conservatively been doubled compared to the uncertainties quoted in sections8and13to account for the extrapolation from the positive-tagging efficiency to the negative one. The resulting uncertainties are generally below 10%.
Long-lived particle decays, material interactions, fake tracks
The products from decays of long-lived particles, e.g. Ks, Λ0, hadronic interactions or photon conversions in the detector material (mainly interactions in the first material layers of the detector), may cause reconstructed secondary vertices in light-flavour jets. While the secondary vertex based algorithms apply a veto to secondary vertices consistent with these decays or interactions, not all of them can be detected and there is a sizable fraction of vertices where one track arising from such decays or interactions is paired with a track from a different source into a vertex. Fake or badly measured tracks may also give rise to additional vertices.
To estimate the resulting systematic uncertainty from an imperfect modelling of the rate of such vertices in simulated events, the fraction of jets containing fake tracks, long-lived particles likeKs andΛ0or material interactions have been varied based on estimates in data, before the application of their suppression criteria. The modelling of fake tracks is evaluated using the fraction of jets containing tracks with χ2/Ndof > 3. The difference in the fraction of such tracks between data and
simulated events is found to be 30%, which is assigned as a systematic uncertainty. The fraction of jets withKs orΛ0 decays in data and simulation are compared by counting the number of events in theKs andΛ0 mass peaks. As the fraction of reconstructedKs andΛ0candidates is consistent between data and simulation, the statistical uncertainty of the estimate, which is approximately 10%, is used as a systematic uncertainty. Finally, the uncertainty associated with jets with a hadronic interaction or photon conversion is estimated in simulated events, considering jets containing a selected track produced at a radial distance from the beam liner > 25 mm. About 80% of all jets have at least one such track, and a systematic uncertainty of 10% is assigned to this fraction, based on the precision with which the material in the detector is known. The resulting uncertainties are up to 7%, with the largest effects originating from hadronic interactions.
Track multiplicity
The simulation does not properly reproduce the multiplicity of tracks associated with jets observed in data. This could be due to imperfect modelling of fragmentation differences in the relative fraction of quark and gluon jets in the light-flavour sample or differences between data and simulation in the track reconstruction efficiency in the core of jets where the track density is high. A higher track multiplicity implies a larger probability of accidentally tagging a light-flavour jet as ab jet for purely combinatorial reasons. The systematic uncertainty in the negative tag analysis due to the track multiplicity is estimated by reweighting the jet sample according to the ratio of distributions of the number of tracks associated to jets in data and simulation. The effect of the track multiplicity reweighting ranges between approximately 5% at low jet pT and over 40% at high jet pT in the
forward region. The track multiplicity systematic uncertainty affects the higher jet pT bins more because the discrepancy between data and simulation is larger in this region, presumably due to an imperfect modelling of track reconstruction in the core of high-pTjets in simulated events as well as
to an imperfect description of the track multiplicities over a wide range of jet transverse momenta in the generator.
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Impact parameter resolution
The secondary vertex reconstruction is very sensitive to the tracking resolution and the proper estimation of the track parameter errors, especially in light-flavour jets where a large contribution of fake vertices is present. It has been shown in section 7.1 that the track impact parameter resolutions in simulation are slightly better than those in data. Therefore, track impact parameters in the simulation have been smeared in order to bring data and simulation into better agreement. The chosen smearing approach does not take into account correlated modifications of the impact parameters of tracks that pass through the same pixel module, as would be needed to model residual misalignments in the Inner Detector. The parameters for the smearing have been chosen to cover the observed discrepancies in the impact parameter resolution between data and simulation. After having applied the track impact parameter smearing to the tracks in simulation, the primary vertex reconstruction andb-tagging have been rerun and the whole analysis repeated. The effect in the negative tag analysis is approximately 5% in the centralη region but can be as large as 22% in the forwardηregion where the modelling of the impact parameter resolution is worse.
Given that the impact parameter sign for tracks associated with a jet depends on the direction of the tracks relative to the jet direction (unless a secondary vertex is found, as detailed in section3.2), the finite jet angular resolution results in a degree of arbitrariness for tracks nearly aligned with the jet direction. The factorskhfandklltherefore are sensitive to this resolution, and the uncertainty on the angular resolution in principle translates into uncertainties onkhfandkll. In practice, however, smearing the jet directions in the simulation as done in section8.3 has a negligible effect on the impact parameter significance distributions, and consequently on the predicted mistag rate.
14.4 Results
The measured mistag rates in data, the mistag rates in simulation and the resulting data-to-simulation scale factors for the MV1 tagging algorithm at 70% efficiency are shown in figure54for two different regions of the jet pseudorapidity.
For the MV1 tagging algorithm at the 70% efficiency operating point the efficiency in data tends to be higher than in simulation, leading to data-to-simulation scale factors that are about 1.2 and 1.4 in the central and forward directions, respectively.
15 Mistag rate calibration of the soft muon tagging algorithm
The probability with which a light-flavour jet is tagged by the SMT algorithm, referred to as the mistag rate, is measured in data using an inclusive jet sample. The method is designed to minimise biases from heavy-flavour jets and to make minimal use of information obtained from simulation.
15.1 Data and simulation samples
To cover a wide transverse momentum range, the events are required to pass one of several inclu- sive jet triggers, with pT thresholds ranging between 10 and 40 GeV. Only events in which the reconstructed primary vertex has at least five tracks associated to it are considered.
The data are compared to the same set of simulated QCD jet samples used in the negative tag analysis (see section14.1).
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[GeV] T Jet p 30 40 50 102 2×102 Mistag rate 0 0.01 0.02 0.03 0.04 0.05 ATLAS∫
L dt = 4.7 fb-1, s = 7 TeV = 70% b ε MV1, | < 1.2 jet η | negative tag Data (stat) Data (stat+syst) Simulation (stat) (a) [GeV] T Jet p 30 40 50 102 2×102Mistag rate scale factor
0 0.5 1 1.5 2 2.5 ATLAS
∫
L dt = 4.7 fb-1, s = 7 TeV negative tag Scale factor (stat)Scale factor (stat+syst) MV1, εb = 70%
| < 1.2 jet η | (b) [GeV] T Jet p 30 40 50 102 2×102 Mistag rate 0 0.02 0.04 0.06 ATLAS
∫
L dt = 4.7 fb-1, s = 7 TeV = 70% b ε MV1, | < 2.5 jet η 1.2 < | negative tag Data (stat) Data (stat+syst) Simulation (stat) (c) [GeV] T Jet p 30 40 50 102 2×102Mistag rate scale factor
0 0.5 1 1.5 2 2.5 ATLAS
∫
L dt = 4.7 fb-1, s = 7 TeV negative tag Scale factor (stat)Scale factor (stat+syst) MV1, εb = 70%
| < 2.5
jet
η
1.2 < |
(d)
Figure 54.The mistag rate in data and simulation (left) and the data-to-simulation scale factor (right) for the MV1 tagging algorithm at 70% efficiency for jets with|η|<1.2 (top) and jets with 1.2<|η| <2.5 (bottom).
15.2 Mistag rate measurement
The method to measure the mistag rate with collision data is based on a system of three equations and three unknowns (among which the mistag rate). The IP3D+JetFitter lifetime tagging algorithm (see section3.4) is used as an auxiliary tagging algorithm to enhance the inclusive jet sample in light-flavour jets. Two samples are selected from events with exactly two jets, one in which one jet is not tagged by the IP3D+JetFitter algorithm (single-veto sample) and one in which neither jet is tagged by the IP3D+JetFitter algorithm (double-veto sample). In the latter sample the fraction of heavy-flavour jets is expected to be considerably suppressed. As the amount of heavy-flavour jets in the double-veto sample largely determines the uncertainty on the mistag rate measurement, the operating point of the IP3D+JetFitter algorithm is chosen to correspond to a high efficiency (80% in simulatedtt¯events).
The number of jets in data which are tagged by the SMT in each of the two above samples is given by NSMT= N× f εSMT HF · fHF + εSMT LF ·[1− fHF] g , (15.1) NSMT0 = N0×fεSMTHF · fHF0 +εSMTLF ·[1− fHF0 ]g, (15.2)