Combined CDF and D0 Upper Limits on Standard Model Higgs Boson Production with up to 8.6 fb{}^{-1} of Data

Combined CDF and D0 Upper Limits on Standard Model Higgs Boson Production with up to 8.6 fb of Data

The TEVNPH Working Group111The Tevatron New-Phenomena and Higgs Working Group can be contacted at TEVNPHWG@fnal.gov. More information can be found at http://tevnphwg.fnal.gov/. for the CDF and D0 Collaborations
July 14, 2019
Abstract

We combine results from CDF and D0 on direct searches for the standard model (SM) Higgs boson () in  collisions at the Fermilab Tevatron at  TeV. Compared to the previous Tevatron Higgs boson search combination more data have been added, additional channels have been incorporated, and some previously used channels have been reanalyzed to gain sensitivity. We use the MSTW08 parton distribution functions and the latest theoretical cross sections when comparing our limits to the SM predictions. With up to 8.2 fb of data analyzed at CDF and up to 8.6 fb at D0, the 95% C.L. our upper limits on Higgs boson production are factors of 1.17, 1.71, and 0.48 times the values of the SM cross section for Higgs bosons of mass 115 GeV/, 140 GeV/, and 165 GeV/, respectively. The corresponding median upper limits expected in the absence of Higgs boson production are 1.16, 1.16, and 0.57. There is a small () excess of data events with respect to the background estimation in searches for the Higgs boson in the mass range  GeV/. We exclude, at the 95% C.L., a new and larger region at high mass between  GeV/, with an expected exclusion region of  GeV/.


Preliminary Results

FERMILAB-CONF-11-354-E

CDF Note 10606

D0 Note 6226

I Introduction

The search for a mechanism for electroweak symmetry breaking, and in particular for a standard model (SM) Higgs boson, has been a major goal of particle physics for many years, and is a central part of the Fermilab Tevatron physics program. Both the CDF and D0 collaborations have performed new combinations CDFHiggs (); DZHiggs () of multiple direct searches for the SM Higgs boson. The new searches include more data, additional channels, and improved analysis techniques compared to previous analyses. The sensitivities of these new combinations significantly exceed those of previous combinations prevhiggs (); WWPRLhiggs ().

In this note, we combine the most recent results of all such searches in  collisions at  TeV. The analyses combined here seek signals of Higgs bosons produced in association with a vector boson (), through gluon-gluon fusion (), and through vector boson fusion (VBF) () corresponding to integrated luminosities up to 8.2 fb at CDF and up to 8.6 fb at D0. The Higgs boson decay modes studied are , , , and .

To simplify the combination, the searches are separated into 165 mutually exclusive final states (71 for CDF and 94 for D0; see Tables 2 and 3) referred to as “analysis sub-channels” in this note. The selection procedures for each analysis are detailed in Refs. cdfWH2J () through dzHgg (), and are briefly described below.

Ii Acceptance, Backgrounds, and Luminosity

Event selections are similar for the corresponding CDF and D0 analyses, consisting typically of a preselection followed by the use of a multivariate analysis technique with a final discriminating variable to separate signal and background. For the case of , an isolated lepton ( electron or muon) and two or three jets required, with one or more -tagged jets, i.e., identified as containing a weakly-decaying hadron. Selected events must also display a significant imbalance in transverse momentum (referred to as missing transverse energy or ). Events with more than one isolated lepton are rejected.

For the D0  analyses, the data are split by lepton type and jet multiplicity (two or three jet sub-channels), and whether there are one or two -tagged jets. As with other D0 analyses targeting the  decay, the  analyses use a new boosted decision tree based -tagging algorithm for this combination. The new algorithm is an upgraded version of the neural network -tagger used previously Abazov:2010ab (), and includes more information relating to the lifetime of the jet and results in a better discrimination between and light jets. Unlike previous versions of the analysis the same “loose” -tagging criterion is applied to both the single (LST) and double (LDT) tag samples, with the output of the -tagger now being used as an input to the final discriminant. This loose -tagging criterion corresponds to an identification efficiency of for true -jets for a mis-identification rate of . Each sub-channel is analyzed separately. The outputs of boosted decision trees, trained separately for each sample and for each Higgs boson mass, are used as the final discriminating variables in the limit setting procedure. In addition for this combination D0 now uses 8.5 fb of data.

For the CDF  analyses, events are analyzed in two and three jet sub-channels separately, and in each of these samples the events are grouped into various lepton and -tag categories. Events are broken into separate analysis categories based on the quality of the identified lepton. Separate categories are used for events with a high quality muon or central electron candidate, an isolated track or identified loose muon in the extended muon coverage, a forward electron candidate, and a loose central electron or isolated track candidate. The final two lepton categories, which provide some acceptance for lower quality electrons and single prong tau decays, are used only in the case of two-jet events. Within the lepton categories there are four -tagging categories considered for two-jet events: two tight -tags (TDT), one tight -tag and one loose -tag (LDT), one tight -tag and one looser -tag (LDTX), and a single, tight, -tag (ST). For three jet events there is no LDTX tagging category and the corresponding events are included within the ST category. In the case of the two jet events, a Bayesian neural network discriminant is trained at each Higgs boson mass within the test range for each of the specific categories (defined by lepton type, -tagging type, and number of jets), while matrix element (ME) discriminants are used for each three jet event category.

For the  analyses, the selection is similar to the selection, except all events with isolated leptons are rejected and stronger multijet background suppression techniques are applied. Both the CDF and D0 analyses use a track-based missing transverse momentum calculation as a discriminant against false . In addition both CDF and D0 utilize multi-variate techniques, a boosted decision tree at D0 and a neural network at CDF, to further discriminate against the multijet background before -tagging. There is a sizable fraction of the  signal in which the lepton is undetected that is selected in the  samples, so these analyses are also referred to as . The CDF analysis uses three non-overlapping categories of -tagged events (TDT, LDT and ST) D0 uses the same loose single (LST) and double tag (LDT) criteria as the  analyses, with the output of the -tagger again being used as an input to the final discriminant. CDF uses neural-network outputs for the final discriminating variables, while D0 uses boosted decision tree outputs. For this combination D0 has analysed the 2-jet sample in an exclusive manner, updating both the 1- and 2 -tag samples to use 8.4 fb of data. The exclusive 3-jet sample is currently not included.

The  analyses require two isolated leptons and at least two jets. D0’s  analyses separate events into non-overlapping samples of events with either one tight -tag (TST) or both one tight and one loose -tags (TLDT). CDF separates events into single tag (ST), double tag (TDT) and loose double tag (LDT) samples. To increase signal acceptance D0 loosens the selection criteria for one of the leptons to include an isolated track not reconstructed in the muon detector () or an electron from the inter-cryostat region of the D0 detector (). Combined with the dielectron () and dimuon () analyses, these provide four orthogonal analyses, and each uses 8.6 fb of data in this combination. CDF uses neural networks to select loose dielectron and dimuon candidates. D0 applies a kinematic fit to optimize reconstruction, while CDF corrects jet energies for  using a neural network approach. D0 uses random forests of decision trees to provide the final variables for setting limits. CDF utilizes a multi-layer discriminant based on neural networks where two discriminant functions are used to define three separate regions of the final discriminant function.

For the  analyses, signal events are characterized by large  and two opposite-signed, isolated leptons. The presence of neutrinos in the final state prevents the accurate reconstruction of the candidate Higgs boson mass. D0 selects events containing electrons and/or muons, dividing the data sample into three final states: , , and . Each final state is further subdivided according to the number of jets in the event: 0, 1, or 2 or more (“2+”) jets. Each of the three final states each uses 8.1 fb of data. Decays involving tau leptons are included in two orthogonal ways. A dedicated analysis () using 7.3 fb of data studying the final state involving a muon and a hadronic tau decay is included in the Tevatron combination. Final states involving other tau decays and mis-identified hadronic tau decays are included in the , , and final state analyses. CDF separates the  events in five non-overlapping samples, split into “high ” and “low ” categories defined by lepton types and the number of reconstructed jets: 0, 1, or 2+ jets. The sample with two or more jets is not split into low and high lepton categories due to the smaller statistics in this channel. A sixth CDF channel is the low dilepton mass () channel, which accepts events with  GeV. A new improvement of the CDF analysis is the ability to recover events with lepton pairs that lie within each other’s isolation cones. This improvement leads to a significant increase in sensitivity from the low channel, in particular.

The division of events into categories based on the number of reconstructed jets allows the analysis discriminants to separate differing contributions of signal and background processes more effectively. The signal production mechanisms considered are , , and vector-boson fusion. The relative fractions of the contributions from each of the three signal processes and background processes, notably production and production, are very different in the different jet categories. Dividing our data into these categories provides more statistical discrimination, but introduces the need to evaluate the systematic uncertainties carefully in each jet category. A discussion of these uncertainties is found in Section III.

The D0 , , and final state channels use boosted decision tree outputs as the final discriminants while the channel uses neural networks. CDF uses neural-network outputs, including likelihoods constructed from calculated matrix-element probabilities as additional inputs for the 0-jet bin.

D0 includes  analyses in which the associated vector boson and the boson from the Higgs boson decay are required to decay leptonically, with like-sign leptons present, thereby defining three like-sign dilepton final states (, , and ). The combined output of two decision trees, trained against the instrumental and diboson backgrounds respectively, is used as the final discriminant. CDF also includes a separate analysis of events with same-sign leptons to incorporate additional potential signal from associated production events in which the two leptons (one from the associated vector boson and one from a boson produced in the Higgs boson decay) have the same charge. CDF additionally incorporates three tri-lepton channels to include additional associated production contributions in which leptons result from the associated boson and the two bosons produced in the Higgs boson decay or where an associated boson decays into a dilepton pair and a third lepton is produced in the decay of either of the bosons resulting from the Higgs boson decay. In the latter case, CDF separates the sample into one jet and two or more jet sub-channels to take advantage of the fact that the Higgs boson candidate mass can be reconstructed from the invariant mass of the two jets, the lepton, and the missing transverse energy.

For the first time CDF includes a search for using four lepton events. A simple four-lepton invariant mass discriminant is used to separate potential Higgs boson signal events from the non-resonant background. CDF has also updated its opposite-sign channels in which one of the two lepton candidates is a hadronic tau. Events are separated into - and - channels. The final discriminants are obtained from boosted decision trees which incorporate both hadronic tau identification and kinematic event variables as inputs. D0 also includes channels in which one of the bosons in the process decays leptonically and the other decays hadronically. Electron and muon final states are studied separately, each with 5.3 fb of data. Random forests are used for the final discriminants.

CDF includes an updated, generic analysis searching for Higgs bosons decaying to tau lepton pairs incorporating contributions from direct production, associated or production, and vector boson production. CDF also includes for the first time an analysis of events that contain one reconstructed lepton ( = or ) in addition to a tau lepton pair focusing on associated production where and an additional lepton is produced in the decay of the or boson. For the generic search, events with either one or two jets are separated into two independent analysis channels. The final discriminant for setting limits is obtained using four boosted decision tree discriminants, each designed to discriminate the signal against one of the major backgrounds (QCD multijets, plus jets, , and where or ). In the new analysis events are separated into three tri-lepton categories (--, --, and --). The final discriminants are likelihoods based on Support Vector Machine (SVM) svm () outputs obtained using separate trainings for the signal against each of the primary backgrounds ( plus jets, , and dibosons). The D0 analysis likewise includes direct production, associated or production, and vector boson production. Decay of the Higgs boson to both tau and boson pairs is considered. A final state consisting of one leptonic tau decay, one hadronic hadronic tau decay and two jets is required. Both muonic and electronic sub-channels use 4.3 fb The output of boosted decision trees is used as the final discriminant.

CDF incorporates an older all-hadronic analysis, which results in two -tagging sub-channels (TDT and LDT) for both and VBF production to the final state. Events with either four or five reconstructed jets are selected, and at least two must be -tagged. The large QCD multijet backgrounds are modeled from the data by applying a measured mistag probability to the non -tagged jets in events containing a single -tag. Neural network discriminants based on kinematic event variables including those designed to separate quark and gluon jets are used to obtain the final limits.

D0 and CDF both contribute analyses searching for Higgs bosons decaying into diphoton pairs. The CDF analysis looks for a signal peak in the diphoton invariant mass spectrum above the smooth background originating from standard QCD production. Signal acceptance has been increased in the updated analysis by including forward (plug) calorimeter candidates as well as central photon conversion candidates. Events are now separated into four independent analysis channels based on the photon candidates contained within the event: two central candidates (CC), one central and one plug candidate (CP), one central and one central conversion candidate (CC-Conv), or one plug and one central conversion candidate (PC-Conv). In the D0 analysis the contribution of jets misidentified as photons is reduced by combining information sensitive to differences in the energy deposition from these particles in the tracker, calorimeter and central preshower in a neural network. The output of boosted decision trees, rather than the diphoton invariant mass, is used as the final discriminating variable. The transverse energies of the leading two photons along with the azimuthal opening angle between them and the diphoton invariant mass and transverse momentum are used as input variables. A sizeable improvement in sensitivity () beyond that achieved with the invariant mass is obtained.

CDF for the first time includes three non-overlapping sets of analysis channels searching for the process . One set of channels selects events with a reconstructed lepton, large missing transverse energy, and four or five reconstructed jets. These events are further sub-divided into five -tagging categories (three tight -tags (TTT), two tight and one loose -tags (TTL) , one tight and two loose -tags (TLL), two tight -tags (TDT), and one tight and one loose -tags (LDT)). Ensembles of neural network discriminants trained at each mass point are used to set limits. A second set of channels selects events with no reconstructed lepton. These events are separated into two categories, one containing events with large missing transverse energy and five to nine reconstructed jets and another containing events with low missing transverse energy and seven to ten reconstructed jets. Events in these two channels are required to have a minimum of two -tagged jets based on a neural network tagging algorithm. Events with three or more -tags are analyzed in separate channels from those with exactly two tags. Two stages of neural network discriminants are used (the first to help reject large multijet backgrounds and the second to separate potential signal events from background events).

For both CDF and D0, events from QCD multijet (instrumental) backgrounds are typically measured in independent data samples using several different methods. For CDF, backgrounds from SM processes with electroweak gauge bosons or top quarks were generated using PYTHIA pythia (), ALPGEN alpgen (), MC@NLO MC@NLO (), and HERWIG herwig () programs. For D0, these backgrounds were generated using PYTHIA, ALPGEN, and COMPHEP comphep (), with PYTHIA providing parton-showering and hadronization for all the generators. These background processes were normalized using either experimental data or next-to-leading order calculations (including MCFM mcfm () for the heavy flavor process).

Iii Signal Predictions

We normalize our Higgs boson signal predictions to the most recent high-order calculations available. The production cross section we use is calculated at next-to-next-to leading order (NNLO) in QCD with a next-to-next-to leading log (NNLL) resummation of soft gluons; the calculation also includes two-loop electroweak effects and handling of the running quark mass anastasiou (); grazzinideflorian (). The numerical values in Table 1 are updates grazziniprivate () of these predictions with set to 173.1 GeV/ tevtop09 (), and with a treatment of the massive top and bottom loop corrections up to next-to-leading-order (NLO) + next-to-leading-log (NLL) accuracy. The factorization and renormalization scale choice for this calculation is . These calculations are refinements of the earlier NNLO calculations of the production cross section harlanderkilgore2002 (); anastasioumelnikov2002 (); ravindran2003 (). Electroweak corrections were computed in Refs. actis2008 (); aglietti (); maltoni (); aglietti1 (). Soft gluon resummation was introduced in the prediction of the production cross section in Ref. catani2003 (). The production cross section depends strongly on the gluon parton density function, and the accompanying value of . The cross sections used here are calculated with the MSTW 2008 NNLO PDF set mstw2008 (), as recommended by the PDF4LHC working group pdf4lhc (). The inclusive Higgs boson production cross sections are listed in Table 1.

For analyses that consider inclusive production but do not split it into separate channels based on the number of reconstructed jets, we use the inclusive uncertainties from the simultaneous variation of the factorization and renormalization scale up and down by a factor of two. We use the prescription of the PDF4LHC working group for evaluating PDF uncertainties on the inclusive production cross section. QCD scale uncertainties that affect the cross section via their impacts on the PDFs are included as a correlated part of the total scale uncertainty. The remainder of the PDF uncertainty is treated as uncorrelated with the QCD scale uncertainty.

For analyses seeking production that divide events into categories based on the number of reconstructed jets, we employ a new approach for evaluating the impacts of the scale uncertainties. Following the recommendations of Ref. bnlaccord (), we treat the QCD scale uncertainties obtained from the NNLL inclusive grazzinideflorian (); anastasiou (), NLO one or more jets anastasiouwebber (), and NLO two or more jets campbellh2j () cross section calculations as uncorrelated with one another. We then obtain QCD scale uncertainties for the exclusive  jet, 1 jet, and 2 or more jet categories by propagating the uncertainties on the inclusive cross section predictions through the subtractions needed to predict the exclusive rates. For example, the +0 jet cross section is obtained by subtracting the NLO  or more jet cross section from the inclusive NNLL+NNLO cross section. We now assign three separate, uncorrelated scale uncertainties which lead to correlated and anticorrelated uncertainty contributions between exclusive jet categories. The procedure in Ref. anastasiouwebber () is used to determine PDF model uncertainties. These are obtained separately for each jet bin and treated as 100% correlated between jet bins and between D0 and CDF.

The scale choice affects the spectrum of the Higgs boson when produced in gluon-gluon fusion, and this effect changes the acceptance of the selection requirements and also the shapes of the distributions of the final discriminants. The effect of the acceptance change is included in the calculations of Ref. anastasiouwebber () and Ref. campbellh2j (), as the experimental requirements are simulated in these calculations. The effects on the final discriminant shapes are obtained by reweighting the spectrum of the Higgs boson production in our Monte Carlo simulation to higher-order calculations. The Monte Carlo signal simulation used by CDF and D0 is provided by the LO generator pythia pythia () which includes a parton shower and fragmentation and hadronization models. We reweight the Higgs boson spectra in our pythia Monte Carlo samples to that predicted by hqt hqt () when making predictions of differential distributions of signal events. To evaluate the impact of the scale uncertainty on our differential spectra, we use the resbos resbos () generator, and apply the scale-dependent differences in the Higgs boson spectrum to the hqt prediction, and propagate these to our final discriminants as a systematic uncertainty on the shape, which is included in the calculation of the limits.

We include all significant Higgs boson production modes in the high-mass search. Besides gluon-gluon fusion through virtual quark loops (ggH), we include Higgs boson production in association with a or vector boson (VH), and vector boson fusion (VBF). For the low-mass searches, we target the , , VBF, and production modes with specific searches, including also those signal components not specifically targeted but which fall in the acceptance nonetheless. Our and cross sections are from Ref. djouadibaglio (). This calculation starts with the NLO calculation of v2hv v2hv () and includes NNLO QCD contributions vhnnloqcd (), as well as one-loop electroweak corrections vhewcorr (). We use the VBF cross section computed at NNLO in QCD in Ref. vbfnnlo (). Electroweak corrections to the VBF production cross section are computed with the hawk program hawk (), and are small and negative (2-3%) in the Higgs boson mass range considered here. We include these corrections in the VBF cross sections used for this result. The production cross sections we use are from Ref. tth ().

In order to predict the kinematic distributions of Higgs boson signal events, CDF and D0 use the PYTHIA pythia () Monte Carlo program, with CTEQ5L and CTEQ6L1 cteq () leading-order (LO) parton distribution functions.

The Higgs boson decay branching ratio predictions used for this result are those of Ref. lhcxs (). In this calculation, the partial decay widths for all Higgs boson decays except to pairs of and bosons are computed with HDECAY hdecay (), and the and pair decay widths are computed with Prophecy4f prophecy4f (). The relevant decay branching ratios are listed in Table 1. The uncertainties on the predicted branching ratios from uncertainties in , , and are presented in Ref. dblittlelhc ().

(GeV/) (fb) (fb) (fb) (fb) (fb) (%) (%) (%) (%) (%) (%)
100 1821.8 291.90 169.8 97.2 8.000 79.1 3.68 8.36 1.11 0.113 0.159
105 1584.7 248.40 145.9 89.7 7.062 77.3 3.59 8.25 2.43 0.215 0.178
110 1385.0 212.00 125.7 82.7 6.233 74.5 3.46 8.03 4.82 0.439 0.197
115 1215.9 174.50 103.9 76.4 5.502 70.5 3.27 7.65 8.67 0.873 0.213
120 1072.3 150.10 90.2 70.7 4.857 64.9 3.01 7.11 14.3 1.60 0.225
125 949.3 129.50 78.5 65.3 4.279 57.8 2.68 6.37 21.6 2.67 0.230
130 842.9 112.00 68.5 60.4 3.769 49.4 2.29 5.49 30.5 4.02 0.226
135 750.8 97.20 60.0 55.9 3.320 40.4 1.87 4.52 40.3 5.51 0.214
140 670.6 84.60 52.7 51.8 2.925 31.4 1.46 3.54 50.4 6.92 0.194
145 600.6 73.70 46.3 48.1 2.593 23.1 1.07 2.62 60.3 7.96 0.168
150 539.1 64.40 40.8 44.6 2.298 15.7 0.725 1.79 69.9 8.28 0.137
155 484.0 56.20 35.9 41.2 2.037 9.18 0.425 1.06 79.6 7.36 0.100
160 432.3 48.50 31.4 38.2 1.806 3.44 0.159 0.397 90.9 4.16 0.0533
165 383.7 43.60 28.4 36.0 1.607 1.19 0.0549 0.138 96.0 2.22 0.0230
170 344.0 38.50 25.3 33.4 1.430 0.787 0.0364 0.0920 96.5 2.36 0.0158
175 309.7 34.00 22.5 31.0 1.272 0.612 0.0283 0.0719 95.8 3.23 0.0123
180 279.2 30.10 20.0 28.8 1.132 0.497 0.0230 0.0587 93.2 6.02 0.0102
185 252.1 26.90 17.9 26.9 1.004 0.385 0.0178 0.0457 84.4 15.0 0.00809
190 228.0 24.00 16.1 25.0 0.890 0.315 0.0146 0.0376 78.6 20.9 0.00674
195 207.2 21.40 14.4 23.3 0.789 0.270 0.0125 0.0324 75.7 23.9 0.00589
200 189.1 19.10 13.0 21.6 0.700 0.238 0.0110 0.0287 74.1 25.6 0.00526
Table 1: The production cross sections and decay branching fractions for the SM Higgs boson assumed for the combination.

Tables 2 and 3 summarize, for CDF and D0 respectively, the integrated luminosities, the Higgs boson mass ranges over which the searches are performed, and references to further details for each analysis.

Channel Luminosity range Reference
(fb) (GeV/)
2-jet channels   4(TDT,LDT,ST,LDTX) 7.5 100-150 cdfWH2J ()
3-jet channels   2(TDT,LDT,ST) 5.6 100-150 cdfWH3J ()
   (TDT,LDT,ST) 7.8 100-150 cdfmetbb ()
   2(TDT,LDT,ST) 7.7 100-150 cdfZHll1 (); cdfZHll2 ()
   2(0 jets,1 jet)+(2 or more jets)+(low-)+(-)+(-) 8.2 110-200 cdfHWW ()
   (same-sign leptons)+(tri-leptons) 8.2 110-200 cdfHWW ()
   (tri-leptons with 1 jet)+(tri-leptons with 2 or more jets) 8.2 110-200 cdfHWW ()
8.2 110-200 cdfHZZ ()
+    (1 jet)+(2 jets) 6.0 100-150 cdfHtt ()
/   (--)+(--)+(--) 6.2 110-150 cdfVHtt ()
   (GF,VBF)(TDT,LDT) 4.0 100-150 cdfjjbb ()
   (CC,CP,CC-Conv,PC-Conv) 7.0 100-150 cdfHgg ()
(lepton)    (4jet,5jet)(TTT,TTL,TLL,TDT,LDT) 6.3 100-150 cdfttHLep ()
(no lepton)    (low met,high met)(2 tags,3 or more tags) 5.7 100-150 cdfttHnoLep ()
Table 2: Luminosity, explored mass range and references for the different processes and final states ( = or ) for the CDF analyses. The generic labels “” and “” refer to separations based on lepton categories.
Channel Luminosity range Reference
(fb) (GeV/)
   (LST,LDT,2,3 jet) 8.5 100-150 dzWHl ()
   (LST,LDT) 8.4 100-150 dzZHv2 ()
   (TST,TLDT,,,,) 8.6 100-150 dzZHll1 ()
+ 4.3 105-200 dzVHt2 ()
5.3 115-200 dzWWW ()
   (0,1,2+ jet) 8.1 115-200 dzHWW ()
7.3 115-200 dzHWWtau ()
5.4 130-200 dzHWWjj ()
8.2 100-150 dzHgg ()
Table 3: Luminosity, explored mass range and references for the different processes and final states () for the D0 analyses.

Iv Distributions of Candidates

All analyses provide binned histograms of the final discriminant variables for the signal and background predictions, itemized separately for each source, and the observed data. The number of channels combined is large, and the number of bins in each channel is large. Therefore, the task of assembling histograms and checking whether the expected and observed limits are consistent with the input predictions and observed data is difficult. We therefore provide histograms that aggregate all channels’ signal, background, and data together. In order to preserve most of the sensitivity gain that is achieved by the analyses by binning the data instead of collecting them all together and counting, we aggregate the data and predictions in narrow bins of signal-to-background ratio, . Data with similar may be added together with no loss in sensitivity, assuming similar systematic errors on the predictions. The aggregate histograms do not show the effects of systematic uncertainties, but instead compare the data with the central predictions supplied by each analysis.

The range of is quite large in each analysis, and so is chosen as the plotting variable. Plots of the distributions of are shown for Higgs boson masses of 115, 140, and 165 GeV/ in Figure 1. These distributions can be integrated from the high- side downwards, showing the sums of signal, background, and data for the most pure portions of the selection of all channels added together. These integrals can be seen in Figure 2. The most significant candidates are found in the bins with the highest ; an excess in these bins relative to the background prediction drives the Higgs boson cross section limit upwards, while a deficit drives it downwards. The lower- bins show that the modeling of the rates and kinematic distributions of the backgrounds is very good. The integrated plots show a slight excess of events in the highest- bins for the analyses seeking a Higgs boson mass of 115 GeV/ and 140 GeV/, and a slight deficit of events in the highest- bins for the analyses seeking a Higgs boson of mass 165 GeV/.

We also show the distributions of the data after subtracting the expected background, and compare that with the expected signal yield for a Standard Model Higgs boson, after collecting all bins in all channels sorted by . These background-subtracted distributions are shown in Figure 3 for Higgs boson masses of 115, 140, and 165 GeV/. These graphs also show the remaining uncertainty on the background prediction after fitting the background model to the data within the systematic uncertainties on the rates and shapes in each contributing channel.

Figure 1: Distributions of , for the data from all contributing channels from CDF and D0, for Higgs boson masses of 115, 140, and 165 GeV/. The data are shown with points, and the expected signal is shown stacked on top of the backgrounds. Underflows and overflows are collected into the leftmost and rightmost bins.
Figure 2: Integrated distributions of , starting at the high side, for Higgs boson masses of 115, 140, and 165 GeV/. The total signal+background and background-only integrals are shown separately, along with the data sums. Data are only shown for bins that have data events in them.
Figure 3: Background-subtracted data distributions for all channels, summed in bins of , for Higgs boson masses of 115, 140, and 165 GeV/. The background has been fit, within its systematic uncertainties, to the data. The points with error bars indicate the background-subtracted data; the sizes of the error bars are the square roots of the predicted background in each bin. The unshaded (blue-outline) histogram shows the systematic uncertainty on the best-fit background model, and the shaded histogram shows the expected signal for a Standard Model Higgs boson.

V Combining Channels

To gain confidence that the final result does not depend on the details of the statistical formulation, we perform two types of combinations, using Bayesian and Modified Frequentist approaches, which yield limits on the Higgs boson production rate that agree within 10% at each value of , and within 1% on average. Both methods rely on distributions in the final discriminants, and not just on their single integrated values. Systematic uncertainties enter on the predicted number of signal and background events as well as on the distribution of the discriminants in each analysis (“shape uncertainties”). Both methods use likelihood calculations based on Poisson probabilities.

v.1 Bayesian Method

Because there is no experimental information on the production cross section for the Higgs boson, in the Bayesian technique CDFHiggs () we assign a flat prior for the total number of selected Higgs boson events. For a given Higgs boson mass, the combined likelihood is a product of likelihoods for the individual channels, each of which is a product over histogram bins:

(1)

where the first product is over the number of channels (), and the second product is over histogram bins containing events, binned in ranges of the final discriminants used for individual analyses, such as the dijet mass, neural-network outputs, or matrix-element likelihoods. The parameters that contribute to the expected bin contents are for the channel and the histogram bin , where and represent the expected background and signal in the bin, and is a scaling factor applied to the signal to test the sensitivity level of the experiment. Truncated Gaussian priors are used for each of the nuisance parameters , which define the sensitivity of the predicted signal and background estimates to systematic uncertainties. These can take the form of uncertainties on overall rates, as well as the shapes of the distributions used for combination. These systematic uncertainties can be far larger than the expected SM Higgs boson signal, and are therefore important in the calculation of limits. The truncation is applied so that no prediction of any signal or background in any bin is negative. The posterior density function is then integrated over all parameters (including correlations) except for , and a 95% credibility level upper limit on is estimated by calculating the value of that corresponds to 95% of the area of the resulting distribution.

v.2 Modified Frequentist Method

The Modified Frequentist technique relies on the method, using a log-likelihood ratio (LLR) as test statistic DZHiggs ():

(2)

where denotes the test hypothesis, which admits the presence of SM backgrounds and a Higgs boson signal, while is the null hypothesis, for only SM backgrounds and ’data’ is either an ensemble of pseudo-experiment data constructed from the expected signal and backgrounds, or the actual observed data. The probabilities are computed using the best-fit values of the nuisance parameters for each pseudo-experiment, separately for each of the two hypotheses, and include the Poisson probabilities of observing the data multiplied by Gaussian priors for the values of the nuisance parameters. This technique extends the LEP procedure pdgstats () which does not involve a fit, in order to yield better sensitivity when expected signals are small and systematic uncertainties on backgrounds are large pflh ().

The technique involves computing two -values, and . The latter is defined by

(3)

where is the value of the test statistic computed for the data. is the probability of observing a signal-plus-background-like outcome without the presence of signal, i.e. the probability that an upward fluctuation of the background provides a signal-plus-background-like response as observed in data. The other -value is defined by

(4)

and this corresponds to the probability of a downward fluctuation of the sum of signal and background in the data. A small value of reflects inconsistency with . It is also possible to have a downward fluctuation in data even in the absence of any signal, and a small value of is possible even if the expected signal is so small that it cannot be tested with the experiment. To minimize the possibility of excluding a signal to which there is insufficient sensitivity (an outcome expected 5% of the time at the 95% C.L., for full coverage), we use the quantity . If for a particular choice of , that hypothesis is deemed to be excluded at the 95% C.L. In an analogous way, the expected , and values are computed from the median of the LLR distribution for the background-only hypothesis.

Systematic uncertainties are included by fluctuating the predictions for signal and background rates in each bin of each histogram in a correlated way when generating the pseudo-experiments used to compute and .

v.3 Systematic Uncertainties

Systematic uncertainties differ between experiments and analyses, and they affect the rates and shapes of the predicted signal and background in correlated ways. The combined results incorporate the sensitivity of predictions to values of nuisance parameters, and include correlations between rates and shapes, between signals and backgrounds, and between channels within experiments and between experiments. More on these issues can be found in the individual analysis notes cdfWH2J () through dzHgg (). Here we consider only the largest contributions and correlations between and within the two experiments.

v.3.1 Correlated Systematics between CDF and D0

The uncertainties on the measurements of the integrated luminosities are 6% (CDF) and 6.1% (D0). Of these values, 4% arises from the uncertainty on the inelastic  scattering cross section, which is correlated between CDF and D0. CDF and D0 also share the assumed values and uncertainties on the production cross sections for top-quark processes ( and single top) and for electroweak processes (, , and ). In order to provide a consistent combination, the values of these cross sections assumed in each analysis are brought into agreement. We use , following the calculation of Moch and Uwer mochuwer (), assuming a top quark mass  GeV/ tevtop09 (), and using the MSTW2008nnlo PDF set mstw2008 (). Other calculations of are similar otherttbar ().

For single top, we use the NLL -channel calculation of Kidonakis kid1 (), which has been updated using the MSTW2008nnlo PDF set mstw2008 () kidprivcomm (). For the -channel process we use kid2 (), again based on the MSTW2008nnlo PDF set. Both of the cross section values below are the sum of the single and single cross sections, and both assume GeV.

(5)
(6)

Other calculations of are similar for our purposes harris ().

MCFM mcfm () has been used to compute the NLO cross sections for , , and production dibo (). Using a scale choice and the MSTW2008 PDF set mstw2008 (), the cross section for inclusive production is

(7)

and the cross section for inclusive production is

(8)

For the , leptonic decays are used in the definition, with both and exchange. The cross section quoted above involves the requirement  GeV for the leptons from the neutral current exchange. The same dilepton invariant mass requirement is applied to both sets of leptons in determining the cross section which is

(9)

For the diboson cross section calculations, for all calculations. Loosening this requirement to include all leptons leads to +0.4% change in the predictions. Lowering the factorization and renormalization scales by a factor of two increases the cross section, and raising the scales by a factor of two decreases the cross section. The PDF uncertainty has the same fractional impact on the predicted cross section independent of the scale choice. All PDF uncertainties are computed as the quadrature sum of the twenty 68% C.L. eigenvectors provided with MSTW2008 (MSTW2008nlo68cl).

In many analyses, the dominant background yields are calibrated with data control samples. Since the methods of measuring the multijet (“QCD”) backgrounds differ between CDF and D0, and even between analyses within the collaborations, there is no correlation assumed between these rates. Similarly, the large uncertainties on the background rates for +heavy flavor (HF) and +heavy flavor are considered at this time to be uncorrelated. The calibrations of fake leptons, unvetoed conversions, -tag efficiencies and mistag rates are performed by each collaboration using independent data samples and methods, and are therefore also treated as uncorrelated.

v.3.2 Correlated Systematic Uncertainties for CDF

The dominant systematic uncertainties for the CDF analyses are shown in the Appendix in Tables 8 and 9 for the  channels, in Table 12 for the channels, in Tables 14 and 15 for the channels, in Tables 17, 18, and 19 for the channels, in Table 20 for the and channels, in Table 21 for the channels, In Table 26 for the channel, in Tables 27, 28, and 29 for the channels, in Table 30 for the channels, in Table 31 for the and channels, in Table 32 for the and VBF channels, and in Table 33 for the channel. Each source induces a correlated uncertainty across all CDF channels’ signal and background contributions which are sensitive to that source. For , the largest uncertainties on signal arise from measured -tagging efficiencies, jet energy scale, and other Monte Carlo modeling. Shape dependencies of templates on jet energy scale, -tagging, and gluon radiation (“ISR” and “FSR”) are taken into account for some analyses (see tables). For , the largest uncertainties on signal acceptance originate from Monte Carlo modeling. Uncertainties on background event rates vary significantly for the different processes. The backgrounds with the largest systematic uncertainties are in general quite small. Such uncertainties are constrained by fits to the nuisance parameters, and they do not affect the result significantly. Because the largest background contributions are measured using data, these uncertainties are treated as uncorrelated for the  channels. The differences in the resulting limits when treating the remaining uncertainties as either correlated or uncorrelated is less than .

v.3.3 Correlated Systematic Uncertainties for D0

The dominant systematic uncertainties for the D0 analyses are shown in the Appendix, in Tables 10, 11, 13, 16, 22, 23, 24, 25, and 34. Each source induces a correlated uncertainty across all D0 channels sensitive to that source. Wherever appropriate the impact of systematic effects on both the rate and shape of the predicted signal and background is included. For the low mass,  analyses, significant sources of uncertainty include the measured -tagging rate and the normalization of the and plus heavy flavor backgrounds. For the and  analyses, significant sources of uncertainty are the measured efficiencies for selecting leptons. For analyses involving jets the determination of the jet energy scale, jet resolution and the multijet background contribution are significant sources of uncertainty. Significant sources for all analyses are the uncertainties on the luminosity and the cross sections for the simulated backgrounds. All systematic uncertainties arising from the same source are taken to be correlated among the different backgrounds and between signal and background.

Figure 4: Distributions of the log-likelihood ratio (LLR) as a function of Higgs boson mass obtained with the method for the combination of all CDF and D0 analyses. The green and yellow bands correspond to the regions enclosing 1- and 2- fluctuations of the background, respectively.

Vi Combined Results

Before extracting the combined limits we study the distributions of the log-likelihood ratio (LLR) for different hypotheses to quantify the expected sensitivity across the mass range tested. Figure 4 displays the LLR distributions for the combined analyses as functions of . Included are the median of the LLR distributions for the background-only hypothesis (LLR), the signal-plus-background hypothesis (LLR), and the observed value for the data (LLR). The shaded bands represent the one and two standard deviation () departures for LLR centered on the median. At  GeV/ a small excess in the data, at the 1- 2-sigma level, has the amplitude expected from a Higgs boson of this mass. Table 6 lists the observed and expected LLR values shown in Figure 4.

These distributions can be interpreted as follows: The separation between the medians of the LLR and LLR distributions provides a measure of the discriminating power of the search. The sizes of the one- and two- LLR bands indicate the width of the LLR distribution, assuming no signal is truly present and only statistical fluctuations and systematic effects are present. The value of LLR relative to LLR and LLR indicates whether the data distribution appears to resemble what we expect if a signal is present (i.e. closer to the LLR distribution, which is negative by construction) or whether it resembles the background expectation more closely; the significance of any departures of LLR from LLR can be evaluated by the width of the LLR bands.

Using the combination procedures outlined in Section III, we extract limits on SM Higgs boson production in  collisions at  TeV for GeV/. To facilitate comparisons with the standard model and to accommodate analyses with different degrees of sensitivity, we present our results in terms of the ratio of obtained limits to the SM Higgs boson production cross section, as a function of Higgs boson mass, for test masses for which both experiments have performed dedicated searches in different channels. A value of the combined limit ratio which is less than or equal to one indicates that that particular Higgs boson mass is excluded at the 95% C.L.

The combinations of results CDFHiggs (); DZHiggs () of each single experiment, as used in this Tevatron combination, yield the following ratios of 95% C.L. observed (expected) limits to the SM cross section: 1.55 (1.49) for CDF and 1.83 (1.90) for D0 at  GeV/, 1.88 (1.55) for CDF and 2.42 (1.79) for D0 at  GeV/, and 0.75 (0.79) for CDF and 0.71 (0.87) for D0 at  GeV/.

The ratios of the 95% C.L. expected and observed limit to the SM cross section are shown in Figure 5 for the combined CDF and D0 analyses. The observed and median expected ratios are listed for the tested Higgs boson masses in Table 4 for  GeV/, and in Table 5 for  GeV/, as obtained by the Bayesian and the methods. In the following summary we quote only the limits obtained with the Bayesian method, which was decided upon a priori. The corresponding limits and expected limits obtained using the method are shown alongside the Bayesian limits in the tables. We obtain the observed (expected) values of 0.68 (0.96) at  GeV/, 1.17 (1.16) at  GeV/, 1.71 (1.16) at  GeV/, 1.08 (0.80) at  GeV/, 0.48 (0.57) at  GeV/, 0.91 (0.80) at  GeV/, and 1.31 (1.22) at  GeV/.

Figure 5: Observed and expected (median, for the background-only hypothesis) 95% C.L. upper limits on the ratios to the SM cross section, as functions of the Higgs boson mass for the combined CDF and D0 analyses. The limits are expressed as a multiple of the SM prediction for test masses (every 5 GeV/) for which both experiments have performed dedicated searches in different channels. The points are joined by straight lines for better readability. The bands indicate the 68% and 95% probability regions where the limits can fluctuate, in the absence of signal. The limits displayed in this figure are obtained with the Bayesian calculation.
Bayesian 100 105 110 115 120 125 130 135 140 145 150
Expected 0.86 0.96 1.03 1.16 1.24 1.31 1.35 1.28 1.16 1.10 0.93
Observed 0.43 0.68 1.12 1.17 1.47 1.81 2.00 1.54 1.71 1.58 1.39
100 105 110 115 120 125 130 135 140 145 150
Expected 0.87 0.95 1.03 1.17 1.26 1.35 1.37 1.29 1.19 1.08 0.95
Observed 0.44 0.70 1.13 1.22 1.57 1.92 2.02 1.59 1.77 1.65 1.32
Table 4: Ratios of median expected and observed 95% C.L. limit to the SM cross section for the combined CDF and D0 analyses as a function of the Higgs boson mass in GeV/, obtained with the Bayesian and with the method.
Bayesian 155 160 165 170 175 180 185 190 195 200
Expected 0.80 0.59 0.57 0.67 0.80 0.97 1.22 1.49 1.71 2.02
Observed 1.08 0.66 0.48 0.62 0.91 1.14 1.31 1.90 2.41 2.91
155 160 165 170 175 180 185 190 195 200
Expected 0.82 0.61 0.58 0.67 0.81 0.98 1.24 1.50 1.77 2.04
Observed 1.03 0.67 0.48 0.61 0.92 1.17 1.34 1.92 2.39 2.82
Table 5: Ratios of median expected and observed 95% C.L. limit to the SM cross section for the combined CDF and D0 analyses as a function of the Higgs boson mass in GeV/, obtained with the Bayesian and with the method.

We also show in Figure 6 and list in Table 7 the observed 1- and its expected distribution for the background-only hypothesis as a function of the Higgs boson mass. This is directly interpreted as the level of exclusion of our search. This figure is obtained using the method. We also show in Figure 6 as a function of , which on a logarithmic scale more clearly shows the strength of the exclusion for values of for which we have a large sensitivity. Figure 7 shows the -value as a function of and also , as well as the expected distributions in the absence of a Higgs boson signal.

We choose to use the intersections of piecewise linear interpolations of our observed and expected rate limits in order to quote ranges of Higgs boson masses that are excluded and that are expected to be excluded. The sensitivities of our searches to Higgs bosons are smooth functions of the Higgs boson mass and depend most strongly on the predicted cross sections and the decay branching ratios (the decay is the dominant decay for the region of highest sensitivity). We therefore use the linear interpolations to extend the results from the 5 GeV/ mass grid investigated to points in between. The regions of Higgs boson masses excluded at the 95% C.L. thus obtained are  GeV/ and  GeV/. The expected exclusion region, given the current sensitivity, is  GeV/ and  GeV/ (masses below  GeV/ were not studied). The excluded region obtained by finding the intersections of the linear interpolations of the observed curve shown in Figure 6 is nearly identical to that obtained with the Bayesian calculation. As previously stated, we make the a priori choice to quote the exclusion region using the Bayesian calculation.

We investigate the sensitivity and observed limits using CDF’s and D0’s searches for taken in combination. These channels contribute the most for values of below around 130 GeV/. The contributing channels for CDF are the channels, the channels, the channels, the channels, and all of the channels. The contributing channels for D0 are the channels, the channels, and the channels. The result of this combination is shown in Figure 8.

In summary, we combine all available CDF and D0 results on SM Higgs boson searches, based on luminosities ranging from 4.0 to 8.6 fb. Compared to our previous combination, more data have been added to the existing channels, additional channels have been included, and analyses have been further optimized to gain sensitivity. The results presented here significantly extend the individual limits of each collaboration and those obtained in our previous combination. The sensitivity of our combined search is sufficient to exclude a Higgs boson at high mass and is, in the absence of signal, expected to grow substantially in the future as more data are added and further improvements are made to our analysis techniques. We observe a small () excess in the range  GeV/ which does not allow exclusion of a Higgs boson to as low a mass as expected. In addition, we combine the CDF and D0 analyses which seek specifically the decay, which dominates at the low end of the allowed mass range for the SM Higgs boson. These are the search modes for which we expect Tevatron sensitivity to remain competitive with the LHC experiments for several years to come.


(a)

(b)

Figure 6: The exclusion strength (a) and 1- (b) as functions of the Higgs boson mass (in steps of 5 GeV/), for the combination of the CDF and D0 analyses. The green and yellow bands correspond to the regions enclosing 1- and 2- fluctuations of the background, respectively.

(a)

(b)

Figure 7: The signal -values (a) and 1- (b) as functions of the Higgs boson mass (in steps of 5 GeV/), for the combination of the CDF and D0 analyses. The green and yellow bands correspond to the regions enclosing 1- and 2- fluctuations of the background, respectively.
Figure 8: Observed and expected (median, for the background-only hypothesis) 95% C.L. upper limits on the ratios to the SM cross section, as functions of the Higgs boson mass for the combination of CDF and D0 analyses focusing on the decay channel. The limits are expressed as a multiple of the SM prediction for test masses (every 5 GeV/) for which both experiments have performed dedicated searches in different channels. The points are joined by straight lines for better readability. The bands indicate the 68% and 95% probability regions where the limits can fluctuate, in the absence of signal. The limits displayed in this figure are obtained with the Bayesian calculation.
(GeV/ LLR LLR LLR LLR LLR LLR LLR
100 13.03 -5.26 13.85 9.40 4.95 0.50 -3.95
105 7.96 -4.51 12.43 8.32 4.22 0.11 -4.00
110 2.43 -3.84 11.28 7.46 3.64 -0.17 -3.99
115 1.01 -2.98 9.59 6.21 2.84 -0.53 -3.90
120 0.24 -2.55 8.71 5.58 2.45 -0.68 -3.81
125 -1.11 -2.24 8.05 5.11 2.17 -0.78 -3.72
130 -1.94 -2.13 7.85 4.97 2.08 -0.80 -3.69
135 0.80 -2.43 8.50 5.43 2.36 -0.71 -3.78
140 -1.01 -2.84 9.35 6.05 2.74 -0.57 -3.88
145 -0.95 -3.41 10.59 6.95 3.31 -0.33 -3.97
150 0.14 -4.38 12.44 8.33 4.22 0.11 -4.00
155 1.68 -5.91 15.02 10.30 5.57 0.85 -3.87
160 7.82 -10.57 21.93 15.74 9.56 3.38 -2.81
165 13.23 -11.52 23.25 16.81 10.37 3.93 -2.51
170 9.00 -8.88 19.36 13.69 8.03 2.36 -3.31
175 4.14 -6.08 15.12 10.37 5.63 0.88 -3.86
180 1.86 -4.20 12.00 8.00 4.00 -0.00 -4.00
185 1.58 -2.63 8.92 5.73 2.54 -0.65 -3.84
190 -0.27 -1.85 7.13 4.46 1.78 -0.89 -3.56
195 -0.62 -1.33 5.85 3.57 1.30 -0.98 -3.26
200 -0.72 -1.02 4.97 2.98 0.99 -1.00 -2.99
Table 6: Log-likelihood ratio (LLR) values for the combined CDF + D0 Higgs boson search obtained using the CL method.
(GeV/) 1-CL 1-CL 1-CL 1-CL 1-CL 1-CL
100 0.999 0.999 0.996 0.974 0.876 0.604
105 0.991 0.999 0.992 0.960 0.835 0.537
110 0.912 0.997 0.988 0.944 0.792 0.473
115 0.824 0.994 0.976 0.908 0.716 0.380
120 0.749 0.991 0.966 0.883 0.669 0.332
125 0.592 0.987 0.956 0.859 0.628 0.294
130 0.484 0.986 0.953 0.851 0.614 0.281
135 0.784 0.990 0.963 0.875 0.654 0.317
140 0.663 0.993 0.974 0.902 0.702 0.365
145 0.712 0.997 0.984 0.931 0.760 0.426
150 0.833 0.999 0.992 0.960 0.832 0.526
155 0.926 1.000 0.997 0.982 0.902 0.655
160 0.996 1.000 1.000 0.998 0.981 0.881
165 1.000 1.000 1.000 0.999 0.986 0.906
170 0.997 1.000 1.000 0.995 0.965 0.821
175 0.969 1.000 0.997 0.982 0.906 0.666
180 0.901 0.998 0.991 0.955 0.818 0.508
185 0.843 0.992 0.969 0.889 0.679 0.341
190 0.639 0.979 0.936 0.818 0.570 0.247
195 0.527 0.959 0.894 0.745 0.478 0.184
200 0.451 0.934 0.851 0.681 0.410 0.145
Table 7: The observed and expected 1-CL values as functions of , for the combined CDF and D0 Higgs boson searches.

Acknowledgments

We thank the Fermilab staff and the technical staffs of the participating institutions for their vital contributions, and we acknowledge support from the DOE and NSF (USA); CONICET and UBACyT (Argentina); ARC (Australia); CNPq, FAPERJ, FAPESP and FUNDUNESP (Brazil); CRC Program and NSERC (Canada); CAS, CNSF, and NSC (China); Colciencias (Colombia); MSMT and GACR (Czech Republic); Academy of Finland (Finland); CEA and CNRS/IN2P3 (France); BMBF and DFG (Germany); INFN (Italy); DAE and DST (India); SFI (Ireland); Ministry of Education, Culture, Sports, Science and Technology (Japan); KRF, KOSEF and World Class University Program (Korea); CONACyT (Mexico); FOM (The Netherlands); FASI, Rosatom and RFBR (Russia); Slovak R&D Agency (Slovakia); Ministerio de Ciencia e Innovación, and Programa Consolider-Ingenio 2010 (Spain); The Swedish Research Council (Sweden); Swiss National Science Foundation (Switzerland); STFC and the Royal Society (United Kingdom); and the A.P. Sloan Foundation (USA).

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\appendixpage\addappheadtotoc

Appendix A Systematic Uncertainties

CDF: tight and loose double-tag (TDT and LDT) channel relative uncertainties (%)

Contribution +HF Mistags Top Diboson Non-
Luminosity () 3.8 0 3.8 3.8 0 3.8
Luminosity Monitor 4.4 0 4.4 4.4 0 4.4
Lepton ID 2.0-4.5 0 2.0-4.5 2.0-4.5 0 2.0-4.5
Jet Energy Scale S 0 S S 0 2(S)
Mistag Rate 0 35 0 0 0 0
-Tag Efficiency 8.6 0 8.6 8.6 0 8.6
Cross Section 0 0 10 0 0 0
Diboson Rate 0 0 0 11.5 0 0
Signal Cross Section 0 0 0 0 0 5
HF Fraction in W+jets 45 0 0 0 0 0
ISR+FSR+PDF 5.0-7.7 0 5.0-7.7 5.0-7.7 0 5.0-7.7
S 0 0 0 0 0
QCD Rate 0 0 0 0 40 0

CDF: looser double-tag (LDTX) channel relative uncertainties (%)

Contribution +HF Mistags Top Diboson Non-
Luminosity () 3.8 0 3.8 3.8 0 3.8
Luminosity Monitor 4.4 0 4.4 4.4 0 4.4
Lepton ID 2.0-4.5 0 2.0-4.5 2.0-4.5 0 2.0-4.5
Jet Energy Scale S S S 2.2(S)
Mistag Rate 0 36 0 0 0 0
-Tag Efficiency 13.6 0 13.6 13.6 0 13.6
Cross Section 0 0 10 0 0 0
Diboson Rate 0 0 0 11.5 0 0
Signal Cross Section 0 0 0 0 0 5
HF Fraction in W+jets 45 0 0 0 0 0
ISR+FSR+PDF 4.9-19.5 0 4.9-19.5 4.9-19.5 0 4.9-19.5
S 0 0 0 0 0
QCD Rate 0 0 0 0 40 0

CDF: single tag (ST) channel relative uncertainties (%)

Contribution +HF Mistags Top Diboson Non-
Luminosity () 3.8 0 3.8 3.8 0 3.8
Luminosity Monitor 4.4 0 4.4 4.4 0 4.4
Lepton ID 2.0-4.5 0 2.0-4.5 2.0-4.5 0 2.0-4.5
Jet Energy Scale S 0 S S 0 2.3-4.7(S)
Mistag Rate 0 35 0 0 0 0
-Tag Efficiency 4.3 0 4.3 4.3 0 4.3
Cross Section 0 0 10 0 0 0
Diboson Rate 0 0 0 11.5 0 0
Signal Cross Section 0 0 0 0 0 5
HF Fraction in W+jets 42 0 0 0 0 0
ISR+FSR+PDF 3.0-8.4 0 3.0-8.4 3.0-8.4 0 3.0-8.4
S 0 0 0 0 0
QCD Rate 0 0 0 0 40 0
Table 8: Systematic uncertainties on the signal and background contributions for CDF’s tight double tag (TDT), loose double tag (LDT), looser double tag (LDTX), and single tag (ST) 2 jet channels. Systematic uncertainties are listed by name; see the original references for a detailed explanation of their meaning and on how they are derived. Systematic uncertainties for shown in this table are obtained for GeV/. Uncertainties are relative, in percent, and are symmetric unless otherwise indicated. Shape uncertainties are labeled with an ”S”.

CDF: tight and loose double-tag (TDT and LDT) channel relative uncertainties (%)

Contribution +HF Mistags Top Diboson Non-
Luminosity () 3.8 0 3.8 3.8 0 3.8
Luminosity Monitor 4.4 0 4.4 4.4 0 4.4
Lepton ID 2 0 2 2 0 2
Jet Energy Scale S 0 S 0 0 13.5(S)
Mistag Rate 0 9 0 0 0 0
-Tag Efficiency 8.4 0 8.4 8.4 0 8.4
Cross Section 0 0 10 0 0 0
Diboson Rate 0 0 0 10 0 0
Signal Cross Section 0 0 0 0 0 10
HF Fraction in W+jets 30 0 0 0 0 0
ISR+FSR+PDF 21.4 0 21.4 21.4 0 21.4
QCD Rate 0 0 0 0 40 0

CDF: single tag (ST) channel relative uncertainties (%)

Contribution +HF Mistags Top Diboson Non-
Luminosity () 3.8 0 3.8 3.8 0 3.8
Luminosity Monitor 4.4 0 4.4 4.4 0 4.4
Lepton ID 2 0 2 2 0 2
Jet Energy Scale S 0 S 0 0 15.8(S)
Mistag Rate 0 13.3 0 0 0 0
-Tag Efficiency 3.5 0 3.5 3.5 0 3.5
Cross Section 0 0 10 0 0 0
Diboson Rate 0 0 0 10 0 0
Signal Cross Section 0 0 0 0 0 10
HF Fraction in W+jets 30 0 0 0 0 0
ISR+FSR+PDF 13.1 0 13.1 13.1 0 13.1
QCD Rate 0 0 0 0 40 0
Table 9: Systematic uncertainties on the signal and background contributions for CDF’s tight double tag (TDT), loose double tag (LDT), and single tag (ST) 3 jet channels. Systematic uncertainties are listed by name; see the original references for a detailed explanation of their meaning and on how they are derived. Systematic uncertainties for shown in this table are obtained for GeV/. Uncertainties are relative, in percent, and are symmetric unless otherwise indicated. Shape uncertainties are labeled with an ”S”.

D0: single tag (ST) channel relative uncertainties (%)

Contribution  WZ/WW Wbb/Wcc Wjj/Wcj single top Multijet    WH
Luminosity 6.1 6.1 6.1 6.1 6.1 0 6.1
EM ID/Trigger eff. (S) 1–5 2–4 2–4 1–2 1–2 0 2–3
Muon Trigger eff. (S) 1–3 1–2 1–3 2–5 2–3 0 2–4
Muon ID/Reco eff./resol. 4.1 4.1 4.1 4.1 4.1 0 4.1
Jet ID/Reco eff. (S) 2–5 1–2 1–3 3–5 2–4 0 2–4
Jet Resolution (S) 4–7 1–3 1–4 2–5 2–4 0 4–6
Jet Energy Scale (S) 4–7 2–5 2–5 2–5 2–4 0 2–5
Vertex Conf. Jet (S) 4–10 5–12 4–10 7–10 5–10 0 4–8
-tag/taggability (S) 1–4 1–2 3–7 3–5 1–2 0 1–2
Heavy-Flavor K-factor 0 20 0 0 0 0 0
Inst.-WH (S) 1–2 2–4 1–3 1–2 1–3 -15 1–2
Inst.-WH 0 2.4 2.4 0 0 -20 0
Cross Section 6 9 9 10 10 0 6
Signal Branching Fraction 0 0 0 0 0 0 1-9
ALPGEN MLM pos/neg(S) 0 SH 0 0 0 0 0
ALPGEN Scale (S) 0 SH SH 0 0 0 0
Underlying Event (S) 0 SH 0 0 0 0 0
PDF, reweighting 2 2 2 2 2 0 2

D0: double tag (DT) channel relative uncertainties (%)

Contribution  WZ/WW Wbb/Wcc Wjj/Wcj single top Multijet    WH
Luminosity 6.1 6.1 6.1 6.1 6.1 0 6.1
EM ID/Trigger eff. (S) 2–5 2–3 2–3 1–2 1–2 0 1–2
Muon Trigger eff. (S) 2–4 1–2 1–2 2–4 1–3 0 2–5
Muon ID/Reco eff./resol. 4.1 4.1 4.1 4.1 4.1 0 4.1
Jet ID/Reco eff. (S) 2–8 2–5 4–9 3–7 2–4 0 3–7
Jet Resolution (S) 4–7 2–7 2–7 2–9 2–4 0 4–6
Jet Energy Scale (S) 4–7 2–6 2–7 2–6 2–7 0 4–6
Vertex Conf. Jet (S) 4–10 5–12 4–10 7–10 5–10 0 4–6
-tag/taggability (S) 3–7 4–6 3–10 5–10 4–10 0 4–9
Heavy-Flavor K-factor 0 20 0 0 0 0 0
Inst.-WH (S) 1–2 2–4 1–3 1–2 1–3 -15 1–2
Inst.-WH 0 2.4 2.4 0 0 -20 0
Cross Section 6 9 9 10 10 0 6
Signal Branching Fraction 0 0 0 0 0 0 1-9
ALPGEN MLM pos/neg(S) 0 SH 0 0 0 0 0
ALPGEN Scale (S) 0 SH SH 0 0 0 0
Underlying Event (S) 0 SH 0 0 0 0 0
PDF, reweighting 2 2 2 2 2 0 2
Table 10: Systematic uncertainties on the signal and background contributions for D0’s loose single (LST) and double tag (LDT) channels. Systematic uncertainties are listed by name, see the original references for a detailed explanation of their meaning and on how they are derived. Systematic uncertainties for shown in this table are obtained for GeV/. Uncertainties are relative, in percent, and are symmetric unless otherwise indicated. Shape uncertainties are labeled with an “S”, and “SH” represents a shape-only uncertainty.

D0: Run IIb channel relative uncertainties (%)

Contribution Signal Signal Signal Top diboson Multijet


Luminosity (D0 specific)
4.1 4.1 4.1 4.1 4.1 4.1 4.1 -
Luminosity (Tevatron common) 4.6 4.6 4.6 4.6 4.6 4.6 4.6 -
ID 2.9 2.9 2.9 2.9 2.9 2.9 2.9 -
trigger 8.6 8.6 8.6 8.6 8.6 8.6 8.6 -
energy correction 9.8 9.8 9.8 9.8 9.8 9.8 9.8 -
track efficiency 1.4 1.4 1.4 1.4 1.4 1.4 1.4 -
selection by type 12,4.2,7 12,4.2,7 12,4.2,7 12,4.2,7 12,4.2,7 12,4.2,7 12,4.2,7 -
Cross section 6.2 4.9 33 6.0 6.0 10.0 7.0 -
ggH Signal PDF - - 29 - - - - -
ggH Reweighting (S) 1.0 1.0 1.0 1.0 1.0 1.0 1.0 -
Signal Branching Fraction 0-7.3 0-7.3 0-7.3 - - - - -
Vertex confirmation for jets 4.0 4.0 4.0 4.0 4.0 4.0 4.0 -


Jet ID(S)
10 10 10 10 10 10 10 -
Jet Energy Resolution (S) 10 10 10 10 10 10 10 -
Jet energy Scale (S) 15 15 15 15 15 15 15 -


Jet pT
5.5 5.5 5.5 5.5 5.5 5.5 5.5 -
PDF reweighting 2 2 2 2 2 2 2 -
Multijet Normalization - - - - - - - 5.3
Multijet Shape - - - - - - - 15

D0: Run IIb relative uncertainties (%)

Contribution Signal Signal Signal Top diboson Multijet
Luminosity (D0 specific) 4.1 4.1 4.1 4.1 4.1 4.1 4.1 -
Luminosity (Tevatron common) 4.6 4.6 4.6 4.6 4.6 4.6 4.6 -
EM ID 4 4 4 4 4 4 4 -
e trigger 2 2 2 2 2 2 2 -
energy correction 9.8 9.8 9.8 9.8 9.8 9.8 9.8 -
track efficiency 1.4 1.4 1.4 1.4 1.4 1.4 1.4 -
selection by type 12,4.2,7 12,4.2,7 12,4.2,7 12,4.2,7 12,4.2,7 12,4.2,7 12,4.2,7 -
Cross section 6.2 4.9 33 6.0 6.0 10.0 7.0 -
ggH Signal PDF - - 29 - - - - -
ggH Reweighting (S) 1.0 1.0 1.0 1.0 1.0 1.0 1.0 -
Signal Branching Fraction 0-7.3 0-7.3 0-7.3 - - - - -
Vertex confirmation for jets 4.0 4.0 4.0 4.0 4.0 4.0 4.0 -

Jet ID(S)
10 10 10 10 10 10 10 -
Jet Energy Resolution (S) 10 10 10 10 10 10 10 -
Jet energy Scale (S) 15 15 15 15 15 15 15 -

Jet pT
5.5 5.5 5.5 5.5 5.5 5.5 5.5 -
PDF reweighting 2 2 2 2 2 2 2 -
Multijet Normalization - - - - - - - 4.7
Multijet Shape - - - - - - - 15


Table 11: Systematic uncertainties on the signal and background contributions for D0’s Run IIb channel. Systematic uncertainties for the Higgs signal shown in this table are obtained for GeV/. Systematic uncertainties are listed by name; see the original references for a detailed explanation of their meaning and on how they are derived. Uncertainties are relative, in percent, and are symmetric unless otherwise indicated. A systematic is denoted as flat if it affects the normalization only, and as a shape “S” uncertainty otherwise.

CDF: tight double-tag (TDT) channel relative uncertainties (%)

Contribution ZH WH Multijet Mistags Top Pair S. Top Di-boson W + HF Z + HF
Luminosity 3.8 3.8 3.8 3.8 3.8 3.8 3.8
Lumi Monitor 4.4 4.4 4.4 4.4 4.4 4.4 4.4
Tagging SF 10.4 10.4 10.4 10.4 10.4 10.4 10.4
Trigger Eff. (S) 0.9 1.4 0.9 0.9 1.6 2.0 1.8 1.2
Lepton Veto 2.0 2.0 2.0 2.0 2.0 2.0 2.0
PDF Acceptance 3.0 3.0 3.0 3.0 3.0 3.0 3.0
JES (S)
ISR/FSR
Cross-Section 5 5 10 10 6 30 30
Multijet Norm. (shape) 2.5
Mistag (S)

CDF: loose double-tag (LDT) channel relative uncertainties (%)

Contribution ZH WH Multijet Mistags Top Pair S. Top Di-boson W + HF Z + HF
Luminosity 3.8 3.8 3.8 3.8 3.8 3.8 3.8
Lumi Monitor 4.4 4.4 4.4 4.4 4.4 4.4 4.4
Tagging SF 8.3 8.3 8.3 8.3 8.3 8.3 8.3
Trigger Eff. (S) 1.2 1.7 1.6 0.9 1.8 2.0 2.5 1.9
Lepton Veto 2.0 2.0 2.0 2.0 2.0 2.0 2.0
PDF Acceptance 3.0 3.0 3.0 3.0 3.0 3.0 3.0
JES (S)