When a b-quark is produced, such as in top quark decay, it hadronizes into a semi-stable par-ticle which lives long enough to travel an often measurable distance within the detector before decaying into a b-jet. Dedicated “b-tagging” algorithms are used to identify them, generally based on either the displacement of the jet or its composition, which differs from light jets.
Two different b-tagging algorithms are used in this thesis, one of each type. A lifetime tagger algorithm, “JetProb” [109], which compares the impact parameter significance to a resolution function is used in the R
Ldt= 35 pb−1 analysis in Chapter 7. A significantly more advanced tagger,“CombNNJetFitter” [110], is used as the discriminant in the top pair cross-section with W heavy flavor analysis in Chapter 9. The performance of these two b-tagging algorithms and others is compared in Figure 4.6. These algorithms can also be used to identify cquarks, owing to their non-negligible mass, although since they are lighter theb-quarks their behavior is some-where in between that of light jets and that of b-jets. The analysis shown in Chapter 9 makes use of this as well.
The JetProb Algorithm
The JetProb algorithm compares the signed impact parameter significance of each track in a jet to a resolution function for prompt tracks, yielding a probability that it is prompt, i.e. that it originates from the primary vertex. The probability for each track is multiplied together, giving a probability that the jet is not constituted of any long-lived particles. This algorithm was widely used in analyses with the 2010 dataset. It is used in the analysis presented in Section 7.
A more complete description of the algorithm can be found, for instance, in [109].
4.4 The b-tagging Algorithms
jet
p
T50 100 150 200 250 300 350 400 450 500
Light jet rejection
200 400 600 800 1000
JetProb SV0 IP3D SV1 IP3D+SV1 JetFitter IP3D+JetFitter
ATLAS Preliminary
=7 TeV s
simulation, t
t
b
=60%
ε
|<2.5, η
jet|
Figure 4.6: The expected performance of various b-tagging algorithms for a working point of εb = 60 % efficiency for jets within |η| < 2.5. The light-jet rejection is plotted as a function of the pT of the jet. The advanced taggers (such as the CombNNJetFitter, called in this plot I3PD+JetFitter, brown circles) show a clearly improved performance over the simple taggers (for instance JetProb, black squares). Here, t¯t MC is used as a source of b-jets. Image from [110].
The CombNNJetFitter Algorithm
The CombNNJetFitter Algorithm is an advanced tagger which became available for the summer 2011 dataset, a result of a considerably more precise knowledge of the detector [110]. This algorithm takes a great deal of information into account. Two separate discriminants, “IP3D”
and “JetFitter”, are constructed before being combined using a neural network. The IP3D algorithm is essentially an extension of the JetProb algorithm described above. It uses both the signed impact parameter significance and the longitudinal impact parameter significance, yielding a 3-dimensional impact parameter algorithm, hence its name. The JetFitter algorithm approximates the flight path of a B-hadron using the decay topology of weak heavy flavor (b,c) decays inside of jets using a Kalman filter [111]. Additional vertex properties, such as its invariant mass, are taken into account in a final likelihood to discriminate betweenb,c, and light jets. A more complete description of the algorithm can be found in [110]. The two algorithms
are combined using a neural network trained on MC samples, achieving a fine discrimination amongst jet flavors.
Calibration of the b-tagging Algorithms and Associated Systematic Uncertainties
A number of complimentary methods exist for calibrating b-tagging algorithms. The essential issue at hand is that a number of effects enter into theb-tagging efficiency and light-jet rejection, such that calibration using data is expected to be necessary. Many methods were used for calibrating the algorithms on theR
Ldt= 35 pb−1dataset, which showed consistent results [112].
The main method is known asprelT , which exploitsb-jet decays in which a muon is present due to the semi-leptonic decay of a B-hadron. The variable is defined as the momentum of the muon transverse to the jet+muon axis, expected to be harder on average for a muon from ab-jet decay than a muon originating from ac-jet or light jet. A MC template fit to data is done before and after b-tagging in order to extract the b-tagging efficiency. This method has also been used to calibrate the JetFitter algorithm for the R
Ldt = 0.7 fb−1 dataset.
Calibration of the algorithms are given as scale factors between the efficiency measured in data and that predicted by the MC. This conveniently allows one to use the ratio as an event weight. In the analyses presented here, no explicit cut on the output of theb-tagging algorithm is made, rather the distribution is used to discriminate amongst the physical processes present.
Many other analyses use the algorithms to select events by explicitly requiring that at least one jet has been “tagged”, that is, the algorithm’s output is above a certain value corresponding to a specific tagging efficiency and light-jet rejection. Such working points are calibrated by defining the ratio of the probability to tag a jet in data to that in the MC, SFi =Ptag,idata/Ptag,iMC. The calibrations for four working points are provided for each algorithm in each dataset used here.
In these analyses, no cut on the algorithm’s output is used but rather the entire distribution is. This requires calibration for the entire algorithm, not just at the working points. In order to calibrate continuously, interpolation is employed. For a value falling in between the calibrated working pointsiand i+1, the scale factor can be interpolated as
SFi,i+1= Ptag,idata−Ptag,i+1data
Ptag,iMC −Ptag,i+1MC = SFi×Ptag,iMC −SFi+1×Ptag,i+1MC Ptag,iMC −Ptag,i+1MC
All values below the lowest point get its calibration, and similarly those above the highest get its.
As a weight, the calibration is used as a multiplicative scale factor for each event. That is, the SF is calculated for each jet in the event and multiplied to get an event weight. In this way, the continuous b-tagging distribution is calibrated. After application, the integral is renormalized back to its previous value, in other words, the shape of this distribution is affected but not the rate.
Uncertainty due to the b-tagging algorithm calibration
The scale factors used to calibrate the distribution have an uncertainty associated with them, which is used to evaluate the associated systematic uncertainty in the analysis. Each of the scale factors are shifted one at a time, then interpolated using the above formula and applied to the distribution in order to distort its shape. Every working point is taken as uncorrelated, a very conservative assumption. The same is done for the mistagging rate of light jets.
5 Modeling of Signal and Background Processes
The physical process expected to contribute to the events selected in data are modeled using either MC simulation or a data-driven technique. The kinematics of contributions from the signal t¯t process and electroweak backgrounds, namely single top, Z+jets, and di-boson production, are modeled using MC simulation. The overall rate is then normalized to the most precise available inclusive cross section using a k-factor or to a measurement in the data. This will be described in the first section of the chapter. Uncertainty on the final analysis caused by the modeling and rate of these processes will be considered as well. The contribution to the selected data of QCD multijet events with a mis-reconstructed lepton and ETmiss are estimated in each dataset. This procedure and its associated uncertainties will be discussed in the second section of this chapter.
5.1 Monte Carlo Simulation of Physical Processes
Monte Carlo simulation is used to make differential predictions used in the analyses presented in this thesis. Different MC generators are used depending on the physical process involved, but all nominal samples use HERWIG [113, 114] for modeling the showering of partons after generation (PS). Most samples use the CTEQ6 PDF set [62], either CTEQ6.1L for the LO MC samples or CTEQ6.6 for NLO samples. In some cases the modified LO MRST2007lomod PDF set has been used, following studies which show that it is expected to better represent the data than CTEQ6.1L [115, 116].
Modeling of Top Processes
For processes involving both top pair and single top production, NLO generators have been available for a few years. The generator MC@NLO [8, 9] is used as the nominal, a generator which uses a diagram subtraction scheme to cancel unphysical contributions which enter the calculations. This leads to about 10% of events having a weight of -1 (instead of the normal +1). The overall cross section is normalized to the inclusive approximate NNLO calculations, discussed in Section 2.3, using a k-factor of 1.117.
Alternative Generators
A number of variations of the MC modelingt¯tproduction have been produced in order to eval-uate systematic uncertainties arising from signal modeling. The difference between the nominal signal sample and each alternate is considered as a systematic uncertainty in the analyses. A second NLO generator, POWHEG [10] is available and used to evaluate uncertainty due to the choice of generator. The two NLO generators, MC@NLO and POWHEG, use different tech-niques to match NLO matrix elements to parton showers in order to avoid double-counting of
phase space [7]. The effects of the two approaches to this, as well as and other differences be-tween the two generators, are investigated in [11]. A comparison of basic kinematic distributions from the two generators is shown in Appendix B.
To model PS uncertainty, the generator is interfaced to PYTHIA[117] instead of HERWIG.
Due to an inability to interface MC@NLO to PYTHIA, POWHEG is used instead. Another set of samples is used to model the initial state radiation (ISR) and final state radiation (FSR) of the system. Neither of the NLO generators are particularly tunable in this respect; indeed there has been much discussion within the collaboration as to wether or not such radiative effects are well defined at NLO at all. In order to vary the ISR and FSR, a LO generator, AcerMC [118] is used. Samples are produced with the nominal settings as well as additional samples with both more and less ISR and FSR.
PDF Uncertainty
The PDF sets used in MC generation are generally provided along with error sets, quantifying the uncertainty of the PDF itself. A prescription based on the PDF4LHC working group is applied to the t¯t signal [119], which uses event reweighting to asses the uncertainty without needing to regenerate the MC. For each parameter in the PDF with an error, an event weight is calculated based on the truth information for each event taking into account the initial state parton type, its longitudinal momentum fraction, and momentum transfer in the interaction.
The signal sample is generated using the CTEQ66 PDF set, which has 22 parameters each with an up and down uncertainty, yielding 44 variations. Each error is first treated independently, creating a systematically shifted MC sample for each. The envelope of these variations is then calculated. For the distribution in question, the difference of the shifted sample with respect to the nominal is taken bin-by-bin, adding in quadrature all contributions with a net “up” effect, and similar for down. In this way, a single up-shifted sample and down-shifted sample with maximum deviation from the nominal is calculated from the error set.
W/Z+Jets Samples
Samples modeling theW+jets andZ+jets (orV+jets, to denote both) processes are produced using ALPGEN [120, 83]. In ALPGEN, an inclusive sample is generated in multiple sub-samples, split in terms of the number of partons in the matrix element (ME). Each sample is then showered using HERWIG, so an individual parton sample does not correspond to a specific jet bin. A procedure known as MLM matching is used to bookkeep the phase space and ensure that no region is double counted; otherwise it would be possible for one parton from the ME in one subsample and the PS in another to both over-represent a part of the phase space [83]. Samples are produced, with 0 to 5 partons in the ME. The 5-parton ME sample is in principle inclusive of the higher jet bins, but in practice it is expected that the kinematics of the samples should be reasonably modeled until the 6th jet bin (accounting for at least one well-modeled jet coming from the PS).
Samples are further split by flavor. It is taken that md =mu=ms= 0, but both c andbare treated as massive. Dedicated heavy-flavor samples are also produced, modeling the processes V +b¯b+jets andW +c¯c+jets [84]. For these samples, there is always QQ¯ in the ME. Samples with 0-3 additional partons in the ME are produced, yielding again a maximum of 5 partons in the ME. Similarly, the process W +c/¯c+jets is produced with up to 4 additional partons in the ME. The processes Z +c/¯c+jets is not modeled, and only the PDF contribution to V +b/¯b+jets is modeled. In the light parton samples, heavy-flavor jets can arise in the PS which could potentially lead to double-counting once dedicated heavy flavor samples are added,
5.1 Monte Carlo Simulation of Physical Processes
and vice-versa. A Heavy Flavor Overlap Removal (HFOR) scheme is used to ensure that flavor contributions are not over counted, in the same vein as the MLM matching [121].
In generation, a filter is applied such that the boson decays in a dedicated channel. Here, samples withW →lνandZ →llare generated, wherel=e, µ, τ. All told, the “W+jets sample”
contains 57 subsamples: (6 different MEs for the W+light jets ×3 leptons)+ (4×3 W+b¯b) + (4 ×3 W+c¯c) + (5×3 W+c/¯c), and similarly forZ+jets without thec/¯ccontribution. These samples are merged using the cross sections given by ALPGEN, which take into account the efficiencies of the MLM procedure. Efficiencies from HFOR are not taken into account explicitly, but heavy flavor contributions are normalized after the fact, discussed below.
Sample Normalization
The normalization is done in several steps. In general these analyses are not particularly sensitive to the overall normalization ofW+jets andZ+jets but are to the relative contribution of heavy flavor final states. The process of normalization begins with applying generic LO to NLO k-factors of 1.20 and 1.25 are to all W+jets and Z+jets subsamples, respectively. For the Z+jets process, a relatively minor background contribution in this analysis, the normalization ends there. For W+jets however, the heavy flavor component is then rescaled to the values measured by the ATLAS collaboration in data. In doing this, the overall W+jets cross section is preserved but the relative contributions of the light and heavy flavor samples changes. This is particularly important for the R
Ldt= 35 pb−1 analysis, which is flavor sensitive but does not measure theW flavor components, rather it is affected by their values and uncertainties. For the dataset analyzed in Chapter 7, the normalization for W+b¯band W+c¯chas been measured to be 1.3±0.65 larger in data than in MC and is therefore scaled accordingly [17]. No measurement of W+c/¯c was available. The overall normalization uncertainty grows from jet bin to jet bin.
For the 2011 analyses in Chapters 8 and 9, one further step was taken. In addition to measuring the heavy flavor fractions, theW+jets normalization in each jet bin was measured, yielding a jet-bin and lepton-channel dependent normalization factor[122]. The charge production asymmetry of W bosons in proton-proton collisions is used. The factors are measured with respect to the LO×k-factor cross sections and summarized in Table 5.1. The different kinematic cuts in the two lepton channels motivate separate treatment of the normalizations despite the fact that the underlying physics is identical. Beyond the overall sample normalization, the W+b¯band W+c¯c fractions were remeasured on the increased dataset and found to be a factor of 1.63±0.76 larger in the data than nominal MC while W+c/¯cis a factor of 1.11 ±0.35 larger, both measured the lepton + 2-jet bin [122]. The values are compared with the measurement in the earlier dataset in Table 5.1. The relative contribution of these processes to the W+jets sample are shifted accordingly, preserving the overall normalization. TheW+jets normalization uncertainty grows with increasing jet bin.
Shape Uncertainty
Given the reliance of the analysis on the modeling of W+jets, the simulated kinematics of the sample are varied to represent a source of systematic uncertainty in the analysis. This “shape”
uncertainty is factorized from the rate uncertainty, where the former is explicitly handled in the fit. The shape uncertainty is taken into account by varying the generator parameters in ALPGEN. A truth-level study was done to study the effects of various parameters. Truth samples with varied parameters for all light parton contributions are generated for the processW →µν + jets. Since the study was undertaken at truth level, the muon sample is taken as representative of both lepton channels. The subsamples were combined using their nominal generator cross
Jet Bin Scaling (µ) Scaling (e)
1 jet 0.983 0.948
2 jets 0.942 0.907
3 jets 0.870 0.881
4 jets 0.849 0.839
4 jet (inclusive) 0.814 0.906 5 jet (inclusive) 0.687 1.098
Table 5.1: Summary of the scaling for each channel in theR
Ldt = 0.7 fb−1 analyses. Values have been measured in [122].
Process Dataset Scaling Uncertainty fWHF R
Ldt= 35 pb−1 1.3 0.65
fWc R
Ldt= 35 pb−1 - -fWHF R
Ldt = 0.7 fb−1 1.63 0.76
fWc R
Ldt = 0.7 fb−1 1.11 0.35
Table 5.2: Summary of the scaling used on the W heavy flavor components. Values represent the scaling factor needed for MC to match the data, as have been measured in [122] and [17].
section to properly account for the contributions of the various parton multiplicities. The overall normalization is arbitrary as the entire sample was always normalized back to the nominal, in order to consider only shape effects.
To be able to use the results of the study in a physics analysis, functions are derived to reweight the nominal reconstructed W+jets MC simulation to behave like the variation. It was found that the transverse momentum of leading jet approximates the overall kinematic differences in the variation quite well. To derive the functions, a basic event selection is applied. A function F(pT) is fit to the ratio of the leading jetpT in the sample with nominal settings to that in the sample with varied settings. The ratio is found to depend on the number of jets present and is therefore considered in each jet bin separately.
The following variations have been investigated:
• Renormalization scale (ktfac), varied up and down by a factor of 2.
• Factorization scale (qfac), varied up and down by a factor of 2.
• Functional form of the factorization scale (iqopt), varied from default (MW2 +P
jetsPT2) to MW2 and MW2 +PT2(W).
• MinimumpT of matrix element partons (ptjmin), varied from default of 15 GeV to 10 and 20 GeV.
• Variations on underlying event and radiation effects.
The study looked at the effects of basic kinematic quantities of objects, namely thepT andη of the objects involved. It has been observed that the shape variations due to iqopt and ptjmin were significantly larger than the others and of a similar magnitude as one another. Other variations were either smaller in magnitude, or not enough statistics were available to discern clear behavior.