We combine the lepton+jets and dilepton top mass measurements using the leptons’ Pt.

The combination of the top mass measurements and the statistical and systematic uncertainties are derived using the Iterative Best Linear Unbiased Estimator “BLUE”.

The lepton+jets top mass measurement is:

This is the result of the combination of the e+jets and μ+jets measurements:

The dilepton top mass measurement is:

The fits to the 2.8 fb-1 b-tagged lepton+jets and dilepton data are shown in Figures 2 and 3 respectively.

For the combination, the e+jets and μ+jets decay modes of the lepton+jets channel are considered as separate measurements as they have different statistical significance and therefore different weight on the total combination.  The “BLUE” algorithm estimates that the weight of the three measurements is:

we+jets   = 0.42

wμ+jets   = 0.40

wdilepton = 0.18

The combined top mass measurement is:

The statistical uncertainty of the combined measurement is δΜtopstat = 7.2 GeV

The mass dependence of the statistical uncertainty is taken into consideration. The details are found here.

The systematic uncertainty of the combined measurement is δΜtopsyst = 2.3 GeV

The systematic uncertainties and the correlation factors for the combination of the three measurements are found here

The statistical significance of the e+jets, μ+jets and dilepton measurements is shown in Figure 1.

Figure 1:The statistical significance of the the e+jets, μ+jets and dilepton top mass measurements at 2.8 fb-1 using the leptons Pt in comparison to their "BLUE" combination (vertical band). The red color denotes the statistical uncertainties (dominant) and the blue color denotes the total uncertainties.

Figure 2: Fit to the 2.8 fb-1 b-tagged lepton+jets data. The top mass measurement in the fit is before any corrections are applied

Figure 3: Fit to the 2.8 fb-1 b-tagged dilepton data. The top mass measurement in the fit after all corrections are applied

The statistical uncertainties of the e+jets, μ+jets and dilepton measurements are not correlated. The mass dependence of the statistical uncertainty is taken into consideration for the measurements that are combined.

The statistical uncertainty of the measurements is linear dependent to the top mass: δΜtopstat = κ + λ Μtop

Table 1 summarizes the κ and λ coefficients for the three measurements:

Table 1: Dependence of the statistical uncertainty to the top mass through coefficients κ and λ.

The statistical uncertainty of the combined measurement is δΜtopstat = 7.2 GeV

Table 2 summarizes the partial systematic uncertainties for the two channels, as well as their combination:

Table 2: Partial and total systematic uncertainty on the top mass for the e+jets, μ+jets, the dilepton channel and their combination. *The "Background shape" systematic is called "Fakes" in the lepton+jets analysis

Table 3 summarizes the correlation coefficients, where the sources that are partially or fully correlated are denoted with ρ=1 and the ones that are uncorrelated with  ρ=0. The sources of systematic uncertainties that have been estimated from statistically independent samples or/and are using a different method or/and one of the errors to be combined is statistically dominated are considered uncorrelated. The correlation coefficient is therefore taken to be ρ=0. The sources of systematic uncertainties that have been estimated from overlapping samples or come from the same origin are considered fully correlated. The correlation coefficient is therefore taken to be ρ=1. In the case that the sources are partially correlated, we conservatively take the coefficient to be  ρ=1.

Table 3:  We denote as ρejets-μjets the correlation between the e+jets and μ+jets components in the lepton + jets channel. We denote as   ρejets-DIL & ρμjets-DIL the correlations between the e+jets/μ+jets and dileptons components respectively. For the sources that are considered fully or partially correlated it has been taken ρ=1 and for the uncorrelated  ρ=0.

The correlation of the individual sources is justified as follows:

Global Pt scale  The e+jets and μ+jets systematics are uncorrelated as the global Pt scale calibration comes from independent Z→ee and Z→μμ  samples. The dilepton systematic is partially correlated with the e/μ+jets ones as the dilepton events have both electrons and muons. The latter ones are conservatively taken to be fully correlated.

Local Pt scale  The systematic uncertainties for all three channels are considered fully correlated, as the local calibration of the electrons is based on the local calibration of the muons.

MC statistics The systematic uncertainties are uncorrelated as the MC e+jets, μ+jets and dilepton sub-samples are independent.

Generator The e+jets systematic uncertainty is statistically dominated and therefore its correlation with the μ+jets and dilepton ones is taken to be 0. Furthermore, as the dilepton uncertainty is also statistically dominated its ρe/μ +jets-DIL is taken to be 0.

IFSR  As the μ+jets and dilepton systematics are statistically dominated all possible three correlations are taken to be 0.

PDF All systematic uncertainties are considered fully correlated as the shifts come from the same origin in all three channels.

Background shape As there is no μ+jets background shape (fakes) systematic error the correlation ρejets +μjets =0. Furthermore ρejets-DIL =0 as the e+jets systematic is estimated using the data sample (anti-electrons) while the dilepton one is based on MC.

Background constrain All sources are uncorrelated as there is no e/μ+jets systematic error from this source.

JES All systematic uncertainties are considered fully correlated as the shifts come from the same origin, the uncertainty on the jets energy, in all three channels.

Multiple Interactions All sources are considered uncorrelated, as the estimation of the e/μ+jets and dilepton systematic error was based on a different approach. The e/μ+jets systematic estimation is based on data while the dilepton one on the high - luminosity MC samples..

Q2 The e+jets and μ+jets sources are of statistical origin and are therefore considered uncorrelated. This systematic does not exist in the dilepton channel.

Bias from the fit This source exists only in the dilepton channel and all correlation coefficients are taken to be 0.