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

The first measurements of production cross sections of polarized same-sign WW 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 WW 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 WW boson pairs. The electroweak production of same-sign WW 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.


Introduction
Vector boson scattering (VBS) processes probe the electroweak (EW) symmetry breaking mechanism at high energy scales. The unitarity of the tree-level amplitude of the scattering of longitudinally polarized gauge bosons at high energies is restored in the standard model (SM) by a Higgs boson with a mass lower than about 1 TeV [1,2]. The observation of a Higgs boson with a mass of about 125 GeV [3][4][5] provides an explanation that W and Z gauge bosons acquire mass via the Brout-Englert-Higgs mechanism, but additional Higgs bosons may still play a role in the EW symmetry breaking. Modifications of the VBS cross section for the longitudinally polarized W and Z bosons are predicted in models of physics beyond the SM through modifications of the Higgs boson couplings to gauge bosons or through the presence of new resonances [6,7]. The measurements of the longitudinally polarized scattering of the W and Z bosons provide complementary information to direct measurements of the Higgs boson couplings to gauge bosons [8,9]. Models of beyond SM physics that modify the cross sections of VBS processes with transversely polarized W and Z bosons are discussed in Ref. [10].
At the CERN LHC, VBS interactions are characterized by the presence of two gauge bosons in association with two forward jets that have a large rapidity separation. They are part of a class of processes contributing to the same-sign W ± W ± production in association with two jets that proceeds via the EW interaction at tree level, O(α 4 ), where α is the EW coupling, referred to as EW W ± W ± production. The leptonic decay mode W ± W ± → ± ν ± ν, where both W bosons decay into electrons or muons, , = e, µ, is a promising final state to study the polarized scattering from gauge bosons. The background contribution of the quantum chromodynamics (QCD) induced production of W ± W ± boson pairs in association with two jets with tree-level contributions at O(α 2 α 2 S ), where α S is the strong coupling, is small. Figure 1 shows representative Feynman diagrams of VBS processes involving self-interactions between gauge bosons through triple and quartic gauge couplings and the t-channel Higgs boson exchange.  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 W ± W ± 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.
The unpolarized EW W ± W ± production has been previously measured at the LHC in the leptonic decay modes at √ s = 8 and 13 TeV [11-15]. The first differential cross section measurements were reported in Ref. [15]. This Letter presents the first measurement of the EW production cross sections for polarized same-sign W ± W ± boson pairs. The data sample of protonproton (pp) collisions at √ s = 13 TeV corresponds to an integrated luminosity of 137 fb −1 [16][17][18], collected with the CMS detector [19] in three LHC operating periods during the years 2016, 2017, and 2018. Candidate events contain exactly two identified same-sign leptons, moderate missing transverse momentum, and two jets with a large rapidity separation and a high dijet mass.
In the W ± W ± channel, each of the W bosons can be polarized either longitudinally (W L ) or transversely (W T ), leading to three distinct contributions W ± L W ± L , W ± L W ± T , and W ± T W ± T . Ideally, we would measure all three contributions separately, but the current data sample size is too limited. Therefore, two maximum-likelihood fits are performed: one for W ± L W ± L and W ± X W ± T ; and another for W ± L W ± X and W ± T W ± T . The index X indicates either of the two polarization states. The event kinematical properties are used to extract the various contributions. Two sets of results are reported with the helicity eigenstates defined either in the WW center-of-mass reference frame or in the initial-state parton-parton one.

The CMS detector
The central feature of the CMS apparatus is a superconducting solenoid of 6 m internal diameter, providing a magnetic field of 3.8 T. Within the solenoid volume are a silicon pixel and strip tracker, a lead tungstate crystal electromagnetic calorimeter (ECAL), and a brass and scintillator hadron calorimeter, each composed of a barrel and two endcap sections. Forward calorimeters extend the pseudorapidity (η) coverage provided by the barrel and endcap detectors. Muons are detected in gas-ionization detectors embedded in the steel flux-return yoke outside the solenoid. A more detailed description of the CMS detector, together with a definition of the coordinate system used and the relevant kinematic variables, is given in Ref. [19].
The first level of the CMS trigger system, composed of custom hardware processors, uses information from the calorimeters and muon detectors to select events of interest with a latency of less than 4 µs. The second level, known as the high-level trigger, consists of a farm of processors running a version of the full event reconstruction software optimized for fast processing, and reduces the event rate to about 1 kHz before data storage [20].

Signal and background simulation
Several Monte Carlo (MC) event generators are used to simulate the signal and background contributions. Three independent sets of simulated events for each process are needed to match the data-taking conditions in the various years. All generated events are processed through a simulation of the CMS detector based on GEANT4 [21] and are reconstructed with the same algorithms used for data. Additional pp interactions in the same and nearby bunch crossings, referred to as pileup, are also simulated. The distribution of the number of pileup interactions in the simulation is adjusted to match the one observed in the data. The average number of pileup interactions was 23 (32) in 2016 (2017 and 2018).
The SM EW W ± L W ± L , W ± L W ± T , and W ± T W ± T signal processes, where both bosons decay leptonically, are separately simulated using MADGRAPH5 aMC@NLO 2.7.2, with the implementation of polarized parton scattering [22][23][24], at leading order (LO) with six EW (O(α 6 )) and zero QCD vertices. The NNPDF 3.1 next-to-next-to-leading-order (NNLO) [25] parton distribution functions (PDFs) are used. Signal processes are simulated with the helicity eigenstates defined either in the W ± W ± center-of-mass reference frame or in the initial parton-parton reference frame. The PHANTOM 1.5.1 generator [26,27] uses the on-shell projection technique for the predictions of the signal processes as discussed in Ref. [28]. The MADGRAPH5 aMC@NLO predictions show satisfactory agreement within the statistical uncertainties with the PHANTOM predictions in the relevant fiducial region, defined in Section 8, for this analysis. The small contributions of off-shell and nonresonant production [28] are not included in the simulated signal samples and amount to 1-2% in the fiducial region.
The full next-to-leading-order (NLO) QCD and EW corrections for the leptonic unpolarized W ± W ± scattering process have been computed [29,30], and they reduce the LO cross section for the EW W ± W ± process by approximately 10-15%, with the correction increasing in magnitude to up to 25% with increasing dilepton and dijet masses. The NLO corrections for the W ± L W ± L , W ± L W ± T , and W ± T W ± T processes are not known. The corrections for the unpolarized EW W ± W ± process at orders of O(α S α 6 ) and O(α 7 ) are applied to the MADGRAPH5 aMC@NLO LO cross sections for the W ± T W ± T process. Only the corrections at order of O(α S α 6 ) are applied to the MADGRAPH5 aMC@NLO LO cross sections for the W ± L W ± L and W ± L W ± T processes because the corrections at order O(α 7 ) are expected to be smaller for the W ± L W ± L and W ± L W ± T processes compared to the size of the corresponding corrections for the unpolarized EW W ± W ± process [31]. There is a negligible effect in the measured cross sections from differences in the event kinematical properties caused by the treatment of the NLO corrections.
The EW WZ background process is simulated with MADGRAPH5 aMC@NLO 2.4.2 at order O(α 6 ). The QCD-induced WZ process is simulated at LO with up to three additional partons in the matrix element calculations using the MADGRAPH5 aMC@NLO generator with at least one QCD vertex at tree level. The different jet multiplicities are merged using the MLM scheme [32] to match matrix element and parton shower jets. The MADGRAPH5 aMC@NLO generator is also used to simulate the QCD-induced W ± W ± process.
The interference between the EW and QCD diagrams for the W ± W ± and WZ processes is generated with MADGRAPH5 aMC@NLO including the contributions of order α S α 5 . The relative contributions in the fiducial region of the interference term between the EW and the QCD diagrams for the W ± L W ± L , W ± L W ± T , and W ± T W ± T processes are comparable to the relative contributions of the W ± L W ± L , W ± L W ± T , and W ± T W ± T processes to the EW W ± W ± cross section. The interferences between the signal processes are expected to be small [24], and good agreement is observed between the incoherent sum of the polarized cross sections and the unpolarized cross sections for the distributions of the observables.
The POWHEG v2 [33][34][35][36][37] generator is used to simulate the tt, tW, and other diboson processes at NLO accuracy in QCD. Production of ttW, ttZ, tt γ, and triple vector boson (VVV) events is simulated at NLO accuracy in QCD using the MADGRAPH5 aMC@NLO 2.2.2 (2.4.2) generator for 2016 (2017 and 2018) [22,23] samples. The tZq process is simulated at NLO in the four-flavor scheme using MADGRAPH5 aMC@NLO 2.3.3. The tZq MC simulation is normalized using a cross section computed at NLO with MADGRAPH5 aMC@NLO in the five-flavor scheme, following the procedure described in Ref. [38]. The double parton scattering W ± W ± production is generated at LO using PYTHIA 8.226 (8.230) [39]

Event reconstruction and selection
Events are reconstructed using the CMS particle-flow (PF) algorithm [44] that reconstructs and identifies each individual particle with an optimized combination of all subdetector information. The missing transverse momentum vector p miss T is defined as the projection onto the plane perpendicular to the beam axis of the negative vector sum of the momenta of all reconstructed PF objects in an event. Its magnitude is referred to as p miss T . Jets are reconstructed by clustering PF candidates using the anti-k T algorithm [45,46] with a distance parameter of 0.4. Jets are calibrated in the simulation, and separately in data, accounting for energy deposits of neutral particles from pileup and any nonlinear detector response [47]. The effect of pileup is mitigated through a charged-hadron subtraction technique, which removes the energy of charged hadrons not originating from the primary vertex (PV) [48] of the event. Corrections to jet energies to account for the detector response are propagated to p miss T [49]. The PV is defined as the vertex with the largest value of summed physics-object p 2 T . The physics objects are derived from only the tracks assigned to the vertex as inputs by clustering them into jets, including leptons. The p miss T is also recalculated only from those jets by summing their negative p T vectors.
Electrons and muons are reconstructed by associating a track reconstructed in the tracking detectors with either a cluster of energy in the ECAL [50, 51] or a track in the muon system [52]. Electron and muon candidates must pass certain identification criteria to be further selected in the analysis. For the "loose" identification, they must satisfy p T > 10 GeV and |η| < 2.5 (2.4) for electrons (muons). At the final stage of the lepton selection the "tight" working points criteria following the definitions provided in Refs. [50,52] are chosen, including requirements on the impact parameter of the candidates with respect to the PV and their isolation with respect to other particles in the event [9].
For electrons, the background contribution coming from a mismeasurement of the track charge is not negligible. The sign of this charge is evaluated using three observables that measure the electron curvature applying different methods; requiring all three charge evaluations to agree reduces this background contribution by a factor of five with an efficiency of about 97% [50]. The charge mismeasurement is negligible for muons [53,54].
Collision events are collected using single-electron (single-muon) triggers that require the presence of an isolated lepton with p T > 27 (24) GeV. In addition, a set of dilepton triggers with lower p T thresholds, with a threshold of 8 GeV for the subleading lepton, are used. This ensures a trigger efficiency above 99% for events that satisfy the subsequent offline selection.
Several selection requirements are used to isolate the W ± W ± topology defining the signal region (SR) while reducing the contributions of background processes. Candidate events contain exactly two isolated same-sign charged leptons and at least two jets with p j T > 50 GeV and |η| < 4.7. Jets that are within ∆R = √ (∆φ) 2 + (∆η) 2 < 0.4 of one of the identified leptons are not used in the analysis. Here ∆φ and ∆η refer to the differences in the azimuthal angle φ and η of the jet and the charged-lepton candidate, respectively. Because of the presence of undetected neutrinos in the signal events, p miss T is required to exceed 30 GeV.
The W ± W ± SR selection requires one of the same-sign leptons to satisfy p T > 25 GeV and the other p T > 20 GeV. The mass of the dilepton pair m must be greater than 20 GeV. Candidate events in the dielectron final state within 15 GeV of the nominal Z boson mass m Z [55] are rejected to reduce the number of Z boson background events where the charge of one of the electron candidates is misidentified.
The VBS topology is targeted by requiring the two highest-p T jets to have a dijet mass m jj > 500 GeV and a pseudorapidity separation |∆η jj | > 2.5. The W bosons in the VBS topologies are mostly produced in the central rapidity region with respect to the two selected jets. The candidate W ± W ± events are required to satisfy max(z * ) < 0.75, where z * = |η − (η j 1 + η j 2 )/2|/|∆η jj | is the Zeppenfeld variable [56], η is the pseudorapidity of one of the selected leptons, and η j 1 and η j 2 are the pseudorapidities of the two candidate VBS jets.
Candidate events with one or more jets with p T > 20 GeV and |η| < 2.4 that are consistent with the fragmentation of a bottom quark are rejected to reduce the number of top quark background events. The DEEPCSV b tagging algorithm [57] is used for this selection. For the chosen working point, the efficiency to select b quark jets is about 70% and the rate for incorrectly tagging jets originating from the hadronization of gluons or u, d, s quarks is about 1%. The rate for incorrectly tagging jets originating from the hadronization of c quarks is about 10%. The selection requirements to define the same-sign W ± W ± SR are summarized in Table 1. Table 1: Summary of the requirements defining the W ± W ± SR. The |m − m Z | requirement is applied to the dielectron final state only.

Variable Requirement Leptons
Exactly 2 same-sign leptons,

Extracting polarization information
In the W ± W ± channel, the W bosons can each be either longitudinally or transversely polarized leading to different kinematic distributions, reflected in the kinematical properties of the two leptons, the two jets, and p miss T . The W L bosons tend to be radiated at a smaller angle with respect to the incoming quark direction, resulting in a smaller W L boson p T compared to the radiated W T boson p T . In addition, there are differences in the behavior of the scattering amplitudes as a function of the W ± W ± center-of-mass energy and the scattering angle [58].
Multivariate techniques are used to enhance the separation between the different processes. We implement boosted decision trees (BDTs) with gradient boosting using the TMVA package [59]. Two different BDTs, referred to as the signal BDTs, are trained on simulated events to separate either the W ± L W ± L and W ± X W ± T processes or the W ± L W ± X and W ± T W ± T processes. Several discriminating observables are used as the inputs to the BDTs, including the jet and lepton kinematical properties and p miss T , as summarized in Table 2. The distributions of these observables are taken from the SM predictions. Hypothetical modifications due to beyond the SM physics are assumed to impact only the production rates, but not the kinematic distributions of sensitive variables. Angular variables are included, such as the difference in the azimuthal angles between the leading and subleading jets (∆φ jj ) and leptons (∆φ ), and the ∆R between the leading (subleading) jet and the dilepton system ∆R j1, (∆R j2, ). The dilepton p T , m , and the transverse diboson mass m WW T as defined in Ref. [15] are also considered. The kinematic variable (p 1 [58] is also included in the BDT inputs. A larger set of discriminating observables was studied, but only variables that improve the sensitivity and show some separation are retained. The distributions of ∆φ jj (upper), ∆φ (middle), and m (lower) at the generator level for the W ± L W ± L , W ± L W ± T , and W ± T W ± T processes with the helic-ity eigenstates defined in the parton-parton (left) and W ± W ± (right) center-of-mass reference frames are shown in Fig. 2. The signal extraction was also compared with a deep neural network using the KERAS [60] deep learning library, interfaced with the TENSORFLOW [61] library, which led to a consistently good performance.

Background estimation
A combination of methods based on control samples in data and simulation is used to estimate background contributions. Uncertainties related to the theoretical and experimental predictions are described in Section 7. The electron charge misidentification in simulation is corrected to reproduce the rate measured in data. Using Z → ee events, the misidentification rate is about 0.01% (0.3%) in the barrel (endcap) region [50]. Oppositely charged dilepton final states from tt, tW, W + W − , and Drell-Yan processes contribute to the background from charge misidentification.
The nonprompt lepton backgrounds originating from leptonic decays of heavy quarks, hadrons misidentified as leptons, and electrons from photon conversion are suppressed by the identification and isolation requirements imposed on electrons and muons. The remaining contribution from the nonprompt lepton background is estimated directly from data following the technique described in Ref.
[12], where the yield in a sample of data events dominated by jet production is extrapolated to the signal region using efficiencies for loosely identified leptons to pass the standard lepton selection criteria. A normalization uncertainty of 20% is assigned for the nonprompt lepton background to include possible differences in the composition of jets , and m (lower) in the fiducial region for the W ± L W ± L , W ± L W ± T , and W ± T W ± T processes with the helicity eigenstates defined in the parton-parton (left) and W ± W ± (right) center-of-mass reference frames. The error bars represent the uncertainties associated with the limited numbers of simulated events.
between the data sample used to derive these efficiencies and the data sample in the W ± W ± SR [9].
Several background-enriched control regions (CRs), disjoint from one another and from the SR, are used to select event samples enriched with WZ, nonprompt lepton, tZq, and ZZ background events. The WZ CR is defined by requiring three leptons where the opposite-sign same-flavor leptons from the Z boson candidate have p T > 25 and 10 GeV with the dilepton mass within 15 GeV of the nominal Z boson mass. In events with three same-flavor leptons, the opposite-sign lepton pair with the dilepton mass closest to m Z is associated with the Z boson. The remaining lepton with p T > 20 GeV is associated with the W boson. In addition, the trilepton mass m is required to be greater than 100 GeV and max(z * ) must be less than 1.0.
The nonprompt lepton CR is defined by requiring the same selection as for the W ± W ± SR, but with the b jet veto requirement inverted. The selected sample is enriched with events from the nonprompt lepton background and dominated by semileptonic tt events. Similarly, the tZq CR is defined by requiring the same selection as the WZ CR, but with the b quark veto requirement inverted. The selected sample is dominated by the tZq background process. Finally, the ZZ CR requirements select events with four leptons with the same VBS requirements as the W ± W ± SR. The four CRs are used to estimate the normalization of the main background processes from data. All other background processes are estimated from simulation after applying corrections to account for small differences between data and simulation as detailed in Section 7.
To distinguish EW W ± W ± production from the SM background processes before extracting the individual polarizations, a BDT is trained using the TMVA package [59]. Several discriminating observables listed in Table 3 are used as inputs to this BDT, which we will refer to as the inclusive BDT. The values of m jj and |∆η jj | are powerful because VBS topologies typically have large values for the dijet mass and pseudorapidity separation [15]. A large training background sample of simulated events is obtained by using oppositely charged dilepton events.  The uncertainty in the calibration of the jet energy scale and resolution directly affects the selection efficiency of the jet multiplicity requirement and the p miss T measurement. These effects are estimated by changing the jet energy in the simulation up-and downwards by one standard deviation. The uncertainty in the jet energy scale and resolution is 2-5%, depending on the p T and η [47], and the impact on the expected signal and background yields is 1-4%.
Discrepancies in the b tagging efficiency between data and simulation are adjusted by applying corrections to the simulated samples [57], which are estimated separately for correctly and incorrectly identified jets. Each set of values results in uncertainties in the b tagging efficiency of about 1-4%, and the impact on the expected signal and background yields is about 1%. The uncertainties in the jet energy scale and b tagging are treated as uncorrelated across the three data sets.
The theoretical uncertainties corresponding to the choice of the QCD renormalization and factorization scales are estimated by varying these scales independently up and down by a factor of two from their nominal values. The largest cross section variation, while excluding the two extreme variations where one scale is varied up and the other one down, is taken as the uncertainty . The PDF uncertainties are evaluated according to the procedure described in Ref. [64]. The scale and PDF uncertainties are treated as fully correlated across bins for the distributions used to extract the results. The effect of O(α 7 ) correction for the unpolarized EW W ± W ± process on the shapes of the distributions for the W ± L W ± L and W ± L W ± T processes is considered as a systematic uncertainty. The correction values are used as a symmetric shape uncertainty. The uncertainties associated with the limited numbers of simulated events and of data events used to estimate the nonprompt lepton background are also included as systematic uncertainties with the latter being the dominant contribution. A summary of the systematic uncertainties in the W ± L W ± L and W ± X W ± T , and in the W ± L W ± X and W ± T W ± T cross section measurements is shown in Table 4. Table 4: Systematic uncertainties of the W ± L W ± L and W ± X W ± T , and W ± L W ± X and W ± T W ± T cross section measurements in units of percent.

Results
Binned maximum-likelihood fits are performed to discriminate between the signals and the remaining backgrounds using the W ± W ± SR and the WZ, nonprompt lepton, tZq, and ZZ CRs. Two separate fits are performed, one for the simultaneous measurements of the W ± L W ± L and W ± X W ± T cross sections and a second for the simultaneous measurements of the W ± L W ± X and W ± T W ± T cross sections. The systematic uncertainties are treated as nuisance parameters and are profiled [65,66] with the shape and normalization of each distribution varying within the respective uncertainties in the fit. The normalization uncertainties are treated as log-normal nuisance parameters. The small QCD W ± W ± contribution is normalized to the SM prediction and allowed to vary within the uncertainties. The normalizations of the tZq, ZZ, and WZ background processes are free parameters of the maximum-likelihood fits, together with the signal cross sections. A two-dimensional distribution is used in the simultaneous fits for the W ± W ± SR with five bins in the inclusive BDT and five bins in the corresponding signal BDT. The m jj distribution is used for the remaining CRs in the fit with four bins. The bin boundaries are chosen to have similar W ± L W ± L and W ± L W ± X contributions across the bins. The interference contributions between the EW and QCD diagrams for the W ± W ± and WZ processes are normalized to the SM predictions within the uncertainties. The impact of treatment of the interference contributions on the results is evaluated by performing a set of alternative fits where the interference contributions between the EW diagrams for the W ± L W ± L and W ± X W ± T or W ± L W ± X and W ± T W ± T processes and QCD diagrams are scaled with the square root of the measured to the predicted cross section ratios. The two approaches yield consistent results.
The distributions of m jj (upper left), ∆φ jj (upper right), ∆φ (lower left), and the output score of the inclusive BDT (lower right) in the W ± W ± SR are shown in Fig. 3. The distributions of the two signal BDT output scores are shown in Fig. 4. The predicted yields are shown with their best fit normalizations from the simultaneous fit. The data yields, together with the SM expectations with the best fit normalizations from the simultaneous fit for the W ± L W ± L and W ± X W ± T cross sections, are given in Table 5. The background yields with the best fit normalizations from the simultaneous fit for the W ± L W ± X and W ± T W ± T cross sections are consistent with the yields shown in Table 5 within a few percent.
The fiducial region for the cross section measurements is defined by requiring two same-sign , and of the output score of the inclusive BDT (lower right) in the W ± W ± SR. The predicted yields are shown with their best fit normalizations from the simultaneous fit. The histograms for the W ± W ± process include the contributions from the W ± L W ± L , W ± L W ± T , and W ± T W ± T processes (shown as solid lines), QCD W ± W ± , and interference. The histograms for other backgrounds include the contributions from double parton scattering, VVV, and from oppositely charged dilepton final states from tt, tW, W + 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.  Figure 4: Distributions of the output score of the signal BDT used for the W ± L W ± L and W ± X W ± T cross section measurements (left) and of the output score of the signal BDT used for the W ± L W ± X and W ± T W ± T cross section measurements (right). The predicted yields are shown with their best fit normalizations from the simultaneous fit. The histograms for the W ± W ± process include the contributions from the W ± L W ± L , W ± L W ± T , and W ± T W ± T processes (shown as solid lines), QCD W ± W ± , and interference. The histograms for other backgrounds include the contributions from double parton scattering, VVV, and from oppositely charged dilepton final states from tt, tW, W + 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. Table 5: Expected yields from various SM processes and observed data events in W ± W ± 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 W ± L W ± L and W ± X W ± T cross sections. The W ± L W ± T and W ± T W ± T yields are obtained from the W ± X W ± T yield assuming the SM prediction for the ratio of the yields. The tVx background yield includes the contributions from ttV and tZq processes.

Process
Yields Total SM 522.9 ± 60.7 Data 524 leptons with p T > 20 GeV, |η| < 2.5, and m > 20 GeV, and two jets with m jj > 500 GeV and |∆η jj | > 2.5. The leptons at the generator level are selected at the so-called dressed level by combining the four-momentum of each lepton after final-state photon radiation with that of photons found within a cone of ∆R = 0.1 around the lepton. The jets at generator level are clustered from stable particles, excluding neutrinos, using the anti-k T clustering algorithm with a distance parameter of 0.4, and are required to satisfy p T > 50 GeV and |η| < 4.7. Jets within ∆R < 0.4 of the selected charged leptons are not included. Electrons and muons produced in the decay of a τ lepton are not included in the definition of the fiducial region. Nonfiducial events, i.e., events selected at the reconstructed level that do not satisfy the fiducial requirements, are included in the simultaneous fit as background processes.
The fit results are shown in Fig. 5 as scans of the negative profile log-likelihood, −2∆lnL, as a function of the W ± L W ± L cross section. The expected distributions include the contribution from the W ± X W ± T process. The corresponding observed (expected) upper limit at 95% confidence level (CL) is 1.17 (0.88) fb. The fiducial cross section measurements for the W ± L W ± L and W ± X W ± T processes and the theoretical predictions are shown in Table 6. The measured cross section values agree with the theoretical predictions within uncertainties.
The fiducial cross section measurements for the W ± L W ± X and W ± T W ± T processes are extracted from a separate fit including the corresponding signal BDT. The measurements and the theoretical predictions are summarized in Table 6. The significance of the measured W ± L W ± X yield is quantified using background-only hypothesis, i.e., assuming no contribution from the W ± L W ± X process, under the asymptotic approximation [67] and corresponds to 2.3 standard deviations. The expected significance is evaluated with an Asimov data set [67] and corresponds to 3.1 standard deviations.
The measurements are also performed for the polarized observables defined using the helicity eigenstates in the initial state parton-parton center-of-mass reference frame. Defining the polarization vectors in the parton-parton center-of-mass reference frame changes the respective contributions of W ± L W ± L , W ± L W ± X and W ± X W ± T , and the distributions of the input observables sensitive to the polarization [68]. The fiducial cross section measurements and the theoretical predictions are summarized in Table 7. The observed (expected) 95% CL upper limit of the production cross section is 1.06 (0.85) fb for the W ± L W ± L process. The observed (expected) significance of the W ± L W ± X process is 2.6 (2.9) standard deviations.

Summary
The first measurements of production cross sections for polarized same-sign W ± W ± 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 W ± W ± boson pairs of 1.17 (0.88) fb is reported with the helicity eigenstates defined in the W ± W ± center-of-mass reference frame. The electroweak production of the W ± W ± 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. 1.94 ± 0.21 Table 7: Measured fiducial cross sections for the W ± L W ± L and W ± X W ± T processes, and for the W ± L W ± X and W ± T W ± 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 O(α S α 6 ) and O(α 7 ) corrections to the MAD-GRAPH5 aMC@NLO LO cross sections, as described in the text, are also shown.

Acknowledgments
We congratulate our colleagues in the CERN accelerator departments for the excellent performance of the LHC and thank the technical and administrative staffs at CERN and at other CMS institutes for their contributions to the success of the CMS effort. In addition, we gratefully acknowledge the computing centers and personnel of the Worldwide LHC Computing Grid for delivering so effectively the computing infrastructure essential to our analyses. Finally, we acknowledge the enduring support for the construction and operation of the LHC and the CMS detector provided by the following funding agencies:  [13] CMS Collaboration, "Observation of electroweak production of same-sign W boson pairs in the two jet and two same-sign lepton final state in proton-proton collisions at √ s = 13 TeV", Phys. Rev. Lett. 120 (2018) 081801, doi:10.1103/PhysRevLett.120.081801, arXiv:1709.05822.
[51] CMS Collaboration, "Electron and photon performance in cms with the full 2017 data sample and additional 2016 highlights for the calor 2018 conference", CMS Detector Performance Summary CMS-DP-2018-017, 2018.