Search for a right-handed W boson and a heavy neutrino in proton-proton collisions at s\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \sqrt{s} $$\end{document} = 13 TeV

A search is presented for a right-handed W boson (WR) and a heavy neutrino (N), in a final state consisting of two same-flavor leptons (ee or μμ) and two quarks. The search is performed with the CMS experiment at the CERN LHC using a data sample of proton-proton collisions at a center-of-mass energy of 13 TeV corresponding to an integrated luminosity of 138 fb−1. The search covers two regions of phase space, one where the decay products of the heavy neutrino are merged into a single large-area jet, and one where the decay products are well separated. The expected signal is characterized by an excess in the invariant mass distribution of the final-state objects. No significant excess over the standard model background expectations is observed. The observations are interpreted as upper limits on the product of WR production cross sections and branching fractions assuming that couplings are identical to those of the standard model W boson. For N masses mN equal to half the WR mass mWR\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {m}_{{\mathrm{W}}_{\mathrm{R}}} $$\end{document} (mN = 0.2 TeV), mWR\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {m}_{{\mathrm{W}}_{\mathrm{R}}} $$\end{document} is excluded at 95% confidence level up to 4.7 (4.8) and 5.0 (5.4) TeV for the electron and muon channels, respectively. This analysis provides the most stringent limits on the WR mass to date.


Introduction
Left-right (LR) symmetric models [1][2][3][4], which extend the electroweak sector of the standard model (SM) by a right-handed SU(2) group, provide a possible explanation for parity violation in the SM as the consequence of spontaneous symmetry breaking at a multi-TeV mass scale. These models predict a heavy partner of the SM W boson, a heavy, right-handed gauge boson W R that is coupled to right-handed fermions. In addition, LR models also provide an explanation for the small mass of SM neutrinos through the seesaw mechanism [5][6][7], which requires the existence of a heavy right-handed neutrino (N) for each lepton flavor. The heavy neutrinos couple exclusively to leptons of the corresponding flavor, and have different masses.
The coupling strength of the W R boson to the SM particles (g R ) is a free parameter in most LR models. We assume LR symmetry, such that g R is the same as the SM coupling constant g L .
The dominant production process for the W R boson at the CERN LHC is the Drell-Yan (DY) mechanism. The leading order Feynman diagram for this process is shown in figure 1. Although the potential Majorana nature of the right-handed neutrinos implies that the final-state charged leptons can have the same sign, we do not impose charge requirements on the final-state leptons, in order to remain sensitive to the widest possible range of models. and 13 TeV. These searches have excluded regions of phase space with masses of the righthanded W boson and heavy neutrino (m W R and m N , respectively) up to several TeV. In this paper, we extend the region of parameter space covered in the previous 2016 CMS search for W R bosons in events with two same-flavor leptons (e or µ) and two jets using 2016 data [12], by including the regime where the W R boson is heavy compared to the N (m W R /m N ≥ 10). In this scenario, the heavy neutrinos are produced with large transverse momentum (p T ) and their decay products are collimated along their direction of motion. Therefore, the heavy neutrino decay is reconstructed in a single jet and identified using jet substructure techniques, similar to those discussed in refs. [16][17][18] and previously applied in ref.
[10]; we refer to these as "boosted" events, in contrast to "resolved" events where the two jets from the heavy neutrino decay are reconstructed separately. The inclusion of boosted events leads to significant improvements in the search sensitivity in the region where m N < 0.5 TeV. To obtain maximum sensitivity, a statistical combination of the resolved and boosted results is performed. For this analysis we use the data sample collected in 2016-2018 with the CMS detector at the LHC corresponding to an integrated luminosity of 138 fb −1 . Tabulated results are provided in HEPData [19].

The CMS detector
A detailed description of the CMS detector, together with a definition of the coordinate system and the relevant kinematic variables, can be found in ref. [20]. 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 (HCAL), 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 chambers embedded in the steel flux-return yoke outside the solenoid.
Events of interest are selected using a two-tiered trigger system [21]. The first level, composed of custom hardware processors, uses information from the calorimeters and muon detectors to select events at a rate of around 100 kHz within a fixed time interval of less than 4 µs [22]. The second level, known as the high-level trigger, consists of a farm of -2 -

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processors running a version of the full event reconstruction software optimized for fast processing, and reduces the event rate to around 1 kHz before data storage.

Simulated samples
All signal events are simulated using the MadGraph5_amc@nlo 2.6.5 [23] Monte Carlo (MC) event generator at leading order (LO) following the prescriptions described in refs. [17,18] for various m W R hypotheses in the range from 0.2 to 7.0 TeV, with m N ranging from 0.1 TeV up to m W R where N is a Majorana neutrino. The events are generated in final states with two same-flavor (SF) leptons (ee or µµ). The production cross sections are scaled to next-to-LO (NLO) in quantum chromodynamics (QCD) using K factors obtained from the same generator.
The background samples are simulated with several MC event generators. The Z and W boson production associated with jets is simulated with the MadGraph5_amc@nlo 2.2.2 (2.4.2) generator for up to four parton-level jets at LO for the 2016 (2017-2018) samples, with the MLM matching scheme between jets from matrix element calculations and parton showers [24]. The powheg 2.0 [25][26][27][28] generator is used to model the tt production, as well as tW and t-channel single top quark production at NLO. The s-channel single top quark production is generated with the MadGraph5_amc@nlo generator at NLO precision. The inclusive decay of tt produced in association with a W and Z boson is simulated by MadGraph5_amc@nlo at NLO and LO precision, respectively. The pythia generator [29] is used to simulate diboson processes (WW, WZ, and ZZ) at LO. Triple vector boson (WWW, WWZ, WZZ, and ZZZ) events are generated at NLO using

MadGraph5_amc@nlo.
The generators used for the signal and background processes are interfaced with pythia 8.226 (8.230) [29]

Event reconstruction and object selection
For this search, the events were selected at the trigger level by requiring the presence of a high-momentum lepton in the event. A combination of three triggers that require an -3 -

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isolated electron with p T > 27 (32) GeV, an electron with p T > 115 GeV, or a photon with p T > 175 (200) GeV is used to collect events that contain at least one electron in 2016 (2018). In 2017, two triggers with the requirement of an isolated electron with p T > 35 GeV or a photon with p T > 200 GeV were used. The single-electron triggers differ in their usage of isolation requirements: while the lower-threshold trigger requires electrons to be well isolated, the higher-threshold trigger does not, which gives an improved efficiency at high p T . Similarly, the single-photon trigger avoids reliance on the online track reconstruction and increases the overall efficiency for electrons with p T > 200 GeV. Events containing at least one isolated muon are collected by triggers that require a muon with a minimum p T of 50 GeV.
The candidate vertex with the largest value of summed physics-object p 2 T is taken to be the primary pp interaction vertex. The physics objects used for this determination are the jets, clustered using the jet finding algorithm [36, 37] with the tracks assigned to candidate vertices as inputs, as well as the remaining single tracks (including identified leptons), and the associated missing transverse momentum, taken as the negative vector sum of the p T of those objects.
The global event reconstruction (also called particle-flow event reconstruction) [38] aims to reconstruct and identify each individual particle in an event, with an optimized combination of all subdetector information. In this process, the identification of the particle type (photon, electron, muon, charged and neutral hadron) plays an important role in the determination of the particle direction and energy. Photons (e.g., coming from π 0 decays or from electron bremsstrahlung) are identified as ECAL energy clusters not linked to the extrapolation of any charged particle trajectory to the ECAL. Each electron (e.g., coming from photon conversions in the tracker material or from B hadron semileptonic decays) is identified as a primary charged particle track and potentially many ECAL energy clusters corresponding to this track extrapolation to the ECAL and to possible bremsstrahlung photons emitted along the way through the tracker material. Muons (e.g., from B hadron semileptonic decays) are identified as tracks in the central tracker consistent with either a track or several hits in the muon system, and associated with calorimeter deposits compatible with the muon hypothesis. Charged hadrons are identified as charged particle tracks neither identified as electrons, nor as muons. Finally, neutral hadrons are identified as HCAL energy clusters not linked to any charged hadron trajectory, or as a combined ECAL and HCAL energy excess with respect to the expected charged hadron energy deposit.
The energy of each photon is obtained from the ECAL measurement. The energy of each electron is determined from a combination of the electron momentum at the primary interaction vertex as determined by the tracker, the energy of the corresponding ECAL cluster, and the energy sum of all bremsstrahlung photons spatially compatible with originating from the electron track. The momentum of each muon is obtained from the trajectory of the corresponding track in the magnetic field. The energy of each charged hadron is determined from a combination of the momentum measured in the tracker and the matching ECAL and HCAL energy deposits, corrected for the response function of the calorimeters to hadronic showers. Finally, the energy of each neutral hadron is obtained from the corresponding corrected ECAL and HCAL energies.

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For each event, the jets are clustered from the reconstructed particles using the infrared and collinear safe anti-k T algorithm [36, 37] with a distance parameter of 0.4 (AK4 jets) or 0.8 (AK8 jets). The jet momentum is determined as the vectorial sum of all particle momenta in the jet, and is found from simulation to be, on average, within 5-10% of the true momentum over the whole p T spectrum and detector acceptance [39].
Pileup interactions can contribute additional tracks and calorimetric energy deposits to the reconstructed jets, increasing their apparent momentum. To mitigate this effect for AK4 jets, charged particles identified as originating from pileup vertices are discarded and an offset correction is applied to correct for the remaining contributions. Jet energy corrections are derived by comparing the average measured energies of jets in data with those of simulated jets. In situ measurements of the momentum balance in dijet, photon+jet, Z+jet, and multijet events are used to account for any residual differences in jet energy scale in data and simulation [39]. The typical jet energy resolution is 15% at 10 GeV, 8% at 100 GeV, and 4% at 1 TeV. Additional selection criteria are applied to each jet to remove jets potentially dominated by anomalous contributions from various subdetector components or reconstruction failures [40]. For AK8 jets, the pileup-per-particle identification algorithm [41, 42] is used to mitigate the effect of pileup at the reconstructed-particle level, making use of local shape information, event pileup properties and tracking information.
The momentum resolution for electrons with p T ≈ 45 GeV from Z → ee decays ranges from 1.7% to 4.5%. It is generally better in the barrel region than in the endcaps, and also depends on the bremsstrahlung energy emitted by the electron as it traverses the material in front of the ECAL [43].
Muons are measured in the range |η| < 2.4, with detection planes made using three technologies: drift tubes, cathode strip chambers, and resistive-plate chambers. The singlemuon trigger efficiency exceeds 90% over the full η range, and the subsequent efficiency to reconstruct and identify muons is greater than 96%. Matching muons to tracks measured in the silicon tracker results in a fractional p T resolution of 1% in the barrel and 3% in the endcaps for muons with p T up to 100 GeV, and of better than 7% in the barrel for muons with p T up to 1 TeV [44].
To reconstruct resolved W R candidates, events with two leptons and at least two AK4 jets are selected. Events with additional leptons are rejected, and if more than two jets exist, the two jets with the highest p T are used. The leading (subleading) lepton is required to have p T > 60(53) GeV and to be within the fiducial acceptance (|η| < 2.4). Electrons are rejected if the cluster lies in the range 1.44 < |η| < 1.57, which corresponds to the transition region between the barrel and endcap sections of the ECAL, where the performance is degraded. To suppress muons originating from hadron decays or pion punch-through in jets, the p T sum of additional tracks that originate at the PV and are inside a cone of ∆R < 0.3, where ∆R ≡ (∆η) 2 + (∆φ) 2 , is required to be less than 10% of the muon p T . Electrons are also required to be isolated, i.e., the p T sum of all tracks in a cone of ∆R < 0.3 centered on the electron candidate, not associated with the electron and originating from the PV, must be below 5 GeV. Dedicated identification algorithms, optimized for the selection of high-momentum leptons [43, 45] are used. The two jet candidates must each have p T > 40 GeV and be within |η| < 2.4. To avoid overlaps between leptons and jets, they are required to be separated in ∆R by at least 0.4. An event is considered resolved if it contains four well-separated final-state objects as described above.
Events that fail the resolved selection criteria are used to reconstruct the boosted W R candidates. The N → qq decay is reconstructed as a single AK8 jet. The boosted signature requires an AK8 jet with p T > 200 GeV and two leptons that have the same p T requirements as in the resolved search. The leading lepton is required to be separated in the azimuthal direction by ∆φ > 2.0 with respect to the AK8 jet. The subleading lepton, with the isolation requirement removed, is required to fall within the AK8 jet cone. The AK8 jet with the highest p T is chosen when multiple jets satisfy the conditions above, and events with additional isolated leptons are rejected. The jet is groomed [46] to remove soft and wide-angle radiation using the soft-drop algorithm [47,48], with the soft radiation fraction parameter z set to 0.1 and the angular exponent parameter β set to 0. The groomed jet is used to compute the soft-drop jet mass (m SD ) and each AK8 jet is required to have m SD > 40 GeV, to optimize the signal selection and background rejection.
The lepton subjet fraction (LSF 3 ) algorithm [49] is used to determine the consistency of the jet with three subjets, where one subjet is dominated by the four-momentum of the lepton. This algorithm clusters the constituents of a jet into three subjets using the exclusive-k T algorithm, and LSF 3 is defined as the ratio of the lepton p T to its associated subjet p T (p T ( )/p T (subjet)). Jets with higher LSF 3 values are considered to have a more isolated lepton within the jet and therefore the lepton is assumed to originate from a prompt decay. A selection of LSF 3 > 0.75 is required for all signal AK8 jets, which removes more than 81 (94)% of dielectron (dimuon) background events that have leptons originating from the decay of particles with non-negligible lifetimes (nonprompt leptons), while keeping 87 (92)% of signal events with (m W R , m N ) = (5.0, 0.2) TeV.
For the resolved events we reconstruct an invariant mass distribution from the two leptons and two AK4 jets (m jj ), and for the boosted events we consider the distribution in invariant mass of the lead lepton and AK8 jet (m J ). We search for deviations from the expected SM background in these distributions in the mass regions with m jj or m J > 0.8 TeV. To reduce the contribution from Z boson production, we also impose a requirement of m > 0. 4

Background estimation
The dominant SM processes that contribute to the background in each SR are DY production of lepton pairs with additional jets in the final state (DY+jets), leptonic decays of pair-produced top quarks, and single top production with an associated W boson. These backgrounds are estimated from simulation and the modeling is corrected using control regions (CRs), as described below. A schematic diagram presenting the CRs and SR is shown in figure 2. The tt events with at least one hadronically decaying W boson, s-and t-channel production of a single top quark, and W boson production in association with jets can contribute to the SRs when nonprompt leptons from, e.g., semileptonic decays of B hadrons, are misidentified as signal-like leptons. These types of background are labeled as nonprompt, and are estimated by means of simulated samples. Multiboson and tt production in association with a gauge boson are rare SM processes that can also contribute to the SRs, and their contributions are obtained from simulation as well.
To correct the mismodeled p T distribution of the Z boson in the DY simulation [50, 51], we apply a K factor as a function of the generator-level Z boson p T ("p T (Z) correction"). The NLO-to-LO K factor in QCD is obtained by taking the ratio between DY samples simulated to NLO and LO precision. The uncertainties from renormalization and factorization scale, PDF variations, and the statistical uncertainties in the MC samples are taken into account. The nNLO electroweak correction (combination of the O(α 2 α S ) contributions and the O(α 3 α S ) electroweak Sudakov logarithms in the next-to-leading log approximation) is taken from ref.
[51]. We define DY CRs to be the same as the SR but modify the dilepton mass requirement to 60 < m < 150 GeV (blue region in figure 2). For the boosted DY CRs, a lepton is not required to be located inside an AK8 jet, and the LSF 3 requirement is removed when collecting the AK8 jets. Owing to a limitation of the DY MC generator, which is restricted to the LO simulation of events with a maximum of four partons in the hard scattering, a shape discrepancy is observed in the leading AK4 and AK8 jet p T distributions in the resolved and boosted DY CRs, respectively. We correct the shape of the jet p T distributions to match with those observed in data by a bin-by-bin rescaling ("DY reshape"). Since this mismodeling is due to the higher-order effect of QCD jet splitting, the dielectron and dimuon events will be affected in a similar way, thus the two event -7 -JHEP04(2022)047 samples are summed when extracting the reweighting values, typically ranging from 0.8 to 1.2. The DY reshape correction modifies the shape of the m jj and m J distributions and brings the distribution in simulation into good agreement with data. The uncertainty assigned to the DY reshape correction is dominated by the statistical uncertainty, and is treated as uncorrelated across bins in the invariant mass spectrum. The normalization of the DY processes is allowed to vary in the fitting procedure, which is described in section 7. Several checks were performed to validate the extrapolation from low to high m , including verifying the agreement in the intermediate region, 150 < m < 400(200) GeV for the resolved (boosted) analysis.
To constrain the normalization of the tt and tW backgrounds in each SR, a corresponding control region (flavor CR) dominated by tt and tW events is defined by requiring the two leptons to have different flavors (the green region in figure 2). For the boosted analysis, separate control regions are used for the dielectron and dimuon searches. These require a lead muon plus a jet with an electron contained within it (e-jet), and a lead electron plus a jet with a muon contained within it (µ-jet), respectively. The normalizations of these backgrounds are extracted by performing a simultaneous fit across the SRs and flavor CRs.
The  decays leptonically and the other decays hadronically and injecting a simulated lepton (e or µ) in the direction of the hadronically decaying W boson, to emulate the 3-prong jet topology. The data-to-simulation scale factor obtained for the LSF 3 requirement, ranging from 0.95 to 1.05, is then applied to the simulated samples. The resulting uncertainty in the yields amounts to less than 10% for both the signal and background.
As described in section 5, the two corrections applied to the DY simulation are varied within their uncertainties to estimate their impact on the invariant mass distributions.
Owing to the imperfect description of nonprompt leptons in the simulation, a conservative 100% normalization uncertainty, cross-checked with a dedicated control region with  zero b jets, is assigned to the nonprompt background estimation. A 50% uncertainty is assigned to the rare SM background. The theoretical uncertainties originating from the strong coupling constant α S , PDFs, and renormalization/factorization scales are the dominant sources of uncertainties for the signal shape estimate. The PDF and α S uncertainties are estimated from the standard deviation of the weights from the PDF replicas provided in the NNPDF3.1 PDF set [33], following the PDF4LHC procedure [55]. shown in figure 5 and no significant excess over the background expectations is observed. A simulated signal distribution corresponding to mass values at the limit of sensitivity is shown for comparison. The shape of this distribution is very similar for the resolved and the boosted analysis, with the peak falling in the last bin. The enhancement visible around 2 TeV in the resolved distribution is due to sculpting of the W R off-shell mass distribution. The upper limits on the product of the cross section for W R production and the branching fractions σ(pp → W R )B(W R → ee(µµ)qq ) for various m W R and m N hypotheses are obtained using the distributions of the likelihood ratio calculated using the asymptotic approximation [56] and the CL s criterion [57,58]. The excluded phase space as a function of m W R obtained from the expected and observed upper limits at 95% confidence level (CL) is shown in figure 6. With m N = m W R /2, the observed (expected) lower limit at 95% CL on the mass of the W R

Summary
A search for right-handed bosons (W R ) and heavy right-handed neutrinos (N) in the leftright symmetric extension of the standard model has been presented. The analysis is based on proton-proton collision data collected at √ s = 13 TeV by the CMS detector, corresponding to an integrated luminosity of 138 fb −1 . The final state consists of events with two same-flavor leptons (ee or µµ) and two quarks, and is identified through two regions: the resolved region, where all four objects are well separated, and the boosted region, where the heavy neutrino decay is identified using jet substructure techniques applied to largearea jets. The addition of the boosted region greatly improves the search sensitivity in the region where m N < 0.5 TeV. No significant excess over the standard model background expectations is observed in the invariant mass distributions. Upper limits are set on the products of the W R and N production cross sections and their branching fraction to two leptons and two quarks assuming that couplings are identical to those of the standard model. For N masses m N equal to half the W R mass m W R (m N = 0.2 TeV), m W R is excluded at 95% confidence level up to 4.7 (4.8) and 5.0 (5.4) TeV for the electron and muon channels, respectively. This analysis provides the most stringent limits on the W R mass to date.

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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 and other centers 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, the CMS detector, and the supporting computing infrastructure provided by the following funding agencies: BMBWF and FWF (Austria);