Physics Modeling

The uncertainties described in this section account for two different effects. First, many processes can lead to a signature similar to tt¯events in the detector, but not all of them can be taken into

account in the simulation and the ensemble testing procedure. Secondly, the description of the processes that are accounted for may still be subject to uncertainties. Such additional uncertainties

6.5. Systematic Uncertainties 99 arise for example from the modeling of the parton distribution functions, the fragmentation of the

bquarks, and the modeling of additional jets from initial- and final-state radiation.

Parton Distribution Functions

As the parton distribution functions yield the probability to find a parton of a certain flavor and mo- mentum fraction inside the proton or antiproton, the kinematic distributions of the Monte Carlo events directly depend on the PDFs. The simulated events used to calibrate the measurement are based on the leading-order PDF set CTEQ6L1. However, systematic uncertainties are only provided for the next-to-leading order PDF set CTEQ6.1M. Therefore, the top quark mass is re- computed using a calibration based on the central CTEQ6.1M PDF set, and the difference between that value and the ones obtained with the systematic variations of the CTEQ6.1M PDF are added according to ∆mPDF+_top = s 20

∑

m+_top,i−m0_top,m_top,− _i−m0_top,02 (6.7)

∆mPDF_top − = s 20

∑

m0_top−m+_top,i,m_top0 ₋m−_top,i,02. (6.8)

wherem0_top denotes the default top mass, and m+_top,i (m−_top,i) the one from the positive (negative)

variation of theith PDF eigenvector. This approach takes into account the sign of the variations

propagated through to the observable, and the maximal positive and negative variations of the physical observable are considered separately. For more details see D. Bourilkovet al.[95].

Technically, each variation of a PDF eigenvector is implemented as an additional event weight which is taken into account when performing ensemble tests. For Run IIa the effect of the PDF uncertainties on the top quark mass is measured to be+0.3

−0.0GeV, and+0.1−0.2GeV for Run IIb. b Quark Fragmentation

Simulations based on different fragmentation and hadronization models predict different average energy fractions in reconstructed jets. This leads to an uncertainty on the relation between the jet and parton energies and thus the jet transfer functions and the measured top quark mass. Data from LEP and SLD on Z _→ bb¯ decays constrain b fragmentation models and yield a precise

determination of the mean energy fraction of the weakly decaying bottom hadron [96]. To simulate top pair events and the corresponding distributions in top quark decays, different fragmentation models that are consistent with theZ data are used. To evaluate the effect of the fragmentation

uncertainties on the top quark mass, the Monte Carlo simulated events are reweighted from the default PYTHIAbfragmentation to a Bowler scheme [97] that has been tuned to LEP or SLD data,

respectively. The maximum difference between the results obtained from the reweighted samples to the unweighted sample is taken as the systematic uncertainty. For Run IIa, it is determined to be±0.1 GeV, for Run IIb,_±0.3 GeV.

Signal Modeling

The main uncertainty in the modeling of the signal events comes from the uncertainty on the modeling of additional jets due to initial- and final-state radiation. As already discussed in Sec- tion 5.4, this has a large impact on the measured top mass. In case of initial-state radiation, the

100 6. Measurement of the Top Quark Mass top pair system is no longer at rest in the transverse plane, while final-state radiation changes the momenta of the final-statebjets. In addition, ISR or FSR may lead to jets that can be misidentified

as one of thett¯decay products.

To evaluate the effect of the jet modeling on the measured top quark mass, the ratio of the numbers of events with exactly two jets (83%) and more than two jets (17%) is determined from data. The signal sample is then reweighted so that the ratio in the signal sample (75% events with exaclty two jets) matches the one in data. The difference between the measured mass based on the default calibration and the calibration from reweighted events is taken as the systematic uncertainty on the signal modeling. For Run IIa, the measured uncertainty is ±0.3 GeV, for

Run IIb, ±0.4 GeV. As the top pair transverse momentum is accounted for in the calculation of

the event likelihoods, this uncertainty is smaller than in other measurements of the top quark mass [7].

Background Fraction

Since the contribution of each source of events in the ensemble testing procedure is taken from the data-to-Monte Carlo comparisons discussed in Section 6.1, the uncertainties on the event yields shown in Table 6.2 may affect the derived calibration curve. Additionally, the contamination from the fake electron and fake isolated muon background is not taken into account when building ensembles.

To achieve a conservative estimate of this uncertainty with the Monte Carlo samples available, the number of background events is scaled up (down) by 1 σ while scaling, at the same time, the number of signal events down (up) by 1 σ. This allows to check the effect of a worst-case scenario in which the background contribution is underestimated while the signal contribution is overestimated. Two new calibration curves are derived taking into account the modified event yields and the difference between this result and the top quark mass based on the default calibration is assigned as the systematic uncertainty on the background fraction. For Run IIa, the effect is measured to be+0.2

−0.0GeV, for Run IIb,+0.2−0.1GeV.