Search for new light gauge bosons in Higgs boson decays to four-lepton final states in pp collisions at √s = 8 TeV with the ATLAS detector at the LHC

This paper presents a search for Higgs bosons decaying to four leptons, either electrons or muons, via one or two light exotic gauge bosons Z d , H → ZZ d → 4 l or H → Z d Z d → 4 l . The search was performed using pp collision data corresponding to an integrated luminosity of about 20 fb − 1 at the center-of-mass energy of ﬃﬃﬃ s p ¼ 8 TeV recorded with the ATLAS detector at the Large Hadron Collider. The observed data are well described by the Standard Model prediction. Upper bounds on the branching ratio of H → ZZ d → 4 l and on the kinetic mixing parameter between the Z d and the Standard Model hypercharge gauge boson are set in the range ð 1 – 9 Þ × 10 − 5 and ð 4 – 17 Þ × 10 − 2 respectively, at 95% confidence level assuming the Standard Model branching ratio of H → ZZ (cid:2) → 4 l , for Z d masses between 15 and 55 GeV. Upper bounds on the effective mass mixing parameter between the Z and the Z d are also set using the branching ratio limits in the H → ZZ d → 4 l search, and are in the range ð 1 . 5 – 8 . 7 Þ × 10 − 4 for 15 < m Z d < 35 GeV. Upper bounds on the branching ratio of H → Z d Z d → 4 l and on the Higgs portal coupling parameter, controlling the strength of the coupling of the Higgs boson to dark vector bosons are set in the range ð 2 – 3 Þ × 10 − 5 and ð 1 – 10 Þ × 10 − 4 respectively, at 95% confidence level assuming the Standard Model Higgs boson production cross sections, for Z d masses between 15 and 60 GeV.

In this paper, we present model-independent searches for dark sector states.We then interpret the results in benchmark models where the dark gauge symmetry is mediated by a dark vector boson Z d .The dark sector could couple to the SM through kinetic mixing with the hypercharge gauge boson [15][16][17].In this hypercharge portal scenario, the kinetic mixing parameter controls the coupling strength of the dark vector boson and SM particles.If, in addition, the U(1) d symmetry is broken by the introduction of a dark Higgs boson, then there could also be a mixing between the SM Higgs boson and the dark sector Higgs boson [5][6][7][8][9][10].In this scenario, the Higgs portal coupling κ controls the strength of the Higgs coupling to dark vector bosons.The observed Higgs boson would then be the lighter partner of the new Higgs doublet, and could also decay via the dark sector.There is an additional Higgs portal scenario where there could be a mass-mixing between the SM Z boson and Z d [7,8].In this scenario, the dark vector boson Z d may couple to the SM Z boson with a coupling proportional to the mass mixing parameter δ.
The presence of the dark sector could be inferred either from deviations from the SM-predicted rates of Drell-Yan (DY) events or from Higgs boson decays through exotic intermediate states.Model-independent upper bounds, from electroweak constraints, on the kinetic mixing parameter of ≤ 0.03 are reported in Refs.[5,18,19] for dark vector boson masses between 1 GeV and 200 GeV.Upper bounds on the kinetic mixing parameter based on searches for dilepton resonances, pp → Z d → , below the Z-boson mass are found to be in range of 0.005-0.020for dark vector boson masses between 20 and 80 GeV [20].The discovery of the Higgs boson [21][22][23] during Run 1 of the Large Hadron Collider (LHC) [24,25] opens a new and rich experimental program that includes the search for exotic decays H → ZZ d → 4 and H → Z d Z d → 4 .This scenario is not entirely excluded by electroweak constraints [5-10, 18, 20].The H → ZZ d process probes the parameter space of and m Z d , or δ and m Z d , where m Z d is the mass of the dark vector boson, and the H → Z d Z d process covers the parameter space of κ and m Z d [5,6].DY production, pp → Z d → , offers the most promising discovery potential for dark vector bosons in the event of no mixing between the dark Higgs boson and the SM Higgs boson.The H → ZZ d → 4 process offers a discovery potential complementary to the DY process for m Z d < m Z [5,20].Both of these would be needed to understand the properties of the dark vector boson [5].If the dark Higgs boson mixes with the SM Higgs boson, the H → Z d Z d → 4 process would be important, probing the dark sector through the Higgs portal coupling [5,6].This paper presents a search for Higgs bosons decaying to four leptons via one or two Z d bosons using pp collision data at √ s = 8 TeV collected at the CERN LHC with the ATLAS experiment.The search uses a dataset corresponding to an integrated luminosity of 20.7 fb −1 with an uncertainty of 3.6% for H → ZZ d → 4 based on the luminosity calibration used in Refs.[26,27], and 20.3 fb −1 with an uncertainty of 2.8% for H → Z d Z d → 4 based on a more recent calibration [28].Same-flavor decays of the Z and Z d bosons to electron and muon pairs are considered, giving the 4e, 2e2µ, and 4µ final states.Final states including τ leptons are not considered in the H → ZZ d → 4 and H → Z d Z d → 4 decays.In the absence of a significant signal, upper bounds are set on the relative branching ratios BR(H → ZZ d → 4 )/BR(H → 4 ) and BR(H → Z d Z d → 4 )/BR(H → ZZ * → 4 ) as functions of the mass of the dark vector boson m Z d .The branching ratio limits are used to set upper bounds on the kinetic mixing, mass mixing, and Higgs boson mixing parameters [5,6].The search is restricted to the mass range where the Z d from the decay of the Higgs boson is on-shell, i.e. 15 GeV < m Z d < m H /2, where m H = 125 GeV.Dark vector boson masses below 15 GeV are not considered in the present search.Although the low-mass region is theoretically well motivated [7,8], the high p T of the Z d boson relative to its mass leads to signatures that are better studied in dedicated searches [29].
The paper is organized as follows.The ATLAS detector is briefly described in Sec. 2. The signal and background modeling is summarized in Sec. 3. The dataset, triggers, and event reconstruction are presented in Sec. 4. Detailed descriptions of the searches are given in Sec. 5 and Sec.6 for H → ZZ d → 4 and H → Z d Z d → 4 processes respectively.Finally, the concluding remarks are presented in Sec. 7.
The background processes considered in the H → ZZ d → 4 and H → Z d Z d → 4 searches follow those used in the H → ZZ * → 4 measurements [39], and consist of: • Higgs boson production via the SM ggF, VBF (vector boson fusion), WH, ZH, and t tH processes with H → ZZ * → 4 final states.In the H → Z d Z d → 4 search, these background processes are normalized with the theoretical cross sections, where the Higgs boson production cross sections and decay branching ratios, as well as their uncertainties, are taken from Refs.[40,41].In the H → ZZ d → 4 search, the normalization of H → 4 is determined from data.The cross section for the ggF process has been calculated to next-to-leading-order (NLO) [42][43][44] and next-to-next-to-leading-order (NNLO) [45][46][47] in QCD.In addition, QCD soft-gluon resummations calculated in the next-to-nextto-leading-logarithmic (NNLL) approximation are applied for the ggF process [48].NLO electroweak (EW) radiative corrections are also applied [49,50].These results are compiled in Refs.[51][52][53] assuming factorization between QCD and EW corrections.For the VBF process, full QCD and EW corrections up to NLO [54][55][56] and approximate NNLO QCD [57] corrections are used to calculate the cross section.The cross sections for the associated WH and ZH production processes are calculated at NLO [58] and at NNLO [59] in QCD, and NLO EW radiative corrections are applied [60].The cross section for associated Higgs boson production with a t t pair is calculated at NLO in QCD [61][62][63][64].
The SM ggF and VBF processes producing H → ZZ * → 4 backgrounds are modeled with Powheg, Pythia8 and CT10 PDFs [33].The SM WH, ZH, and t tH processes producing H → ZZ * → 4 backgrounds are modeled with Pythia8 with CTEQ6L1 PDFs.• SM ZZ * production.The rate of this background is estimated using simulation normalized to the SM cross section at NLO.The ZZ * → 4 background is modeled using simulated samples generated with Powheg [65] and Pythia8 [35] for q q → ZZ * , and gg2ZZ [66] and Jimmy [67] for gg → ZZ * , and CT10 PDFs for both.• Z+jets and t t.The rates of these background processes are estimated using data-driven methods.However Monte Carlo (MC) simulation is used to understand the systematic uncertainty on the data-driven techniques.The Z+jets production is modeled with up to five partons using Alpgen [68] and is divided into two sources: Z+light-jets, which includes Zcc in the massless c-quark approximation and Zb b with b b from parton showers; and Zb b using matrix-element calculations that take into account the b-quark mass.The matching scheme of matrix elements and parton shower evolution (see Ref. [69] and the references therein) is used to remove any double counting of identical jets produced via the matrix-element calculation and the parton shower, but this scheme is not implemented for b-jets.Therefore, b b pairs with separation ∆R ≡ (∆φ) 2 + (∆η) 2 > 0.4 between the b-quarks are taken from the matrix-element calculation, whereas for ∆R < 0.4 the parton-shower b b pairs are used.For comparison between data and simulation, the NNLO QCD FEWZ [70,71] and NLO QCD MCFM [72,73] cross-section calculations are used to normalize the simulations for inclusive Z boson and Zb b production, respectively.The t t background is simulated with MC@NLO-4.06[74] with parton showers and underlying-event modeling as implemented in Herwig 6.5.20 [75] and Jimmy.The AUET2C [76] tune for the underlying events is used for t t with CT10 PDFs.
• SM WZ and WW production.The rates of these backgrounds are normalized to theoretical calculations at NLO in perturbative QCD [77].The simulated event samples are produced with Sherpa [78] and CT10 PDFs.• Backgrounds containing J/ψ and Υ, namely Z J/ψ and ZΥ.These backgrounds are normalized using the ATLAS measurements described in Ref. [79].These processes are modeled with Pythia8 [35] and CTEQ6L1 PDFs.
Differing pileup conditions (multiple proton-proton interactions in the same or neighboring bunch-crossings) as a function of the instantaneous luminosity are taken into account by overlaying simulated minimumbias events generated with Pythia8 onto the hard-scattering process and reweighting them according to the distribution of the mean number of interactions observed in data.The MC generated samples are processed either with a full ATLAS detector simulation [80] based on the GEANT4 program [81] or a fast simulation based on the parameterization of the response to the electromagnetic and hadronic showers in the ATLAS calorimeters [82] and a detailed simulation of other parts of the detector and the trigger system.The results based on the fast simulation are validated against fully simulated samples and the difference is found to be negligible.The simulated events are reconstructed and analyzed with the same procedure as the data, using the same trigger and event selection criteria.

Event Reconstruction
A combination of single-lepton and dilepton triggers is used to select the data samples.The singleelectron trigger has a transverse energy (E T ) threshold of 25 GeV while the single-muon trigger has a transverse momentum (p T ) threshold of 24 GeV.The dielectron trigger has a threshold of E T = 12 GeV for both electrons.In the case of muons, triggers with symmetric thresholds at p T = 13 GeV and asymmetric thresholds at 18 GeV and 8 GeV are used.Finally, electron-muon triggers are used with electron E T thresholds of 12 GeV or 24 GeV depending on the electron identification requirement, and a muon p T threshold of 8 GeV.The trigger efficiency for events passing the final selection is above 97% [39] in each of the final states considered.
Data events recorded during periods when significant portions of the relevant detector subsystems were not fully functional are rejected.These requirements are applied independently of the lepton final state.Events in a time window around a noise burst in the calorimeter are removed [83].Further, all triggered events are required to contain a reconstructed primary vertex formed from at least 3 tracks, each with p T > 0.4 GeV.
Electron candidates consist of clusters of energy deposited in the electromagnetic calorimeter and associated with ID tracks [84].The clusters matched to tracks are required to satisfy a set of identification criteria such that the longitudinal and transverse shower profiles are consistent with those expected from electromagnetic showers.The electron transverse momentum is computed from the cluster energy and the track direction at the interaction point.Selected electrons must satisfy E T > 7 GeV and |η| < 2.47.Each electron must have a longitudinal impact parameter (z 0 ) of less than 10 mm with respect to the reconstructed primary vertex, defined as the vertex with at least three associated tracks for which the p 2 T of the associated tracks is the highest.Muon candidates are formed by matching reconstructed ID tracks with either complete or partial tracks reconstructed in the muon spectrometer [85].If a complete track is present, the two independent momentum measurements are combined; otherwise the momentum is measured using the ID.The muon reconstruction and identification coverage is extended by using tracks reconstructed in the forward region (2.5 < |η| < 2.7) of the MS, which is outside the ID coverage.In the center of the barrel region (|η| < 0.1), where there is no coverage from muon chambers, ID tracks with p T > 15 GeV are identified as muons if their calorimetric energy deposits are consistent with a minimum ionizing particle.Only one muon per event is allowed to be reconstructed in the MS only or identified with the calorimeter.Selected muons must satisfy p T > 6 GeV and |η| < 2.7.The requirement on the longitudinal impact parameter is the same as for electrons except for the muons reconstructed in the forward region without an ID track.To reject cosmic-ray muons, the impact parameter in the bending plane (d 0 ) is required to be within 1 mm of the primary vertex.
In order to avoid double-counting of leptons, an overlap removal procedure is applied.If two reconstructed electron candidates share the same ID track or are too close to each other in η and φ (∆R < 0.1), the one with the highest transverse energy deposit in the calorimeter is kept.An electron within ∆R = 0.2 of a muon candidate is removed, and a calorimeter-based reconstructed muon within ∆R = 0.2 of an electron is removed.
Once the leptons have been selected with the aforementioned basic identification and kinematic requirements, events with at least four selected leptons are kept.All possible combinations of four leptons (quadruplets) containing two same-flavor, opposite-charge sign (SFOS) leptons, are made.The selected leptons are ordered by decreasing transverse momentum and the three highest-p T leptons should have respectively p T > 20 GeV, p T > 15 GeV and p T > 10 GeV.It is then required that one (two) leptons match the single-lepton (dilepton) trigger objects.The leptons within each quadruplet are then ordered in SFOS pairs, and denoted 1 to 4, indices 1 and 2 being for the first pair, 3 and 4 for the second pair.

Search strategy
The H → ZZ d → 4 search is conducted with the same sample of selected 4 events as used in Refs.[26,27] with the four-lepton invariant mass requirement of 115 < m 4 < 130 GeV.This collection of events is referred to as the 4 sample.The invariant mass of the opposite-sign, same-flavor pair closest to the Z-boson pole mass of 91.2 GeV [86] is denoted m 12 .The invariant mass of the remaining dilepton pair is defined as m 34 .The H → 4 yield, denoted n(H → 4 ), is determined by subtracting the relevant backgrounds from the 4 sample as shown in Eq. (1): The other backgrounds from WW, WZ, Z J/ψ and ZΥ are negligible and not considered.
The search is performed by inspecting the m 34 mass spectrum and testing for a local excess consistent with the decay of a narrow Z d resonance.This is accomplished through a template fit of the m 34 distribution, using histogram-based templates of the H → ZZ d → 4 signal and backgrounds.The signal template is obtained from simulation and is described in Sec.5.2.The m 34 distributions and the expected normalizations of the t t and Z+jets backgrounds, along with the m 34 distributions of the H → ZZ * → 4 background, as shown in Fig. 1, are determined as described in Sec.5.4.The pre-fit signal and H → ZZ * → 4 background event yields are set equal to the H → 4 observed yield given by Eq. ( 1).The expected yields for the 4 sample are shown in Table 1.
In the absence of any significant local excess, the search can be used to constrain a relative branching ratio R B , defined as:  where R B is zero in the Standard Model.A likelihood function (L) is defined as a product of Poisson probability densities (P) in each bin (i) of the m 34 distribution, and is used to obtain a measurement of R B : where µ H is the normalization of the H → ZZ * → 4 background (and allowed to float in the fit), ρ the parameter of interest related to the H → ZZ d → 4 normalization and ρ × µ H the normalization of the H → ZZ d → 4 signal.The symbol ν represents the systematic uncertainties on the background estimates that are treated as nuisance parameters, and N bins the total number of bins of the m 34 distribution.The likelihood to observe the yield in some bin, n obs i , given the expected yield , and the contribution of backgrounds b i (ν).
An upper bound on ρ is obtained from the binned likelihood fit to the data, and used in Eq. ( 2) to obtain a measurement of R B , taking into account the detector acceptance (A) and reconstruction efficiency (ε): where C is the ratio of the products of the acceptances and reconstruction efficiencies in H → ZZ d → 4 and H → ZZ * → 4 events: The acceptance is defined as the fraction of generated events that are within a fiducial region.The reconstruction efficiency is defined as the fraction of events within the fiducial region that are reconstructed and selected as part of the 4 signal sample.acceptances and efficiencies are derived with H → ZZ d → 4 and H → ZZ * → 4 MC samples where the Higgs boson is produced via ggF.The product of acceptance and reconstruction efficiency for VBF differs from ggF by only 1.2% and the contribution of V H and t tH production modes is negligible: the products of acceptance and reconstruction efficiency obtained using the ggF production mode are used also for VBF, V H and t tH.

Event selection
The Higgs boson candidate is formed by selecting two pairs of SFOS leptons.The value of m 12 is required to be between 50 GeV and 106 GeV.The value of m 34 is required to be in the range 12 GeV ≤ m 34 ≤ 115 GeV.The four-lepton invariant mass m 4 is required to be in the range 115 < m 4 < 130 GeV.After applying the selection to the 8 TeV data sample, 36 events are left as shown in Table 1.The events are grouped into four channels based on the flavor of the reconstructed leptons.Events with four electrons are in the 4e channel.Events in which the Z boson is reconstructed with electrons, and m 34 is formed from muons, are in the 2e2µ channel.Similarly, events in which the Z is reconstructed from muons and m 34 is formed from electrons are in the 2µ2e channel.Events with four muons are in the 4µ channel.

Background estimation
The search is performed using the same background estimation strategy as the H → ZZ * → 4 measurements.The expected rates of the t t and Z+jets backgrounds are estimated using data-driven methods as described in detail in Refs.[26,27].The results of the expected t t and Z+jets background estimations from data control regions are summarized in Table 2.In the "m 12 fit method", the m 12 distribution of t t is fitted with a second-order Chebychev polynomial, and the Z+jets component is fitted with a Breit-Wigner lineshape convolved with a Crystal Ball resolution function [26].In the " + e ± e ∓ relaxed requirements" method, a background control region is formed by relaxing the electron selection criteria for electrons of the subleading pairs [26].Since a fit to the data using m 34 background templates is carried out in the

Systematic uncertainties
The sources of the systematic uncertainties in the H → ZZ d → 4 search are the same as in the H → ZZ * → 4 measurements.Uncertainties on the lepton reconstruction and identification efficiencies, as well as on the energy and momentum reconstruction and scale are described in detail in Refs.[26,27], and shown in Table 3.The lepton identification is the dominant contribution to the systematic uncertainties on the ZZ * background.The largest uncertainty in the H → ZZ d → 4 search is the normalization of the t t and Z+jets backgrounds.Systematic uncertainties related to the determination of selection efficiencies of isolation and impact parameters requirements are shown to be negligible in comparison with other systematic uncertainties.The uncertainty in luminosity [28] is applied to the ZZ * background normalization.The electron energy scale uncertainty is determined from Z → ee samples and for energies below 15 GeV from J/ψ → ee decays [26,27].Final-state QED radiation modeling and background contamination affect the mass scale uncertainty negligibly.The muon momentum scale systematic uncertainty is determined from Z → µµ samples and from J/ψ → µµ as well as Υ → µµ decays [26,27].Theory related systematic uncertainties on the Higgs production cross section and branching ratios are discussed in Refs.[39][40][41], but do not apply in this search since the H → 4 normalization is obtained from data.
Uncertainties on the m 34 shapes arising from theory uncertainties on the PDFs and renormalization and factorization scales are found to be negligible.Theory cross-section uncertainties are applied to the ZZ * background.Normalization uncertainties are taken into account for the Z+jets and t t backgrounds based on the data-driven determination of these backgrounds.

Results and interpretation
A profile-likelihood test statistic is used with the CL s modified frequentist formalism [88][89][90][91] implemented in the RooStats framework [92] to test whether the data are compatible with the signal-plusbackground and background-only hypotheses.Separate fits are performed for different m Z d hypotheses from 15 GeV to 55 GeV, with 1 GeV spacing.After scanning the m 34 mass spectrum for an excess consistent with the presence of a H → ZZ d → 4 signal, no significant deviation from SM expectations is observed.
The asymptotic approximation [90] is used to estimate the expected and observed exclusion limits on ρ for the combination of all the final states, and the result is shown in Fig. 2. The relative branching ratio R B as a function of m Z d is extracted using Eqs.( 2) and ( 4) where the value of C as a function of m 34 is shown in Fig. 3, for the combination of all four final states.This is then used with ρ to constrain the value of R B , and the result is shown in Fig. 4 for the combination of all four final states.
The simplest benchmark model adds to the SM Lagrangian [6][7][8]10] a U(1) d gauge symmetry that introduces the dark vector boson Z d .The dark vector boson may mix kinetically with the SM hypercharge gauge boson with kinetic mixing parameter [6,10].This enables the decay H → ZZ d through the Hypercharge Portal.The Z d is assumed to be narrow and on-shell.Furthermore, the present search assumes prompt Z d decays consistent with current bounds on from electroweak constraints [18,19].The coupling of the Z d to SM fermions is given in Eq. (47) of Ref. [6] to be linear in , so that BR(Z d → ) is independent of due to cancellations [6].In this model, the H → ZZ d → 4 search can be used to constrain the hypercharge kinetic mixing parameter as follows: the upper limit on R B shown in Fig. 4 leads to an upper limit on BR(H → ZZ d → 4 ) assuming the SM branching ratio of H → ZZ * → 4 of 1.25 × 10 −4 [40,41] as shown in Fig. 5.The limit on can be obtained directly from the BR(H → ZZ d → 4 ) upper bounds and by using Table 2 of Ref. [5].The 95% CL upper bounds on are shown in Fig. 6 as a function of m Z d in the case κ where κ is the Higgs portal coupling.
The measurement of the relative branching ratio R B as shown in Fig. 4 can also be used to constrain the mass-mixing parameter of the model described in Refs.[7,8] where the SM is extended with a dark vector boson and another Higgs doublet, and a mass mixing between the dark vector boson and the SM Z boson is introduced.This model explores how a U(1) d gauge interaction in the hidden sector may manifest itself in the decays of the Higgs boson.The model also assumes that the Z d , being in the hidden sector, does not couple directly to any SM particles including the Higgs boson (i.e. the SM particles do not carry dark charges).However where Γ SM is the total width of the SM Higgs boson and Γ(H → ZZ d ) Γ SM .From Eqs. ( 4), (A.3) and (A.4) of Ref. [7], Γ(H → ZZ d ) ∼ δ 2 .It therefore follows from Eq. ( 6), with the further assumption where v is the vacuum expectation value of the SM Higgs field.The limit is set on the product δ 2 × BR(Z d → 2 ) since both δ and BR(Z d → 2 ) are model-dependent: in the case where kinetic mixing dominates, BR(Z d → 2 ) ∼ 30% for the model presented in Ref. [6] but it could be smaller when Z-Z d mass mixing dominates [8].In the m Z d mass range of 15 GeV to (m H − m Z ), the upper bounds on δ 2 × BR(Z d → 2 ) are in the range ∼ (1.5-8.7)× 10 −5 as shown in Fig. 7, assuming the same signal acceptances shown in Fig. 3.
events are selected as discussed in Sec.6.2.The Z, J/ψ, Υ vetoes are applied as also discussed in Sec.6.2.Subsequently, the analysis exploits the small mass difference between the two SFOS lepton pairs of the selected quadruplet to perform a counting experiment.After the small mass difference requirements between the SFOS lepton pairs, the estimated background contributions, coming from H → ZZ * → 4 and ZZ * → 4 , are small.These backgrounds are normalized with the theoretical calculations of their cross sections.The other backgrounds are found to be negligible.Since there is no significant excess, upper bounds on the signal strength, defined as the ratio of the H → Z d Z d → 4 rate normalized to the SM H → ZZ * → 4 expectation are set as a function of the hypothesized m Z d .In a benchmark model where the SM is extended with a dark vector boson and a dark Higgs boson, the measured upper bounds on the signal strength are used to set limits on the branching ratio of H → Z d Z d and on the Higgs boson mixing parameter as a function of m Z d [5,6]. [GeV]

Event selection
For the H → Z d Z d → 4 search, unlike in the H → ZZ * → 4 study [93], there is no distinction between a primary pair (on-shell Z) and a secondary pair (off-shell Z), since both Z d bosons are considered to be on-shell.Among all the different quadruplets, only one is selected by minimizing the mass difference ∆m = |m 12 − m 34 | where m 12 and m 34 are the invariant masses of the first and second pairs, respectively.The mass difference ∆m is expected to be minimal for the signal since the two dilepton systems should have invariant masses consistent with the same m Z d .No requirement is made on ∆m; it is used only to select a unique quadruplet with the smallest ∆m.Subsequently, isolation and impact parameter significance requirements are imposed on the leptons of the selected quadruplet as described in Ref. [39]. Figure 8 shows the minimal value of ∆m for the 2e2µ final state after the impact parameter significance requirements.Similar distributions are found for the 4e and 4µ final states.The dilepton and four-lepton invariant mass distributions are shown in Figs. 9 and 10 respectively for m 12 and m 34 combined.
For the H → Z d Z d → 4 search with hypothesized m Z d , after the impact parameter significance requirements on the selected leptons, four final requirements are applied: (1) 115 < m 4 < 130 GeV where m 4 is the invariant mass of the four leptons in the quadruplet, consistent The shaded area shows both the statistical and systematic uncertainties.The bottom plots show the significance of the observed number of events in the data compared to the expected number of events from the backgrounds.These distributions are obtained after the impact parameter significance requirement.

Background estimation
For the H → Z d Z d → 4 search, the main background contributions in the signal region come from the H → ZZ * → 4 and ZZ * → 4 processes.These backgrounds are suppressed by the requirements of the tight signal region, as explained in Sec.6.2.Other backgrounds with smaller contributions come from the Z+jets and t t, WW and WZ processes as shown in Fig. 11.The H → ZZ * → 4 , ZZ * → 4 , WW and WZ backgrounds are estimated from simulation and normalized with theoretical calculations of their cross sections.After applying the tight signal region requirements described in Sec.6.2, the Z+jets, t t and diboson backgrounds are negligible.In the case where the Monte Carlo calculation yields zero expected background events in the tight signal region, an upper bound at 68% CL on the expected events is estimated using 1.14 events [86], scaled to the data luminosity and normalized to the background cross section: where L is the total integrated luminosity, σ the cross section of the background process, and N tot the total number of weighted events simulated for the background process.
Events / 5 GeV The bottom plots show the significance of the observed number of events in the data compared to the expected number of events from the backgrounds.These distributions are obtained after the impact parameter significance requirement.
To validate the background estimation, a signal depleted control region is defined by reversing the fourlepton invariant mass requirement with an m 4 < 115 GeV or m 4 > 130 GeV requirement.Good agreement between expectation and observation is found in this validation control region as shown in Fig. 12.

Systematic uncertainties
The systematic uncertainties on the theoretical calculations of the cross sections used in the event selection and identification efficiencies are taken into account.The effects of PDFs, α S , and renormalization and factorization scale uncertainties on the total inclusive cross sections for the Higgs production by ggF, VBF, V H and t tH are obtained from Refs.[40,41].The renormalization, factorization scales and PDFs and α S uncertainties are applied to the ZZ * background estimates.The uncertainties due to the limited number of MC events in the t t, Z+jets, Z J/ψ, ZΥ and WW/WZ background simulations are estimated as described in Sec.6.3.The luminosity uncertainty [28] is applied to all signal yields, as well as to the background yields that are normalized with their theory cross sections.The detector systematic uncertainties due to uncertainties in the electron and muon identification efficiencies are estimated within the acceptance of the signal region requirements.There are several components to these uncertainties.For the muons, Entries / 5 GeV uncertainties in the reconstruction and identification efficiency, and in the momentum resolution and scale, are included.For the electrons, uncertainties in the reconstruction and identification efficiency, the isolation and impact parameter significance requirements, the energy scale and energy resolution are considered.The systematic uncertainties are summarized in Table 4.  Events / 5 GeV range 20.5 ≤ m Z d ≤ 21.0 GeV.In the m Z d range of 15 to 30 GeV where four data events pass the loose signal region requirements, histogram interpolation [87] is used in steps of 0.5 GeV to obtain the signal acceptances and efficiencies at the hypothesized m Z d .The expected numbers of signal, background and data events, after applying the tight signal region requirements, are shown in Table 5.

Results and interpretation
For each m Z d , in the absence of any significant excess of events consistent with the signal hypothesis, the upper limits are computed from a maximum-likelihood fit to the numbers of data and expected signal and background events in the tight signal regions, following the CL s modified frequentist formalism [88,89] with the profile-likelihood test statistic [90,91].The nuisance parameters associated to the systematic uncertainties described in Sec.6.4 are profiled.The parameter of interest in the fit is the signal strength µ d defined as the ratio of the H → Z d Z d → 4 rate relative to the SM H → ZZ * → 4 rate: The systematic uncertainties in the electron and muon identification efficiencies, renormalization and factorization scales and PDF are 100% correlated between the signal and backgrounds.Pseudoexperiments are used to compute the 95% CL upper bound µ d in each of the final states and their combination, and   9), as shown in Fig. 15.
The simplest benchmark model is the SM plus a dark vector boson and a dark Higgs boson as discussed in Refs.[6,10], where the branching ratio of Z d → is given as a function of m Z d .This can be used to convert the measurement of the upper bound on the signal strength µ d into an upper bound on the branching ratio BR(H → Z d Z d ) assuming the SM Higgs boson production cross section.Figure 16 shows the 95% CL upper limit on the branching ratio of H → Z d Z d as a function of m Z d using the combined µ d of the three final states.The weaker bound at higher m Z d is due to the fact that the branching ratio Z d → drops slightly at higher m Z d [6] as other decay channels become accessible.The H → Z d Z d decay can be used to obtain a m Z d -dependent limit on an Higgs mixing parameter κ [6]: where κ is the size of the Higgs portal coupling and m S is the mass of the dark Higgs boson.The partial width of H → Z d Z d is given in terms of κ [5].In the regime where the Higgs mixing parameter dominates The Higgs portal coupling parameter κ is obtained using Eq. ( 53) of Ref. [6] or Table 2 of Ref. [5]: where   An interpretation for H → Z d Z d is not done in the Z-Z d mass mixing scenario described in Refs.[7,8] since in this model the rate of H → Z d Z d is highly suppressed relative to that of H → ZZ d .

Conclusions
Two searches for an exotic gauge boson Z d that couples to the discovered SM Higgs boson at a mass around 125 GeV in four-lepton events are presented, using the ATLAS detector at the LHC.  the final states.For relative branching ratios above 0.4 (observed) and 0.2 (expected), the entire mass range of 15 < m Z d < 55 GeV is excluded at 95% CL.Upper bounds at 95% CL on the branching ratio of H → ZZ d → 4 are set in the range (1-9) × 10 −5 for 15 < m Z d < 55 GeV, assuming the SM branching ratio of H → ZZ * → 4 .
The H → Z d Z d → 4 search covers the exotic gauge boson mass range from 15 GeV up to the kinematic limit of m H /2.An integrated luminosity of 20.3 fb −1 at 8 TeV is used in this search.One data event is observed to pass all the signal region selections in the 4e channel, and has dilepton invariant masses of 21.8 GeV and 28.1 GeV.This 4e event is consistent with a Z d mass in the range 23.5 < m Z d < 26.5 GeV.Another data event is observed to pass all the signal region selections in the 4µ channel, and has dilepton invariant masses of 23.2 GeV and 18.0 GeV.This 4µ event is consistent with a Z d mass in the range 20.5 < m Z d < 21.0 GeV.In the absence of a significant excess, upper bounds on the signal strength (and thus on the cross section times branching ratio) are set for the mass range of 15 < m Z d < 60 GeV using the combined 4e, 2e2µ, 4µ final states.
Using a simplified model where the SM is extended with the addition of an exotic gauge boson and a dark Higgs boson, upper bounds on the gauge kinetic mixing parameter (when κ), are set in the range (4-17) × 10 −2 at 95% CL, assuming the SM branching ratio of H → ZZ * → 4 , for 15 < m Z d < 55 GeV.The crucial computing support from all WLCG partners is acknowledged gratefully, in particular from CERN and the ATLAS Tier-1 facilities at TRIUMF (Canada), NDGF (Denmark, Norway, Sweden), CC-IN2P3 (France), KIT/GridKA (Germany), INFN-CNAF (Italy), NL-T1 (Netherlands), PIC (Spain), ASGC (Taiwan), RAL (UK) and BNL (USA) and in the Tier-2 facilities worldwide.
e Also at Department of Physics, California State University, Fresno CA, United States of America f Also at Department of Physics, University of Fribourg, Fribourg, Switzerland g Also at Departamento de Fisica e Astronomia, Faculdade de Ciencias, Universidade do Porto, Portugal h Also at Tomsk State University, Tomsk, Russia i Also at CPPM, Aix-Marseille Université and CNRS/IN2P3, Marseille, France j Also at Universita di Napoli Parthenope, Napoli, Italy k Also at Institute of Particle Physics (IPP), Canada l Also at Particle Physics Department, Rutherford Appleton Laboratory, Didcot, United Kingdom m Also at Department of Physics, St. Petersburg State Polytechnical University, St. Petersburg, Russia n Also at Louisiana Tech University, Ruston LA, United States of America o Also at Institucio Catalana de Recerca i Estudis Avancats, ICREA, Barcelona, Spain p Also at Department of Physics, National Tsing Hua University, Taiwan q Also at Department of Physics, The University of Texas at Austin, Austin TX, United States of America r Also at Institute of Theoretical Physics, Ilia State University, Tbilisi, Georgia s Also at CERN, Geneva, Switzerland t Also at Georgian Technical University (GTU),Tbilisi, Georgia u Also at Ochadai Academic Production, Ochanomizu University, Tokyo, Japan v Also at Manhattan College, New York NY, United States of America w Also at Hellenic Open University, Patras, Greece x Also at Institute of Physics, Academia Sinica, Taipei, Taiwan y Also at LAL, Université Paris-Sud and CNRS/IN2P3, Orsay, France z Also at Academia Sinica Grid Computing, Institute of Physics, Academia Sinica, Taipei, Taiwan aa Also at School of Physics, Shandong University, Shandong, China ab Also at Moscow Institute of Physics and Technology State University, Dolgoprudny, Russia ac Also at Section de Physique, Université de Genève, Geneva, Switzerland ad Also at International School for Advanced Studies (SISSA), Trieste, Italy ae Also at Department of Physics and Astronomy, University of South Carolina, Columbia SC, United States of America a f Also at School of Physics and Engineering, Sun Yat-sen University, Guangzhou, China ag Also at Faculty of Physics, M.V.

Figure 1 :
Figure 1: The distribution of the mass of the second lepton pair, m 34 , of the √ s= 8 TeV data (filled circles with error bars) and the expected (pre-fit) backgrounds.The H → ZZ * → 4 expected (pre-fit) normalization, for a mass hypothesis of m H =125 GeV, is set by subtracting the expected contributions of the ZZ * , Z+jets and t t backgrounds from the total number of observed 4 events in the data.

A
signal would produce a narrow peak in the m 34 mass spectrum.The width of the m 34 peak for the Z d signal is dominated by detector resolution for all Z d masses considered.For the individual decay channels and their combination, the resolutions of the m 34 distributions are determined from Gaussian fits.The m 34 resolutions show a linear trend between m Z d = 15 GeV and m Z d = 55 GeV and vary from 0.3 GeV to 1.5 GeV respectively, for the combination of all the final states.The resolutions of the m 34 distributions are smaller than the mass spacing between the generated signal samples (5 GeV), requiring an interpolation to probe intermediate values of m Z d .Histogram-based templates are used to model the Z d signal where no simulation is available; these templates are obtained from morphed signals produced with the procedure defined in Ref. [87].The morphed signal templates are generated with a mass spacing of 1 GeV.

Figure 2 :
Figure2: The observed (solid line) and median expected (dashed line) 95% confidence level (CL) upper limits on the parameter ρ related to the H → ZZ d → 4 normalization as a function of m Z d , for the combination of all four channels (4µ, 4e, 2µ2e, 2e2µ).The ±1σ and ±2σ expected exclusion regions are indicated in green and yellow, respectively.

Figure 3 :
Figure 3: The ratio C of the products of the acceptances and reconstruction efficiencies in H → ZZ d → 4 and H → ZZ * → 4 events as a function of m 34 .

Figure 4 :
Figure 4: The 95% CL upper limits on the relative branching ratio, R B = BR(H→ZZ d →4 ) BR(H→4 ) as a function of m Z d .The ±1σ and ±2σ expected exclusion regions are indicated in green and yellow, respectively.

Figure 5 :
Figure 5: The 95% CL upper limits on the branching ratio of H → ZZ d → 4 as a function of m Z d using the combined upper limit on R B and the SM branching ratio of H → ZZ * → 4 . m

Figure 6 :
Figure6: The 95% CL upper limits on the gauge kinetic mixing parameter as a function of m Z d using the combined upper limit on the branching ratio of H → ZZ d → 4 and Table2of Ref.[5].

Figure 7 :
Figure7: The 95% CL upper limits on the product of the mass-mixing parameter δ and the branching ratio of Z d decays to two leptons (electrons, or muons), δ 2 × BR(Z d → 2 ), as a function of m Z d using the combined upper limit on the relative branching ratio of H → ZZ d → 4 and the partial width of H → ZZ d computed in Refs.[7,8].

Figure 8 :Figure 9 :
Figure 8: Absolute mass difference between the two dilepton pairs, ∆m = |m 12 − m 34 | in the 2e2µ channel, for m H = 125 GeV.The shaded area shows both the statistical and systematic uncertainties.The bottom plot shows the significance of the observed number of events in the data compared to the expected number of events from the backgrounds.These distributions are obtained after the impact parameter significance requirements.

Figure 10 :
Figure10: Four-lepton invariant mass, in the combined 4e + 2e2µ + 4µ final state, for m H = 125 GeV.The shaded area shows both the statistical and systematic uncertainties.The bottom plots show the significance of the observed number of events in the data compared to the expected number of events from the backgrounds.These distributions are obtained after the impact parameter significance requirement.

Figure 11 :
Figure11: Dilepton invariant mass, m ≡ m 12 or m 34 after the loose signal region requirements described in Sec.6.2 for the 4e, 4µ and, 2e2µ final states combined, for m H = 125 GeV.The data is represented by the black dots, and the backgrounds are represented by the filled histograms.The shaded area shows both the statistical and systematic uncertainties.The bottom plots show the significance of the observed data events compared to the expected number of events from the backgrounds.The dashed vertical line is the kinematic limit (m 12 or m 34 < 63 GeV) of the loose signal region requirements as discussed in Sec.6.2.

Figures 11 and 13 Figure 12 :
Figures 11 and 13  show the distributions of the dilepton invariant mass (for m 12 and m 34 combined) and the absolute mass difference ∆m = |m 12 −m 34 | after the loose signal region requirements.Four data events pass the loose signal region requirements, one in the 4e channel, two in the 4µ channel and one in the 2e2µ channel.Two of these four events pass the tight signal region requirements: the event in the 4e channel and one of the events in the 4µ channel.The event in the 4e channel has dilepton masses of 21.8 GeV and 28.1 GeV as shown in Fig.11, and is consistent with a Z d mass in the range 23.5 ≤ m Z d ≤ 26.5 GeV.For the event in the 4µ channel that passes the tight signal region requirements, the dilepton invariant masses are 23.2GeV and 18.0 GeV as shown in Fig.11, and they are consistent with a Z d mass in the

Figure 13 :
Figure 13: Absolute mass difference, ∆m = |m 12 − m 34 | after the loose signal region requirements described in Sec.6.2 for the 4e, 4µ and, 2e2µ final states combined, for m H = 125 GeV.The data is represented by the black dots, and the backgrounds are represented by the filled histograms.The shaded area shows both the statistical and systematic uncertainties.The bottom plots show the significance of the observed data events compared to the expected number of events from the backgrounds.

3 × 10 − 3 1 0Table 5 :
Total background < 5.3 × 10 −2 < 5.1 × 10 −2 < 6.4 × 10 −2 Data 0 The expected and observed numbers of events in the tight signal region of the H → Z d Z d → 4 search for each of the three final states, for the hypothesized mass m Z d = 25 GeV and 20.5 GeV.Statistical and systematic uncertainties are given respectively for the signal and the background expectations.One event in data passes all the selections in the 4e channel and is consistent with 23.5 ≤ m Z d ≤ 26.5 GeV.One other data event passes all the selections in the 4µ channel and is consistent with 20.5 ≤ m Z d ≤ 21.0 GeV.The H → ZZ * → 4 numbers are summed over the ggF, VBF, ZH, WH and t tH processes.for each of the hypothesized m Z d .The 95% confidence-level upper bounds on the H → Z d Z d → 4 rates are shown in Fig. 14 relative to the SM Higgs boson process H → ZZ * → 4 as a function of the hypothesized m Z d for the combination of the three final states 4e, 2e2µ and 4µ.Assuming the SM Higgs boson production cross section and using BR(H → ZZ * → 4 ) SM = 1.25 × 10 −4 [40, 41], upper bounds on the branching ratio of H → Z d Z d → 4 can be obtained from Eq. (

Figure 15 :
Figure 15: The 95% confidence level upper bound on the branching ratio of H → Z d Z d → 4 as a function of m Z d , in the combined 4e + 2e2µ + 4µ final state, for m H = 125 GeV.The ±1σ and ±2σ expected exclusion regions are indicated in green and yellow, respectively.

Figure 17
Figure 17 shows the upper bound on the effective Higgs mixing parameter as a function of m Z d : for m H /2 < m S < 2m H , this would correspond to an upper bound on the Higgs portal coupling in the range κ ∼ (1-10) × 10 −4 .
The H → ZZ d → 4 analysis uses the events resulting from Higgs boson decays to four leptons to search for an exotic gauge boson Z d , by examining the m 34 mass distribution.The results obtained in this search cover the exotic gauge boson mass range of 15 < m Z d < 55 GeV, and are based on proton-proton collisions data at √ s = 8 TeV with an integrated luminosity of 20.7 fb −1 .Observed and expected exclusion limits on the branching ratio of H → ZZ d → 4 relative to H → 4 are estimated for the combination of all

Figure 16 :
Figure 16: The 95% confidence level upper bound on the branching ratio of H → Z d Z d in the combined 4e + 2e2µ + 4µ final state, for m H = 125 GeV.The ±1σ and ±2σ expected exclusion regions are indicated in green and yellow, respectively.

Figure 17 : 2 H /|m 2 H − m 2 S
Figure 17: The 95% confidence level upper bound on the Higgs mixing parameter κ × m 2 H /|m 2 H − m 2 S | as a function of m Z d , in the combined 4e + 2e2µ + 4µ final state, for m H = 125 GeV.The ±1σ and ±2σ expected exclusion regions are indicated in green and yellow, respectively.

Table 1 :
The estimated pre-fit background yields of (MC) ZZ * , (data-driven) t t + Z+jets, their sum, the observed 4 event yield and the estimated pre-fit H → 4 contribution in the 4 sample.The H → 4 estimate in the last column is obtained as the difference between the observed event yield and the sum of the ZZ * and t t + Z+jets backgrounds.The pre-fit H → ZZ * → 4 background and H → ZZ d → 4 signal events are normalized to the H → 4 observed events.The uncertainties are statistical and systematic respectively.The systematic uncertainties are discussed in Section 5.5.Uncertainties on the H → 4 rates do not include the statistical uncertainty from the observed number.

Table 2 :
± e ∓ relaxed requirements: sum of Z + jets and t t contributions 5.2 ± 0.4 ± 0.5 4e + e ± e ∓ relaxed requirements: sum of Z + jets and t t contributions 3.2 ± 0.5 ± 0.4 Summary of the estimated expected numbers of Z+jets and t t background events for the 20.7 fb −1 of data at √ s = 8 TeV for the full mass range after kinematic selections, for the H → ZZ d → 4 search.The first uncertainty is statistical while the second is systematic.The uncertainties are given on the event yields.Approximately 80% of the t t and Z+jets backgrounds have m 4 < 160 GeV.
The acceptances and reconstruction efficiencies of the H → ZZ d → 4 signal and H → ZZ * → 4 background are used in Eqs.(4) and (5) to obtain the measurement of the relative branching ratio R B .The

Table 3 :
The relative systematic uncertainties on the event yields in the H → ZZ d → 4 search.
search, both the distribution in m 34 and normalization of the backgrounds are relevant.For all relevant backgrounds (H → ZZ * → 4 , ZZ * , t t and Z+jets) the m 34 distribution is obtained from simulation.

Table 4 :
The relative systematic uncertainties on the event yields in the H → Z d Z d → 4 search.