Inclusive b-jet Production in ATLAS

The production of high-pT b-jets at the Large Hadron Collider LHC is an important process probing perturbative QCD at next-to-leading order. High-pT b-jets also form a significant background to many Standard Model and Beyond the Standard Model physics channels at the LHC. Measurements of the inclusive differential and dijet cross section of b-jets in proton-proton collisions at √ s = 7TeV, using data collected with the ATLAS experiment corresponding to an integrated luminosity of 3pb−1 is presented. These results are compared to NLO QCD predictions.


INTRODUCTION
The new energy regimes available with the LHC provide an excellent testing ground for probing production of b-jets in proton-proton collisions using perturbative QCD (pQCD).The measurement of the b-jet production cross section not only is a test of theoretical predictions in pQCD, but also can be used to constrain the heavy flavour content in proton PDFs.Furthermore, understanding a substantial fraction of background events in many searches for physics beyond the Standard Model depends on the precise measurements of the inclusive b-jet cross section.
In this paper details of the b-jet cross section measurements with the ATLAS detector [1] at the LHC are highlighted.The identification of b-jets is described in the first part, results on the cross section measurements are summarised in the second part.The next-to-leading order (NLO) calculations in pQCD have been used to produce particle final states, which have been compared to data.

TRIGGER AND RECONSTRUCTION
All results presented in this paper are based on data that have been collected between March and August 2010 at the ATLAS detector, corresponding to an integrated luminosity of about 3.0 pb −1 of proton-proton collisions at √ s = 7 TeV.Events are triggered by a combination of Level-1 jet triggers and a minimum bias trigger for low-p T jets, resulting in a trigger efficiency for b-jets of more then 98 %.Jets are reconstructed using the anti-k t algorithm [2] with a radius of R = ∆η 2 + ∆φ 2 < 0.4.Depending on the jet p T , the systematic uncertainty on the jet energy scale varies between 5 % and 9 %, the reconstruction and selection efficiency of b-jets is above 99 % [3].
Jets originating from bor b-quarks are identified by b-tagging algorithms.The lifetime of B hadrons of about 1.5 ps and consequently a typical flight time of a few millimetres leads to a jet topology with a displaced secondary vertex.The SV0 b-tagging algorithm [4] explicitly tries to reconstruct a displaced vertex by taking into account all particle tracks and muons associated to a jet.From those tracks, two-track vertices are built and merged into one common vertex.Two-track vertices compatible with the primary vertex or the radii of one of the three Pixel Detector layers are removed.From the common vertex, tracks contributing with a large χ 2 are iteratively removed, until the reconstructed vertex fulfils several quality criteria, e.g. the largest χ 2 contribution from any track is 7 or less and the invariant vertex mass is required to be less then 6 GeV.
The final output of the SV0 tagging algorithm is the signed decay length significance L/σ (L), which is used as b-tagging weight, where L is the signed decay length and σ (L) its error.The b-tagging weight distribution is shown in the Figure 1 (left) for three different kinds of jets: b-jets, c-jets and light flavoured jets.The b-tagging efficiency is determined in a sub-sample of the data, containing at least one muon with p T > 4 GeV associated to a jet.Muons originating from B hadrons have a harder p rel T spectrum than non-b-jets, where p rel T is the momentum component perpendicular to the axis of an associated jet.Template p rel T spectra are created for band non-b-jets using simulated data and fitted to the data using a binned maximum likelihood fit.The relative contributions of the templates in the fit correspond to the b-tagging efficiency, as shown in the Figure 1 (right) for events with L/σ (L) > 5.72.This cut corresponds to a b-tagging efficiency of 50 % in simulated events and is also used in the cross section measurement.More details on the p rel T template fit method can be found in [5].

MEASUREMENT OF THE b-JET PRODUCTION CROSS SECTION
The differential cross sections for inclusive b-jets in bins of jet transverse momentum p T and rapidity y and for pairs of b-jets (dijets) in bins of the dijet mass M can be written as where N b is the total number of b-jets tagged by the SV0 algorithm and f rac b is the fraction of true b-jets determined by applying a Monte Carlo template fit to the spectrum of the invariant mass of the secondary vertex.N bb is the number of events events with two b-jets and f rac bb is the fraction of events with two true b-jets, determined by a template fit of the sum of the two secondary vertices.ε trig and ε sel are the trigger and jet reconstruction efficiencies, ε btag (ε btag,bb ) is the b-tagging efficiency for b-jets (dijets) and L is the total integrated luminosity.Finally, C is a bin-by-bin unfolding correction applied to the cross section taking into account bin migrations between reconstructed jet p T and the p T of a truth jet containing a true B hadron.All above values have been measured in bins of p T and y or in bins of the dijet mass M. The following measurements are compared to predictions from Pythia 6 and NLO calculations derived by POWHEG.
Figure 2 (left) shows the inclusive double-differential b-jet cross section as a function of p T and |y|, in the range 20 GeV < p T < 260 GeV and for |y| < 2.1.As Pythia is a leading-logarithmic parton power shower generator, it is not expected to get the normalisation correct [3], therefore the Pythia results are scaled by a factor of 0.52.While both cross sections from Pythia and POWHEG fall more quickly than the measured one, the model shapes are consistent with data within indicated uncertainties.The systematic uncertainty is dominated by the b-jet energy scale followed by uncertainties due to the determination of b-tagging efficiency and purity.
The ratio of b-jet to inclusive jet cross section is shown in the Figure 2 (right), again as a function of jet p T and |y|.The b-jet fraction is underestimated by POWHEG by approximately 30 %, corresponding to about 1 σ of the systematic uncertainty, whereas the Pythia predictions are closer to the measured ratio.As the jet scale uncertainty largely cancels in the ratio, the dominant uncertainties arise from b-tagging efficiency and purity determination.
Figure 3 shows the differential b b dijet cross section as a function of the dijet mass M. Both b-jets are required to have a transverse momentum of of p T > 40 GeV and to be within |y| < 2.1 in order to be fully reconstructed.With the same scaling factor of 0.52, the measured data is well described by Pythia, whereas it can be seen, that POWHEG overestimates the b b cross section at lower dijet mass.The systematic uncertainty of this measurement is dominated by the determination of the b-tagging efficiency, followed by jet scale uncertainty.

CONCLUSION
The differential inclusive and dijet cross section of b-jets has been measured at ATLAS using the SV0 b-tagging algorithm and compared to predictions of Pythia and with the NLO QCD calculations performed within a framework of the POWHEG generator.This paper was supported by the Austrian Ministry of Science and Research BM.WF and the Austrian Science Fund FWF project P22982.Copyright CERN for the benefit of the ATLAS collaboration.

FIGURE 1 .
FIGURE 1. Left: The SV0 signed decay length significance L/σ (L) for simulated events.Right: The result of a template fit to the p rel T distribution for jets with 40 GeV < p T (jet) < 60 GeV.Figures taken from [5].

FIGURE 2 . 3 FIGURE 3 .
FIGURE 2. Inclusive double-differential b-jet cross section (left) and ratio of b-jet to inclusive jet cross section (right) as a function of jet p T for different bins of rapidity.Data is compared to Pythia predictions (rescaled by a factor of 0.52) and to POWHEG.Figures taken from [3].