Search for Dark Matter Produced in Association with a Higgs Boson Decaying to $b\bar b$ using 36 fb$^{-1}$ of $pp$ collisions at $\sqrt s=13$ TeV with the ATLAS Detector

Several extensions of the Standard Model predict associated production of dark-matter particles with a Higgs boson. Such processes are searched for in final states with missing transverse momentum and a Higgs boson decaying to a $b\bar b$ pair with the ATLAS detector using 36.1 fb$^{-1}$ of $pp$ collisions at a center-of-mass energy of 13 TeV at the LHC. The observed data are in agreement with the Standard Model predictions and limits are placed on the associated production of dark-matter particles and a Higgs boson.

using calculations at next-to-next-to-leading order (NNLO) in QCD including next-to-next-to-leading logarithmic corrections for soft-gluon radiation [48].The single-top-quark processes are normalized with cross-sections at NLO in QCD [49][50][51][52][53]. Background processes involving a vector boson V = W, Z decaying leptonically in association with jets, V +jets, were simulated with Sherpa 2.2.1 [54] including mass effects for b-and c-quarks and using NNPDF3.0PDFs.The perturbative calculations for V + jets were performed at NLO for up to two partons and at leading order for up to four partons [55,56], and matched to the parton shower [57] using the ME+PS@NLO prescription from Ref. [58].The normalizations are determined at NNLO in QCD [59].Diboson processes (VV) were simulated at NLO in QCD with Sherpa 2.1.1 and CT10 PDFs.Backgrounds from associated Vh production were generated with Pythia 8.186 using NNPDF3.0PDFs for qq → Vh, and Powheg interfaced to Pythia 8.186 using CT10 PDFs for gg → Vh.
Events are selected by an E miss T trigger based on calorimeter information [60].Its threshold was 110 GeV for most of the data taking period, and lower in the first third.Events are required to have at least one pp collision vertex reconstructed from at least two inner detector (ID) tracks with p track T > 0.4 GeV.The primary vertex (PV) for each event is the vertex with the highest (p track T ) 2 .Reconstruction of muons (µ) incorporates tracks or track segments found in the muon spectrometer and matched ID tracks.Identified muons must satisfy the "loose" quality criteria [61] and have |η| < 2.7.Electrons (e) are reconstructed by matching an ID track to a cluster of energy in the calorimeter.Electron candidates are identified through a likelihood-based method [62] and must satisfy the "loose" operating point and be within |η| < 2.47.Muon and electron candidates must have p T > 7 GeV and are required to be isolated by limiting the sum of p T for tracks within a cone in ∆R around the lepton direction, as in Ref. [31].
Jets reconstructed from three-dimensional clusters of calorimeter cells [63] with the anti-k t algorithm [64] are used to identify the h → b b decay.For small to moderate h momenta, the decay products can be resolved using jets with a radius parameter R = 0.4 (small-R jets or j).The decay products of highmomenta h become collimated and are reconstructed using a single jet with R = 1.0 (large-R jet or J).Small-R jets with |η| < 2.5 must satisfy p T > 20 GeV and are called "central", while those with 2.5 < |η| < 4.5 must have p T > 30 GeV and are called "forward".Small-R jets are corrected for pileup [65], and central small-R jets with 20 GeV < p T < 60 GeV and |η| < 2.4 are additionally required to be identified as originating from the PV using associated tracks [66].Small-R jets closer than ∆R = 0.2 to an electron candidate are rejected.Large-R jets are reconstructed independently of small-R jets and trimmed [67,68] to reduce the effects of pileup and the underlying event.Furthermore, large-R jets must fulfill p T > 200 GeV and |η| < 2.0.To improve the resolution and minimize uncertainties, the mass of large-R jets is determined by the resolution-weighted mean of the mass measured using calorimeter information alone and the track-assisted jet mass [69].The latter is obtained by scaling the mass determined using ID tracks alone by the ratio of jet p T measured in the calorimeter and in the ID.
Multivariate algorithms are used to identify jets containing b-hadrons (b-tagging), which are expected in h → b b decays [68,70].These algorithms are applied directly to small-R jets, while for large-R jets they are applied to track-jets matched to large-R jets.Track-jets are reconstructed from ID tracks matched to the PV using the anti-k t algorithm with R = 0.2, and must fulfill p T > 10 GeV and |η| < 2.5.
The E miss T observable is calculated as the negative of the vector sum of the transverse momenta of e, µ, and jet candidates in the event.The transverse momenta not associated with any e, µ, or jet candidates are accounted for using ID tracks [71,72].Similarly, p miss,trk T is defined as the negative of the vector sum of the transverse momenta of tracks with p T > 0.5 GeV associated with the PV and within |η| < 2.5.
The signal is characterized by high E miss T , no isolated leptons, and an invariant mass of the h candidate m h compatible with the observed Higgs boson mass of 125 GeV [73].In the signal region (SR) described below, the dominant backgrounds from Z(νν) + jets, W + jets, and t t production contribute respectively 30-60%, 10-25%, and 15-50% of the total background, depending on E miss T and the b-tag multiplicity.The models for V + jets and t t are constrained using two control regions (CR): the single-muon control region (1µ-CR) is designed to constrain the t t and W + jets backgrounds, while the two-lepton control region (2 -CR) constrains the Z +jets background contribution.
The SR requires E miss T > 150 GeV, and no isolated e or µ.The multijet background contributes due to mismeasured jet momenta.To suppress it, additional selections are required: min ∆φ E miss T , p j T > π/9 for the three highest-p T (leading) small-R jets, ∆φ E miss T , p miss,trk T < π/2, and p miss,trk T > 30 GeV for events with fewer than two central b-tagged small-R jets.The requirements using p miss,trk T also reduce non-collision backgrounds.
In the "resolved" regime, defined by E miss T < 500 GeV, the h candidate is reconstructed from two leading b-tagged central small-R jets, or, if only one b-tag is present in the event, from the b-tagged central small-R jet and the leading non-b-tagged central small-R jet.At least one of the jets comprising the h candidate must satisfy p T > 45 GeV.A separation in ∆φ between the h candidate and E miss T of more than 2π/3 is required following the back-to-back configuration of the Higgs boson recoiling against DM.To improve the trigger efficiency modeling, events are retained only if the scalar sum H T of the p T of the two (three) leading jets fulfills H T,2 j > 120 GeV (H T,3 j > 150 GeV) if two (more than two) central jets are present.Further optimization of the event selection described below provides an additional background reduction of up to 60% relative to Ref. [31], for a small signal loss.Events with a hadronic τ-lepton candidate, identified either by an algorithm based on a boosted decision tree [74] or as small-R jets containing one to four tracks within the jet core and ∆φ E miss T , p j T < π/8, are rejected to reduce the t t background, which can enter the SR if at least one top quark decays as t → Wb → τνb.This background is further reduced by removing events with more than two b-tagged central jets, which typically happens for t t events with t → Wb → csb decays.Since most of the hadronic activity in a signal event is expected from the h → b b decay, the scalar sum of the p T of the two jets forming the h candidate and, if present, the highest-p T additional jet must be larger than 0.63 × H T,all jets .Finally, ∆R p j 1 h , p j 2 h < 1.8 is required for the two jets forming the h candidate.
In the "merged" regime, defined by E miss T > 500 GeV, the leading large-R jet represents the h candidate.Further selection optimization reduces backgrounds, primarily t t production, by up to 30% relative to Ref. [31], for a small signal loss: events containing τ-lepton candidates with ∆R p τ , p J > 1.0 are vetoed; no b-tagged central small-R jets with ∆R p j,b-tag , p J > 1.0 are allowed in the event; and the scalar sum of p T of the small-R jets with ∆R p j , p J > 1.0 is required to be smaller than 0.57 times that sum added to p J T .The resolution in m h is improved using muons associated with small-R jets in the resolved regime or with track-jets matched to large-R jets in the merged regime [68,75].
The event selection in the 1µ-CR is identical to the SR, except that exactly one isolated µ candidate with p µ T > 27 GeV is required, and that p µ T is added to E miss T to mimic the behavior of events contaminating the SR when the charged lepton is not detected.
Events in the 2 -CR are collected using a single-e or single-µ trigger, and selected by requiring one pair of isolated e or µ, one of which must have p T > 27 GeV.Events with a Z boson candidate are retained, The effect is expressed as the fractional uncertainty on the signal yield.Total is the quadrature sum of statistical and total systematic uncertainties.The impact of the luminosity uncertainty, which does not affect backgrounds with free normalizations, varies due to the changing background composition with increasing E miss T .
Source of uncert.identified as having 83 GeV < m ee < 99 GeV or 71 GeV < m µµ < 106 GeV with an opposite-charge requirement in the µµ case.In addition, a measure of the E miss T significance given by the ratio of the E miss T to the square root of the scalar sum of p T of all leptons and small-R jets in the event must be less than 3.5 GeV 1/2 .This requirement separates Z( )+jets processes from t t production, as E miss T originates from finite detector resolution for the former and mainly from neutrinos for the latter.To mimic Z → νν decays in the SR, the E miss T is set to the p T of the dilepton system, which is then ignored in the subsequent analysis.All other selection requirements are identical between the 2 -CR and the SR.
Subdominant backgrounds, including diboson, Vh, single top quark, and multijet production, contribute less than 10% of the total background in the SR.Multijet production is negligible for E miss T > 350 GeV.Its m h distribution is determined from data in a dedicated multijet-enriched sideband, defined by inverting the min ∆φ E miss T , p j T requirement.Dominant sources of experimental systematic uncertainty arise from the number of background MC events, the calibration of the b-tagging efficiency and integrated luminosity, as well as the scale and resolution of the energy and the mass of jets.Uncertainties associated with the τ vetoes are found to be negligible.Dominant sources of theoretical systematic uncertainty originate from the modeling of the signal and background processes such as t t, V +jets, Vh, diboson, and multijet production.The few relevant changes in the estimation of systematic uncertainties relative to Ref. [31] encompass: the improved calibrations of the b-tagging efficiency using t t events [68,70] as well as of the jet energy and mass scales using various in situ methods [69,76]; the reduced uncertainty from the new jet-mass observable [68,69]; and the uncertainty of 3.4% on the integrated luminosity of data collected in 2016.Table 1 quantifies dominant sources of uncertainty after the fit to data assuming three representative Z -2HDM-scenarios.This search is statistically limited for E miss T 300 GeV.
A fit to the m h observable based on a binned likelihood approach [77,78] is used to search for a signal.Systematic uncertainties are included in the likelihood function as nuisance parameters with Gaussian or categories that are used as inputs to the fit.The upper panels show a comparison of data to the SM expectation before (dashed lines) and after the fit (solid histograms) with no signal included.The lower panels display the ratio of data to SM expectations after the fit, with its systematic uncertainty considering correlations between individual contributions indicated by the hatched band.The expected signal from a representative Z -2HDM model is also shown (long-dashed line).log-normal constraints and profiled [75].To account for changes in the background composition and to benefit from a higher signal sensitivity with increasing E miss T and b-tag multiplicity, the data are split into categories that are fit simultaneously.Eight categories are defined for the SR and each of the two CRs: four ranges in E miss T /GeV as [150, 200), [200,350), [350, 500), and [500, ∞), which are each split into two subregions with one and two b-tags.In the 1µ-CR, the electric charge of the µ is used to separate t t from V + jets since the former provides an equal number of µ + and µ − , while a prevalence of µ + is expected from the latter process due to PDFs [79].Only the total event yield is considered in the 2 -CR due to limited data statistics.The normalizations of t t, W+HF, and Z+HF processes are free parameters in the fit, where HF represents jets containing b-or c-quarks.In the SR, the contribution from Z +jets is increased by about 50% by the fit relative to theory predictions, staying within uncertainties, while t t is reduced by up to 30% at high E miss T .The normalizations of other backgrounds modeled using MC simulations are constrained to theory predictions within uncertainties, as detailed in Ref. [31].
The distributions of m h for SR events with two b-tags provide the highest signal sensitivity and are shown in the four E miss T regions in Figure 1.No significant deviation from SM predictions is observed.
The results are interpreted as exclusion limits at 95% confidence level (CL) on the production crosssection of h + DM events σ h+DM times B(h → b b) with the CL s formalism [80] using a profile likelihood ratio [81] as test statistic.Exclusion contours in the (m Z , m A ) space in the Z -2HDM scenario are presented in Figure 2 2. To minimize the dependence on the E miss T distribution of a potential h + DM signal, the standard fit approach is modified to analyze one E miss T range at a time in the SR.The Z -2HDM model is used to evaluate the dependence of the σ vis,h(b b)+DM limits and of A × ε on the event kinematics within a given E miss T bin.A range of (m Z , m A ) parameters that yield a sizable contribution of 10% × σ h+DM × B(h → b b) in a given E miss T bin is considered.Corresponding variations of 25% (70%) in the expected limits and of 50% (25%) in A × ε are found in the resolved (merged) regime.Table 2 quotes the least stringent limit and the lowest A × ε value in a given E miss T bin after rounding.The limits are valid for p T,h 1.5 TeV.
In summary, a search for DM produced in association with a Higgs boson in final states with E miss T and a b b pair from the h → b b decay was conducted using 36.1 fb −1 of pp collisions at √ s = 13 TeV recorded by the ATLAS detector at the LHC.The results are in agreement with SM predictions, and a substantial region of the parameter space of a representative Z -2HDM model is excluded, significantly improving upon previous results.Stringent limits are also placed on the production cross-section of non-SM events with large E miss T and a Higgs boson without extra model assumptions.
We thank CERN for the very successful operation of the LHC, as well as the support staff from our institutions without whom ATLAS could not be operated efficiently.

Figure 1 :
Figure 1: Distributions of the invariant mass of the Higgs boson candidates m h = m j j , m J with two b-tags in the SR for the four E miss T

Figure 2 :
Figure 2: Exclusion contours for the Z -2HDM scenario in the (m Z , m A ) plane for tan β = 1, g Z = 0.8, and m χ = 100 GeV.The observed limits (solid line) are consistent with the expectation under the SM-only hypothesis (dashed line) within uncertainties (filled band).Observed limits from previous ATLAS results at √ s = 13 TeV (dash-dotted line) [31] are also shown.

Table 2 :
Observed (obs) and expected (exp) upper limits at 95% CL on σ vis,h(b b)+DM ≡ σ h+DM × B(h → b b) × A × ε of h(b b) + DM events.Also shown are the acceptance × efficiency (A × ε) probabilities to reconstruct and select an event in the same E miss T bin as generated.Range in σ obs vis,h(b b)+DM σ exp vis,h(b b)+DM particles.For this, limits are set on σ vis,h(b b)+DM ≡ σ h+DM × B(h → b b) × A × ε of h(b b) + DM events per E miss T bin at detector level, after all SR selections except the requirements on b-tag multiplicity and m h range as used in the fit.The A × ε term quantifies the probability for an event to be reconstructed in the same E miss T bin as generated and to pass all σ vis,h(b b)+DM selections, where A represents the kinematic acceptance and ε accounts for the experimental efficiency.The results are shown in Table and NSFC, China; COLCIENCIAS, Colombia; MSMT CR, MPO CR and VSC CR, Czech Republic; DNRF and DNSRC, Denmark; IN2P3-CNRS, CEA-DSM/IRFU, France; SRNSF, Georgia; BMBF, HGF, and MPG, Germany; GSRT, Greece; RGC, Hong Kong SAR, China; ISF, I-CORE and Benoziyo Center, Israel; INFN, Italy; MEXT and JSPS, Japan; CNRST, Morocco; NWO, Netherlands; RCN, Norway; MNiSW and NCN, Poland; FCT, Portugal; MNE/IFA, Romania; MES of Russia and NRC KI, Russian Federation; JINR; MESTD, Serbia; MSSR, Slovakia; ARRS and MIZŠ, Slovenia; DST/NRF, South Africa; MINECO, Spain; SRC and Wallenberg Foundation, Sweden; SERI, SNSF and Cantons of Bern and Geneva, Switzerland; MOST, Taiwan; TAEK, Turkey; STFC, United Kingdom; DOE and NSF, United States of America.In addition, individual groups and members have received support from BCKDF, the Canada Council, CANARIE, CRC, Compute Canada, FQRNT, and the Ontario Innovation Trust, Canada; EPLANET, ERC, ERDF, FP7, Horizon 2020 and Marie Skłodowska-Curie Actions, European Union; Investissements d'Avenir Labex and Idex, ANR, Région Auvergne and Fondation Partager le Savoir, France; DFG and AvH Foundation, Germany; Herakleitos, Thales and Aristeia programmes co-financed by EU-ESF and the Greek NSRF; BSF, GIF and Minerva, Israel; BRF, Norway; CERCA Programme Generalitat de Catalunya, Generalitat Valenciana, Spain; the Royal Society and Leverhulme Trust, United Kingdom.