Search for standard-model Z and Higgs bosons decaying into a bottom-antibottom quark pair in proton-antiproton collisions at 1.96 TeV

The Collider Detector at Fermilab collected a unique sample of jets originating from bottom-quark fragmentation ($b$-jets) by selecting online proton-antiproton ($p\bar{p}$) collisions with a vertex displaced from the $p\bar{p}$ interaction point, consistent with the decay of a bottom-quark hadron. This data set, collected at a center-of-mass energy of $\sqrt{s}=$1.96 TeV, and corresponding to an integrated luminosity of $5.4~\rm{fb}^{-1}$, is used to measure the $Z$-boson production cross section times branching ratio into $b\bar{b}$. The number of $Z\rightarrow b\bar{b}$ events is determined by fitting the dijet-mass distribution while constraining the dominant $b$-jet background, originating from QCD multijet events, with data. The result, $\sigma(p\bar{p} \rightarrow Z) \times \mathcal{B}(Z \rightarrow b\bar{b})= 1.11\pm 0.08(\text{stat}) \pm 0.14(\text{syst})~\text{nb}$, is the most precise measurement of this process, and is consistent with the standard-model prediction. The data set is also used to search for Higgs-boson production. No significant signal is expected in our data and the first upper limit on the cross section for the inclusive $p\bar p \rightarrow H\rightarrow b\bar b$ process at $\sqrt{s}=$1.96 TeV is set, corresponding to 33 times the expected standard-model cross section, or $\sigma = 40.6$ pb, at the 95\% confidence level.

The Collider Detector at Fermilab collected a unique sample of jets originating from bottom-quark fragmentation (b-jets) by selecting online proton-antiproton (pp) collisions with a vertex displaced from the pp interaction point, consistent with the decay of a bottom-quark hadron. This data set, collected at a center-of-mass energy of √ s =1.96 TeV, and corresponding to an integrated luminosity of 5.4 fb −1 , is used to measure the Z-boson production cross section times branching ratio into bb. The number of Z → bb events is determined by fitting the dijet-mass distribution while constraining the dominant b-jet background, originating from QCD multijet events, with data. The result, σ(pp → Z) × B(Z → bb) = 1.11 ± 0.08(stat) ± 0.14(syst) nb, is the most precise measurement of this process, and is consistent with the standard-model prediction. The data set is also used to search for Higgs-boson production. No significant signal is expected in our data and the first upper limit on the cross section for the inclusive pp → H → bb process at √ s =1.96 TeV is set, corresponding to 33 times the expected standard-model cross section, or σ = 40.6 pb, at the 95% confidence level.
PACS numbers: 13.38.Dg, 14.80.Bn This Letter reports the most precise measurement of the σ(pp → Z) × B(Z → bb) production cross section times branching ratio and the first inclusive search for the pp → H → bb process in proton-antiproton (pp) collisions at a center-of-mass energy of 1.96 TeV. These results arise from the analyses of the data set collected by the Collider Detector at Fermilab (CDF) by an online requirement of one jet with a displaced vertex from the primary pp interaction vertex (secondary vertex), consistent with a b-hadron decay (b-jet).
The identification of the Z → bb decay is challenging at hadron colliders due to the overwhelming irreducible background from multijet production (as is predicted by quantum chromodynamics, QCD), but it represents a benchmark measurement as it validates the experimental techniques used in searches with b quarks in the final states. In addition, it can be used for a direct test of the calibration of the jet-energy scale (JES) for b-jets, defined by a factor that measures the discrepancy between the effect of detector response and energy corrections in real and simulated b-jets. Finally, a large sample of Z → bb events, combined with an algorithm for the identification of the charge of the b quarks, can allow the measurement of the bb forward-backward asymmetry. Such a measurement near the Z-pole can be sensitive to interference effects between tree-level Z exchange and possible non-standard-model amplitudes [1].
The CMS [2], ATLAS [3] and LHCb [4] Collaborations have measured the pp → Z → bb process at various Zboson momenta and rapidities at the Large Hadron Collider (LHC). At the Tevatron the only determination of the Z → bb decay was reported by the CDF Collaboration, which determined the σ(pp → Z)×B(Z → bb) cross section with a relative uncertainty of 29% [5]. Owing to a new and unique data set with increased size, and an analysis technique that uses data for the determination of the invariant-mass spectrum of the various multijet background contributions, the measurement reported in this Letter improves the precision of the previous CDF analysis by almost a factor of two.
Beyond its intrinsic value, the Z → bb measurement allows validation of the background description for the first inclusive search of the pp → H → bb process. Despite its large branching ratio [6], the coupling of Higgs boson to b quarks has not yet been well established [7]. In addition, the search in the inclusive mode is sensitive to a broad class of non-standard-model contributions. A first inclusive search for the Higgs boson at the LHC has been recently reported by the CMS Collaboration [2].
The data used in this analysis were collected during Run II at the Tevatron with the CDF II detector [8]. The CDF II detector was a multipurpose azimuthallysymmetric magnetic spectrometer with a large tracking volume inside a magnet solenoid. Outside the solenoid, there were sampling calorimeters, surrounded by the steel flux return of the solenoid and by muon detectors.
Data were collected with a dedicated online eventselection (trigger) algorithm [10], designed and optimized to select H → bb events. This algorithm operated only in the second part of the Run II data taking and was used for a total of 5.4 fb −1 of integrated luminosity. A stringent requirement on the impact parameter [11] of charged-particle trajectories (tracks) within the jets is used to select those coming from the b-hadron decay vertex. This requirement allowed the collection of a sample enriched in b-jets without saturating the total CDF datataking bandwidth. The threshold on the jet energy was kept as low as possible to limit the sculpting on the dijetmass distribution in the mass range of the Z and Higgs bosons. The trigger algorithm was structured with three levels. At the first level, at least two central (|η| < 1.5 [9]) calorimetric energy deposits with E T > 5 GeV [9] and two charged particles with p T > 2 GeV/c [9] must be reconstructed. At level 2 jets with E T > 15 GeV and |η| < 1.0 are reconstructed using a fixed-cone algorithm [12] with a radius, R = ∆η 2 + ∆φ 2 [9], of 0.7. At least two tracks with transverse distance of closest approach to the primary vertex (impact parameter) d 0 > 90 µm matched to one of the jets have to be identified. The distance of the secondary vertex from the primary vertex in the transverse plane, R b [13], is required to be greater than 0.1 cm. At level 3 the trigger algorithm confirms level-2 requirements using offline-quality tracks and jets variables.
Jets are reconstructed offline using a fixed-size cone algorithm [12] with a cone radius R = 0.7. The event selection requires two central (|η| < 1) jets with E T > 22 GeV. Identification of b-hadrons in the event is performed with the SECVTX algorithm [14]. The algorithm looks for a vertex displaced from the collision point, which is likely to be produced by the decay of a b-hadron. The b-jet candidates selected by the trigger are required to contain a secondary vertex identified by the SECVTX algorithm, and are referred to as the b-tagged trigger jet. The sample of events containing the two leading-E T jets, of which one is the b-tagged trigger jet and the other is not required to be b-tagged (other jet) is referred to as the single-tagged sample. The sample used to search for bb resonances is required to have two SECVTX btagged jets. If more than two SECVTX b-tagged jets are identified in an event, the two with the largest E T are chosen. We refer to this subset of the single-tagged sample as the double-tagged sample. The double-tagged sample contains 925 338 events.
Simulated events are used to evaluate the acceptance for the Z → bb, and H → bb signal processes, and to determine the efficiencies of the SECVTX algorithm for the various jet-flavor hypotheses by exploiting bb, cc and light-quark samples. Samples are generated using Pythia [15] with the CTEQ5L [16] set of parton distribution functions (PDF). The different efficiencies of the online and the offline b-tagging algorithms in data and simulated jets are reconciled by using correction scale factors obtained from a dijet control sample in which a muon with p T > 8 GeV/c is reconstructed inside the jet cone. The fraction of bb events in the control sample is determined by fitting the distribution of the muon transverse momentum with respect to the jet axis, p T,rel . Then the b-tagging efficiencies, and therefore the factors to scale such efficiencies from simulation to data, are determined as functions of the jet E T . The difference response of the tagging algorithm to b-jets with a muon and to hadronic b-jets is included in its systematic uncertainty.
The search for Z → bb and H → bb candidates is conducted by looking for an enhancement over the continuum background in the invariant-mass distribution of the two leading-E T b-tagged jets, m 12 , in the doubletagged sample. This sample is predominantly composed of b-jet pairs from multijet production, but the fraction of events with one jet initiated by a charm or light quark and wrongly identified as a b-jet is not negligible a priori.
The multijet background composition of the sample cannot be determined reliably from simulation, which is affected by large theoretical uncertainties. A data-driven method is used to evaluate and model this background contribution following Ref. [17]. This method allows a determination of the shapes of the invariant-mass distribution of the backgrounds from data, by exploiting the single-tagged sample. We refer to these shapes as background templates. The normalizations are determined with a fit to the binned mass distribution of the doubletagged sample and are part of the results of the analysis. The signal templates are derived from the double-tagged samples selected from simulated samples of Z-and Higgsboson decays.
In order to determine the background templates, the flavor-dependent bias introduced by the SECVTX tagging is reproduced on the other jet of the single-tagged sample by weighting it with tagging probabilities for b-, c-and light-quark jets; we refer to this jet as the simulated flavor-tagged jet. The invariant mass of the dijet formed by the b-tagged trigger jet and the simulated flavor-tagged jet is calculated under the various flavor hypotheses.
This method allows for predictions of the shape of the background by using the single-tagged sample, which is expected to have negligible signal contamination (0.3% estimated using a simulated signal sample). Simulated bb, cb and light-quark samples are employed only to determine the per-jet probabilities that a jet initiated by a b, c, or light quark is tagged by the SECVTX algorithm as functions of jet E T and η [9]. These probabilities are referred to as tagging matrices.
This procedure relies on the assumption that the btagged trigger jet in the single-tagged sample is initiated  nating from b quarks have larger M SV values than those originating from c quarks. Figure 1 shows the M SV distribution of b-tagged trigger jets from the single-tagged sample, fitted with a binned likelihood as the sum of three contributions: jets initiated by b quarks, c quarks, and light quarks. The M SV templates of the b-, c-, and light-quark jets are obtained from simulated dijet bb, cc, and light-quark jets samples, respectively. In the singletagged sample, the fraction of the b-tagged trigger jets originating from b quarks is (75 ± 2)%, with (7 ± 1)% from c quarks and (18 ± 2)% from light quarks, where the uncertainties are the quadratic sum of the statistical uncertainty and the systematic uncertainty due to the finite size of the simulated templates. The reduced χ 2 is 0.76, with 21 degrees of freedom.
By requiring M SV > 1.8 GeV/c 2 for the b-tagged trigger jets in the single-tagged sample, we strongly reduce the contamination from c and light quarks, thus achieving a nearly pure sample of b-tagged trigger jets originating from b quarks. The tagging matrices are applied to the other jet to determine the invariant-mass distributions for the various multijet background components, bb, bc, and bq. The contribution of multiple non-b tags, cc and qq jets, is expected to be negligible and it is not considered.
The background components are classified as Bb, bB, Bc, cB, Bq and qB. The uppercase B indicates the btagged trigger jet of the single-tagged sample, while lowercase letters give the flavor hypotheses obtained from the tagging matrices, where q indicates the light quarks, applied to the untagged jet. The order of the letters follows the decreasing-E T ordering of the jets. Since the dijet-mass distribution templates built with the b-tagging and the c-tagging matrices are indistinguishably similar (Bb and Bc, as well as bB and cB pairs, respectively), they are merged assuming a fixed 5% c-jet contribution. A systematic uncertainty is assigned for this assumption. Therefore, four different templates are used to model the The dijet-mass signal templates are obtained from simulated events. The fit is performed by maximizing a binned likelihood, defined as where L is the product, over all bins, of the probabilities that the event in the ith bin of invariant mass belongs to a signal or background process. These probabilities are described by the background probability density functions (pdf) P b (m 12 ) plus the Z-and the H-boson signal pdfs P s (m 12 ). The free parameters are the number of signal (n i s ) and background (n i b ) events, which are constrained to be non-negative. Figure 2 shows the result of the fit to the dijet-mass distribution for the double-tagged sample. The resulting yields are listed in Table I where the uncertainties are statistical only. The fit returns a sizable Z → bb signal component, while no H → bb signal is found. We expect about 36 Higgs-boson events in this sample, according to the predicted total Higgs-boson production cross section and branching ratio into a pair of b quarks. The Higgs-boson event selection efficiency is 1.5%, which is evaluated with the simulated signal sample. In Figure 2, for illustrative purposes, the Higgs-boson component is magnified 10 3 times with respect to this expectation. The light-quark component is compatible with zero, indicating that the data sample is dominated by pairs of heavyflavor jets. The reduced χ 2 is 0.87, with 31 degrees of freedom. If the Z and H signal components are removed in the fit, the reduced χ 2 is 7.48, with 33 degrees of freedom.
From the Z → bb yield, the product of the Z-boson production cross section and the branching ratio is de- termined using where trig =6.4%, kin =56%, and tag =13%, are the efficiencies for the trigger, offline selections and tagging requirement, respectively; SF trig =0.68 and SF tag =0.86 are the online and offline scale factors that match the simulated b-tagging performance to that on data, and L is the integrated luminosity.
The Z → bb event sample allows for a measurement of the scale factor that matches simulated and observed calorimeter energy scales for b-jets. The scale factor is determined by fitting the bb dijet-mass distribution in data multiple times, using in each a different Z-signal mass template corresponding to a specific choice of the jet-energy scale. The Z → bb yield is determined independently in each fit. The energy of each jet of the Z → bb simulated sample is multiplied by a factor k JES , which varies between 0.90 and 1.10 in steps of 0.01. This range largely covers the possible variation of this parameter, as established in a previous CDF analysis [5]. The value k min JES that minimizes the χ 2 is chosen as the central jet-energy scale that matches simulation to data. The standard deviation on k min JES is determined to be the k JES interval corresponding to a symmetric unit variation in χ 2 .
The Z → bb cross section and jet-energy scale measurements are affected by systematic uncertainties. Some of them are related to differences between data and simulation, while others are related to the signal extraction procedure. The systematic uncertainty due to the statistical fluctuations of the background templates is estimated by generating simplified simulated experiments that fluctuate the number of events in each bin of the background templates and measuring the resulting bias. The effect of the finite size of the simulated signal template is evaluated analogously, and it affects both the cross section and the jet energy scale measurement. The systematic uncertainty due to the fixed proportion of cjets in the Bb and bB background templates is set by varying this percentage from 0 to 10%. The data-tosimulation online and offline b-tagging scale factors are affected by systematic uncertainties that propagate to the evaluation of the signal cross section. Two separate scale factors are evaluated. One parametrizes the combined data-to-simulation response of the trigger and the offline b-tagging, and it is applied to the b-tagged trigger jet. The other parametrizes the offline b-tagging scale factor, and it is applied to the second b-tagged jet. The systematic uncertainties related to these two sources are considered 100% correlated. Their energy dependence is also taken into account. The systematic uncertainty on the signal efficiency due to the CDF jet-energy correction is estimated by shifting the energy of simulated jets by the amount prescribed by the standard correction. Finally, the effect of decreased or increased final state radiation on the simulated signal is evaluated by generating samples with different final-state radiation tunings. The effect on the measurement of a particular choice of PDF is measured by generating samples using the CTEQ6L PDF set. Not all the PDF sets are considered since the impact of these variations is negligible. A summary of the systematic effects considered is shown in Table II. The Z-boson production cross section times the Z → bb branching ratio is calculated from Eq. (2). The measured value of σ Z × B(Z → bb) = 1.11 ± 0.08(stat) ± 0.14(syst) nb is consistent with the NLO theoretical calculation [18] which predicts σ Z × B(Z → bb) = 1.13 ± 0.02 nb. The significance of the signal observation is determined using simplified simulated experiments, including statistical and systematic uncertainties and it exceeds 5σ. The measured b-jet-energy scale is k JES = 0.993 ± 0.022(stat) ± 0.008(syst).
Since no significant H → bb signal is found, a 95% confidence-level (C.L.) upper limit is set to the cross section for inclusive Higgs-boson production followed by decay into a bb pair using the modified frequentist CL s method [19,20]. Simplified simulated experiments are generated based on the background description and the various assumed signal strengths. As test statistic we use the distribution of the difference in χ 2 between fits with a signal-plus-background model or background-only model, as resulting from fits of the simplified simulated experiments. The systematic uncertainties associated with the Higgs-boson search are the same as those considered for the Z-boson measurement. These uncertainties may affect both the normalization and the shape of the invariant-mass distributions. In the limit calculation they are introduced, using a Bayesian technique, as nuisance parameters over which the posterior probability is marginalized assuming Gaussian prior densities. Figure 3 shows the expected and observed CL s values as functions of the cross section times the branching ratio normalized to the standard-model H → bb prediction. The observed (expected) upper limit at 95% C.L. on the pp → H → bb process is measured to be 33 (46) times the standard-model cross section, which corresponds to a cross section of 40.6 (56.6) pb. This represents the first inclusive limit of the pp → H → bb process at √ s = 1.96 TeV.
The measurements reported in this Letter can be considered the CDF legacy for the σ(pp → Z) × B(Z → bb) determination and the inclusive Higgs boson production cross section limit.