Search for the standard model Higgs boson in +jets final states in 9.7 fb of collisions with the D0 detector
We present, in detail, a search for the standard model Higgs boson, , in final states with a charged lepton (electron or muon), missing energy, and two or more jets in data corresponding to 9.7 fb of integrated luminosity collected at a center of mass energy of = 1.96 TeV with the D0 detector at the Fermilab Tevatron Collider. The search uses -jet identification to categorize events for improved signal versus background separation and is sensitive to associated production of the with a boson, ; gluon fusion with the Higgs decaying to boson pairs, ; and associated production with a vector boson where the Higgs decays to boson pairs, production (where or ). We observe good agreement between data and expected background. We test our method by measuring and production with and find production rates consistent with the standard model prediction. For a Higgs boson mass of 125 GeV, we set a 95% C.L. upper limit on the production of a standard model Higgs boson of 5.8, where is the standard model Higgs boson production cross section, while the expected limit is 4.7. We also interpret the data considering models with fourth generation fermions, or a fermiophobic Higgs boson.
The D0 Collaboration111with visitors from Augustana College, Sioux Falls, SD, USA, The University of Liverpool, Liverpool, UK, UPIITA-IPN, Mexico City, Mexico, DESY, Hamburg, Germany, SLAC, Menlo Park, CA, USA, University College London, London, UK, Centro de Investigacion en Computacion - IPN, Mexico City, Mexico, ECFM, Universidad Autonoma de Sinaloa, Culiacán, Mexico, Universidade Estadual Paulista, São Paulo, Brazil, Karlsruher Institut für Technologie (KIT) - Steinbuch Centre for Computing (SCC) and Office of Science, U.S. Department of Energy, Washington, D.C. 20585, USA. Visitor from Bradley University, Peoria, IL, USA.
The Higgs boson is the massive physical state that emerges from electroweak symmetry breaking in the Higgs mechanism Englert:1964et ; Higgs:1964pj ; Guralnik:1964eu . This mechanism generates the masses of the weak gauge bosons and explains the fermion masses through their Yukawa couplings to the Higgs boson field. The mass of the Higgs boson () is a free parameter in the standard model (SM). Precision measurements of various SM electroweak parameters constrain to be less than GeV at the 95% C.L. Aaltonen:2012bp ; Abazov:2012bv ; bib:LEPEWWG . Direct searches at the CERN Collider (LEP) Barate:2003sz exclude GeV at the 95% C.L. The ATLAS and CMS Collaborations, using collisions at the CERN LHC, exclude masses from GeV, except for a narrow region between 122 and 127 GeV Atlas-jul2012 ; CMS-PAS-HIG-12-008 . Both experiments observe a resonance at a mass of GeV, primarily in the and final states, with a significance greater than 5 standard deviations (s.d.) that is consistent with SM Higgs boson production atlas-obs ; cms-obs . The CDF and D0 Collaborations at the Fermilab Tevatron Collider report a combined analysis that excludes the region GeV CDFandD0:2012aa and shows evidence at the 3 s.d. level for a particle decaying to , produced in association with a or boson, consistent with SM production tevatron-bbbar . Demonstrating that the observed resonance is the SM Higgs boson requires also observing it at the predicted rate in the final state, which is the dominant decay mode for masses below GeV.
The dominant production process for the Higgs boson at the Tevatron Collider is gluon fusion (), followed by the associated production of a Higgs boson with a vector boson (), then via vector boson fusion (). At masses below GeV, the Higgs boson mainly decays to a pair of quarks, while for larger masses, the dominant decay is to a pair of bosons. Because the process is difficult to distinguish from background at hadron colliders, it is more effective to search for the Higgs boson produced in association with a vector boson for this decay channel.
This Article presents a search by the D0 collaboration for the SM Higgs boson using events containing one isolated charged lepton ( or ), a significant imbalance in transverse energy (), and two or more jets. It includes a detailed description of the search, initially presented in Ref. Abazov:2012wh97 and used as an input to the result presented in Ref. tevatron-bbbar , differing from and superseding that result due to an updated treatment of some systematic uncertainties as described in Sec. X below. The complete analysis comprises searches for the production and decay channels: , (where ), and (where or ). This search also considers contributions from production and from the decay when one of the charged leptons from decay is not identified in the detector. We optimize the analysis by subdividing data into mutually exclusive subchannels based on charged lepton flavor, jet multiplicity, and the number and quality of candidate quark jets. This search also extends the most recent D0 search Abazov:2012wh97 by adding subchannels with looser -quark jet identification requirements and subchannels with four or more jets. These additional subchannels are primarily sensitive to and production and extend the reach of our search to GeV. We present a measurement of production with as a cross check on our methodology in Sec. XI. In addition to our standard model interpretation, we consider interpretations of our result in models with a fourth generation of fermions, and models with a fermiophobic Higgs as described in Sec. XIII.
Several other searches for production have been reported at a center-of-mass energy of TeV, most recently by the CDF Collaboration Aaltonen:2012wh . The results presented here supersede previous searches by the D0 Collaboration, presented in Refs. Abazov:2005aa ; Abazov:2007hk ; Abazov:2008eb ; Abazov:2010hn ; Abazov:2012wh , which used subsamples of the data presented in this Article. They also supersede a previous search for Higgs boson production in the final state by the D0 Collaboration Abazov:2011bc .
Ii The D0 Detector
This analysis relies on all major components of the D0 detector: tracking detectors, calorimeters, and muon identification system. These systems are described in detail in Ref. Abachi:1993em ; Abazov:2005pn ; Abolins:2007yz ; Angstadt:2009ie .
Closest to the interaction point is the silicon microstrip tracker (SMT) followed by the central scintillating fiber tracker (CFT). These detector subsystems are located inside a 2 T magnetic field provided by a superconducting solenoid. They track charged particles and are used to reconstruct primary and secondary vertices for pseudorapidities defseta of . Outside the solenoid is the liquid argon/uranium calorimeter consisting of one central calorimeter (CC) covering and two end calorimeters (EC) extending coverage to . Each calorimeter contains an innermost finely segmented electromagnetic layer followed by two hadronic layers, with fine and coarse segmentation, respectively. The main functions of the calorimeters are to measure energies and help identify electrons, photons, and jets using coordinate information of significant energy clusters. They also give a measure of the . A preshower detector between the solenoidal magnet and central calorimeter consists of a cylindrical radiator and three layers of scintillator strips covering the region . The outermost system provides muon identification. It is divided into a central section that covers and forward sections that extend coverage out to . The muon system is composed of three layers of drift tubes and scintillation counters, one layer before and two layers after a 1.8 T toroidal magnet.
Iii Event Trigger
Events in the electron channel are triggered by a logical OR of triggers that require an electromagnetic object and jets, as described in Ref. Abazov:2012wh . Trigger efficiencies are modeled in the Monte Carlo (MC) simulation by applying the trigger efficiency, measured in data, as an event weight. This efficiency is parametrized as a function of electron , azimuthal angle defphi , and transverse momentum . For the events selected in our analysis, these triggers have an efficiency of depending on the trigger and the region of the detector.
The muon channel uses an inclusive trigger approach, based on the logical OR of all available triggers, except those containing lifetime-based requirements that can bias the performance of -jet identification. To determine the trigger efficiency, we compare data events selected with a well-modeled logical OR of the single muon and muon+jets triggers (), which are about 70% efficient, to events selected using all triggers. The increase in event yield in the inclusive trigger sample is used to determine an inclusive trigger correction for the MC trigger efficiency, , relative to the trigger ensemble:
where the numerator is the difference between the number of data events in the inclusive trigger sample and the trigger sample, after subtracting off instrumental multijet (MJ) backgrounds, and the denominator is the number of MC events (after the event selection and normalization to data described in Sec. VIII and the MC corrections are applied as described in Sec. VI.1) with the trigger efficiency set to 1. The total trigger efficiency estimate for events in the muon channel is , limited to be .
Triggers based on jets and make the most significant contributions to the inclusive set of triggers beyond those included in the well-modeled trigger set. To account for these contributions, the correction from triggers to the inclusive set of triggers is parametrized as a function of the scalar sum of the transverse momenta of all jets, , and the , and is derived for separate regions in muon .
For , events are dominantly triggered by single muon triggers, while for , triggers based on the logical OR of muon+jets prevail. The third region, , is a mixture of single muon and muon+jets triggers. In the and regions the detector support structure allows only partial coverage by the muon system. This impacts the muon trigger efficiency in the region . In these regions, we therefore derive separate corrections. The inclusive trigger approach results in a gain of about 30% in efficiency over using only muon and the muon+jets triggers. Examples of these corrections, are shown in Fig. 1.
Iv Identification of Leptons, Jets,
To reconstruct the candidate boson, our selected events are required to contain a single identified electron or muon together with significant . To ensure statistical independence with channels that contain more than one lepton, we do not consider events with more than one electron or muon. Two or more jets are also required in order to study , , and production. Two sets of lepton identification criteria are applied for each lepton channel in order to form a “loose” sample, used to estimate the multijet background from data as described in Sec. VII, and a “tight” sample used to perform the search. The event selection procedure, prior to -jet categorization, is similar to that described in Ref. Abazov:2012wh and described in more detail below.
Electrons with GeV are selected in the pseudorapidity regions and , corresponding to the CC and EC, respectively. A multivariate discriminant is used to identify electrons. The discriminant is based on a boosted decision tree narsky-0507157 ; Breiman1984 ; schapire01boostapproach ; schapireFreund ; friedman (BDT) as implemented in the tmva package Hocker:2007ht with input variables that are listed below. The BDTs are discussed in more detail in Sec. IX. The loose and tight electron samples are defined by different requirements on the response of this multivariate discriminant that are chosen to retain high electron selection efficiencies while suppressing backgrounds at differing rates.
Leptons coming from the leptonic decays of bosons tend to be isolated from jets. Isolated electromagnetic showers are identified within a cone in - space of defsDR . In the CC (EC), an electromagnetic shower is required to deposit of its total energy within a cone of radius in the electromagnetic calorimeter. The showers must have transverse and longitudinal distributions that are consistent with those expected from electrons. In the CC region, a reconstructed track, isolated from other tracks, is required to have a trajectory that extrapolates to the electromagnetic (EM) shower. The isolation criteria restrict the sum of the scalar of tracks with GeV within a hollow cone of radius surrounding the electron candidate to be less than 2.5 GeV. The BDT is constructed using additional information such as: the number and scalar sum of tracks in the cone of radius surrounding the candidate cluster, track-to-cluster-matching probability, the ratio of the transverse energy of the cluster to the transverse momentum of the track associated with the shower, the EM energy fraction, lateral and longitudinal shower shape characteristics, as well as the number of hits in the various layers of the tracking detector, and information from the central preshower detector. The discriminants are trained using data events.
We select muons with GeV and . They are required to have reconstructed track segments in layers of the muon system both before and after the toroidal magnet, except where detector support structure limits muon system coverage, for which the presence of track segments in any layer is sufficient. The local muon system track must be spatially matched to a track in the central tracker.
Muons originating from semi-leptonic decays of heavy flavored hadrons are typically not isolated due to jet fragmentation and secondary particles from the partial hadronic decays. We employ a loose muon definition, requiring minimal separation of between the muon and any jet, while the tight identification has additional isolation requirements. For tight muons, the scalar sum of the of tracks with around the muon candidate is required to be less than . Furthermore, the transverse energy deposits in the calorimeter in a hollow cone of around the muon must be less than . To suppress cosmic ray muons, scintillator timing information is used to require hits in the detector to coincide with a beam crossing.
To reduce backgrounds from jets and production, we reject events containing more than one tight-isolated charged lepton.
Jets are reconstructed in the calorimeters in the region using an iterative midpoint cone algorithm, with a cone size of Blazey:2000qt . To minimize the possibility that jets are caused by noise or spurious energy deposits, the fraction of the total jet energy contained in the electromagnetic layers of the calorimeter is required to be between 5% and 95%, and the energy fraction in the coarse hadronic layers of the calorimeter is required to be less than 40%. To suppress noise, different energy thresholds are also applied to clustered and to isolated cells Abazov:2011vi . The energy of the jets is scaled by applying a correction determined from jet events using the same jet-finding algorithm. This scale correction accounts for additional energy (e.g., residual energy from previous bunch crossings and energy from multiple interactions) that is sampled within the finite cone size, the calorimeter energy response to particles produced within the jet cone, and energy flowing outside the cone or moving into the cone via detector effects Abazov:2011vi . We also apply an additional correction that accounts for the flavor composition of jets Abazov:2011ck .
Jet energy calibration and resolution are adjusted in simulated events to match those measured in data. This correction is derived from jet events from the imbalance between the boson and the recoiling jet in MC simulation when compared to that observed in data, and applied to jet samples in MC events. Differences in reconstruction thresholds in simulation and data are also taken into account, and the jet identification efficiency and jet resolution are adjusted in the simulation to match those measured in data. All selected jets are required to have GeV and . We require that jets originate from the primary vertex (PV), such that each selected jet is matched to at least two tracks with GeV that have at least one hit in the SMT detector and a distance of closest approach with respect to the PV of less than 0.5 cm in the transverse plane and less than 1 cm along the beam axis (). Interaction vertices are reconstructed from tracks that have GeV with at least two hits in the SMT. The primary vertex is the reconstructed vertex with the highest average of its tracks. Vertex reconstruction is described in more detail in Ref. Abazov:2010ab . We also require that the PV be reconstructed within of the center of the detector.
The is calculated from individual calorimeter cell energies in the electromagnetic and fine hadronic sections of the calorimeter and is required to satisfy GeV for the electron channel and GeV for the muon channel. Energy from the coarse hadronic layers that is contained within a jet is also included in the calculation. A correction for the presence of any muons and all energy corrections applied to electrons and jets are propagated to the value of .
V Tagging of -Quark Jets
The -tagging algorithm for identifying jets originating from quarks is based on a multivariate discriminant using a combination of variables sensitive to the presence of tracks or secondary vertices displaced significantly in the - plane from the interaction vertex. This algorithm provides improved performance over the neural network algorithm described in Ref. Abazov:2010ab .
Jets considered by the -tagging algorithm are required to be “taggable,” i.e., contain at least two tracks with each having at least one hit in the SMT. The efficiency of this requirement accounts for variations in detector acceptance and track reconstruction efficiencies at different locations of the PV prior to the application of the -tagging algorithm, and depends on the position of the PV and the and of the jet. For jets that pass through the geometrical acceptance of the tracking system, this efficiency is typically about 97%. The efficiency for -tagging is determined with respect to taggable jets. The correction for taggability is measured in the selected data sample, while the corrections for -tagging are determined in an independent heavy-flavor jet enriched sample of events that include a jet containing a muon, as described in Ref. Abazov:2010ab . The efficiency for jets to be taggable and to satisfy -tagging requirements in the simulation is corrected to reproduce the respective efficiencies in data.
We define six independent tagging samples with zero, one loose, one tight, two loose, two medium, or two tight -tagged jets. An inclusive “pretag” sample is also considered for parts of this analysis. Events with no jets satisfying the -tagging criteria are included in the zero -tag sample. If exactly one jet is -tagged, and the -identification discriminant output for that jet, , satisfies the tight selection threshold (), that event is considered part of the one tight -tag sample. Events with exactly one -tagged jet that fails the tight selection threshold, but passes the loose selection threshold () are included in the one loose -tag sample. Events with two or more -tagged jets are assigned to either the two loose -tags, two medium -tags, or two tight -tags category, depending on the value of the average -identification discriminant of the two jets with the highest discriminant values, i.e., the double tight category is required to satisfy ; the medium category is ; and the loose category is (see Fig. 2). The operating point for the loose (medium, tight) threshold has an identification efficiency of 79% (57%, 47%) for individual jets, averaged over selected jet and distributions, with a -tagging misidentification rate of 11% (0.6%, 0.15%) for light quark jets (), calculated by the method described in Ref. Abazov:2010ab .
Vi Monte Carlo Simulation
We account for all Higgs boson production and decay processes that can lead to a final state containing exactly one charged well isolated lepton, , and two or more jets. The signal processes considered are:
Associated production of a Higgs boson with a vector boson where the Higgs boson decays to , , , or . The associated weak vector boson decays leptonically in the case of and either leptonically or hadronically in the case of . Contributions from production arise from identifying only one charged lepton in the detector, with the other contributing to the .
Higgs boson production via gluon fusion with the subsequent decay , where one weak vector boson decays leptonically (with exactly one identified lepton).
Higgs boson production via vector boson fusion with the subsequent decay , where one weak vector boson decays leptonically (with exactly one identified lepton).
Various SM processes can mimic expected signal signatures, including jets, diboson (), MJ, , and single top quark production.
All signal processes and most of the background processes are estimated from MC simulation, while the MJ background is evaluated from data, as described in Sec. VII. We use pythia Sjostrand:2006za to simulate all signal processes and diboson processes. The jets and samples are simulated with the alpgen Mangano:2002ea MC generator interfaced to pythia for parton showering and hadronization, while the singletop event generator Boos:2004kh ; Boos:2006af interfaced to pythia is used for single top quark events. To avoid overestimating the probability of further partonic emissions in pythia, the MLM factorization (“matching”) scheme Alwall:2007fs is used. All of these simulations use CTEQ6L1 Lai:1996mg ; Pumplin:2002vw parton distribution functions (PDF).
A full geant-based geant detector simulation is used to process signal and background events. To account for residual activity from previous beam crossings and contributions from the presence of additional interactions, events from randomly selected beam crossings with the same instantaneous luminosity profile as the data are overlaid on the simulated events. All events are then reconstructed using the same software as used for data.
The signal cross sections and branching fractions are normalized to the SM predictions CDFandD0:2012aa . The and cross sections are calculated at next-to-next-to-leading order (NNLO) Baglio:2010um , with MSTW2008 NNLO PDFs Martin:2009iq . The gluon fusion process uses the NNLO+next-to-next-to-leading log (NNLL) calculation deFlorian:2009hc , and the vector boson fusion process is calculated at NNLO in QCD Bolzoni:2011cu . The Higgs boson decay branching fractions are obtained with hdecay Djouadi:1997yw ; Butterworth:2010ym . We use NLO cross sections to normalize single top quark Kidonakis:2006bu and diboson Campbell:1999ah ; mcfm_code production, while we use an approximate NNLO calculation for production Langenfeld:2009wd . The of the boson in jets events is corrected to match that observed in data Abazov:2007jy . The of the boson in +jets events is corrected using the same dependence but taking into account the differences between the spectra of the and bosons in NNLO QCD Melnikov:2006kv . Additional scale factors to account for higher order terms in the alpgen MC for the +heavy flavor jets, , are obtained from mcfm Campbell:2001ik ; mcfm_code . The +jets processes are then normalized to data for each lepton flavor and jet multiplicity separately as described in Sec. VIII.
vi.1 MC Reweighting
Motivated by previous comparisons of alpgen with data Abazov:2008ez and with other event generators Alwall:2007fs , we develop corrections to and MC samples to correct for the shape discrepancies in kinematic distributions between data and simulation. The corrections are derived based on the direct comparison between data and MC samples prior to the application of -tagging, where any contamination from signal is very small.
To improve the description of jet directions, we correct the distributions of the leading and second leading jets in +jets events. The correction function is a fourth-order polynomial determined from the ratio of the +jets events in MC and data minus non-+jets backgrounds. The modeling of the lepton in +jets events is adjusted by applying a second-order polynomial correction. Correlated discrepancies observed in the leptonically decaying boson transverse momentum, , and the jet angular separation, , are corrected through two reweighting functions in the two-dimensional - plane Abazov:2012wh . The reweighting is applied only to events, while the reweighting is applied to both and events. Each of these corrections is designed to change differential distributions, but to preserve normalization. Corrections are on the order of a few percent in the highly populated region of each distribution and may exceed 10% for extreme values of each distribution.
All corrections are derived in events selected with muon+jets triggers to minimize uncertainties due to contamination from MJ events, and are applied to both the electron and muon channels. Additional , , and lepton corrections and corresponding systematic uncertainties are determined from events selected with inclusive muon triggers and are applied to events containing muons, accounting for variations in modeling distributions of the inclusively triggered events.
Vii Multijet Background
The MJ background, events where a jet is misidentified as a lepton, is determined from the data prior to the application of -tagging, using a method similar to the one used in Ref. Abazov:2012wh . This method involves applying event weights that depend on the relative efficiency , of a lepton passing loose requirements to subsequently pass the tight requirements and a similar relative probability, , for a MJ event to pass these sequential selections. A MJ template is constructed by selecting events from data in which the lepton passes the loose isolation requirement, but fails the tight requirement, as described in Sec. IV. Each event in the MJ template is weighted by
where is a function of the event kinematics. Since the MJ template contains a contribution from events with real leptons originating from leptonic decays of bosons, we correct the normalization of the +jets MC using the event weight
where and are functions of event kinematics. The efficiencies are functions of lepton , and they are determined from events. The probabilities are determined in the region GeV from the measured ratio of the number of events with tight leptons and those with loose leptons after correcting each sample for the expected MC contribution from real leptons in the specific kinematic interval. Electron channel probabilities are parametrized in , calorimeter detector , and while probabilities in the muon channel are parametrized in for different regions in muon detector and .
Viii Event Selection
Events are required to have one isolated charged lepton, large , and two or more jets, as described in Sec. IV. To suppress MJ backgrounds, events must satisfy the additional requirement that , where is the transverse mass defwtm of the boson. We then perform the final normalization of the +jets and MJ backgrounds via a simultaneous fit to data in the distribution after subtracting the other SM background predictions from the data as described in Refs. Abazov:2012wh97 ; Abazov:2010hn ; Abazov:2012wh . The distribution of after this normalization procedure is shown in Fig. 3(a). We perform separate fits for each lepton flavor and jet multiplicity category before dividing events into categories based on the number and quality of identified jets, as described in Sec. V. All events passing these selection criteria constitute the pretag sample, and each pretag event also belongs to exactly one of the six independent -tag categories. Only the zero and one-loose -tag categories are considered when searching for the signal in events with four or more jets because production dominates the small amount of signal present in higher -tag categories.
The expected number of events from each signal and background category is compared to the observed data for each -jet identification category for events with two jets, three jets, and four or more jets in Tables 1, 2, and 3, respectively. Selected kinematic distributions are shown for all selected events in Figs. 3 and 4, and the dijet invariant mass for events with two jets is shown for all -tag categories in Figs. 5 and 6. In all plots, data points are shown with error bars that reflect the statistical uncertainty only. Discrepancies in data-MC agreement are within our systematic uncertainties described in Sec. X.
|Pretag||0 -tags||1 loose -tag||1 tight -tag||2 loose -tags||2 med. -tags||2 tight -tags|
|-jets||182 271||148 686||26 421||6174||1762||132||13|
|27 443||15 089||4872||5236||978||691||691|
|top ( + single top)||3528||758||455||1289||247||333||462|
|Multijet||58 002||43 546||9316||3700||946||298||195|
|Total expectation||276 930||212 114||42 032||16 935||4043||1496||1400|
|Total uncertainty||14 998||11 352||2438||1696||362||117||175|
|Observed events||276 929||211 169||42 774||16 406||4057||1358||1165|
|Pretag||0 -tags||1 loose -tag||1 tight -tag||2 loose -tags||2 med. -tags||2 tight -tags|
|-jets||24 086||18 078||4577||976||582||34||3|
|top ( + single top)||3695||563||419||1123||365||460||570|
|Total expectation||45 908||29 209||8746||4395||1768||867||830|
|Observed events||45 907||28 924||8814||4278||1815||879||797|
|Pretag||0 -tags||1 loose -tag|
|top ( + single top)||2889||311||268|
Ix Multivariate Signal Discriminants
We employ multivariate analysis (MVA) techniques to separate signal from background events. To separate signal from the MJ events, we use a boosted decision tree implemented with the tmva package Hocker:2007ht . This multivariate analysis is described in Sec. IX.1. A BDT is also used to separate signal from other specific background sources in events with four or more jets (see Sec. IX.4). For the final multivariate analysis, we use a BDT in the one tight -tag channel and all three two -tag channels, and we use a random forest decision tree (RF) Breiman:2001:RF:570181.570182 implemented in the statpatternrecognition (SPR) package narsky-0507143 ; narsky-0507157 for events in the zero and one loose -tag channels.
The BDT and the RF are forms of machine learning techniques known as decision trees. Decision trees operate on a series of yes/no splits on events that are known to be classified as either signal or background. The splitting is done to maximally separate signal from background. The resulting nodes are continually split to optimally separate signal from background until either a minimum number of events in a node is reached or the events in a node are pure signal or pure background. The technique of boosting in the BDT builds up a series of trees where each tree is retrained, boosting the weights for events that are misclassified in the previous training. The RF technique creates a collection of decision trees where each tree is trained on a subset of the training data that is randomly sampled.
We train separate BDTs and RFs for each lepton flavor, jet multiplicity, and tagging category, and for each hypothesized Higgs boson mass in steps of 5 GeV. Since the branching fraction for the Higgs decay to quarks is only significant over the mass range 90–150 GeV, we restrict the search in the one tight and two -tag channels to this range of . In the zero and one loose -tag channels, the primary signal contribution is from Higgs decays to vector bosons, the search is performed over the mass range of 100–200 GeV.
Each of the final BDTs and RFs are trained to distinguish the signal from all of the backgrounds. We choose variables to train the BDTs and RFs that have good agreement between data and background simulation (since the expected contribution from signal events is small), and so that there is a good separation between signal and at least one background. Background and signal samples are each split into three independent samples for use in training, testing, and performing the final statistical analysis with each multivariate discriminant. We ensure that the discriminant is not biased towards statistical fluctuations in the training sample by comparing the training output to the testing sample. The independent sample used for the limit setting procedure ensures that any optimizations performed based on the output of the training and testing samples do not bias the final limits.
ix.1 Multivariate multijet discriminators
We train two separate BDTs to separate the MJ background from signal events: one for signals, , and one for signals, . The variables used in training these BDTs are chosen to exploit kinematic differences between the MJ and signal events, and are documented in Appendix A. To improve the training statistics, we combine signal events for , 125, and 130 GeV in training. We find that a BDT trained on this combination of Higgs boson masses has a similar performance when applied to other masses, eliminating the need for a mass dependent MJ discriminant. The BDT outputs and are shown in Fig. 7. The and discriminant outputs are used as input variables to the final MVAs, as detailed in Appendix A.
ix.2 Final MVA analysis
In events with two or three jets and one tight -tag or two -tags, the process provides the dominant signal contribution. To separate signal from background, we train a BDT on the signal and all backgrounds. The lists of input variables to the MVA and their descriptions are included in Appendix A. Figures 8 and 9 show examples of some of the most effective discriminating variables used in our BDTs for the two-jet and three-jet channels, respectively, in the one tight -tag and all two -tags channels. Figures 10 and 11 show the BDT output for the two and three-jet channels, respectively, in the one tight -tag and all the two -tag channels.
ix.3 Final MVA analysis
The process provides the dominant signal in events with two or three jets and zero -tags or one loose -tag, since the boson decays producing a quark are rare. For signal searches in these channels, we apply a multivariate technique based on the RF discriminant. Events in the above tagging categories are examined for GeV. Since we do not perform the search in the one tight and two -tag channels for GeV, events having exactly two or three jets in all -tagging categories (i.e. pretag events) are used in the search for GeV.
To suppress MJ background in the electron channel in these subchannels, we select events with for GeV in events with zero or one loose tag, and for GeV in all events. These requirements were optimized to maximize the ratio of number of signal events to the square root of the number of background events. The MJ component in the zero or one loose -tag muon channel is small, so there is no cut applied to the MJ MVA outputs.
We train a RF on the total signal and background from all considered physics processes. We optimize the RF independently in the electron and muon channels for each -tag and jet multiplicity category. As the signal shape is strongly driven by the signal mass hypothesis, we optimize the MVA variable list at two different mass points: at GeV for masses below 150 GeV and at GeV for masses above 150 GeV. Because the resolution of the reconstructed Higgs boson mass is about 20 GeV for channels presented in this Article, optimizing the input variable list at only these mass points is sufficient. Each RF is trained using between 14 and 30 well modeled discriminating variables formed from kinematic properties of either elementary objects like jets or leptons, or composite objects, such as reconstructed boson candidates (see Figs. 12 and 13). The lists of input variables and their descriptions are included in Appendix A. The final RF discriminants for the electron and muon channels are shown in Figs. 14 and 15.
ix.4 Final MVA analysis
The majority of signal events with four or more jets and zero -tags or one loose -tag are from the process, but there are significant contributions from direct production via gluon fusion and vector boson fusion. Identification of the Higgs boson decay products in events is complicated by the combinatorics of pairing four jets into two hadronically decaying vector boson candidates and then two of the three total vector boson candidates into the Higgs boson candidate. The discriminating variables are different for fully hadronic and semileptonic Higgs boson decays, and determining the Higgs boson candidate for an event also determines which of these two decay scenarios is considered. Variables unique to a particular decay scenario are set to a default value outside of the physical range of that variable in events reconstructed under the alternate decay scenario. To reconstruct the two hadronically decaying vector boson candidates, we examine the leading four jets in an event and choose the jet pairings that minimize:
where () is the invariant mass of the and ( and ) jets, and GeV Beringer:2012 . The Higgs boson candidate is then determined by considering the semileptonically decaying boson and the two hadronically decaying vector bosons and selecting the vector boson candidate pair with the minimum separation in an event, out of the three possible pairings.
Diverse signal processes contribute to the inclusive four-jet channel with relative contributions varying with . To help mitigate the effect of having many signal and background contributions to this search channel, we use two layers of multivariate discriminants to improve the separation of signal from background. The first layer of training focuses on separating the sum of all signal processes from specific sets of backgrounds. Input variables for each background-specific discriminant are selected based on the separation power between the total signal and the backgrounds being considered. Background-specific discriminants are trained to separate the sum of all Higgs boson signal processes from three specific background categories: and single top quark production, +jets production, and diboson production. The input variables and their descriptions are listed in Appendix A. Separate background-specific discriminants are trained for each Higgs boson mass point considered. Sample inputs and output responses of the background-specific discriminants are shown in Figs. 16 and 17, respectively, for GeV.
The background-specific discriminants are used as inputs to the final RF discriminant that is trained to discriminate all signal processes from the total background contributions. Additional input variables for the final discriminant are selected based on their separation power between the total signal and the total background, and are required to be well modeled. The input variables for each lepton and -tag category are listed in Appendix A. Sample inputs and output responses of the final discriminants are shown in Figs. 18 and 19, respectively, for GeV.
X Systematic Uncertainties
We assess systematic uncertainties on signals and backgrounds for each of the jet multiplicity and -tag channels by repeating the full analysis after varying each source of uncertainty by s.d. We consider uncertainties that affect both the normalizations and the shapes of our MVA outputs.
We include theoretical uncertainties on the and single top quark production cross sections (7% Langenfeld:2009wd ; Kidonakis:2006bu ), diboson production cross section (6% Campbell:1999ah ), production (6%), and production (20%, estimated from mcfm Campbell:2001ik ; mcfm_code ). Since the +jets experimental scaling factors for the three- and four-jet channels are different from unity, we apply an additional systematic uncertainty on the +jets samples that is uncorrelated across jet multiplicity and lepton flavor bins. The size of this uncertainty is taken as the uncertainty from the +jets fit to data, described in Sec. VII.
An uncertainty on the integrated luminosity (6.1% Andeen:2007zc ) affects the normalization of the expected signal and simulated backgrounds. Uncertainties that affect the final MVA distribution shapes include jet taggability (3% per jet), -tagging efficiency (2.5%–3% per heavy-quark jet), the light-quark jet misidentification rate (10% per jet), jet identification efficiency (5%), and jet energy calibration and resolution (varying between 5% and 15%, depending on the process and channel) as described in Ref. Abazov:2012wh . We also include uncertainties from modeling that affect both the shapes and normalizations of the final MVA distributions. These include an uncertainty on the trigger efficiency in the muon channel as derived from the data (3%–5%), lepton identification and reconstruction efficiency (5%–6%), the MLM matching Mangano:2002ea applied to +light-flavor events (%), the alpgen renormalization and factorization scales, and the choice of parton distribution functions (2%) as described in Ref. Abazov:2012wh . The trigger uncertainty in the muon channel is calculated as the difference between applying a trigger correction calculated using the alpgen reweightings derived on the trigger sample and applying the nominal trigger correction. Since we reweight our alpgen samples, we include separate uncertainties on each of the five functions used to apply the reweighting. The adjusted functions are calculated by shifting the parameter responsible for the largest shape variation of the fit by s.d. then calculating the remaining parameters for the function using the covariance matrix obtained from the functional fit.
We determine the uncertainty on the MJ background shape by relaxing the requirement from Sec. VIII on to and repeating the analysis with this selection in place. The positive and negative variations are taken to be symmetric. The uncertainty on the MJ rate is () for the electron (muon) channel. Since our MJ sample is statistically limited, we do not correlate the uncertainties on the rate and shape across the subchannels. Since we simultaneously fit MJ and +jets to match data, we apply a normalization uncertainty to the +jets samples that is anticorrelated with the MJ normalization systematics and scales as the relative MJ to +jets normalization.
Xi and Production with
The SM processes and where one of the leptons from the decay is not reconstructed, result in the same final state signature as the Higgs boson in this search. Therefore, we search for these processes to validate our analysis methodology. The only change in the analysis is in the training of the final discriminant in events with two or three jets with one tight -tag or two -tags. We train using the and diboson processes as signal while leaving the process as a background. The output of this discriminant is used to measure the combined and cross section by performing a maximum likelihood fit to data using signal plus background models, with maximization over the systematic uncertainties as described in detail in Sec. XII. The expected significance of the measurement using the MVA output is 1.8 s.d. We measure a cross section of 0.50 0.34 (stat.) 0.36 (syst.) times the expected SM cross section of 4.4 0.3 pb. Figure 20 shows the MVA discriminant output for the diboson cross section () with background-subtracted data and signal scaled to the best fit value.
Xii Upper Limits on the Higgs Boson Production Cross Section
We derive upper limits on the Higgs boson production cross section multiplied by the corresponding branching fraction in units of the SM prediction. The limits are calculated using the modified frequentist approach Junk:1999kv ; Read:2002hq ; wade_tm , and the procedure is repeated for each assumed value of .
Two hypotheses are considered: the background-only hypothesis (B), in which only background contributions are present, and the signal-plus-background (S+B) hypothesis in which both signal and background contributions are present.
The limits are determined using the MVA output distributions, together with their associated uncertainties, as inputs to the limit setting procedure. To preserve the stability of the limit derivation procedure in regions of small background statistics in the one tight -tag and all two -tags categories, the width of the bin at the largest MVA output value is adjusted by comparing the total background and signal+background expectations until the statistical significances for B and S+B are, respectively, greater than 3.6 and 5.0 s.d. from zero. The remaining part of the distribution is then divided into equally sized bins. In the zero -tags and one loose -tag categories, the width of the bin at largest MVA output is set such that the relative statistical uncertainty on the signals plus background entries is less than 0.15. The remaining bins are distributed uniformly. The rebinning procedure is checked for potential biases in the determination of the final limits, and no such bias is observed.
We evaluate the compatibility of the data with the background-only and signal+background hypotheses. This is done using the log likelihood ratio (), which is twice the negative logarithm of the ratio of the Poisson likelihoods, , of the signal+background hypothesis to the background only hypothesis, .
Systematic uncertainties are included through nuisance parameters that are assigned Gaussian probability distributions (priors). The signal and background predictions are functions of the nuisance parameters. Each common source of systematic uncertainty (such as the uncertainties on predicted SM cross sections, identification efficiencies, and energy calibration, as described in Sec. X) is taken to be correlated across all channels except as otherwise noted in Sec. X.
The inclusion of systematic uncertainties in the generation of pseudoexperiments has the effect of broadening the expected distributions and, thus, reducing the ability to resolve signal-like excesses. This degradation can be partially reduced by performing a maximum likelihood fit to each pseudoexperiment (and data), once for the B hypothesis and once for the S+B hypothesis. The maximization is performed over the systematic uncertainties. The is evaluated for each outcome using the ratio of maximum likelihoods for the fit to each hypothesis. The resulting degradation of the limits due to systematic uncertainties is for searches in the vicinity of GeV.
The medians of the obtained distributions for the B and S+B hypotheses for each tested mass are presented in Fig. 21. The corresponding s.d. and s.d. values for the background-only hypothesis at each mass point are represented by the shaded regions in the figure. The values obtained from the data are also presented in the figure.
The MVA discriminant distributions, for the Higgs boson mass point GeV, after subtracting the total posterior background expectation are shown in Fig. 22. The signal expectation is shown scaled to the observed upper limit (described later) and the uncertainties in the background after the constrained fit are shown by the solid lines.
|Combined 95% C.L. Limit|
|2 or 3 jets with one tight -tag or two -tags|
|2 or 3 jets with zero -tags or one loose -tag|
|4 or more jets with zero -tags or one loose -tag|
|All channels combined|
Upper limits are calculated at 23 discrete values of the Higgs boson mass, spanning the range 90–200 GeV and spaced in increments of 5 GeV, by scaling the expected signal contribution to the value at which it can be excluded at the 95% C.L. The expected limits are calculated from the background-only distribution whereas the observed limits are quoted with respect to the values measured in data. The expected and observed 95% C.L. upper limits results for the Higgs boson production cross section multiplied by the decay branching fraction are shown, as a function of the Higgs boson mass , in units of the SM prediction in Fig. 23. The values obtained for the expected and observed limit to SM ratios at each mass point are listed in Table 4 for all one-tight, two-loose, two-medium, and two-tight -tag subchannels together, for the two-jet and three-jet, zero and one loose -tag subchannels (all -tag categories for GeV) together, the -jet subchannels, and the combination of all subchannels.
Xiii Interpretations in fourth generation and fermiophobic Higgs models
Extensions of the minimal electroweak symmetry breaking mechanism of the SM may be allowed, including models with a fourth generation of fermions or with a Higgs boson that has modified couplings to fermions, as in fermiophobic Higgs models (FHM). We interpret our results in these scenarios using the subchannels that are sensitive to decays: events with two or more jets and zero or one loose -tag for GeV, extended to include pretag two- and three-jet events for GeV. These are the first results for these models in the jets final state.
Previous results from the Tevatron Collider experiments in the context of a fourth generation of fermions set a limit on the of GeV Aaltonen:2010sv . The ATLAS Aad:2011qi and CMS Chatrchyan:2011tz collaborations exclude GeV and GeV, respectively. Previous searches for the fermiophobic Higgs boson in and channels, with two leptons in the final state, were carried out at the LEP Collider Heister:2002ub ; Abdallah:2003xf ; Achard:2003jb ; Abbiendi:2002vu , by the CDF Collaboration:2012pa and D0 Abazov:2011ix Collaborations, and by the ATLAS Aad:2012yq and CMS CMS:2012bd Collaborations, with the most stringent limits being set by the CMS experiment where the excluded range is GeV.
The coupling is enhanced in fourth-generation models, which leads to a higher rate of production and a larger decay width of than in the SM Holdom:2009rf ; Kribs:2007nz ; Arik:2005ed ; Anastasiou:2010bt . However, since is loop-mediated, the decay mode dominates for GeV, as in the SM. We consider two scenarios for the presence of a fourth generation. In the “low-mass” scenario, we assume a fourth-generation neutrino mass of GeV and a value for the fourth-generation charged lepton mass of GeV, while in the “high-mass” scenario, we assume values for the fourth-generation neutrino and lepton masses of TeV. Both scenarios set the fourth-generation quark masses to the values in Ref. Anastasiou:2010bt . After applying our selection criteria, the total expected signal for production in the low-mass (high-mass) fourth-generation model is enhanced by a factor of 7.2 (7.5) over the SM production rate for GeV. We only consider gluon fusion Higgs boson production, and we set limits on . These limits are compared with the predicted production cross section results from hdecay Djouadi:1997yw , as shown in Fig. 24. We exclude the “low-mass” scenario for GeV, and the “high-mass” scenario for GeV.
In the FHM, the Higgs boson does not couple to fermions at tree level but is otherwise SM-like. This suppresses production via gluon fusion to a negligible rate and forbids direct decay to fermions. Production in association with a vector boson or via vector boson fusion is allowed. For this interpretation, we set the contribution from production to zero and scale the contributions from other production and decay mechanisms to reflect the predicted rate in the FHM. After applying our selection criteria, the total expected signal for vector boson fusion and production in the FHM is enhanced by a factor of 4.2 over the SM production rate for GeV. The expected and observed cross section times branching fraction limits are compared to the FHM predictions in Fig. 25.
We have presented a search for SM Higgs boson production in lepton + + jets final states with a dataset corresponding to 9.7 fb of integrated luminosity collected with the D0 detector. The search is sensitive to , , and production and decay, and supersedes previous and searches published by D0. To maximize our signal sensitivity, we subdivide the dataset into 36 independent subchannels according to lepton flavor, jet multiplicity, and the number and quality of -tagged jets and apply multivariate analysis techniques to further discriminate between signal and background. We test our method by examining SM and production with decay and find production rates consistent with the SM prediction. We observe no significant excess over the background prediction as expected from the amplitude of a 125 GeV SM Higgs boson signal, given the sensitivity of this single channel. Significance is achieved by combining this channel with the other low mass channels analyzed at the Tevatron tevatron-bbbar , while here we set 95% C.L. upper limits on the Higgs boson production cross section for masses between 90 and 200 GeV. For GeV, the observed (expected) upper limit is 5.8 (4.7) times the SM prediction. We interpret the data also in models with fourth generation fermions, or a fermiophobic Higgs boson. In these interpretations, we exclude GeV in the “low-mass” (“high-mass”) fourth generation fermion scenario, and provide 95% C.L limits on the production cross section in the fermiophobic model.
We thank the staffs at Fermilab and collaborating institutions, and acknowledge support from the DOE and NSF (USA); CEA and CNRS/IN2P3 (France); MON, NRC KI and RFBR (Russia); CNPq, FAPERJ, FAPESP and FUNDUNESP (Brazil); DAE and DST (India); Colciencias (Colombia); CONACyT (Mexico); NRF (Korea); FOM (The Netherlands); STFC and the Royal Society (United Kingdom); MSMT and GACR (Czech Republic); BMBF and DFG (Germany); SFI (Ireland); The Swedish Research Council (Sweden); and CAS and CNSF (China).
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Appendix A Multivariate Discriminator Input Variables
The multivariate discriminators used in this search use input variables from five general categories: final state particle information, as measured in the D0 detector; kinematics of reconstructed objects, such as boson candidates reconstructed from the leptonic or hadronic decay products; angular distributions between final state particles and reconstructed objects; topological variables that examine the net properties of all final state particles in an event; and special variables focused on discriminating Higgs boson candidate events from specific backgrounds. Certain multivariate discriminants trained to separate a Higgs boson signal from a specific background are also used as inputs for a final discriminant that is trained to separate the Higgs boson signal from all backgrounds.
Individual input variables are described in detail below. In the descriptions, refers to the electron or muon in a selected event, refers to the neutrino candidate, and refers to jets as ordered by where is the jet with highest . The of the neutrino candidate is estimated by constraining the charged lepton and the neutrino system to the mass of the boson and choosing the lowest magnitude solution.
Input variable lists for each multivariate discriminant appear in Tables 5–18. The ranking by importance of the variables is determined in the BDT by counting how often the variables are used to split decision tree nodes, and by weighting each split occurrence by the separation gain-squared it has achieved and by the number of events in the node Hocker:2007ht . In the RF, the importance of variables are estimated after training in an independent sample of validation events. These events are run through the RF, once for each variable used. On each pass the class of each event is randomized whenever the variable under test is encountered and the change in the quadratic loss figure of merit is estimated:
where is an event weight, =1 for signal, 0 for background, and is the output of the RF classifier for a given event. Whenever the RF makes an incorrect assignment for an event the FOM increases in value. In this test the assignments are randomized for one variable at a time, effectively removing the predictive power of that variable, and the FOM will increase more when more powerful variables are removed in this manner.
The input variable distributions are defined as follows:
a.1 Final State Particle Information
: Energy of the leading jet
: of the leading jet
: of the second leading jet
: of the third leading jet
: Product of the lepton charge and its pseudorapidity
: Smaller absolute value solution for of the reconstructed neutrino, reconstructed with the assumption all is originating from boson
: Larger absolute value solution for of the reconstructed neutrino
: Missing as determined from charged particle tracks in central tracking detector
: Scaled is defined as