, $ {\mathrm{W} ^\pm _{\mathrm {L}}\mathrm{W} ^\pm _{\mathrm {T}}} $, and $ {\mathrm{W} ^\pm _{\mathrm {T}}\mathrm{W} ^\pm _{\mathrm {T}}} $ processes with the helicity eigenstates defined in the parton-parton center-of-mass reference frame. The error bars represent the uncertainties associated with the limited numbers of simulated events.
png pdf	Figure 2-b: Generator level distributions of $ {\Delta \phi _{{\mathrm {j}} {\mathrm {j}}}} $ in the fiducial region for the $ {\mathrm{W} ^\pm _{\mathrm {L}}\mathrm{W} ^\pm _{\mathrm {L}}} $, $ {\mathrm{W} ^\pm _{\mathrm {L}}\mathrm{W} ^\pm _{\mathrm {T}}} $, and $ {\mathrm{W} ^\pm _{\mathrm {T}}\mathrm{W} ^\pm _{\mathrm {T}}} $ processes with the helicity eigenstates defined in the $ {\mathrm{W} ^\pm \mathrm{W} ^\pm} $ center-of-mass reference frame. The error bars represent the uncertainties associated with the limited numbers of simulated events.
png pdf	Figure 2-c: Generator level distributions of $\Delta \phi _{\ell \ell}$ in the fiducial region for the $ {\mathrm{W} ^\pm _{\mathrm {L}}\mathrm{W} ^\pm _{\mathrm {L}}} $, $ {\mathrm{W} ^\pm _{\mathrm {L}}\mathrm{W} ^\pm _{\mathrm {T}}} $, and $ {\mathrm{W} ^\pm _{\mathrm {T}}\mathrm{W} ^\pm _{\mathrm {T}}} $ processes with the helicity eigenstates defined in the parton-parton center-of-mass reference frame. The error bars represent the uncertainties associated with the limited numbers of simulated events.
png pdf	Figure 2-d: Generator level distributions of $\Delta \phi _{\ell \ell}$ in the fiducial region for the $ {\mathrm{W} ^\pm _{\mathrm {L}}\mathrm{W} ^\pm _{\mathrm {L}}} $, $ {\mathrm{W} ^\pm _{\mathrm {L}}\mathrm{W} ^\pm _{\mathrm {T}}} $, and $ {\mathrm{W} ^\pm _{\mathrm {T}}\mathrm{W} ^\pm _{\mathrm {T}}} $ processes with the helicity eigenstates defined in the $ {\mathrm{W} ^\pm \mathrm{W} ^\pm} $ center-of-mass reference frame. The error bars represent the uncertainties associated with the limited numbers of simulated events.
png pdf	Figure 2-e: Generator level distributions of $ {m_{\ell \ell}} $ in the fiducial region for the $ {\mathrm{W} ^\pm _{\mathrm {L}}\mathrm{W} ^\pm _{\mathrm {L}}} $, $ {\mathrm{W} ^\pm _{\mathrm {L}}\mathrm{W} ^\pm _{\mathrm {T}}} $, and $ {\mathrm{W} ^\pm _{\mathrm {T}}\mathrm{W} ^\pm _{\mathrm {T}}} $ processes with the helicity eigenstates defined in the parton-parton center-of-mass reference frame. The error bars represent the uncertainties associated with the limited numbers of simulated events.
png pdf	Figure 2-f: Generator level distributions of $ {m_{\ell \ell}} $ in the fiducial region for the $ {\mathrm{W} ^\pm _{\mathrm {L}}\mathrm{W} ^\pm _{\mathrm {L}}} $, $ {\mathrm{W} ^\pm _{\mathrm {L}}\mathrm{W} ^\pm _{\mathrm {T}}} $, and $ {\mathrm{W} ^\pm _{\mathrm {T}}\mathrm{W} ^\pm _{\mathrm {T}}} $ processes with the helicity eigenstates defined in the $ {\mathrm{W} ^\pm \mathrm{W} ^\pm} $ center-of-mass reference frame. The error bars represent the uncertainties associated with the limited numbers of simulated events.
png pdf	Figure 3: Distributions of the $ {m_{{\mathrm {j}} {\mathrm {j}}}} $ (upper left), $ {\Delta \phi _{{\mathrm {j}} {\mathrm {j}}}} $ (upper right), $\Delta \phi _{\ell \ell}$ (lower left), and of the output score of the inclusive BDT (lower right) in the $ {\mathrm{W} ^\pm \mathrm{W} ^\pm} $ SR. The predicted yields are shown with their best fit normalizations from the simultaneous fit. The histograms for the $ {\mathrm{W} ^\pm \mathrm{W} ^\pm} $ process include the contributions from the $ {\mathrm{W} ^\pm _{\mathrm {L}}\mathrm{W} ^\pm _{\mathrm {L}}} $, $ {\mathrm{W} ^\pm _{\mathrm {L}}\mathrm{W} ^\pm _{\mathrm {T}}} $, and $ {\mathrm{W} ^\pm _{\mathrm {T}}\mathrm{W} ^\pm _{\mathrm {T}}} $ processes (shown as solid lines), QCD $ {\mathrm{W} ^\pm \mathrm{W} ^\pm} $, and interference. The histograms for other backgrounds include the contributions from double parton scattering, VVV, and from oppositely charged dilepton final states from ${\mathrm{t} \mathrm{\bar{t}}} $, $\mathrm{t} \mathrm{W} $, $\mathrm{W} ^{+}\mathrm{W} ^{-}$, and Drell-Yan processes. The overflow is included in the last bin. The bottom panel in each figure shows the ratio of the number of events observed in data to that of the total SM prediction. The gray bands represent the uncertainties in the predicted yields. The vertical bars represent the statistical uncertainties in the data.
png pdf	Figure 3-a: Distribution of $ {m_{{\mathrm {j}} {\mathrm {j}}}} $ in the $ {\mathrm{W} ^\pm \mathrm{W} ^\pm} $ SR. The predicted yields are shown with their best fit normalizations from the simultaneous fit. The histograms for the $ {\mathrm{W} ^\pm \mathrm{W} ^\pm} $ process include the contributions from the $ {\mathrm{W} ^\pm _{\mathrm {L}}\mathrm{W} ^\pm _{\mathrm {L}}} $, $ {\mathrm{W} ^\pm _{\mathrm {L}}\mathrm{W} ^\pm _{\mathrm {T}}} $, and $ {\mathrm{W} ^\pm _{\mathrm {T}}\mathrm{W} ^\pm _{\mathrm {T}}} $ processes (shown as solid lines), QCD $ {\mathrm{W} ^\pm \mathrm{W} ^\pm} $, and interference. The histograms for other backgrounds include the contributions from double parton scattering, VVV, and from oppositely charged dilepton final states from ${\mathrm{t} \mathrm{\bar{t}}} $, $\mathrm{t} \mathrm{W} $, $\mathrm{W} ^{+}\mathrm{W} ^{-}$, and Drell-Yan processes. The overflow is included in the last bin. The bottom panel shows the ratio of the number of events observed in data to that of the total SM prediction. The gray bands represent the uncertainties in the predicted yields. The vertical bars represent the statistical uncertainties in the data.
png pdf	Figure 3-b: Distribution of $ {\Delta \phi _{{\mathrm {j}} {\mathrm {j}}}} $ in the $ {\mathrm{W} ^\pm \mathrm{W} ^\pm} $ SR. The predicted yields are shown with their best fit normalizations from the simultaneous fit. The histograms for the $ {\mathrm{W} ^\pm \mathrm{W} ^\pm} $ process include the contributions from the $ {\mathrm{W} ^\pm _{\mathrm {L}}\mathrm{W} ^\pm _{\mathrm {L}}} $, $ {\mathrm{W} ^\pm _{\mathrm {L}}\mathrm{W} ^\pm _{\mathrm {T}}} $, and $ {\mathrm{W} ^\pm _{\mathrm {T}}\mathrm{W} ^\pm _{\mathrm {T}}} $ processes (shown as solid lines), QCD $ {\mathrm{W} ^\pm \mathrm{W} ^\pm} $, and interference. The histograms for other backgrounds include the contributions from double parton scattering, VVV, and from oppositely charged dilepton final states from ${\mathrm{t} \mathrm{\bar{t}}} $, $\mathrm{t} \mathrm{W} $, $\mathrm{W} ^{+}\mathrm{W} ^{-}$, and Drell-Yan processes. The overflow is included in the last bin. The bottom panel shows the ratio of the number of events observed in data to that of the total SM prediction. The gray bands represent the uncertainties in the predicted yields. The vertical bars represent the statistical uncertainties in the data.
png pdf	Figure 3-c: Distribution of $\Delta \phi _{\ell \ell}$ in the $ {\mathrm{W} ^\pm \mathrm{W} ^\pm} $ SR. The predicted yields are shown with their best fit normalizations from the simultaneous fit. The histograms for the $ {\mathrm{W} ^\pm \mathrm{W} ^\pm} $ process include the contributions from the $ {\mathrm{W} ^\pm _{\mathrm {L}}\mathrm{W} ^\pm _{\mathrm {L}}} $, $ {\mathrm{W} ^\pm _{\mathrm {L}}\mathrm{W} ^\pm _{\mathrm {T}}} $, and $ {\mathrm{W} ^\pm _{\mathrm {T}}\mathrm{W} ^\pm _{\mathrm {T}}} $ processes (shown as solid lines), QCD $ {\mathrm{W} ^\pm \mathrm{W} ^\pm} $, and interference. The histograms for other backgrounds include the contributions from double parton scattering, VVV, and from oppositely charged dilepton final states from ${\mathrm{t} \mathrm{\bar{t}}} $, $\mathrm{t} \mathrm{W} $, $\mathrm{W} ^{+}\mathrm{W} ^{-}$, and Drell-Yan processes. The overflow is included in the last bin. The bottom panel shows the ratio of the number of events observed in data to that of the total SM prediction. The gray bands represent the uncertainties in the predicted yields. The vertical bars represent the statistical uncertainties in the data.
png pdf	Figure 3-d: Distribution of the output score of the inclusive BDT in the $ {\mathrm{W} ^\pm \mathrm{W} ^\pm} $ SR. The predicted yields are shown with their best fit normalizations from the simultaneous fit. The histograms for the $ {\mathrm{W} ^\pm \mathrm{W} ^\pm} $ process include the contributions from the $ {\mathrm{W} ^\pm _{\mathrm {L}}\mathrm{W} ^\pm _{\mathrm {L}}} $, $ {\mathrm{W} ^\pm _{\mathrm {L}}\mathrm{W} ^\pm _{\mathrm {T}}} $, and $ {\mathrm{W} ^\pm _{\mathrm {T}}\mathrm{W} ^\pm _{\mathrm {T}}} $ processes (shown as solid lines), QCD $ {\mathrm{W} ^\pm \mathrm{W} ^\pm} $, and interference. The histograms for other backgrounds include the contributions from double parton scattering, VVV, and from oppositely charged dilepton final states from ${\mathrm{t} \mathrm{\bar{t}}} $, $\mathrm{t} \mathrm{W} $, $\mathrm{W} ^{+}\mathrm{W} ^{-}$, and Drell-Yan processes. The overflow is included in the last bin. The bottom panel shows the ratio of the number of events observed in data to that of the total SM prediction. The gray bands represent the uncertainties in the predicted yields. The vertical bars represent the statistical uncertainties in the data.
png pdf	Figure 4: Distributions of the output score of the signal BDT used for the $ {\mathrm{W} ^\pm _{\mathrm {L}}\mathrm{W} ^\pm _{\mathrm {L}}} $ and $ {\mathrm{W} ^\pm _{X}\mathrm{W} ^\pm _{\mathrm {T}}} $ cross section measurements (left) and of the output score of the signal BDT used for the $ {\mathrm{W} ^\pm _{\mathrm {L}}\mathrm{W} ^\pm _{X}} $ and $ {\mathrm{W} ^\pm _{\mathrm {T}}\mathrm{W} ^\pm _{\mathrm {T}}} $ cross section measurements (right). The predicted yields are shown with their best fit normalizations from the simultaneous fit. The histograms for the $ {\mathrm{W} ^\pm \mathrm{W} ^\pm} $ process include the contributions from the $ {\mathrm{W} ^\pm _{\mathrm {L}}\mathrm{W} ^\pm _{\mathrm {L}}} $, $ {\mathrm{W} ^\pm _{\mathrm {L}}\mathrm{W} ^\pm _{\mathrm {T}}} $, and $ {\mathrm{W} ^\pm _{\mathrm {T}}\mathrm{W} ^\pm _{\mathrm {T}}} $ processes (shown as solid lines), QCD $ {\mathrm{W} ^\pm \mathrm{W} ^\pm} $, and interference. The histograms for other backgrounds include the contributions from double parton scattering, VVV, and from oppositely charged dilepton final states from ${\mathrm{t} \mathrm{\bar{t}}} $, $\mathrm{t} \mathrm{W} $, $\mathrm{W} ^{+}\mathrm{W} ^{-}$, and Drell-Yan processes. The bottom panel in each figure shows the ratio of the number of events observed in data to that of the total SM prediction. The gray bands represent the uncertainties in the predicted yields. The vertical bars represent the statistical uncertainties in the data.
png pdf	Figure 4-a: Distribution of the output score of the signal BDT used for the $ {\mathrm{W} ^\pm _{\mathrm {L}}\mathrm{W} ^\pm _{\mathrm {L}}} $ and $ {\mathrm{W} ^\pm _{X}\mathrm{W} ^\pm _{\mathrm {T}}} $ cross section measurements. The predicted yields are shown with their best fit normalizations from the simultaneous fit. The histograms for the $ {\mathrm{W} ^\pm \mathrm{W} ^\pm} $ process include the contributions from the $ {\mathrm{W} ^\pm _{\mathrm {L}}\mathrm{W} ^\pm _{\mathrm {L}}} $, $ {\mathrm{W} ^\pm _{\mathrm {L}}\mathrm{W} ^\pm _{\mathrm {T}}} $, and $ {\mathrm{W} ^\pm _{\mathrm {T}}\mathrm{W} ^\pm _{\mathrm {T}}} $ processes (shown as solid lines), QCD $ {\mathrm{W} ^\pm \mathrm{W} ^\pm} $, and interference. The histograms for other backgrounds include the contributions from double parton scattering, VVV, and from oppositely charged dilepton final states from ${\mathrm{t} \mathrm{\bar{t}}} $, $\mathrm{t} \mathrm{W} $, $\mathrm{W} ^{+}\mathrm{W} ^{-}$, and Drell-Yan processes. The bottom panel in each figure shows the ratio of the number of events observed in data to that of the total SM prediction. The gray bands represent the uncertainties in the predicted yields. The vertical bars represent the statistical uncertainties in the data.
png pdf	Figure 4-b: Distribution of the output score of the signal BDT used for the $ {\mathrm{W} ^\pm _{\mathrm {L}}\mathrm{W} ^\pm _{X}} $ and $ {\mathrm{W} ^\pm _{\mathrm {T}}\mathrm{W} ^\pm _{\mathrm {T}}} $ cross section measurements. The predicted yields are shown with their best fit normalizations from the simultaneous fit. The histograms for the $ {\mathrm{W} ^\pm \mathrm{W} ^\pm} $ process include the contributions from the $ {\mathrm{W} ^\pm _{\mathrm {L}}\mathrm{W} ^\pm _{\mathrm {L}}} $, $ {\mathrm{W} ^\pm _{\mathrm {L}}\mathrm{W} ^\pm _{\mathrm {T}}} $, and $ {\mathrm{W} ^\pm _{\mathrm {T}}\mathrm{W} ^\pm _{\mathrm {T}}} $ processes (shown as solid lines), QCD $ {\mathrm{W} ^\pm \mathrm{W} ^\pm} $, and interference. The histograms for other backgrounds include the contributions from double parton scattering, VVV, and from oppositely charged dilepton final states from ${\mathrm{t} \mathrm{\bar{t}}} $, $\mathrm{t} \mathrm{W} $, $\mathrm{W} ^{+}\mathrm{W} ^{-}$, and Drell-Yan processes. The bottom panel in each figure shows the ratio of the number of events observed in data to that of the total SM prediction. The gray bands represent the uncertainties in the predicted yields. The vertical bars represent the statistical uncertainties in the data.
png pdf	Figure 5: Profile likelihood scan as a function of the $ {\mathrm{W} ^\pm _{\mathrm {L}}\mathrm{W} ^\pm _{\mathrm {L}}} $ cross section. The red (blue) line represents the expected values in the background-only hypothesis, i.e., assuming no contribution from the $ {\mathrm{W} ^\pm _{\mathrm {L}}\mathrm{W} ^\pm _{\mathrm {L}}} $ process, considering all systematic uncertainties (only statistical ones). The green line shows the expected values for the signal-plus-background hypothesis. The observed values are represented by the black line.

Tables
png pdf	Table 1: Summary of the requirements defining the $ {\mathrm{W} ^\pm \mathrm{W} ^\pm} $ SR. The $ {| {m_{\ell \ell}} - m_{\mathrm{Z}} |}$ requirement is applied to the dielectron final state only.
png pdf	Table 2: List and description of all the input variables for the signal BDT trainings.
png pdf	Table 3: List and description of the input variables for the inclusive BDT training.
png pdf	Table 4: Systematic uncertainties of the $ {\mathrm{W} ^\pm _{\mathrm {L}}\mathrm{W} ^\pm _{\mathrm {L}}} $ and $ {\mathrm{W} ^\pm _{X}\mathrm{W} ^\pm _{\mathrm {T}}} $, and $ {\mathrm{W} ^\pm _{\mathrm {L}}\mathrm{W} ^\pm _{X}} $ and $ {\mathrm{W} ^\pm _{\mathrm {T}}\mathrm{W} ^\pm _{\mathrm {T}}} $ cross section measurements in units of percent.
png pdf	Table 5: Expected yields from various SM processes and observed data events in $ {\mathrm{W} ^\pm \mathrm{W} ^\pm} $ SR. The combination of the statistical and systematic uncertainties is shown. The expected yields are shown with their best fit normalizations from the simultaneous fit for the $ {\mathrm{W} ^\pm _{\mathrm {L}}\mathrm{W} ^\pm _{\mathrm {L}}} $ and $ {\mathrm{W} ^\pm _{X}\mathrm{W} ^\pm _{\mathrm {T}}} $ cross sections. The $ {\mathrm{W} ^\pm _{\mathrm {L}}\mathrm{W} ^\pm _{\mathrm {T}}} $ and $ {\mathrm{W} ^\pm _{\mathrm {T}}\mathrm{W} ^\pm _{\mathrm {T}}} $ yields are obtained from the $ {\mathrm{W} ^\pm _{X}\mathrm{W} ^\pm _{\mathrm {T}}} $ yield assuming the SM prediction for the ratio of the yields. The $ {\mathrm{t} \mathrm{V} \mathrm {x}} $ background yield includes the contributions from ${\mathrm{t} \mathrm{\bar{t}}} \mathrm{V} $ and $ {\mathrm{t} \mathrm{Z} \mathrm{q}} $ processes.
png pdf	Table 6: Measured fiducial cross sections for the $ {\mathrm{W} ^\pm _{\mathrm {L}}\mathrm{W} ^\pm _{\mathrm {L}}} $ and $ {\mathrm{W} ^\pm _{X}\mathrm{W} ^\pm _{\mathrm {T}}} $ processes, and for the $ {\mathrm{W} ^\pm _{\mathrm {L}}\mathrm{W} ^\pm _{X}} $ and $ {\mathrm{W} ^\pm _{\mathrm {T}}\mathrm{W} ^\pm _{\mathrm {T}}} $ processes for the helicity eigenstates defined in the $ {\mathrm{W} ^\pm \mathrm{W} ^\pm} $ center-of-mass frame. The combination of the statistical and systematic uncertainties is shown. The theoretical predictions including the $\mathcal {O}({\alpha _\mathrm {S}} \alpha ^6)$ and $\mathcal {O}(\alpha ^7)$ corrections to the MadGraph 5\_aMC@NLO LO cross sections, as described in the text, are also shown. The theoretical uncertainties include statistical, PDF, and LO scale uncertainties; $\mathcal {B}$ is the branching fraction for $\mathrm{W} \mathrm{W} \to \ell \nu \ell '\nu $ [55].
png pdf	Table 7: Measured fiducial cross sections for the $ {\mathrm{W} ^\pm _{\mathrm {L}}\mathrm{W} ^\pm _{\mathrm {L}}} $ and $ {\mathrm{W} ^\pm _{X}\mathrm{W} ^\pm _{\mathrm {T}}} $ processes, and for the $ {\mathrm{W} ^\pm _{\mathrm {L}}\mathrm{W} ^\pm _{X}} $ and $ {\mathrm{W} ^\pm _{\mathrm {T}}\mathrm{W} ^\pm _{\mathrm {T}}} $ processes for the helicity eigenstates defined in the parton-parton center-of-mass frame. The combination of the statistical and systematic uncertainties is shown. The theoretical predictions including the $\mathcal {O}({\alpha _\mathrm {S}} \alpha ^6)$ and $\mathcal {O}(\alpha ^7)$ corrections to the MadGraph 5\_aMC@NLO LO cross sections, as described in the text, are also shown. The theoretical uncertainties include statistical, PDF, and LO scale uncertainties; $\mathcal {B}$ is the branching fraction for $\mathrm{W} \mathrm{W} \to \ell \nu \ell '\nu $ [55].

Summary

The first measurements of production cross sections for polarized same-sign ${\mathrm{W}^\pm\mathrm{W}^\pm} $ boson pairs are reported. The measurements are based on a sample of proton-proton collisions at a center-of-mass energy of 13 TeV collected by the CMS detector at the LHC, corresponding to an integrated luminosity of 137 fb$^{-1}$ . Events are selected by requiring exactly two same-sign leptons (electrons or muons), moderate missing transverse momentum, and two jets with a large rapidity separation and a high dijet mass. Boosted decision trees are used to separate between the polarized scattering processes by exploiting the kinematic differences. An observed (expected) 95% confidence level upper limit on the production cross section for longitudinally polarized same-sign ${\mathrm{W}^\pm\mathrm{W}^\pm} $ boson pairs of 1.17 (0.88) fb is reported with the helicity eigenstates defined in the ${\mathrm{W}^\pm\mathrm{W}^\pm} $ center-of-mass reference frame. The electroweak production of the ${\mathrm{W}^\pm\mathrm{W}^\pm} $ boson pairs where at least one of the W bosons is longitudinally polarized is measured with an observed (expected) significance of 2.3 (3.1) standard deviations. Results are also reported with the polarizations defined in the parton-parton center-of-mass reference frame. The measured cross section values agree with the standard model predictions.

Additional Figures
png pdf	Additional Figure 1: Distributions of the output score of the signal BDT used for the $ {{\mathrm {W}}^\pm _{\mathrm {L}} {\mathrm {W}}^\pm _{\mathrm {L}}} $ and $ {{\mathrm {W}}^\pm _{\mathrm {X}} {\mathrm {W}}^\pm _{\mathrm {T}}} $ cross section measurements (left) and of the output score of the signal BDT used for the $ {{\mathrm {W}}^\pm _{\mathrm {L}} {\mathrm {W}}^\pm _{\mathrm {X}}} $ and $ {{\mathrm {W}}^\pm _{\mathrm {T}} {\mathrm {W}}^\pm _{\mathrm {T}}} $ cross section measurements (right), after requiring the output score of the inclusive BDT greater than 0. The predicted yields are shown with their best fit normalizations from the simultaneous fit. The histograms for $ {{\mathrm {W}}^\pm {\mathrm {W}}^\pm} $ process include the contributions from the $ {{\mathrm {W}}^\pm _{\mathrm {L}} {\mathrm {W}}^\pm _{\mathrm {L}}} $, $ {{\mathrm {W}}^\pm _{\mathrm {L}} {\mathrm {W}}^\pm _{\mathrm {T}}} $, and $ {{\mathrm {W}}^\pm _{\mathrm {T}} {\mathrm {W}}^\pm _{\mathrm {T}}} $ processes (shown as solid lines), QCD $ {{\mathrm {W}}^\pm {\mathrm {W}}^\pm} $, and interference. The histograms for $\mathrm{tVx}$ backgrounds include the contributions from $ {{\mathrm {t}\overline {\mathrm {t}}}} \mathrm{V}$ and $ {\mathrm {t} {\mathrm {Z}} {\mathrm {q}}} $ processes. The histograms for other backgrounds include the contributions from double parton scattering and VVV processes. The bottom panel in each figure shows the ratio of the number of events observed in data to that of the total SM prediction. The gray bands represent the uncertainties in the predicted yields.
png pdf	Additional Figure 1-a: Distribution of the output score of the signal BDT used for the $ {{\mathrm {W}}^\pm _{\mathrm {L}} {\mathrm {W}}^\pm _{\mathrm {L}}} $ and $ {{\mathrm {W}}^\pm _{\mathrm {X}} {\mathrm {W}}^\pm _{\mathrm {T}}} $ cross section measurements, after requiring the output score of the inclusive BDT greater than 0. The predicted yields are shown with their best fit normalizations from the simultaneous fit. The histograms for $ {{\mathrm {W}}^\pm {\mathrm {W}}^\pm} $ process include the contributions from the $ {{\mathrm {W}}^\pm _{\mathrm {L}} {\mathrm {W}}^\pm _{\mathrm {L}}} $, $ {{\mathrm {W}}^\pm _{\mathrm {L}} {\mathrm {W}}^\pm _{\mathrm {T}}} $, and $ {{\mathrm {W}}^\pm _{\mathrm {T}} {\mathrm {W}}^\pm _{\mathrm {T}}} $ processes (shown as solid lines), QCD $ {{\mathrm {W}}^\pm {\mathrm {W}}^\pm} $, and interference. The histograms for $\mathrm{tVx}$ backgrounds include the contributions from $ {{\mathrm {t}\overline {\mathrm {t}}}} \mathrm{V}$ and $ {\mathrm {t} {\mathrm {Z}} {\mathrm {q}}} $ processes. The histograms for other backgrounds include the contributions from double parton scattering and VVV processes. The bottom panel shows the ratio of the number of events observed in data to that of the total SM prediction. The gray bands represent the uncertainties in the predicted yields.
png pdf	Additional Figure 1-b: Distribution of the output score of the signal BDT used for the $ {{\mathrm {W}}^\pm _{\mathrm {L}} {\mathrm {W}}^\pm _{\mathrm {X}}} $ and $ {{\mathrm {W}}^\pm _{\mathrm {T}} {\mathrm {W}}^\pm _{\mathrm {T}}} $ cross section measurements, after requiring the output score of the inclusive BDT greater than 0. The predicted yields are shown with their best fit normalizations from the simultaneous fit. The histograms for $ {{\mathrm {W}}^\pm {\mathrm {W}}^\pm} $ process include the contributions from the $ {{\mathrm {W}}^\pm _{\mathrm {L}} {\mathrm {W}}^\pm _{\mathrm {L}}} $, $ {{\mathrm {W}}^\pm _{\mathrm {L}} {\mathrm {W}}^\pm _{\mathrm {T}}} $, and $ {{\mathrm {W}}^\pm _{\mathrm {T}} {\mathrm {W}}^\pm _{\mathrm {T}}} $ processes (shown as solid lines), QCD $ {{\mathrm {W}}^\pm {\mathrm {W}}^\pm} $, and interference. The histograms for $\mathrm{tVx}$ backgrounds include the contributions from $ {{\mathrm {t}\overline {\mathrm {t}}}} \mathrm{V}$ and $ {\mathrm {t} {\mathrm {Z}} {\mathrm {q}}} $ processes. The histograms for other backgrounds include the contributions from double parton scattering and VVV processes. The bottom panel shows the ratio of the number of events observed in data to that of the total SM prediction. The gray bands represent the uncertainties in the predicted yields.
png pdf	Additional Figure 2: Generator level distributions of $ {\Delta \phi _{{\mathrm {j}} {\mathrm {j}}}} $ (upper), $\Delta \phi _{\ell \ell}$ (center), and $ {m_{\ell \ell}} $ (lower) in the fiducial region for the $ {{\mathrm {W}}^\pm _{\mathrm {L}} {\mathrm {W}}^\pm _{\mathrm {L}}} $, $ {{\mathrm {W}}^\pm _{\mathrm {L}} {\mathrm {W}}^\pm _{\mathrm {T}}} $, and $ {{\mathrm {W}}^\pm _{\mathrm {T}} {\mathrm {W}}^\pm _{\mathrm {T}}} $ processes with the helicity eigenstates defined in the parton-parton (left) and $ {{\mathrm {W}}^\pm {\mathrm {W}}^\pm} $ (right) center-of-mass reference frames. The distributions are also shown for the unpolarized EW $ {{\mathrm {W}}^\pm {\mathrm {W}}^\pm} $ process. The bottom panel in each figure shows the ratio of the contribution of the unpolarized $ {{\mathrm {W}}^\pm {\mathrm {W}}^\pm} $ process to that of the sum of the $ {{\mathrm {W}}^\pm _{\mathrm {L}} {\mathrm {W}}^\pm _{\mathrm {L}}} $, $ {{\mathrm {W}}^\pm _{\mathrm {L}} {\mathrm {W}}^\pm _{\mathrm {T}}} $, and $ {{\mathrm {W}}^\pm _{\mathrm {T}} {\mathrm {W}}^\pm _{\mathrm {T}}} $ processes. The gray bands represent the statistical uncertainties associated with the limited number of simulated events.
png pdf	Additional Figure 2-a: Generator level distributions of $ {\Delta \phi _{{\mathrm {j}} {\mathrm {j}}}} $ in the fiducial region for the $ {{\mathrm {W}}^\pm _{\mathrm {L}} {\mathrm {W}}^\pm _{\mathrm {L}}} $, $ {{\mathrm {W}}^\pm _{\mathrm {L}} {\mathrm {W}}^\pm _{\mathrm {T}}} $, and $ {{\mathrm {W}}^\pm _{\mathrm {T}} {\mathrm {W}}^\pm _{\mathrm {T}}} $ processes with the helicity eigenstates defined in the parton-parton center-of-mass reference frame. The distributions are also shown for the unpolarized EW $ {{\mathrm {W}}^\pm {\mathrm {W}}^\pm} $ process. The bottom panel shows the ratio of the contribution of the unpolarized $ {{\mathrm {W}}^\pm {\mathrm {W}}^\pm} $ process to that of the sum of the $ {{\mathrm {W}}^\pm _{\mathrm {L}} {\mathrm {W}}^\pm _{\mathrm {L}}} $, $ {{\mathrm {W}}^\pm _{\mathrm {L}} {\mathrm {W}}^\pm _{\mathrm {T}}} $, and $ {{\mathrm {W}}^\pm _{\mathrm {T}} {\mathrm {W}}^\pm _{\mathrm {T}}} $ processes. The gray bands represent the statistical uncertainties associated with the limited number of simulated events.
png pdf	Additional Figure 2-b: Generator level distributions of $ {\Delta \phi _{{\mathrm {j}} {\mathrm {j}}}} $ in the fiducial region for the $ {{\mathrm {W}}^\pm _{\mathrm {L}} {\mathrm {W}}^\pm _{\mathrm {L}}} $, $ {{\mathrm {W}}^\pm _{\mathrm {L}} {\mathrm {W}}^\pm _{\mathrm {T}}} $, and $ {{\mathrm {W}}^\pm _{\mathrm {T}} {\mathrm {W}}^\pm _{\mathrm {T}}} $ processes with the helicity eigenstates defined in the $ {{\mathrm {W}}^\pm {\mathrm {W}}^\pm} $ center-of-mass reference frame. The distributions are also shown for the unpolarized EW $ {{\mathrm {W}}^\pm {\mathrm {W}}^\pm} $ process. The bottom panel shows the ratio of the contribution of the unpolarized $ {{\mathrm {W}}^\pm {\mathrm {W}}^\pm} $ process to that of the sum of the $ {{\mathrm {W}}^\pm _{\mathrm {L}} {\mathrm {W}}^\pm _{\mathrm {L}}} $, $ {{\mathrm {W}}^\pm _{\mathrm {L}} {\mathrm {W}}^\pm _{\mathrm {T}}} $, and $ {{\mathrm {W}}^\pm _{\mathrm {T}} {\mathrm {W}}^\pm _{\mathrm {T}}} $ processes. The gray bands represent the statistical uncertainties associated with the limited number of simulated events.
png pdf	Additional Figure 2-c: Generator level distributions of $\Delta \phi _{\ell \ell}$ in the fiducial region for the $ {{\mathrm {W}}^\pm _{\mathrm {L}} {\mathrm {W}}^\pm _{\mathrm {L}}} $, $ {{\mathrm {W}}^\pm _{\mathrm {L}} {\mathrm {W}}^\pm _{\mathrm {T}}} $, and $ {{\mathrm {W}}^\pm _{\mathrm {T}} {\mathrm {W}}^\pm _{\mathrm {T}}} $ processes with the helicity eigenstates defined in the parton-parton center-of-mass reference frame. The distributions are also shown for the unpolarized EW $ {{\mathrm {W}}^\pm {\mathrm {W}}^\pm} $ process. The bottom panel shows the ratio of the contribution of the unpolarized $ {{\mathrm {W}}^\pm {\mathrm {W}}^\pm} $ process to that of the sum of the $ {{\mathrm {W}}^\pm _{\mathrm {L}} {\mathrm {W}}^\pm _{\mathrm {L}}} $, $ {{\mathrm {W}}^\pm _{\mathrm {L}} {\mathrm {W}}^\pm _{\mathrm {T}}} $, and $ {{\mathrm {W}}^\pm _{\mathrm {T}} {\mathrm {W}}^\pm _{\mathrm {T}}} $ processes. The gray bands represent the statistical uncertainties associated with the limited number of simulated events.
png pdf	Additional Figure 2-d: Generator level distributions of $\Delta \phi _{\ell \ell}$ in the fiducial region for the $ {{\mathrm {W}}^\pm _{\mathrm {L}} {\mathrm {W}}^\pm _{\mathrm {L}}} $, $ {{\mathrm {W}}^\pm _{\mathrm {L}} {\mathrm {W}}^\pm _{\mathrm {T}}} $, and $ {{\mathrm {W}}^\pm _{\mathrm {T}} {\mathrm {W}}^\pm _{\mathrm {T}}} $ processes with the helicity eigenstates defined in the $ {{\mathrm {W}}^\pm {\mathrm {W}}^\pm} $ center-of-mass reference frame. The distributions are also shown for the unpolarized EW $ {{\mathrm {W}}^\pm {\mathrm {W}}^\pm} $ process. The bottom panel shows the ratio of the contribution of the unpolarized $ {{\mathrm {W}}^\pm {\mathrm {W}}^\pm} $ process to that of the sum of the $ {{\mathrm {W}}^\pm _{\mathrm {L}} {\mathrm {W}}^\pm _{\mathrm {L}}} $, $ {{\mathrm {W}}^\pm _{\mathrm {L}} {\mathrm {W}}^\pm _{\mathrm {T}}} $, and $ {{\mathrm {W}}^\pm _{\mathrm {T}} {\mathrm {W}}^\pm _{\mathrm {T}}} $ processes. The gray bands represent the statistical uncertainties associated with the limited number of simulated events.
png pdf	Additional Figure 2-e: Generator level distributions of $ {m_{\ell \ell}} $ in the fiducial region for the $ {{\mathrm {W}}^\pm _{\mathrm {L}} {\mathrm {W}}^\pm _{\mathrm {L}}} $, $ {{\mathrm {W}}^\pm _{\mathrm {L}} {\mathrm {W}}^\pm _{\mathrm {T}}} $, and $ {{\mathrm {W}}^\pm _{\mathrm {T}} {\mathrm {W}}^\pm _{\mathrm {T}}} $ processes with the helicity eigenstates defined in the parton-parton center-of-mass reference frame. The distributions are also shown for the unpolarized EW $ {{\mathrm {W}}^\pm {\mathrm {W}}^\pm} $ process. The bottom panel shows the ratio of the contribution of the unpolarized $ {{\mathrm {W}}^\pm {\mathrm {W}}^\pm} $ process to that of the sum of the $ {{\mathrm {W}}^\pm _{\mathrm {L}} {\mathrm {W}}^\pm _{\mathrm {L}}} $, $ {{\mathrm {W}}^\pm _{\mathrm {L}} {\mathrm {W}}^\pm _{\mathrm {T}}} $, and $ {{\mathrm {W}}^\pm _{\mathrm {T}} {\mathrm {W}}^\pm _{\mathrm {T}}} $ processes. The gray bands represent the statistical uncertainties associated with the limited number of simulated events.
png pdf	Additional Figure 2-f: Generator level distributions of $ {m_{\ell \ell}} $ in the fiducial region for the $ {{\mathrm {W}}^\pm _{\mathrm {L}} {\mathrm {W}}^\pm _{\mathrm {L}}} $, $ {{\mathrm {W}}^\pm _{\mathrm {L}} {\mathrm {W}}^\pm _{\mathrm {T}}} $, and $ {{\mathrm {W}}^\pm _{\mathrm {T}} {\mathrm {W}}^\pm _{\mathrm {T}}} $ processes with the helicity eigenstates defined in the $ {{\mathrm {W}}^\pm {\mathrm {W}}^\pm} $ center-of-mass reference frame. The distributions are also shown for the unpolarized EW $ {{\mathrm {W}}^\pm {\mathrm {W}}^\pm} $ process. The bottom panel shows the ratio of the contribution of the unpolarized $ {{\mathrm {W}}^\pm {\mathrm {W}}^\pm} $ process to that of the sum of the $ {{\mathrm {W}}^\pm _{\mathrm {L}} {\mathrm {W}}^\pm _{\mathrm {L}}} $, $ {{\mathrm {W}}^\pm _{\mathrm {L}} {\mathrm {W}}^\pm _{\mathrm {T}}} $, and $ {{\mathrm {W}}^\pm _{\mathrm {T}} {\mathrm {W}}^\pm _{\mathrm {T}}} $ processes. The gray bands represent the statistical uncertainties associated with the limited number of simulated events.
png pdf	Additional Figure 3: Generator level distribution of diboson mass for the SM $ {{\mathrm {W}}^\pm {\mathrm {W}}^\pm} $ (black) and $ {{\mathrm {W}}^\pm _{\mathrm {L}} {\mathrm {W}}^\pm _{\mathrm {L}}} $ (blue) processes with the helicity eigenstates defined in the $ {{\mathrm {W}}^\pm {\mathrm {W}}^\pm} $ center-of-mass reference frame. The distributions are shown requiring jets with $ {p_{\mathrm {T}}} > $ 30 GeV and $ {| \eta |} < $ 5.0, with a dijet mass $ {m_{{\mathrm {j}} {\mathrm {j}}}} > $ 400 GeV and a pseudorapidity separation $ {{| \Delta \eta _{{\mathrm {j}} {\mathrm {j}}} |}} > $ 2.4. The dashed lines show the distributions of the $ {{\mathrm {W}}^\pm {\mathrm {W}}^\pm} $ and $ {{\mathrm {W}}^\pm _{\mathrm {L}} {\mathrm {W}}^\pm _{\mathrm {L}}} $ processes with the value of the Higgs boson coupling to W bosons scaled by a factor of 0.8.

Additional Tables

png pdf

Additional Table 1: Relative systematic uncertainties in the $ {{\mathrm {W}}^\pm _{\mathrm {L}} {\mathrm {W}}^\pm _{\mathrm {L}}} $ and $ {{\mathrm {W}}^\pm _{\mathrm {X}} {\mathrm {W}}^\pm _{\mathrm {T}}} $, and in the $ {{\mathrm {W}}^\pm _{\mathrm {L}} {\mathrm {W}}^\pm _{\mathrm {X}}} $ and $ {{\mathrm {W}}^\pm _{\mathrm {T}} {\mathrm {W}}^\pm _{\mathrm {T}}} $ cross section measurements in units of percent, using the helicity eigenstates in the initial state parton-parton center-of-mass reference frame.

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