Measurements of properties of the Higgs boson decaying into the four-lepton final state in pp collisions at sqrt(s) = 13 TeV

Properties of the Higgs boson are measured in the H to ZZ to 4l (l= e, mu) decay channel. A data sample of proton-proton collisions at sqrt(s) = 13 TeV, collected with the CMS detector at the LHC and corresponding to an integrated luminosity of 35.9 inverse femtobarns is used. The signal strength modifier mu, defined as the ratio of the observed Higgs boson rate in the H to ZZ to 4l decay channel to the standard model expectation, is measured to be mu = 1.05 +0.19/-0.17 at m[H ]= 125.09 GeV, the combined ATLAS and CMS measurement of the Higgs boson mass. The signal strength modifiers for the individual Higgs boson production modes are also measured. The cross section in the fiducial phase space defined by the requirements on lepton kinematics and event topology is measured to be 2.92 +0.48/-0.44 (stat) +0.28/-0.24 (syst) fb, which is compatible with the standard model prediction of 2.76 +/- 0.14 fb. Differential cross sections are reported as a function of the transverse momentum of the Higgs boson, the number of associated jets, and the transverse momentum of the leading associated jet. The Higgs boson mass is measured to be m[H] = 125.26 +/- 0.21 GeV and the width is constrained using on-shell production to be Gamma[H]<1.10 GeV, at 95% confidence level.


Introduction
In 2012, the ATLAS and CMS Collaborations reported the observation of a new particle with a mass of approximately 125 GeV and properties consistent with that of the standard model (SM) Higgs boson [1][2][3]. Further studies by the two experiments [4][5][6], using the entire LHC Run 1 data set at center-of-mass energies of 7 and 8 TeV indicate agreement within their uncertainties between the measured properties of the new boson and those predicted for the SM Higgs boson [7][8][9][10][11][12]. The ATLAS and CMS Collaborations have also published a combined measurement of the Higgs boson mass of m H = 125.09 ± 0.21 (stat) ± 0.11 (syst) GeV [13].
The H → ZZ → 4 decay channel ( = e, µ) has a large signal-to-background ratio, and the precise reconstruction of the final-state decay products allows the complete determination of the kinematics of the Higgs boson. This makes it one of the most important channels to measure the properties of the Higgs boson. Measurements performed by the ATLAS and CMS Collaborations using this decay channel with the LHC Run 1 data include the determination of the mass and spin-parity of the boson [14][15][16][17][18], its width [19][20][21], the fiducial cross sections [22,23], and the tensor structure of its interaction with a pair of neutral gauge bosons [16,18,20].
In this paper measurements of properties of the Higgs boson decaying into the four-lepton final state in proton-proton (pp) collisions at √ s = 13 TeV are presented. Events are classified into categories optimized with respect to those used in Ref. [14] to provide increased sensitivity to subleading production modes of the Higgs boson such as vector boson fusion (VBF) and associated production with a vector boson (WH, ZH) or top quark pair (ttH). The signal strength modifier, defined as the ratio of the measured Higgs boson rate in the H → ZZ → 4 decay channel to the SM expectation, is measured. The signal strength modifiers for the individual Higgs boson production modes are constrained. In addition, cross section measurements and dedicated measurements of the mass and width of the Higgs boson are performed. This paper is structured as follows: the apparatus and the data samples are described in Section 2 and Section 3. Section 4 summarizes the event reconstruction and selection. Kinematic discriminants and event categorization are discussed in Section 5 and Section 6. The background estimation and the signal modelling are reported in Section 7 and Section 8. We then discuss the systematic uncertainties in Section 9. Finally, Section 10 presents event yields, kinematic distributions, and measured properties.

The CMS detector
A detailed description of the CMS detector, together with a definition of the coordinate system used and the relevant kinematic variables, can be found in Ref. [24].
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.
The silicon tracker measures charged particles within the pseudorapidity range |η| < 2.5. It consists of 1440 silicon pixel and 15 148 silicon strip detector modules. For non-isolated particles with transverse momentum p T between 1 and 10 GeV and |η| < 1.4, the track resolutions are typically 1.5% in p T and 25-90  µm in the transverse (longitudinal) impact parame-ter [25].
The electromagnetic calorimeter consists of 75 848 lead tungstate crystals, which provide coverage in pseudorapidity |η| < 1.479 in the barrel region (EB) and 1.479 < |η| < 3.0 in the two endcap regions (EE). A preshower detector consisting of two planes of silicon sensors interleaved with a total of 3X 0 of lead is located in front of the EE. The electron momentum is estimated by combining the energy measurement in the ECAL with the momentum measurement in the tracker. The momentum resolution for electrons with p T ≈ 45 GeV from Z → ee decays ranges from 1.7% for electrons in the barrel region that do not shower in the tracker volume to 4.5% for electrons in the endcaps that do shower in the tracker volume [26].
Muons are measured in the pseudorapidity range |η| < 2.4, with detection planes made using three technologies: drift tubes, cathode strip chambers, and resistive plate chambers. Matching muons to tracks measured in the silicon tracker results in a relative transverse momentum resolution for muons with 20 < p T < 100 GeV of 1.3-2.0% in the barrel (|η| < 0.9) and better than 6% in the endcaps (|η| > 0.9). The p T resolution in the barrel is better than 10% for muons with p T up to 1 TeV [27].
The first level (L1) of the CMS trigger system [28], composed of custom hardware processors, uses information from the calorimeters and muon detectors to select the most interesting events in a fixed time interval of less than 4 µs. The high-level trigger (HLT) processor farm further decreases the event rate from around 100 kHz to less than 1 kHz, before data storage.

Data and simulated samples
This analysis makes use of pp collision data recorded by the CMS detector in 2016, corresponding to an integrated luminosity of 35.9 fb −1 . Collision events are selected by high-level trigger algorithms that require the presence of leptons passing loose identification and isolation requirements. The main triggers of this analysis select either a pair of electrons or muons, or an electron and a muon. The minimal transverse momentum with respect to the beam axis of the leading electron (muon) is 23 (17) GeV, while that of the subleading lepton is 12 (8) GeV. To maximize the signal acceptance, triggers requiring three leptons with lower p T thresholds and no isolation requirement are also used, as are isolated single-electron and single-muon triggers with the thresholds of 27 GeV and 22 GeV, respectively. The overall trigger efficiency for simulated signal events that pass the full selection chain of this analysis (described in Section 4) is larger than 99%. The trigger efficiency is measured in data with a method based on the "tag-and-probe" technique [29] using a sample of 4 events collected by the single-lepton triggers. Leptons passing the single-lepton triggers are used as tags and the other three leptons are used as probes. The efficiency in data is found to be in agreement with the expectation from simulation.
The Monte Carlo (MC) simulation samples for the signals and the relevant background processes are used to estimate backgrounds, optimize the event selection, and evaluate the acceptance and systematic uncertainties. The SM Higgs boson signals are generated at next-toleading order (NLO) in perturbative quantum chromodynamics (pQCD) with the POWHEG 2.0 [30][31][32] generator for the five main production modes: gluon fusion (gg → H), vector boson fusion (qq → qqH), and associated production (WH, ZH, and ttH). For WH and ZH the MINLO HVJ [33] extension of POWHEG 2.0 is used. The cross sections for the various signal processes are taken from Ref. [34], and in particular the cross section for the dominant gluon fusion production mode is taken from Ref. [35]. The default set of parton distribution functions (PDFs) used in all simulations is NNPDF30 nlo as 0118 [36]. The decay of the Higgs boson to four leptons is modeled with JHUGEN 7.0.2 [37,38]. In the case of ZH and ttH, the Higgs boson is also allowed to decay as H → ZZ → 2 2X where X stands for either a quark or a neutrino, thus accounting for four-lepton events where two leptons originate from the decay of the associated Z boson or top quarks. In all of the simulated samples, vector bosons are allowed to decay to τ-leptons such that this contribution is included in all estimations.
To generate a more accurate signal model, the p T spectrum of the Higgs boson was tuned in the POWHEG simulation of the dominant gluon fusion production mode to better match predictions from full phase space calculations implemented in the HRES 2.3 generator [39,40].
The SM ZZ background contribution from quark-antiquark annihilation is generated at NLO pQCD with POWHEG 2.0, while the gg → ZZ process is generated at leading order (LO) with MCFM [41].
All signal and background generators are interfaced with PYTHIA 8.212 [42] tune CUETP8M1 [43] to simulate multiple parton interactions, the underlying event, and the fragmentation and hadronization effects. The generated events are processed through a detailed simulation of the CMS detector based on GEANT4 [44,45] and are reconstructed with the same algorithms that are used for data. The simulated events include overlapping pp interactions (pileup) and have been reweighted so that the distribution of the number of interactions per LHC bunch crossing in simulation matches that observed in data.

Event reconstruction and selection
Event reconstruction is based on the particle-flow (PF) algorithm [46], which exploits information from all the CMS subdetectors to identify and reconstruct individual particles in the event.
The PF candidates are classified as charged hadrons, neutral hadrons, photons, electrons, or muons, and they are then used to build higher-level observables such as jets and lepton isolation quantities.
Electrons with p e T > 7 GeV are reconstructed within the geometrical acceptance defined by a pseudorapidity |η e | < 2.5. Electrons are identified using a multivariate discriminant that includes observables sensitive to the presence of bremsstrahlung along the electron trajectory, the geometrical and momentum-energy matching between the electron trajectory and the associated energy cluster in the ECAL, the shape of the electromagnetic shower in the ECAL, and variables that discriminate against electrons originating from photon conversions such as the number of expected but missing pixel hits and the conversion vertex fit probability.
Muons within the geometrical acceptance |η µ | < 2.4 and p µ T > 5 GeV are reconstructed by combining information from the silicon tracker and the muon system [27]. The matching between the inner and outer tracks proceeds either outside-in, starting from a track in the muon system, or inside-out, starting from a track in the silicon tracker. In the latter case, tracks that match track segments in only one or two planes of the muon system are also considered in the analysis to collect very low-p T muons that may not have sufficient energy to penetrate the entire muon system. The muons are selected among the reconstructed muon track candidates by applying minimal requirements on the track in both the muon system and inner tracker system, and taking into account compatibility with small energy deposits in the calorimeters.
To suppress muons originating from in-flight decays of hadrons and electrons from photon conversions, we require each lepton track to have the ratio of the impact parameter in three dimensions, computed with respect to the chosen primary vertex position, and its uncertainty to be less than 4. The primary vertex is defined as the reconstructed vertex with the largest value of summed physics-object p 2 T , where the physics objects are the objects returned by a jet finding algorithm [47,48] applied to all charged tracks associated with the vertex, plus the corresponding associated missing transverse energy, E miss T , defined as the magnitude of the vector sum of the transverse momenta of all reconstructed PF candidates (charged or neutral) in the event.
To discriminate between prompt leptons from Z boson decay and those arising from electroweak decays of hadrons within jets, an isolation requirement for leptons of I < 0.35 is imposed, where the relative isolation is defined as The isolation sums involved are all restricted to a volume bounded by a cone of angular radius ∆R = 0.3 around the lepton direction at the primary vertex, where the angular distance between two particles i and j is ∆R is the scalar sum of the transverse momenta of charged hadrons originating from the chosen primary vertex of the event. The ∑ p neutral T and ∑ p γ T are the scalar sums of the transverse momenta for neutral hadrons and photons, respectively. Since the isolation variable is particularly sensitive to energy deposits from pileup interactions, a p PU T ( ) contribution is subtracted, using two different techniques. For muons, we define p PU T (µ) ≡ 0.5 ∑ i p PU,i T , where i runs over the momenta of the charged hadron PF candidates not originating from the primary vertex, and the factor of 0.5 corrects for the different fraction of charged and neutral particles in the cone. For electrons, the FASTJET technique [48][49][50] is used, in which p PU T (e) ≡ ρ A eff , where the effective area A eff is the geometric area of the isolation cone scaled by a factor that accounts for the residual dependence of the average pileup deposition on the η of the electron, and ρ is the median of the p T density distribution of neutral particles within the area of any jet in the event.
An algorithm is used to recover the final-state radiation (FSR) from leptons. Photons reconstructed by the PF algorithm within |η γ | < 2.4 are considered as FSR candidates if they pass p γ T > 2 GeV and I γ < 1.8, where the photon relative isolation I γ is defined as for the leptons in Eq. 1. Associating every such photon to the closest selected lepton in the event, we discard photons that do not satisfy ∆R(γ, )/(p γ T ) 2 < 0.012 GeV −2 and ∆R(γ, ) < 0.5. We finally retain the lowest-∆R(γ, )/(p γ T ) 2 photon candidate of every lepton, if any. Photons thus identified are excluded from any isolation computation.
The momentum scale and resolution for electrons and muons are calibrated in bins of p T and η using the decay products of known dilepton resonances. The electron momentum scale is corrected with a Z → e + e − sample by matching the peak of the reconstructed dielectron mass spectrum in data to the one in simulation. A pseudorandom Gaussian smearing is applied to electron energies in simulation to make the Z → e + e − mass resolution match the one in data [51]. Muon momenta are calibrated using a Kalman filter approach [52], using J/ψ meson and Z boson decays.
A "tag-and-probe" technique based on inclusive samples of Z boson events in data and simulation is used to measure the efficiency of the reconstruction and selection for prompt electrons and muons in several bins of p T and η . The difference in the efficiencies measured in simulation and data, which on average is 1% (4%) per muon (electron), is used to rescale the selection efficiency in the simulated samples.
Jets are reconstructed from the PF candidates, clustered by the anti-k T algorithm [47,48] with a distance parameter of 0.4, and with the constraint that the charged particles are compatible with the primary vertex. The jet momentum is determined as the vector sum of all particle momenta in the jet, and is found in the simulation to reproduce the true momentum at the 5 to 10% level over the whole p T spectrum and detector acceptance. Jet energy scale corrections are derived from the simulation and confirmed with measurements examining the energy balance in dijet, multijet, γ + jet, and leptonic Z/γ + jet events [53,54]. Jet energies in simulation are smeared to match the resolution in data. To be considered in the analysis, jets must satisfy p jet T > 30 GeV and |η jet | < 4.7, and be separated from all selected lepton candidates and any selected FSR photon by ∆R( /γ, jet) > 0.4.
For event categorization, jets are tagged as b-jets using the Combined Secondary Vertex algorithm [55,56] which combines information about the impact parameter significance, the secondary vertex and the jet kinematics. The variables are combined using a multilayer perceptron approach to compute the b tagging discriminator. Data-to-simulation scale factors for the b tagging efficiency are applied as a function of jet p T , η, and flavor. The E miss T is also used for the event categorization.
The event selection is designed to extract signal candidates from events containing at least four well-identified and isolated leptons, each originating from the primary vertex and possibly accompanied by an FSR photon candidate. In what follows, unless otherwise stated, FSR photons are included in invariant mass computations.
First, Z boson candidates are formed with pairs of leptons (e + e − , µ + µ − ) of the same flavor and opposite sign (OS) and required to pass 12 < m + − < 120 GeV. They are then combined into ZZ candidates, wherein we denote as Z 1 the Z candidate with an invariant mass closest to the nominal Z boson mass (m Z ) [57], and as Z 2 the other one. The flavors of the leptons involved define three mutually exclusive subchannels: 4e, 4µ, and 2e2µ.
To be considered for the analysis, ZZ candidates have to pass a set of kinematic requirements that improve the sensitivity to Higgs boson decays. The Z 1 invariant mass must be larger than 40 GeV. All leptons must be separated in angular space by at least ∆R( i , j ) > 0.02. At least two leptons are required to have p T > 10 GeV and at least one is required to have p T > 20 GeV. For Z 1 Z 2 candidates composed of four same flavor leptons, an alternative pairing Z a Z b can be formed out of the same four leptons. We discard the Z 1 Z 2 candidate if m(Z a ) is closer to m Z than m(Z 1 ) and m(Z b ) < 12 GeV. This protects against events that contain an on-shell Z and a low-mass dilepton resonance. In events with only four leptons this requirement leads to the event being discarded, while in events with more than four leptons other ZZ candidates are considered. To further suppress events with leptons originating from hadron decays in jet fragmentation or from the decay of low-mass hadronic resonances, all four OS lepton pairs that can be built with the four leptons (irrespective of flavor) are required to satisfy m + − > 4 GeV, where selected FSR photons are disregarded in the invariant mass computation. Finally, the four-lepton invariant mass m 4 must be larger than 70 GeV.
In events where more than one ZZ candidate passes the above selection, the candidate with the highest value of D kin bkg (defined in Section 5) is retained, except when two candidates consist of the same four leptons in which case the candidate with the Z 1 mass closest to m Z is retained. The additional leptons that do not form the ZZ candidate but pass identification, vertex compatibility, and isolation requirements are used in the event categorization, see Section 6.

Kinematic discriminants and event-by-event mass uncertainty
The full kinematic information from each event using either the Higgs boson decay products or associated particles in its production is extracted using matrix element calculations and is used to form several kinematic discriminants. These computations rely on the MELA package [37,38,58] and use JHUGEN matrix elements for the signal and MCFM matrix elements for the background. The decay kinematics of the scalar H boson and the production kinematics of gluon fusion in association with one jet (H+1 jet) or two jets (H+2 jets), VBF, ZH, and WH associated production are explored in this analysis. The kinematics of the full event are described by decay observables Ω H→4 or observables describing associated production Ω H+JJ . The definition of these observables can be found in Refs. [37,38,58].
The discriminant sensitive to the gg/qq → 4 kinematics is calculated as [2,16] where P gg sig is the probability density for an event to be consistent with the signal and P qq bkg is the corresponding probability density for the dominant qq → ZZ → 4 background process, all calculated either with the JHUGEN or MCFM matrix elements within the MELA framework.
Four discriminants are used to enhance the purity of event categories as described in Section 6. D 2 jet is the discriminant sensitive to the VBF signal topology with two associated jets, D 1 jet is the discriminant sensitive to the VBF signal topology with one associated jet, and D WH or D ZH are the discriminants sensitive to the ZH or WH signal topologies with two associated jets from the decay of the Z→ qq or the W→ qq : where P VBF , P HJJ , P HJ , and P VH are probability densities obtained from the JHUGEN matrix elements for the VBF, H + 2 jets, H + 1 jet, and VH (V = W, Z) processes, respectively. The expression dη J P VBF is the integral of the two-jet VBF matrix element probability density discussed above over the η J values of the unobserved jet with the constraint that the total transverse momentum of the H + 2 jets system is zero. By construction, all discriminants defined in Eqs. 2 and 3 have values bounded between 0 and 1.
The uncertainty in the momentum measurement can be predicted for each lepton. For muons, the full covariance matrix is obtained from the muon track fit, and the directional uncertainties are negligibly small. For the electrons, the momentum uncertainty is estimated from the combination of the ECAL and tracker measurements, neglecting the uncertainty in the track direction. The uncertainty in the kinematics at the per-lepton level is then propagated to the four-lepton candidate to predict the mass uncertainty (D mass ) on an event-by-event basis. For FSR photons, a parametrization obtained from simulation is used for the uncertainty in the photon p T . The per-lepton momentum uncertainties are corrected in data and simulation using Z boson events. Events are divided into different categories based on the predicted dilepton mass resolution. A Breit-Wigner parameterization convolved with a double-sided Crystal Ball function [59] is then fit to the dilepton mass distribution in each category to extract the resolution and compare it to the predicted resolution. Corrections to the lepton momentum uncertainty are derived through an iterative procedure in different bins of lepton p T and η. After the corrections are derived, a closure test of the agreement between the predicted and fitted 4 mass resolution is performed in data and in simulation, in bins of the predicted 4 mass resolution, confirming that the calibration brings it close to the fitted value. A systematic uncertainty of 20% in the 4 mass resolution is assigned to cover the residual differences between the predicted and fitted resolutions.

Event categorization
To improve the sensitivity to the various Higgs boson production mechanisms, the selected events are classified into mutually exclusive categories. The category definitions exploit the jet multiplicity, the number of b-tagged jets, the number of additional leptons (defined as leptons that pass identification, vertex compatibility, and isolation requirements, but do not form the ZZ candidate), and requirements on the kinematic discriminants described in Section 5.
Seven categories are defined, using the criteria applied in the following order (i.e. an event is considered for the subsequent category only if it does not satisfy the requirements of the previous category): • The VBF-2jet-tagged category requires exactly four leptons. In addition, there must be either two or three jets of which at most one is b tagged, or four or more jets none of which are b-tagged. Finally, D 2 jet > 0.5 is required. • The VH-hadronic-tagged category requires exactly four leptons. In addition, there must be two or three jets, or four or more jets none of which are b-tagged. D VH ≡ max(D ZH , D WH ) > 0.5 is required. • The VH-leptonic-tagged category requires no more than three jets and no b-tagged jets in the event, and exactly one additional lepton or one additional pair of OS, same-flavor leptons. This category also includes events with no jets and at least one additional lepton.
• The ttH-tagged category requires at least four jets of which at least one is b tagged, or at least one additional lepton.
• The VH-E miss T -tagged category requires exactly four leptons, no more than one jet and E miss T greater than 100 GeV.
• The VBF-1jet-tagged category requires exactly four leptons, exactly one jet and D 1 jet > 0.5.
• The Untagged category consists of the remaining selected events.
The definitions of the categories were chosen to achieve high signal purity whilst maintaining high efficiency for each of the main Higgs boson production mechanisms. The order of the categories is chosen to maximize the signal purity target in each category. Figure 1 shows the relative signal purity of the seven event categories for the various Higgs boson production processes. The VBF-1jet-tagged and VH-hadronic-tagged categories are expected to have substantial contamination from gluon fusion, while the purity of the VBF process in the VBF-2jet-tagged category is expected to be about 49%.
7 Background estimation

Irreducible backgrounds
The irreducible backgrounds to the Higgs boson signal in the 4 channel, which come from the production of ZZ via qq annihilation or gluon fusion, are estimated using simulation. The   Figure 1: Relative signal purity in the seven event categories in terms of the five main production mechanisms of the Higgs boson in the 118 < m 4 < 130 GeV mass window are shown. The WH, ZH, and ttH processes are split according to the decay of the associated particles, where X denotes anything other than an electron or a muon. Numbers indicate the total expected signal event yields in each category.
fully differential cross section for the qq → ZZ process has been computed at next-to-next-toleading order (NNLO) [60], and the NNLO/NLO K-factor as a function of m ZZ has been applied to the POWHEG sample. This K-factor varies from 1.0 to 1.2 and is 1.1 at m ZZ = 125 GeV. Additional NLO electroweak corrections, which depend on the initial state quark flavor and kinematics, are also applied in the region m ZZ > 2m Z where the corrections have been computed [61]. The uncertainty due to missing electroweak corrections in the region m ZZ < 2m Z is expected to be small compared to the uncertainties in the pQCD calculation.
The production of ZZ via gluon fusion contributes at NNLO in pQCD. It has been shown [62] that the soft-collinear approximation is able to describe the background cross section and the interference term at NNLO. Further calculations also show that at NLO the K-factor for the signal and background [63] and at NNLO the K-factor for the signal and interference terms [64] are very similar. Therefore, the same K-factor used for the signal is also used for the background [65]. The NNLO K-factor for the signal is obtained as a function of m ZZ using the HNNLO v2 program [40,66,67] by calculating the NNLO and LO gg → H → 2 2 cross sections at the small H boson decay width of 4.1 MeV and taking their ratios. The NNLO/LO K-factor for gg → ZZ varies from 2.0 to 2.6 and is 2.27 at m ZZ = 125 GeV; a systematic uncertainty of 10% in its determination when applied to the background process is used in the analysis.

Reducible backgrounds
Additional backgrounds to the Higgs boson signal in the 4 channel arise from processes in which heavy flavor jets produce secondary leptons, and also from processes in which decays of heavy flavor hadrons, in-flight decays of light mesons within jets, or (for electrons) the decay of charged hadrons overlapping with π 0 decays, are misidentified as prompt leptons. We denote these reducible backgrounds as "Z+X" since the dominant process producing them is Z + jets, while subdominant processes in order of importance are tt + jets, Zγ + jets, WZ + jets, and WW + jets. In the case of Zγ + jets, the photon may convert to an e + e − pair with one of the decay products not being reconstructed, giving rise to a signature with three prompt leptons. The contribution from the reducible background is estimated using two independent methods having dedicated control regions in data. The control regions are defined by a dilepton pair satisfying all the requirements of a Z 1 candidate and two additional leptons, OS or same-sign (SS), satisfying certain relaxed identification requirements when compared to those used in the analysis. These four leptons are then required to pass the ZZ candidate selection. The event yield in the signal region is obtained by weighting the control region events by the lepton misidentification probability (or misidentification rate) f , defined as the fraction of nonsignal leptons that are identified by the analysis selection criteria.
The lepton misidentification rates f e and f µ are determined from data, separately for the SS and OS methods, using a control region defined by a Z 1 candidate and exactly one additional lepton passing the relaxed selection. The Z 1 candidate consists of a pair of leptons, each of which passes the selection requirements used in the analysis. For the OS method, the mass of the Z 1 candidate is required to satisfy |m(Z 1 ) − m Z | < 7 GeV to reduce the contribution of (asymmetric) photon conversions, which is estimated separately. In the SS method, the contribution from photon conversions is estimated by determining an average misidentification rate. Furthermore the E miss T is required to be less than 25 GeV to suppress contamination from WZ and tt processes. The fraction of these events in which the additional lepton passes the selection requirements used in the analysis gives the lepton misidentification rate f . The lepton misidentification rates is measured as a function of p T and |η | and is assumed to be independent of the presence of any additional leptons.

Method using OS leptons
The control region for the OS method consists of events with a Z 1 candidate and two additional OS leptons of the same-flavor. The expected yield in the signal region is obtained from two categories of events.
The first category is composed of events with two leptons that pass (P) the tight lepton identification requirements and two leptons that pass the loose identification but fail (F) the tight identification, and is denoted as the 2P2F region. Backgrounds, which intrinsically have only two prompt leptons, such as Z + jets and tt, are estimated with this control region. To obtain the expected yield in the signal region, each event i in the 2P2F region is weighted by a fac- ], where f i 3 and f i 4 are the misidentification rates for the third and fourth lepton, respectively.
The second category consists of events where exactly one of the two additional leptons passes the analysis selection, and is referred to as the 3P1F region. Backgrounds with three prompt leptons, such as WZ + jets and Zγ + jets with the photon converting to e + e − , are estimated using this region. To obtain the expected yield in the signal region, each event j in the 3P1F region is weighted by a factor f is the misidentification rate for the lepton that does not pass the analysis selection. The contribution from ZZ events to the 3P1F region (N ZZ 3P1F ), which arises from events where a prompt lepton fails the identification requirements, is estimated from simulation and scaled with a factor w ZZ appropriate to the integrated luminosity of the analyzed data set.
The contamination of 2P2F-type processes in the 3P1F region is estimated as } to the expected yield in the signal region. This amount is subtracted from the total background estimate to avoid double counting.
The total reducible background estimate in the signal region coming from the two categories 2P2F and 3P1F without double counting, N reducible SR , can be written as: where N 3P1F and N 2P2F are the number of events in the 3P1F and 2P2F regions, respectively.

Method using SS leptons
The control region for the SS method, referred to as the 2P2L SS region, consists of events with a Z 1 candidate and two additional SS leptons of same-flavor. These two additional leptons are required to pass the loose selection requirements for leptons.
The contribution of photon conversions to the electron misidentification probability f is estimated. Its linear dependence on the fraction of loose electrons in the sample with tracks having one missing hit in the pixel detector, r miss , is used to derive a corrected misidentification ratef . The dependence is determined by measuring f in samples with different values of r miss formed by varying the requirements on |m 1 2 − m Z | and |m 1 2 e loose − m Z |. Here 1 and 2 are the leptons which form the Z 1 candidate and e loose is the additional electron passing the loose selection.
The expected number of reducible background events in the signal region can then be written as: where the ratio r OS/SS between the number of events in the 2P2L OS and 2P2L SS control regions is obtained from simulation. The 2P2L OS region is defined analogously to the 2P2L SS region but with an OS requirement for the additional pair of loose leptons.

Prediction and uncertainties
The predicted yield in the signal region of the reducible background from the two methods are in agreement within their statistical uncertainties, and since they are mutually independent, the results of the two methods are combined. The final estimate is obtained by weighting the individual mean values of both methods according to their corresponding variances. The shape of the m 4 distribution for the reducible background is obtained by combining the prediction from the OS and SS methods and fitting the distributions with empirical functional forms built from Landau [68] and exponential distributions.
The dominant systematic uncertainty in the reducible background estimation arises from the limited number of events in the control regions as well as in the region where the misidentification rate is applied. Additional sources of systematic uncertainty, estimated using simulated samples, come from the fact that the composition of the regions used to compute the misidentification rates typically differs from that of control regions where they are applied. The subdominant systematic uncertainty in the m 4 shape is determined by taking the envelope of differences among the shapes from the OS and SS methods in the three different final states. The combined systematic uncertainty is estimated to be about 40%.

Signal modeling
The signal shape of a narrow resonance around m H ∼ 125 GeV is parametrized using a doublesided Crystal Ball function. The signal shape is parametrized as a function of m H by performing a simultaneous fit of several mass points for gg → H production around 125 GeV. Each parameter of the double-sided Crystal Ball function is given a linear dependence on m H for a total of 12 free parameters. Of these parameters, 10 are left free in the simultaneous fits. The parameters that control the prominence of the tails in the two Crystal Ball functions are forced to have a unique value at all m H values, to remove large correlations and because they are constant within the uncertainty. This parameterization, derived separately for each 4 final state, is found to provide a good description of the resonant part of the signal for all production modes and event categories. An additional non-resonant contribution from WH, ZH, and ttH production arises when one of the leptons from the Higgs boson decay is lost or is not selected. This contribution is modeled by a Landau distribution which is added to the total probability density function for those production modes.
For the measurement of the width the signal shape for a broad resonance around m H ∼ 125 GeV is parameterized in the following way. First, the gluon fusion or electroweak (VBF and VH) signal production is treated jointly with the corresponding background and their interference as: where µ i is the signal strength in the production type i, gluon fusion or electroweak, and the small ttH contribution is treated jointly with gluon fusion. The general parameterization of the probability density function in Eq. (6)  ). (7)

Systematic uncertainties
The experimental uncertainties common to all measurements include the uncertainty in the integrated luminosity measurement (2.5%) [69] and the uncertainty in the lepton identification and reconstruction efficiency (ranging from 2.5 to 9% on the overall event yield for the 4µ and 4e channels), which affect both signal and background. Experimental uncertainties in the reducible background estimation, described in Section 7.2, vary between 36% (4µ) and 43% (4e).
The uncertainty in the lepton energy scale, which is the dominant source of systematic uncertainty in the Higgs boson mass measurement, is determined by considering the Z → mass distributions in data and simulation. Events are separated into categories based on the p T and η of one of the two leptons, selected randomly, and integrating over the other. A Breit-Wigner parameterization convolved with a double-sided Crystal Ball function is then fit to the dilepton mass distributions. The offsets in the measured peak position with respect to the nominal Z boson mass in data and simulation are extracted, and the results are shown in Fig. 2. In the case of electrons, since the same data set is used to derive and validate the momentum scale corrections, the size of the corrections is taken into account for the final value of the uncertainty. The 4 mass scale uncertainty is determined to be 0.04%, 0.3%, and 0.1% for the 4µ, 4e, and 2e2µ channels, respectively. The uncertainty in the 4 mass resolution coming from the uncertainty in the per-lepton energy resolution is 20%, as described in Section 5. Theoretical uncertainties that affect both the signal and background estimation include uncertainties from the renormalization and the factorization scales and the choice of the PDF set. The uncertainty from the renormalization and factorization scale is determined by varying these scales between 0.5 and 2 times their nominal value while keeping their ratio between 0.5 and 2. The uncertainty from the PDF set is determined following the PDF4LHC recommendations [70]. An additional uncertainty of 10% in the K factor used for the gg → ZZ prediction is applied as described in Section 7.1. A systematic uncertainty of 2% [34] in the H → 4 branching fraction only affects the signal yield. The theoretical uncertainties in the background yield are included for all measurements, while the theoretical uncertainties in the overall signal yield are not included in the measurement uncertainties when cross sections, rather than signal strength modifiers, are extracted.
In the case of the measurements which use event categorization, experimental and theoretical uncertainties that account for possible migration of signal and background events between categories are included. The main sources of uncertainty in the event categorization include the renormalization and factorization scales, PDF set, and the modeling of the fragmentation, hadronization, and the underlying event. These uncertainties amount to 4-20% for the signal and 3-20% for the background, depending on the category, and are largest for the prediction of the gg → H yield in the VBF-2jet-tagged category. Additional uncertainties come from the imprecise knowledge of the jet energy scale (from 2% for the gg → H yield in the untagged category to 15% for the gg → H yield in the VBF-2jet-tagged category) and b tagging efficiency and mistag rate (up to 6% in the ttH-tagged category).

Results
The reconstructed four-lepton invariant mass distribution is shown in Fig. 3 for the sum of the 4e, 4µ, and 2e2µ channels, and compared with the expectations from signal and background processes. The error bars on the data points correspond to the so-called Garwood confidence intervals at 68% confidence level (CL) [71]. The observed distribution agrees with the expectation within the statistical uncertainties over the whole spectrum. In Fig. 4, the reconstructed four-lepton invariant mass distributions are split by event category, for the low-mass range.  Table 1 for m 4 > 70 GeV. Table 2 shows the expected and observed yields for each of the seven event categories and their total. The reconstructed dilepton invariant masses for the selected Z 1 and Z 2 candidates are shown in Fig. 5 for 118 < m 4 < 130 GeV, along with their correlation. Figure 6 shows the correlation between the kinematic discriminant D kin bkg with the four-lepton invariant mass, the two variables used in the likelihood fit to extract the results (see Section 10.1). The gray scale represents the expected combined relative density of the ZZ background and the Higgs boson signal. The points show the data and the measured four-lepton mass uncertainties D mass as horizontal bars. Different marker colors and styles are used to denote the final state and the categorization of the events, respectively. This distribution shows that the two observed events around 125 GeV in the VH-E miss T -tagged and ttH-tagged categories (empty star and square markers) have low  ), and the ZZ backgrounds are normalized to the SM expectation, whilst the Z+X background is normalized to the estimation from data. For the categories other than the untagged category, the SM Higgs boson signal is separated into two components: the production mode that is targeted by the specific category, and other production modes, where the gluon fusion dominates. The order in perturbation theory used for the normalization of the irreducible backgrounds is described in Section 7.1. values of D kin bkg , implying that these events are more compatible with the background than the signal hypothesis. The distribution of the discriminants used for event categorization and the corresponding working point values are shown in Fig. 7.    ), and the ZZ backgrounds are normalized to the SM expectation, whilst the Z+X background is normalized to the estimation from data. The vertical gray dashed lines denote the working points used in the event categorization. The SM Higgs boson signal is separated into two components: the production mode that is targeted by the specific discriminant, and other production modes, where the gluon fusion dominates. The order in perturbation theory used for the normalization of the irreducible backgrounds is described in Section 7.1.

Signal strength modifiers
To extract the signal strength modifier we perform a multi-dimensional fit that relies on two variables: the four-lepton invariant mass m 4 and the D kin bkg discriminant. We define the twodimensional likelihood function as: The mass dimension is unbinned and uses the model described in Section 8. The conditional term is implemented by creating a two-dimensional template of m 4 vs. D kin bkg normalized to 1 for each bin of m 4 . Based on the seven event categories and the three final states (4e, 4µ, 2e2µ), the (m 4 , D kin bkg ) unbinned distributions are split into 21 categories. A simultaneous fit to all categories is performed to extract the signal strength modifier. The relative fraction of 4e, 4µ, and 2e2µ signal events is fixed to the SM prediction. Systematic uncertainties are included in the form of nuisance parameters and the results are obtained using an asymptotic approach with a test statistic based on the profile likelihood ratio [72,73]. The individual contributions of statistical and systematic uncertainties are separated by performing a likelihood scan removing the systematic uncertainties to determine the statistical uncertainty. The systematic uncertainty is then taken as the difference in quadrature between the total uncertainty and the statistical uncertainty. At the ATLAS and CMS Run 1 combined mass value of m H = 125.09 GeV, the signal strength modifier is µ = 1.05 +0. 15 −0.14 (stat) +0.11 −0.09 (syst) = 1.05 +0.19 −0.17 . It is compared to the measurement for each of the seven event categories in Fig. 8 (top left).
The observed values are consistent with the SM prediction of µ = 1 within the uncertainties. The dominant sources of experimental systematic uncertainty are the uncertainties in the lepton identification efficiencies and integrated luminosity measurement, while the dominant theoretical sources are the uncertainty in the total gluon fusion cross section as well as the uncertainty in the category migration for the gluon fusion process. The contributions to the total uncertainty from experimental and theoretical sources are found to be similar in magnitude.
A fit is performed for five signal strength modifiers (µ ggH , µ VBF , µ VHhad , µ VHlep , and µ ttH , all constrained to positive values) that control the contributions of the main SM Higgs boson production modes. The WH and ZH processes are merged, and then split based on the decay of the associated vector boson into either hadronic decays (VHhad) or leptonic decays (VHlep). The results are reported in Fig. 8 (top right) and compared to the expected signal strength modifiers in Table 3. The expected uncertainties are evaluated by generating an Asimov data set [73], which is a representative event sample that provides both the median expectation for an experimental result and its expected statistical variation, in the asymptotic approximation. The coverage of the quoted intervals has been verified for a subset of results using the Feldman-Cousins method [74]. The low observed signal strengths for the VBF, VH, and ttH processes can be explained by the mild excess in the untagged category, which leads to a higher than expected signal strength for the gg → H process that contributes significantly to the total signal yield in categories that are based on the hadronic activity in the event. In the categories that are not based on hadronic event activity, events with m 4 near 125 GeV have low D kin bkg values, and are therefore more compatible with the background than the signal hypothesis.
Two signal strength modifiers µ ggH, ttH and µ VBF,VH are introduced as scale factors for the fermionand vector-boson induced contribution to the expected SM cross section. A two-parameter fit is performed simultaneously to all categories assuming a mass of m H = 125.09 GeV, leading to the measurements of µ ggH, ttH = 1.19 +0. 21 −0.20 and µ VBF,VH = 0.00 +0.81 −0.00 . The 68% and 95% CL contours in the (µ ggH, ttH , µ VBF,VH ) plane are shown in Fig. 8 (bottom). The SM predictions of µ ggH, ttH = 1 and µ VBF,VH = 1 lie within the 68% CL regions of this measurement.

Cross section measurements
In this section we present various measurements of the cross section for Higgs boson production. First we show cross section measurements for five SM Higgs boson production processes (σ ggH , σ VBF , σ VHhad , σ VHlep , and σ ttH ) in a simplified fiducial volume defined using a selection on the Higgs boson rapidity |y H | < 2.5. Outside of this volume the analysis has a negligible acceptance. The separation of the production processes is achieved through the categorization of events described in Section 6. This measurement corresponds to the 'stage-0' simplified template cross sections from Ref. [34]. This approach allows one to reduce the dependence of the measurements on the theoretical uncertainties in the SM predictions, avoiding extrapolation of the measurements to the full phase space which carries nontrivial or sizeable theoretical uncertainties. The measured cross sections, normalized to the SM prediction [34], which is denoted as σ theo , are shown in Fig. 9. The dominant sources of experimental systematic uncertainty are the same as in the measurement of the signal strength modifier, while the dominant theoretical source is the uncertainty in the category migration for the gluon fusion process.  The cross section for the production and decay pp → H → 4 in a tight fiducial phase space is also presented. This measurement has minimal dependence on the assumptions of the relative fraction or kinematic distributions of the separate production modes. The definition of the generator-level fiducial volume, chosen to match closely the reconstruction-level selection, is very similar to the definition used in Ref. [22]. The differences with respect to Ref. [22] are that leptons are defined as "dressed" leptons, as opposed to Born-level leptons, and the lepton isolation criterion is updated to match the reconstruction-level selection. Leptons are "dressed" by adding the four-momenta of photons within ∆R < 0.3 to the bare leptons, and leptons are considered isolated if the scalar sum of transverse momenta of all stable particles, excluding electrons, muons, and neutrinos, within ∆R < 0.3 from the lepton is less than 0.35p T (GeV). For the measurement of differential cross sections related to jet observables, only well mea-sured central jets with p T > 30 GeV and |η| < 2.5 are considered in both the fiducial and reconstruction-level selections. To simplify the definition of the fiducial volume, the D kin bkg discriminant is not used to select the ZZ candidate at the generator level. Instead the Z 1 candidate is chosen to be the one with m(Z 1 ) closest to the nominal Z boson mass, and in cases where multiple Z 2 candidates satisfy all criteria, the pair of leptons with the highest sum of the transverse momenta is chosen. The same candidate selection is also used at the reconstruction level for the fiducial cross section measurements to align the reconstruction-and fiducial-level selections as closely as possible. The full definition of the fiducial volume is detailed in Table 4 and the acceptance A fid for various SM production modes is given in Table 5. Table 4: Summary of requirements and selections used in the definition of the fiducial phase space for the pp → H → 4 cross section measurements.
Lepton kinematics and isolation Leading lepton p T p T > 20 GeV Subleading lepton p T p T > 10 GeV Additional electrons (muons) p T p T > 7 (5) GeV Pseudorapidity of electrons (muons) |η| < 2.5 (2.4) Sum p T of all stable particles within ∆R < 0.3 from lepton <0.35p T Event topology Existence of at least two same-flavor OS lepton pairs, where leptons satisfy criteria above Invariant mass of the Z 1 candidate 40 < m Z 1 < 120 GeV Invariant mass of the Z 2 candidate 12 < m Z 2 < 120 GeV Distance between selected four leptons ∆R( i , j ) > 0.02 for any i = j Invariant mass of any opposite-sign lepton pair m + − > 4 GeV Invariant mass of the selected four leptons 105 < m 4 < 140 GeV A maximum likelihood fit of the signal and background parameterizations to the observed 4 mass distribution, N obs (m 4 ), is performed to extract the integrated fiducial cross section σ fid for pp → H → 4 . The fit is done without any event categorization targeting different production modes and does not use the D kin bkg observable to minimize the model dependence. The fit is performed simultaneously in all final states assuming a Higgs boson mass of m H = 125.09 GeV, and the branching fraction of the Higgs boson decays to different final states (4e, 4µ, 2e2µ) is allowed to float.
The number of expected events in each final state f and in each bin i of an observable considered is expressed as a function of m 4 as: The shape of the resonant signal contribution, P res (m 4 ), is modelled by a double-sided Crystal Ball function, as described in Section 8, and the normalization is proportional to the fiducial cross section. The non-resonant contribution from WH, ZH, and ttH production, N nonres , is modeled by a Landau distribution, P nonres (m 4 ), whose shape parameters are constrained in the fit to be within a range determined from signal samples with full detector simulation and is treated as a background in this measurement.
The f i,j factor represents the detector response matrix that maps the number of expected events in a given observable bin j at the fiducial level to the number of expected events in the bin i at the reconstruction level. This response matrix is measured using signal samples with full detector simulation and corrected for residual differences between data and simulation. This procedure accounts for the unfolding of detector effects from the observed distributions and is the same as in Refs. [75] and [22]. In the case of the integrated fiducial cross section measurement the efficiencies reduce to single values, which for different SM production modes are listed in Table 5.
An additional resonant contribution arises from events which are reconstructed, but do not originate from the fiducial phase space, N nonfid . These events are due to detector effects that cause differences between the quantities used for the fiducial phase space definition and the analogous quantities at the reconstruction level. This contribution is treated as background and is referred to as the "nonfiducial signal" contribution. The shape of these events is verified using signal samples with full detector simulation to be identical to the shape of the fiducial signal, and its normalization is fixed to be a fraction of the fiducial signal component. The value of this fraction, which we denote as f nonfid , has been determined from signal samples with full detector simulation for each of the signal production modes studied. The value of f nonfid for different signal production modes is shown in Table 5. Table 5: Summary of the fraction of signal events for different SM signal production modes within the fiducial phase space (acceptance A fid ), reconstruction efficiency ( ) for signal events from within the fiducial phase space, and ratio of reconstructed events which are from outside the fiducial phase space to reconstructed events which are from within the fiducial phase space ( f nonfid ). For all production modes the values given are for m H = 125 GeV. Also shown in the last column is the factor (1 + f nonfid ) which regulates the signal yield for a given fiducial cross section, as shown in Eq. 9. The uncertainties listed are statistical only. The theoretical uncertainty in A fid for the SM is less than 1%.
The integrated fiducial cross section is measured to be σ fid = 2.92 +0.48 −0.44 (stat) +0.28 −0.24 (syst) fb. This can be compared to the SM expectation obtained from NNLOPS of σ SM fid = 2.76 ± 0.14 fb. The integrated fiducial cross section as a function of √ s is also shown in Fig. 10. The compatibility of the integrated fiducial cross sections measured in the 4e, 4µ, and 2e2µ final states with the SM prediction is estimated using a likelihood ratio with the three cross sections at their best fit values in the numerator and the three cross sections fixed to the SM predictions in the denominator. The compatibility, defined as the asymptotic p-value of the fit, is found to be 88%. The measured differential cross section results for p T (H), N(jets), and p T (jet) of the leading associated jet can also be seen in Fig. 10. The dominant sources of systematic uncertainty are the experimental uncertainties in the lepton identification efficiencies and integrated luminosity measurement, and the theoretical sources of uncertainty are found to be subdominant. To estimate the model dependence of the measurement, the unfolding procedure is repeated us-ing different response matrices created by varying the relative fraction of each SM production mode within its experimental constraints. The uncertainty is determined to be negligible with respect to the experimental systematic uncertainties. . The acceptance is calculated using NNLOPS at √ s = 13 TeV and HRES [39,40] at √ s = 7 and 8 TeV and the total cross sections and uncertainties are taken from Ref. [34]. The fiducial volume for √ s = 7 and 8 TeV uses the lepton isolation definition from Ref. [22], while for √ s = 13 TeV the definition described in the text is used. The results of the differential cross section measurements are shown for p T (H) (top right), N(jets) (bottom left) and p T (jet) of the leading associated jet (bottom right). The acceptance and theoretical uncertainties in the differential bins are calculated using POWHEG and NNLOPS. The subdominant component of the signal (VBF + VH + ttH) is denoted as XH. In the differential cross section measurement for p T (H), the last bin represents the integrated cross section for p T (H) > 200 GeV and is scaled by 1/50 for presentation purposes. No events are observed with p T (H) > 200 GeV.

Higgs boson mass measurement
In this section we show the results of the measurement of the mass of the resonance, using additional information in the likelihood fit with respect to the signal strength and cross section measurements.
To improve the four-lepton invariant mass resolution, a kinematic fit is performed using a mass constraint on the intermediate Z resonance. Previous studies [14] of the Higgs boson mass show that the selected Z 1 has a significant on-shell component, while the invariant mass distribution for the selected Z 2 is wider than the detector resolution. Therefore only the Z 1 candidate is considered when performing the kinematic constraint.
The likelihood to be maximized is constructed as follows: where p 1 T and a 2 are the reconstructed transverse momenta of the two leptons forming the Z 1 candidate, σ p 1 T and σ p 2 T are the corresponding per-lepton resolutions,p 1 T andp 2 T are the refitted transverse momenta, and m 12 is the invariant mass calculated from the refitted four-momenta. The term L(m 12 |m Z , m H ) is the mass constraint term. For a Higgs boson mass near 125 GeV, the selected Z 1 is not always on-shell, so a Breit-Wigner shape does not perfectly describe the Z 1 shape at the generator level. We therefore choose L(m 12 |m Z , m H ) to be the m(Z 1 ) shape at the generator level from the SM Higgs boson sample with m H = 125 GeV, where the same algorithm for selecting the Z 1 and Z 2 candidates, as described in Section 4, is used. For each event, the likelihood is maximized and the refitted transverse momenta are used to recalculate the four-lepton mass and mass uncertainty, which are denoted as m 4 and D mass , respectively. These distributions are then used to build the likelihood used to extract the Higgs boson mass.
The 1D likelihood scans vs. m H , while profiling the signal strength modifier µ along with all other nuisance parameters for the 1D L(m 4 ), 2D L(m 4 , D mass ), and 3D L(m 4 , D mass , D kin bkg ) fits, including the m(Z 1 ) constraint, are shown in Fig. 11. All systematic uncertainties described in Section 9 are included. When estimating separately the systematic and statistical uncertainties, the signal strength is profiled in the likelihood scan with the systematic uncertainties removed, so that its uncertainty is included in the statistical uncertainty. As in the measurement of the signal strengths, the relative fraction of 4e, 4µ, and 2e2µ signal events is fixed to the SM prediction. If the relative fractions are allowed to float, the change in the fitted mass value is much smaller than the uncertainty.
The best fit masses and the expected increase in the uncertainty relative to the 3D fit with the m(Z 1 ) constraint for each of the six fits are shown in Table 6. The nominal result for the mass measurement is obtained from the 3D fit with the m(Z 1 ) constraint, for which the fitted value of m H in the three subchannels is m 4µ H = 124.94 ± 0.25 (stat) ± 0.08 (syst) GeV, m 4e H = 124.37 ± 0.62 (stat) ± 0.38 (syst) GeV, and m 2e2µ H = 125.95 ± 0.32 (stat) ± 0.14 (syst) GeV leading to a combined value m H = 125.26 ± 0.20 (stat) ± 0.08 (syst) GeV. The systematic uncertainty in the mass measurement is completely dominated by the uncertainty in the lepton momentum scale. The expected uncertainty in the mass measurement using the 3D fit with the m(Z 1 ) constraint is evaluated with two Asimov data sets. The "prefit" expected uncertainty is ±0.24 (stat) ± 0.09 (syst) GeV. Here m H = 125 GeV, µ = 1, and all nuisance parameters are fixed to their nominal values. The "postfit" expected uncertainty with m H , µ, and all nuisance parameters fixed to their best-fit estimates from the data is ±0.23 (stat) ± 0.08 (syst) GeV. The probability of the "prefit" uncertainty being less than or equal to the observed value is determined from an ensemble of pseudo-experiments to be about 18%. The mutual compat-ibility of the m H results from the three individual channels is tested using a likelihood ratio with three masses in the numerator and a common mass in the denominator, and thus two degrees of freedom. The signal strength is profiled in both the numerator and denominator. The resulting compatibility, defined as the asymptotic p-value of the fit, is 2.5%. The tension between the three individual channels is driven by the difference between the 4µ and 2e2µ channels, where the compatibility of the 1D mass measurements without the m(Z 1 ) constraint is 8%. In the 1D mass measurement the main potential source of systematic bias is the lepton momentum scale; this possibility is disfavored by the fact that the measured mass in the 2e2µ channel is not in between the measurements in the 4e and 4µ channels. This bias has also been checked by performing the 1D mass measurements without the m(Z 1 ) constraint using Z → 4 events, and the resulting mass is measured to be m 4µ Z = 90.85 ± 0.27 (stat) ± 0.04 (syst) GeV, m 4e Z = 90.85 ± 0.74 (stat) ± 0.28 (syst) GeV, and m 2e2µ Z = 90.61 ± 0.48 (stat) ± 0.10 (syst) GeV leading to a combined value m Z = 90.84 ± 0.23 (stat) ± 0.07 (syst) GeV. The compatibility with the nominal Z-boson mass from Ref. [57] is 14% and the mutual compatibility between the three individual channels is 90%. The modelling of the event-by-event mass uncertainties is a possible source of systematic bias in the 2D and 3D measurements. It is checked by performing a Kolmogorov-Smirnov compatibility test of the expected and observed distributions in an expanded m 4 range yielding p-values of 10% for the 2e2µ channel, 55% for the 4e channel, and 94% for the 4µ channel.

Measurement of the Higgs boson width using on-shell production
In this section, we describe a model-independent measurement of the width performed using the m 4 distribution in the range 105 < m 4 < 140 GeV. This measurement is limited by the four-lepton invariant mass resolution and is therefore sensitive to a width of about 1 GeV. Therefore, we take into account the interference between the signal and background production of the 4 final state in this analysis.
An unbinned maximum likelihood fit to the m 4 distribution is performed. The strengths of fermion and vector boson induced couplings are independent and are left unconstrained in the fit. By splitting events into two categories, namely those with a VBF-like two-jet topology and the rest, it is possible to constrain the two sets of couplings. The general parameterization of the probability density function is described in Section 8.
The joint constraint on the width Γ H and mass m H of the Higgs boson is shown in Fig. 12 (left). Figure 12 (right) shows the likelihood as a function of Γ H with the m H parameter unconstrained. The width is constrained to be Γ H < 1.10 GeV at 95% CL. The observed and expected results are summarized in Table 7 and are consistent with the expected detector resolution. The dominant sources of uncertainty are the uncertainty in the lepton momentum scale when determining the mass and the uncertainty in the four-lepton mass resolution when determining the width.

Summary
The first results on Higgs boson production in the four-lepton final state at √ s = 13 TeV have been presented, using 35.9 fb −1 of pp collisions collected by the CMS experiment at the LHC. The signal strength modifier µ, defined as the ratio of the observed Higgs boson rate in the H → ZZ → 4 decay channel to the standard model expectation, is measured to be µ = 1.05 +0. 15 −0.14 (stat) +0.11 −0.09 (syst) = 1.05 +0.19 −0.17 at m H = 125.09 GeV, the combined ATLAS and CMS measurement of the Higgs boson mass. Two signal strength modifiers associated with the fermion-and vector-boson induced contributions to the expected standard model cross section are measured to be µ ggH, ttH = 1.19 +0. 21 −0.20 and µ VBF,VH = 0.00 +0.81 −0.00 , respectively. The cross section at √ s = 13 TeV in a fiducial phase space defined to match the experimental acceptance in terms of the lepton kinematics and event topology, predicted in the standard model to be 2.76 ± 0.14 fb, is measured to be 2.92 +0. 48 −0.44 (stat) +0.28 −0.24 (syst) fb. Differential cross sections are reported as a function of the transverse momentum of the Higgs boson, the number of associated jets, and the transverse momentum of the leading associated jet. The mass is measured to be m H = 125.26 ± 0.20 (stat) ± 0.08 (syst) GeV and the width is constrained to be Γ H < 1.10 GeV at 95% confidence level. The production and decay properties of the Higgs boson are consistent, within their uncertainties, with the expectations for the standard model Higgs boson. [5] ATLAS Collaboration, "Measurements of the Higgs boson production and decay rates and coupling strengths using pp collision data at √ s = 7 and 8 TeV in the ATLAS experiment", Eur. Phys. J. C 76 (2016) 6, doi:10.1140/epjc/s10052-015-3769-y, arXiv:1507.04548.