Measurement of the ppbar ->W+b+X production cross section at \sqrt{s}=1.96 TeV

We present a measurement of the cross section for $W$ boson production in association with at least one {$b$-quark} jet in proton-antiproton collisions. The measurement is made using data corresponding to an integrated luminosity of 6.1\ifb recorded with the D0 detector at the Fermilab Tevatron \ppbar Collider at $\sqrt{s}=1.96$ TeV. We measure an inclusive cross section of {$\sigma(W \sim(\to\mu\nu) + b + X) = 1.04 \pm 0.05\thinspace$(stat.) $\pm 0.12 \thinspace$(syst.) pb} and $\sigma(W (\to e\nu) + b + X) = 1.00$ \pm 0.04 \thinspace$(stat.) $\pm 0.12 \thinspace$(syst.) pb in the phase space defined by $p_T^\nu>25$ GeV, $p_T^{\text{$b$-jet}}>20$ GeV, $|\eta^{\text{$b$-jet}}|<1.1$, and a muon (electron) with $p_T^\ell>20$ GeV and $|\eta^\mu|<1.7$ ($|\eta^e|<1.1$ or $1.5<|\eta^e|<2.5$). The combined result per lepton family is $\sigma(W (\to \ell \nu) + b + X) = 1.05$ $\pm 0.12 \thinspace$(stat.+syst.) for $|\eta^\ell|<1.7$. The results are in agreement with predictions from next-to-leading order QCD calculations using \textsc{mcfm}, $\sigma(W+b)\cdot {\cal B}(W \to \ell \nu)= 1.34 ^{+0.41}_{-0.34}\thinspace(\textrm{syst.})$, and also with predictions from the \textsc{sherpa} and \textsc{madgraph} Monte Carlo event generators.

We present a measurement of the cross section for W boson production in association with at least one b-quark jet in proton-antiproton collisions. The measurement is made using data corresponding to an integrated luminosity of 6.1 fb −1 recorded with the D0 detector at the Fermilab Tevatron pp Collider at √ s = 1.96 TeV. We measure an inclusive cross section of σ(W (→ µν) + b + X) = 1.04 ± 0.05 (stat.) ± 0.12 (syst.) pb and σ(W (→ eν) + b + X) = 1.00 ± 0.04 (stat.) ± 0.12 (syst.) pb in the phase space defined by p ν T > 25 GeV, p b-jet T > 20 GeV, |η b-jet | < 1.1, and a muon (electron) with p ℓ T > 20 GeV and |η µ | < 1.7 (|η e | < 1.1 or 1.5 < |η e | < 2.5). The combined result per lepton family is σ(W (→ ℓν) + b + X) = 1.05 ± 0.12 (stat.+syst.) for |η ℓ | < 1.7. The results are in agreement with predictions from next-to-leading order QCD calculations using mcfm, σ(W + b) · B(W → ℓν) = 1.34 +0.41 −0.34 (syst.), and also with predictions from the sherpa and madgraph Monte Carlo event generators. The measurement of the production cross section of a W boson in association with a b-quark jet provides a stringent test of quantum chromodynamics (QCD). Processes involving W/Z bosons in association with b quarks are also the largest backgrounds in studies of the standard model (SM) Higgs boson decaying to two b quarks, in measurements of top quark properties in both single and pair production, and in numerous searches for physics beyond the SM. The cross section for the process pp → W + b + X has been calculated with nextto-leading order (NLO) precision [1,2]. Subprocesses at NLO include qq → W bb, qq → W bbg, and qg → W bbq ′ . An additional small contribution comes from sea b quarks in the incoming proton or antiproton, * with visitors from a Augustana College, Sioux Falls, SD, USA, b bq → W bq ′ .
In this letter we describe a measurement of the cross section for W boson production in association with bquark jets in pp interactions, where a W boson is identified via its electronic or muonic decay modes. A measurement of W +b production cross section with up to two jets at √ s = 1.96 TeV has been published by the CDF Collaboration [3] and an inclusive measurement has been published by the ATLAS Collaboration [4] at √ s = 7 TeV. The measured production cross section reported by CDF is σ · B(W → ℓν) = 2.74 ± 0.27 (stat.) ± 0.42 (syst.) pb (ℓ = e, ν), while the theoretical expectation for this quantity based on NLO calculations is 1.22 ± 0.14 (syst.) pb [3]. With the CDF measurement of W + b production exceeding significantly the NLO prediction, while the ATLAS result is in agreement with the expectation, an independent measurement is important to understand the production of W bosons in association with b jets at hadron colliders.
The data used in this analysis were collected between July 2006 and December 2010 using the D0 detector at the Fermilab Tevatron Collider at √ s = 1.96 TeV, and correspond to an integrated luminosity of 6.1 fb −1 .
We first briefly describe the main components of the D0 Run II detector [5] relevant to this analysis. The D0 detector has a central tracking system consisting of a silicon microstrip tracker (SMT) [6] and a central fiber tracker (CFT), both located within a 2 T superconducting solenoidal magnet, with designs optimized for tracking and vertexing at pseudorapidities |η| < 3 and |η| < 2.5, respectively [7]. A liquid argon and uranium calorimeter has a central section (CC) covering pseudorapidities |η| 1.1, and two end calorimeters (EC) that extend coverage to |η| ≈ 4.2, with all three housed in separate cryostats [8]. An outer muon system, at |η| < 2, consists of a layer of tracking detectors and scintillation trigger counters in front of 1.8 T toroids, followed by two similar layers after the toroids. Luminosity is measured using plastic scintillator arrays located in front of the EC cryostats. The trigger and data acquisition systems are designed to accommodate the high instantaneous luminosities of Run II. The W + b candidates are selected by triggering on single lepton or lepton-plus-jet signatures with a three-level trigger system. The trigger efficiencies are approximately 70% for the muon channel and 95% for the electron channel.
W boson candidates are identified in the µ+ν and e+ν decay channels whereas a small fraction of selected events arises from leptonical decaying tau leptons. Offline event selection requires a reconstructed primary pp interaction primary vertex (PV) that has at least three associated tracks and is located within 60 cm of the center of the detector along the beam direction. The vertex selection for W + b events is about 97% efficient as measured in simulations.
Electrons are identified using calorimeter and tracking information. The selection requires exactly one electron with transverse momentum p e T > 20 GeV identified by an electromagnetic (EM) shower in the central (|η e | < 1.1) or endcap (1.5 < |η e | < 2.5) calorimeter by comparing the longitudinal and transverse shower profiles to those of simulated electrons. The showers must be spatially isolated from other energetic particles, deposit most of their energy in the EM part of the calorimeter, and pass a likelihood criterion that includes a spatial track match. In the central detector region, an E/p requirement is applied, where E is the energy of the calorimeter cluster and p is the momentum of the track. The transverse momentum measurement of electrons is based on calorimeter energy information.
The muon selection requires the candidate to be reconstructed from hits in the muon system and matched to a reconstructed track in the central tracker. The transverse momentum of the muon must exceed p µ T > 20 GeV, with |η µ | < 1.7. Muons are required to be spatially isolated from other energetic particles using information from the central tracking detectors and calorimeter [9]. Muons from cosmic rays are rejected by applying a timing crite-rion on the hits in the scintillator layers and by applying restrictions on the displacement of the muon track with respect to the selected PV.
Candidate W + jets events are then selected by requiring at least one reconstructed jet with |η jet | < 1.1 and p jet T > 20 GeV. Jets are reconstructed from energy deposits in the calorimeter using the iterative midpoint cone algorithm [10] and a cone of radius ∆R = 0.5 in y-ϕ space [7]. The energies of jets are corrected for detector response, the presence of noise and multiple pp interactions, and for energy deposited outside of the jet reconstruction cone. To enrich the sample with W bosons, events are required to have missing transverse energy E / T > 25 GeV due to the neutrino escaping detection.
Background processes for this analysis are electroweak W + jets/γ production, Z/γ * production, tt and single top quark production, diboson production, and multijet events with jets misidentified as leptons. The W +b signal and SM background processes are simulated using a combination of pythia v6.409 [11] and alpgen v2.3 [12] with pythia providing parton showering and hadronization. We use pythia Tune A with CTEQ6L1 [13] parton distribution functions (PDFs) and perform a detailed geant-based [14] simulation of the D0 detector. The V +jets (V = W/Z) processes are normalized to the inclusive W and Z-boson cross sections calculated at NNLO [15]. The Z-boson p T distribution is modeled to match the distribution observed in data [16], taking into account the dependence on the number of reconstructed jets. To reproduce the W -boson p T distribution in simulated events, the product of the measured Z-boson p T spectrum and the ratio of W to Z-boson p T distributions at NLO is used as correction. NLO+NNLL (nextto-next-to-leading log) calculations are used to normalize tt production [17], while single top quark production is normalized to NNLO [18]. The NLO W W , W Z, and ZZ production cross section values are obtained with mcfm program [19]. For the W +heavy-flavor jet (b or c quark) events, the ratio of the alpgen prediction to the NLO prediction for W + bb and W + cc is obtained from mcfm [19] and applied as a correction factor. The simulation is also corrected for the trigger efficiencies measured in data.
Instrumental backgrounds and those from semileptonic decays of hadrons, referred to as "multijet" background, are estimated from data. The instrumental background is important for the electron channel, where a jet with a high electromagnetic fraction can pass electron identification criteria, or a photon can be misidentified as an electron. In the muon channel, the multijet background is less significant and arises mainly from the semileptonic decay of heavy quarks in which the muon satisfies the isolation requirements. We require that the W boson candidates have a transverse mass M T [20] satisfying 40 GeV + 1 2 E / T < M T < 120 GeV to suppress multijet background and mis-reconstructed events. The average efficiency determined in simulation for a W + b signal to pass these requirements is about 82%.
Identification of b jets is crucial for this measurement. Once the inclusive W +jets sample is defined, the jets considered for b tagging are subject to a requirement called taggability. This requirement is imposed to decouple the performance of the b-jet identification from detector effects. For a jet to be taggable, it must contain at least two tracks with at least one hit in the SMT, p T > 1 GeV for the highest-p T track and p T > 0.5 GeV for the nextto-highest p T track. The efficiency for a jet to be taggable is about 90% in the selected phase space.
The D0 b-tagging algorithm for identifying heavy flavor jets is based on a combination of variables sensitive to the presence secondary vertices (SV) or tracks displaced from the PV. This analysis uses an updated b tagger utilizing a multivariate analysis (MVA) [21,22] that provides improved performance over the previous neural network based algorithm [23]. The most sensitive input variables to the MVA are the number of reconstructed secondary vertices in the jet, the invariant mass of charged particles associated with the SV (M SV ), the number of tracks used to reconstruct the SV, the twodimensional decay length significance of the SV in the plane transverse to the beam, a weighted combination of the tracks' transverse impact parameter significances, and the probability that the tracks from the jet originate from the PV, which is referred to as the jet lifetime probability (JLIP). The MVA provides a continuous output value that tends towards one for b jets and zero for non-b jets. Events are considered in which at least one jet passes a tight MVA requirement corresponding to an efficiency of ≈ 50% for b jets. The likelihood for a light jet (u, d, s quarks and gluons) to be misidentified for the corresponding MVA selection is about 0.5%. Simulated events are corrected to have the same efficiencies for taggability and b-tagging requirements as found in data. These corrections are derived in a flavor dependent manner [23], using independent QCD enriched data samples and simulated events with enriched light and heavy jet contributions. Jets containing b quarks have a different energy response and receive an additional energy correction of about 6% as determined from simulation. Figure 1 shows the transverse mass of the candidate events before and after applying b-jet identification.
In addition to the MVA output, we perform further selections using M SV and JLIP variables. M SV provides good discrimination between b, c, and light quark jets due to their different masses [22]. The two variables together take into account the kinematics of the event and, in order to further improve the separation power, they are combined in a single variable D MJL = 1 2 (M SV /(5 GeV) − ln(JLIP)/20) [24].A loose criterion for an event to pass at least D MJL > 0.1 is applied to remove poorly reconstructed events. The efficiency for signal events to pass this selection is about 97%.
The numbers of expected and observed events before and after applying the b-jet identification in data and simulation are listed in Table I   We measure the fraction of W +b+X events in the final selected sample by performing a binned maximum likelihood fit to the observed data distribution of the D MJL discriminant in our sample shown in Fig. 2. The templates for W +light flavor, W +b, and W +c jets shown in Fig. 2 are taken from the efficiency-corrected simulation. Expected contributions from Z+jets, single top quark, tt, diboson, and multijet production are subtracted from the data. After performing the fits, we obtain the number of events with different jet flavors listed in Table II. The measured cross sections are presented at the particle level by correcting for detector acceptance, selectionefficiencies, and b-jet identification. We quote our result as a cross section in a restricted phase space: at least one b-jet with p b-jet T > 20 GeV, |η b-jet | < 1.1 and a muon with p µ T > 20 GeV and |η µ | < 1.7 or an electron with p e T > 20 GeV and |η e | < 1.1 or 1.5 < |η e | < 2.5. For the neutrino momentum we require p ν T > 25 GeV.  Systematic uncertainties are determined by varying experimental parameters and efficiency/acceptance corrections by one standard deviation and propagating the effect on D MJL . The systematic uncertainties are dominated by effects related to the measurement of jets. The contributions from jet energy resolution, jet modeling, and detector effects are about 2.5%, 3%, and 4%, respectively. Uncertainties on b-jet identification are determined in data and simulations by using b-jet-enriched samples and are about 2%−5% per jet. The uncertainties due to lepton identification are about 2%. The integrated luminosity is known to a precision of 6.1% [25]. The uncertainty of the template fit is estimated by varying the normalization and shape from the data corrections of the W boson processes and the fit parameters (about 6%). By summing the uncertainties in quadrature we obtain a final total systematic uncertainty on the cross section measurements of approximately 12%.
The cross section times branching fraction is calculated by dividing the number of signal events measured by integrated luminosity (L), acceptance (A), and efficiencies (ǫ) of the selection requirements: where ǫ is given by the product of the trigger, object reconstruction, and selection efficiencies. We first present results separately for the muon channel and electron channel because they are performed in slightly different requirements on the phase space of the lepton and then combine using a common phase space. We measure from the cross section in the muon channel where W → µν in a visible phase space defined by p µ T > 20 GeV, |η µ | < 1.7 with at least one b-jet limited to p b-jet T > 20 GeV and |η b-jet | < 1.1 as, σ(W + b) · B(W → µν) = 1.04 ± 0.05 (stat.) ± 0.12 (syst.) pb.
We perform an NLO QCD prediction using mcfm v6.1, based on CTEQ6M PDF [13] and a central scale of GeV is the mass of the b quark. Uncertainties are estimated by varying renormalization and factorization scales by a factor of two in each direction, varying m b between 4.2 and 5 GeV, and by using an alternative PDF set. The mcfm calculation predicts σ(W + b) · B(W → µν) = 1.34 +0.40 −0.33 (scale) ± 0.06 (PDF) +0.09 −0.05 (m b ) pb. Predictions obtained using sherpa v1.4 and CTEQ6.6 PDFs [13] lead to a value 1.21 ± 0.03 (stat.) pb. Using madgraph5 [26] with CTEQ6L1 PDFs, we obtain 1.52±0.02 (stat.) pb. Uncertainties for scale variations, PDFs, and the b-quark mass are on the order of about 30%.
Using the mcfm prediction we extrapolate the measurement in the electron final state to the same selection requirements as the muon final state to allow for a consistent combination. Combining the results in W → µν and W → eν decays we obtain σ(W + b) · B(W → ℓν) = 1.05 ± 0.03 (stat.) ± 0.12 (syst.) pb.
The small experimental uncertainty should allow to further constrain theoretical predictions. In summary, we have performed a measurement of the inclusive cross section for W boson production in association with at least one b-jet at √ s = 1.96 TeV, considering final states with W → µν (W → eν) events in a restricted phase space of p ℓ T > 20 GeV, |η µ | < 1.7 (|η e | < 1.1 or 1.5 < |η e | < 2.5), with b jets limited to p b-jet T > 20 GeV and |η b-jet | < 1.1. The measured cross sections agree within uncertainties with NLO QCD calculations and predictions obtained using the sherpa and madgraph generators.