Search for dark matter produced in association with a dark Higgs boson decaying into $W^\pm W^\mp$ or $ZZ$ in fully hadronic final states from $\sqrt{s}=13$ TeV $pp$ collisions recorded with the ATLAS detector

Several extensions of the Standard Model predict the production of dark matter particles at the LHC. An uncharted signature of dark matter particles produced in association with $VV=W^\pm W^\mp$ or $ZZ$ pairs from a decay of a dark Higgs boson $s$ is searched for using 139 fb$^{-1}$ of $pp$ collisions recorded by the ATLAS detector at a center-of-mass energy of 13 TeV. The $s\to V(q\bar q)V(q\bar q)$ decays are reconstructed with a novel technique aimed at resolving the dense topology from boosted $VV$ pairs using jets in the calorimeter and tracking information. Dark Higgs scenarios with $m_s>160$ GeV are excluded.

Overwhelming astrophysical evidence [1][2][3][4] suggests the existence of dark matter (DM).DM cannot be accounted for within the Standard Model (SM) and its nature is one of the major questions in physics.Several extensions of the SM postulate stable, electrically neutral, weakly interacting massive particles () [4] as DM candidates that can potentially be produced in high-energy collisions at the CERN LHC.Once produced,  would escape detection, producing an imbalance in the measured transverse momentum 1 , resulting in missing transverse momentum  miss T (with magnitude  miss T ).A wide class of models probed at the LHC postulate processes where one or more SM particles  are produced recoiling against , resulting in an " +  miss T " signature.Searches at the LHC have considered  to be a hadronic jet [5,6], top or bottom quarks [7][8][9][10], a photon [11,12], a  or  boson [13][14][15], or a Higgs boson [16][17][18].This Letter presents a pioneering search for DM using the  +  miss T signature where  is a hypothetical particle that decays into a vector-boson pair  =  +  − or  .This signature was not explored for large  miss T and resonant  production with an invariant mass    > 160 GeV.The signal region (SR) requires large  miss T from DM particles, and targets the  →  q q decay, which has the largest branching ratio B. The background is dominated by vector-boson production in association with jets, referred to as  +jets.The analysis employs control regions (CRs) requiring either a single muon () or a pair of leptons ℓ ± ℓ ∓ (ℓ = , ) in the final state to improve background modeling in the SR.
The discovery of a new boson with SM Higgs properties [19][20][21] confirmed the mechanism for electroweak symmetry breaking [22][23][24][25][26][27] and the generation of mass for SM particles.This success motivates a similar mechanism in the dark sector that contains the DM particle, where  obtains mass via its Yukawa interactions with a dark Higgs boson  [28].Furthermore,  alleviates the strict constraints from the observed DM relic density [29] by opening up a new annihilation channel into SM particles, when , rather than , is the lightest state in the dark sector.
A two-mediator-based DM model [30] containing a new  (1) gauge symmetry, which yields an additional massive spin-1 vector  boson via the new scalar boson , is used for the optimization and interpretation of the search presented in this Letter.The relevant model parameters are the Majorana DM particle mass   , the  mass   , the dark Higgs mass   , and the  couplings   to quarks and   to DM particles.The Born-level Feynman diagrams for the process are shown in Figure 1.The  +   signal is produced through  q →  →   , requiring an off-shell intermediate state such as a  or .The  →  ±  ∓ and  →   processes become relevant for   160 GeV and   180 GeV, respectively [31].The proposed framework shares similarities with previously explored spin-1 simplified DM models [32][33][34][35][36], with  being the only addition and  being a Majorana rather than a Dirac fermion.Within this framework, searches for spin-1 mediators provide complementary sensitivity [37].
The search is performed using 139 fb −1 of   collisions at √  = 13 TeV recorded with the ATLAS detector [38,39] in 2015-2018.Events in the SR and the single-muon CR were collected by triggering on  miss T reconstructed from calorimeter information [40] above a threshold that varied from 90 to 110 GeV.Events in the dilepton CR were recorded using single-lepton triggers with transverse momentum ( T ) thresholds of 24 GeV and higher, depending on the data-taking period, for electrons and muons.SM background processes and the  +   signal were simulated using Monte Carlo (MC) event generators, except the multĳet background, which is found to be negligible using a data-driven method.A detailed 1 ATLAS uses a right-handed coordinate system with its origin at the nominal interaction point (IP) in the center of the detector and the -axis along the beam pipe.The -axis points from the IP to the center of the LHC ring, and the -axis points upwards.Cylindrical coordinates (, ) are used in the transverse plane,  being the azimuthal angle around the -axis.
The pseudorapidity is defined in terms of the polar angle  as  = − ln tan(/2).Angular distance is measured in units of Δ ≡ √︁ (Δ) 2 + (Δ) 2 .q q q q q q Z 0 s Z 0 W, Z W, Z q q q q q q Z 0 s W, Z W, Z Figure 1: Born-level Feynman diagrams for the  q →  →   ,  →  ( q) ( q) process.The left diagram typically dominates.simulation of the ATLAS detector [41] based on G 4 [42] was used to simulate the detector response for all MC event samples.Contributions from additional   interactions (pileup) were simulated with P 8.186 [43] using the NNPDF23 LO parton distribution function (PDF) set [44] and corrected to match data.Parton shower simulations with P use the A14 set of tuned parameters [45] with the NNPDF23 LO PDF set.
Signal samples for the   →  →    →    →  q q   process were generated at leading order (LO) in QCD with up to one additional parton in the event, using M G 5_aMC@NLO 2.6.2 [46] interfaced to P 8.230, both using the NNPDF23 LO PDF set.Samples were generated in the (  ,   ) plane for   = 0.5, 1, 1.7, 2.5 TeV and in steps of 25 GeV for 160 <   /GeV < 360, with   = 200 GeV to avoid  →   decays.Other parameters were chosen as   = 1.0,   = 0.25 [35,36], and sin  = 0.01, where  is the mixing angle between SM and dark Higgs bosons [28], set to a small value [47].
The +jets processes were simulated with S 2.2.1 [48], including mass effects for -and -quarks and using NNPDF3.0PDFs [49].The perturbative calculations for  +jets were performed at next-to-leading order (NLO) in QCD for up to two partons and at LO for up to four partons [50,51], and matched to the parton shower [52] using the ME+PS@NLO prescription [53].The  +jets samples are normalized using calculations at next-to-next-to-leading order (NNLO) in QCD [54].Backgrounds from top quark pair ( t) production and single top quark production were generated at NLO in QCD with P -B [55-58] v2 using the NNPDF3.0NLO PDF set, interfaced to P 8.230 for parton showering and hadronization.The  t samples are normalized using calculations at NNLO in QCD including next-to-next-to-leading logarithmic corrections for soft-gluon radiation [59][60][61][62][63][64][65].The single-top-quark processes are normalized to cross sections at NLO in QCD from Hathor v2.1 [66,67].Diboson () samples were simulated with S 2.2.1 at NLO in QCD and normalized using calculations at NNLO in QCD using NNPDF3.0NNLO PDFs.Backgrounds from associated   production were generated at NLO in QCD with P -B interfaced to P 8.186 using NNPDF3.0NLO PDFs.The  →   and  →   processes were normalized using calculations at NNLO in QCD and at NLO in QCD combined with next-to-leading-logarithmic order corrections, respectively.
At least one   collision vertex reconstructed from at least two inner detector (ID) tracks with  track T > 0.5 GeV is required in the event.The vertex with the highest (  track T ) 2 in the event is designated the primary vertex (PV).The ID tracks must have at least seven hits and satisfy  T > 0.5 GeV and || < 2.5 requirements [68,69].Their transverse and longitudinal impact parameters relative to the PV must satisfy | 0 | < 2 mm and | 0 sin()| < 3 mm, respectively.
Muons are reconstructed by matching a track or track segment found in the muon spectrometer to an ID track.Muons must satisfy "medium" or "loose" requirements [70] such that "medium" ("loose") muons must have || < 2.5 (2.7).Electrons are reconstructed by matching a cluster of energy in the calorimeter to an ID track.Electron candidates are identified using a likelihood-based method [71] and must satisfy the "loose" requirement and have || < 2.47.Electrons and muons must be isolated according to the track proximity criteria in Ref. [72].Hadronic -lepton decays are identified by an algorithm based on a boosted decision tree [73].
Jets are formed from three-dimensional clusters of calorimeter cells with the anti-  algorithm [74,75].Small- jets use a radius parameter  = 0.4 and are referred to as "central" if they satisfy || < 2.5 and  T > 20 GeV, and "forward" if they fulfill 2.5 < || < 4.5 and  T > 30 GeV.Corrections for pileup [76] and the energy scale and resolution [77] are applied to small- jets.In addition, central small- jets with 20 <  T /GeV < 60 and || < 2.4 are identified as originating from the PV using associated tracks [78].Small- jets closer than Δ = 0.2 to an , , or hadronic -decay candidate are rejected.
To better reconstruct the challenging multi-prong  →  ( q) ( q) decay, the novel track-assisted reclustering (TAR) algorithm [79] is used.This technique improves the resolution of jet substructure observables by considering both tracking and calorimeter information, combined with the flexibility of jet reclustering.The TAR jets are formed from small- jets reclustered into larger jets with  = 0.8 using trimming parameters optimized for ATLAS [80].The mass and other substructure observables of TAR jets are reconstructed using ID tracks.For this, ID tracks are first matched to the small- jets that constitute the  = 0.8 jets.Subsequently, the  T of tracks matched to a given small- jet are rescaled such that their sum equals the  T of that jet, in order to compensate for the neutral jet components missed by the tracker [79].The TAR algorithm is estimated to improve the sensitivity of the search by a factor of up to 2.5 in expected median discovery significance compared to the conventional large- jet approach [81], neglecting systematic uncertainties.
In order to suppress contributions from background processes that involve top quarks, which decay almost exclusively to -quarks, a multivariate algorithm is used to identify jets containing -hadrons (-tagging) with an efficiency of 77% [82].The algorithm is applied to variable-radius track-jets with  T > 10 GeV and || < 2.5 formed from ID tracks using the anti-  algorithm [83] and a  T -dependent radius parameter.
The  miss T vector is computed as the negative vector sum of the transverse momenta of the , , and small- jet candidates in the event.The transverse momenta not associated with any , , or jet candidates are accounted for using ID tracks [84].In addition, an  miss T significance S is computed from the expected resolutions for all the objects used in the  miss T calculation [85] and is used to reject multĳet background processes.
The signal is characterized by high  miss T from DM particles, and substantial hadronic activity from  →  ( q) ( q) decays that results in an invariant mass consistent with   .Thus, the SR requires  miss T > 200 GeV, no isolated  or , no  lepton decays, and two or more small- jets.Events in the SR are rejected if a "loose" electron or muon with  T > 7 GeV is present.In addition, events in the SR and CRs are not considered if they contain hadronic -decay candidates with  T > 20 GeV within || < 2.5.The smallest azimuthal angle between the  miss T and any of the three highest- T (leading) small- jets is required to be at least /9 in order to reduce the multĳet background arising from mismeasured jet momenta.This background is further suppressed by requiring S > 15.
The  t and diboson processes contribute 1%-7% and 2%-8% of the background in the SR, respectively, while the dominant SM  () + jets and  (ℓ) + jets processes contribute 59%-73% and 15%-32%, respectively, depending on the topology.The modeling of  + jets is improved using two CRs: the single-muon CR (1-CR) enriched in  +jets, and the two-lepton CR (2ℓ-CR) enriched in  +jets.The 1-CR follows the same selection as the SR, except that events must contain exactly one "medium" muon with  T > 27 GeV and no "loose" electrons with  T > 7 GeV.Events in the 2ℓ-CR are selected using the same requirements as the SR, except that events must contain exactly two "loose" electrons or two oppositely charged "medium" muons, and satisfy S < 15.The leading lepton must fulfill  T > 27 (25) GeV for electrons (muons), while for the subleading one  T > 7 GeV is required.The dilepton system is required to be consistent with an energetic  boson, i.e.  ℓℓ T > 200 GeV and 83 <  ℓℓ /GeV < 99.In order to optimize the sensitivity over a broad -pair momentum range, two selection categories, merged and intermediate, are defined.For large  momenta, the dark Higgs boson's decay products become collimated and are reconstructed inside a single TAR jet.These topologies are targeted in the merged category, defined as containing at least one TAR jet with  TAR T > 300 GeV, and mass  TAR between 100 GeV and 400 GeV.TAR jet substructure variables are employed to discriminate between the four-prong topology of  →  ( q) ( q) decays and backgrounds with lower multiplicities.This is done using combinations of -subjettiness [86] variables   by requiring 0 <  4 / 2 < 0.3 and 0 <  4 / 3 < 0.6, which were also experimentally studied in Ref. [87].The -candidate mass is identified with  TAR .The merged category dominates the sensitivity, and the product of acceptance and selection efficiency for (   →   ) × B ( → ) lies around 1%.
Moderate -candidate momenta result in less-collimated decay products, which may not be captured by the nominal TAR jet.In such cases, events failing the merged-category requirements are considered in the intermediate category, where the  candidate is reconstructed from a TAR jet with  TAR > 60 GeV that is supplemented by up to two additional small- jets within Δ = 2.5 of the TAR jet.If the mass of the TAR jet is compatible with   , i.e. 60 <  TAR /GeV < 100, the TAR jet is supplemented with the two small- jets whose combined invariant mass is closest to   .If  TAR > 100 GeV, it is assumed that only one prong of the  decay was not reconstructed within the TAR jet, and thus it is supplemented with exactly one small- jet.The -candidate mass is required to lie between 100 GeV and 400 GeV.The product of acceptance and selection efficiency for (   →   ) × B ( → ) ranges between 10% and 20%.
To account for changes in the background composition and benefit from increased signal sensitivity with higher  miss T , events in the merged category are further classified into ranges in  miss T /GeV: [300, 500] and [500, ∞).The DM signal is extracted via a simultaneous maximum-likelihood fit [88,89] of signal and background simulations to the binned -candidate mass distributions in the SR and to total yields in the CR categories.The normalizations of  +jets and  +jets processes are free parameters in the fit and are constrained by the total event yields, summed over  miss T -bin and category, in the 1-CR and 2ℓ-CR.Experimental uncertainties related to the calibration of the scale and resolution of the jet energy [77] as well as to tracking efficiencies [69] affect the reconstruction of   using TAR jets.Other leading experimental systematic uncertainties arise from the finite number of MC events and the calibration of the lepton identification efficiencies [70,71].Dominant theoretical systematic uncertainties originate from the modeling of the signal and the +jets and +jets background processes.These encompass uncertainties from the choice of PDFs and factorization and normalization scales.In addition, to estimate the uncertainty from the choice of matrix element and parton shower generator for  +jets and  +jets, alternative MC samples generated with M G 5_aMC@NLO 2.6.2 at LO in QCD with up to four parton emissions using the NNPDF23 LO PDF set and interfaced to P 8.230 using a merging scale of  cut = 30 GeV are considered.All other systematic uncertainties are estimated similarly to Ref. [16], except for the  t normalization, for which Table 1: Dominant sources of uncertainty for three dark Higgs scenarios after the fit to Asimov data generated from the expected values of the maximum-likelihood estimators including predicted signals with   = 1 TeV and   of (a) 160 GeV, (b) 235 GeV, and (c) 310 GeV.The uncertainty in the fitted signal yield relative to the theory prediction is presented.Total is the quadrature sum of statistical and total systematic uncertainties, which consider correlations.

Source of uncertainty
Uncertainty theoretical uncertainties [64] are considered.The systematic uncertainties, parameterized as nuisance parameters with Gaussian or log-normal prior probabilities, are profiled and used to constrain the template shapes and the normalizations varied in the fit [90].Dominant uncertainties after the fit to Asimov data for three representative dark Higgs scenarios are quantified in Table 1.
A first fit to the SM backgrounds is performed using only data from the CRs.The observed and fitted yields in the CR categories obtained after this fit are shown in Figure 2. Also shown are the background yields predicted in the SR when using the observed parameter values from the CR-only fit.The fit reduces the MC-predicted  +jets contribution in the merged category.The overall yields in the CRs and the SR are found to be well described by SM simulations.The normalization and the   T dependence of both  +jets and  +jets are consistent within uncertainties with SM predictions in the SR and CRs. Figure 3 shows the mass distributions    of the  candidate in two representative SR categories and the two corresponding categories in the 1-CR, obtained after a simultaneous fit to the SR and the CRs under the hypothesis that only SM predictions are present.The data distributions agree well with MC simulations in the CRs, indicating that  +jets background processes reconstructed with the novel TAR algorithm are well modeled.The observed results in the SR indicate that the data are in general well described by SM predictions.A mild excess around    = 160 GeV is observed, yielding a 2.3 local significance and 1.3 global significance when considering nine independent   hypotheses.The excess in the intermediate region is narrower than the experimental resolution for   .
Upper limits are set on the product of the   →    production cross section and B ( → ), using a modified frequentist approach (CL s ) [91] with a test statistic based on the profile likelihood in the asymptotic approximation [92].Exclusion contours in the (  ,   ) plane for the dark Higgs model are presented in Figure 4, and exclude   up to 1.8 TeV for   = 210 GeV at 95% confidence level (C.L.).The observed exclusion range in   becomes narrower than expected at low   owing to the small excess in data near    = 160 GeV discussed above.The merged SR provides the maximal sensitivity attained at low   and high   , while the intermediate SR provides complementary sensitivity.The ratio of the data to SM expectations after the CR-only fit is shown in the lower panel, along with the red line representing the ratio of the pre-fit to the post-fit background prediction.Pre-fit uncertainties cover differences between the data and pre-fit background prediction.The upper panels compare the data with the SM expectation before and after the background-only fit.The lower panels display the ratio of data to SM expectations after the fit, with its systematic uncertainty.Also shown is the ratio of SM expectations before and after the fit.The expected signal, with a cross section of 214 fb, from a representative dark Higgs model with   = 0.25,   = 1.0, and sin  = 0.01, is scaled for presentation purposes.No    shape information in the CRs is considered in the fit.Pre-fit uncertainties cover differences between the data and pre-fit background prediction.In conclusion, this Letter presents a novel search for DM in previously uncovered final states with large  miss T and hadronic decays of resonant  =  ±  ∓ or   pairs, with    > 160 GeV, using the ATLAS detector at the LHC.No significant excess over the predicted background is found in 139 fb −1 of 13 TeV   collision data.This search excludes previously uncharted parameter space of the dark Higgs model for   > 160 GeV, and provides sensitivity complementary to other DM searches using  +  miss The range [200, ∞) is used in the intermediate category.The same ranges are defined consistently in the 1-CR and the 2ℓ-CR.To ensure kinematic similarity to the  miss T arising from the  +jets in the SR,  miss, no  T =  miss T +   T , which corresponds to the  T carried by the  boson, is used in the 1-CR.Similarly,  ℓℓ T in the 2ℓ-CR corresponds to  miss T in the SR.

Figure 2 :
Figure 2: Data overlaid on SM background post-fit yields stacked in each SR and CR category and  miss T bin with the maximum-likelihood estimators set to the conditional values of the CR-only fit, and propagated to SR and CRs.The ratio of the data to SM expectations after the CR-only fit is shown in the lower panel, along with the red line representing the ratio of the pre-fit to the post-fit background prediction.Pre-fit uncertainties cover differences between the data and pre-fit background prediction.

Figure 3 :
Figure3: Distributions of the invariant mass of the dark Higgs boson candidates in the 1-CR and 2ℓ-CR (upper row) and in the SR (lower row) in two representative categories, after the fit to data.The upper panels compare the data with the SM expectation before and after the background-only fit.The lower panels display the ratio of data to SM expectations after the fit, with its systematic uncertainty.Also shown is the ratio of SM expectations before and after the fit.The expected signal, with a cross section of 214 fb, from a representative dark Higgs model with   = 0.25,   = 1.0, and sin  = 0.01, is scaled for presentation purposes.No    shape information in the CRs is considered in the fit.Pre-fit uncertainties cover differences between the data and pre-fit background prediction.

Figure 4 :
Figure 4: Observed (expected) exclusion regions at 95% C.L. for the dark Higgs model in the (  ,   ) plane, encircled by the solid (dashed) line.The expected ±1 (±2) uncertainty is shown as the filled green (yellow) band.The observed relic density[29] is obtained for   = 850 GeV (dotted line).