CMSTOP12030 ; CERNEP2016062  
Measurement of the top quark mass using charged particles in pp collisions at $ \sqrt{s} = $ 8 TeV  
CMS Collaboration  
21 March 2016  
Phys. Rev. D 93 (2016) 092006  
Abstract: A novel technique for measuring the mass of the top quark that uses only the kinematic properties of its charged decay products is presented. Top quark pair events with final states with one or two charged leptons and hadronic jets are selected from the data set of 8 TeV protonproton collisions, corresponding to an integrated luminosity of 19.7 fb$^{1}$. By reconstructing secondary vertices inside the selected jets and computing the invariant mass of the system formed by the secondary vertex and an isolated lepton, an observable is constructed that is sensitive to the top quark mass that is expected to be robust against the energy scale of hadronic jets. The main theoretical systematic uncertainties, concerning the modeling of the fragmentation and hadronization of b quarks and the reconstruction of secondary vertices from the decays of b hadrons, are studied. A top quark mass of 173.68 $\pm$ 0.20 (stat) $^{+1.58}_{0.97}$ (syst) GeV is measured. The overall systematic uncertainty is dominated by the uncertainty in the b quark fragmentation and the modeling of kinematic properties of the top quark.  
Links: eprint arXiv:1603.06536 [hepex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; CADI line (restricted) ; 
Figures  
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Figure 1a:
Distributions of the transverse decay length of secondary vertices with respect to the primary vertex in dilepton (a) and semileptonic channels (b). The expectations from simulation and estimates from the data for the multijet background are compared to the reconstructed data. The last bin contains the overflow events. 
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Figure 1b:
Distributions of the transverse decay length of secondary vertices with respect to the primary vertex in dilepton (a) and semileptonic channels (b). The expectations from simulation and estimates from the data for the multijet background are compared to the reconstructed data. The last bin contains the overflow events. 
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Figure 2a:
Distributions of the ratio of the transverse momentum of secondary vertices to the charged component of the jet with three, four, and five tracks (from (a,d) to (b,e) to (c,f)) in Z+jets dilepton (a,b,c) and $ {\mathrm{ t \bar{t} } } $ dilepton events (d,e,f), compared to the expected shape using the Z2* LEP $r_{\mathrm{ b } }$ fragmentation tune. In each plot, the top panels compare the average of the distribution measured in data and its statistical uncertainty (shaded area) with that expected from different choices of the b quark fragmentation function in PYTHIA. For Z2* LEP $r_{\mathrm{ b } }$ , the error bar represents the $\pm $ variations of Z2* LEP $r_{\mathrm{ b } }$ . 
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Figure 2b:
Distributions of the ratio of the transverse momentum of secondary vertices to the charged component of the jet with three, four, and five tracks (from (a,d) to (b,e) to (c,f)) in Z+jets dilepton (a,b,c) and $ {\mathrm{ t \bar{t} } } $ dilepton events (d,e,f), compared to the expected shape using the Z2* LEP $r_{\mathrm{ b } }$ fragmentation tune. In each plot, the top panels compare the average of the distribution measured in data and its statistical uncertainty (shaded area) with that expected from different choices of the b quark fragmentation function in PYTHIA. For Z2* LEP $r_{\mathrm{ b } }$ , the error bar represents the $\pm $ variations of Z2* LEP $r_{\mathrm{ b } }$ . 
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Figure 2c:
Distributions of the ratio of the transverse momentum of secondary vertices to the charged component of the jet with three, four, and five tracks (from (a,d) to (b,e) to (c,f)) in Z+jets dilepton (a,b,c) and $ {\mathrm{ t \bar{t} } } $ dilepton events (d,e,f), compared to the expected shape using the Z2* LEP $r_{\mathrm{ b } }$ fragmentation tune. In each plot, the top panels compare the average of the distribution measured in data and its statistical uncertainty (shaded area) with that expected from different choices of the b quark fragmentation function in PYTHIA. For Z2* LEP $r_{\mathrm{ b } }$ , the error bar represents the $\pm $ variations of Z2* LEP $r_{\mathrm{ b } }$ . 
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Figure 2d:
Distributions of the ratio of the transverse momentum of secondary vertices to the charged component of the jet with three, four, and five tracks (from (a,d) to (b,e) to (c,f)) in Z+jets dilepton (a,b,c) and $ {\mathrm{ t \bar{t} } } $ dilepton events (d,e,f), compared to the expected shape using the Z2* LEP $r_{\mathrm{ b } }$ fragmentation tune. In each plot, the top panels compare the average of the distribution measured in data and its statistical uncertainty (shaded area) with that expected from different choices of the b quark fragmentation function in PYTHIA. For Z2* LEP $r_{\mathrm{ b } }$ , the error bar represents the $\pm $ variations of Z2* LEP $r_{\mathrm{ b } }$ . 
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Figure 2e:
Distributions of the ratio of the transverse momentum of secondary vertices to the charged component of the jet with three, four, and five tracks (from (a,d) to (b,e) to (c,f)) in Z+jets dilepton (a,b,c) and $ {\mathrm{ t \bar{t} } } $ dilepton events (d,e,f), compared to the expected shape using the Z2* LEP $r_{\mathrm{ b } }$ fragmentation tune. In each plot, the top panels compare the average of the distribution measured in data and its statistical uncertainty (shaded area) with that expected from different choices of the b quark fragmentation function in PYTHIA. For Z2* LEP $r_{\mathrm{ b } }$ , the error bar represents the $\pm $ variations of Z2* LEP $r_{\mathrm{ b } }$ . 
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Figure 2f:
Distributions of the ratio of the transverse momentum of secondary vertices to the charged component of the jet with three, four, and five tracks (from (a,d) to (b,e) to (c,f)) in Z+jets dilepton (a,b,c) and $ {\mathrm{ t \bar{t} } } $ dilepton events (d,e,f), compared to the expected shape using the Z2* LEP $r_{\mathrm{ b } }$ fragmentation tune. In each plot, the top panels compare the average of the distribution measured in data and its statistical uncertainty (shaded area) with that expected from different choices of the b quark fragmentation function in PYTHIA. For Z2* LEP $r_{\mathrm{ b } }$ , the error bar represents the $\pm $ variations of Z2* LEP $r_{\mathrm{ b } }$ . 
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Figure 3a:
Fits to the invariant mass peaks of the three considered charmed mesons in ${\mathrm{ t \bar{t} } } $ events in the data, as described in the text: $\mathrm{ J } / \psi $ (a), $ \mathrm{D}^0 $ (b), and $ \mathrm{D}^{*}(2010)^+ $ (c). 
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Figure 3b:
Fits to the invariant mass peaks of the three considered charmed mesons in ${\mathrm{ t \bar{t} } } $ events in the data, as described in the text: $\mathrm{ J } / \psi $ (a), $ \mathrm{D}^0 $ (b), and $ \mathrm{D}^{*}(2010)^+ $ (c). 
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Figure 3c:
Fits to the invariant mass peaks of the three considered charmed mesons in ${\mathrm{ t \bar{t} } } $ events in the data, as described in the text: $\mathrm{ J } / \psi $ (a), $ \mathrm{D}^0 $ (b), and $ \mathrm{D}^{*}(2010)^+ $ (c). 
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Figure 4a:
Distribution of the relative transverse momentum of $\mathrm{ J } / \psi $ (a), $ \mathrm{D}^0 $ (b), and $ \mathrm{D}^{*}(2010)^+ $ (c) meson candidates with respect to the charged components of the jet in ${\mathrm{ t \bar{t} } } $ events for the data and the nominal Z2* LEP $r_{\mathrm{ b } }$ fragmentation function. The top panels show the average of the distributions observed in the data and its statistical uncertainty (shaded area), as well as expectations obtained with different b quark fragmentation functions and with an alternative generator setup using HERWIG 6 with the AUET2 tune. 
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Figure 4b:
Distribution of the relative transverse momentum of $\mathrm{ J } / \psi $ (a), $ \mathrm{D}^0 $ (b), and $ \mathrm{D}^{*}(2010)^+ $ (c) meson candidates with respect to the charged components of the jet in ${\mathrm{ t \bar{t} } } $ events for the data and the nominal Z2* LEP $r_{\mathrm{ b } }$ fragmentation function. The top panels show the average of the distributions observed in the data and its statistical uncertainty (shaded area), as well as expectations obtained with different b quark fragmentation functions and with an alternative generator setup using HERWIG 6 with the AUET2 tune. 
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Figure 4c:
Distribution of the relative transverse momentum of $\mathrm{ J } / \psi $ (a), $ \mathrm{D}^0 $ (b), and $ \mathrm{D}^{*}(2010)^+ $ (c) meson candidates with respect to the charged components of the jet in ${\mathrm{ t \bar{t} } } $ events for the data and the nominal Z2* LEP $r_{\mathrm{ b } }$ fragmentation function. The top panels show the average of the distributions observed in the data and its statistical uncertainty (shaded area), as well as expectations obtained with different b quark fragmentation functions and with an alternative generator setup using HERWIG 6 with the AUET2 tune. 
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Figure 5:
LeptonSV invariant mass distribution for a combination of all five channels, for a simulation of three different top quark mass values (166.5, 172.5, and 178.5 GeV), and the observed data distribution. Note that all possible leptonvertex combinations for each event enter the distribution. 
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Figure 6a:
Template fits to the observed ${m_{\mathrm {svl}}} $ distributions for the three dilepton channels ($ {\mathrm{ e } \mu } $, ${\mathrm{ e } \mathrm{ e } } $, ${\mu \mu } $ from (a,b,c) to (d,e,f) to (g,h,i)), and for exactly three, four, and five tracks assigned to the secondary vertex (from (a,d,g) to (b,e,h) to (c,f,i)). The top panels show the binbybin difference between the observed data and the fit result, divided by the statistical uncertainty (pull). The inset shows the scan of the negative loglikelihood as a function of the calibrated top quark mass, accounting only for the statistical uncertainty, when performed exclusively in each event category. 
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Figure 6b:
Template fits to the observed ${m_{\mathrm {svl}}} $ distributions for the three dilepton channels ($ {\mathrm{ e } \mu } $, ${\mathrm{ e } \mathrm{ e } } $, ${\mu \mu } $ from (a,b,c) to (d,e,f) to (g,h,i)), and for exactly three, four, and five tracks assigned to the secondary vertex (from (a,d,g) to (b,e,h) to (c,f,i)). The top panels show the binbybin difference between the observed data and the fit result, divided by the statistical uncertainty (pull). The inset shows the scan of the negative loglikelihood as a function of the calibrated top quark mass, accounting only for the statistical uncertainty, when performed exclusively in each event category. 
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Figure 6c:
Template fits to the observed ${m_{\mathrm {svl}}} $ distributions for the three dilepton channels ($ {\mathrm{ e } \mu } $, ${\mathrm{ e } \mathrm{ e } } $, ${\mu \mu } $ from (a,b,c) to (d,e,f) to (g,h,i)), and for exactly three, four, and five tracks assigned to the secondary vertex (from (a,d,g) to (b,e,h) to (c,f,i)). The top panels show the binbybin difference between the observed data and the fit result, divided by the statistical uncertainty (pull). The inset shows the scan of the negative loglikelihood as a function of the calibrated top quark mass, accounting only for the statistical uncertainty, when performed exclusively in each event category. 
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Figure 6d:
Template fits to the observed ${m_{\mathrm {svl}}} $ distributions for the three dilepton channels ($ {\mathrm{ e } \mu } $, ${\mathrm{ e } \mathrm{ e } } $, ${\mu \mu } $ from (a,b,c) to (d,e,f) to (g,h,i)), and for exactly three, four, and five tracks assigned to the secondary vertex (from (a,d,g) to (b,e,h) to (c,f,i)). The top panels show the binbybin difference between the observed data and the fit result, divided by the statistical uncertainty (pull). The inset shows the scan of the negative loglikelihood as a function of the calibrated top quark mass, accounting only for the statistical uncertainty, when performed exclusively in each event category. 
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Figure 6e:
Template fits to the observed ${m_{\mathrm {svl}}} $ distributions for the three dilepton channels ($ {\mathrm{ e } \mu } $, ${\mathrm{ e } \mathrm{ e } } $, ${\mu \mu } $ from (a,b,c) to (d,e,f) to (g,h,i)), and for exactly three, four, and five tracks assigned to the secondary vertex (from (a,d,g) to (b,e,h) to (c,f,i)). The top panels show the binbybin difference between the observed data and the fit result, divided by the statistical uncertainty (pull). The inset shows the scan of the negative loglikelihood as a function of the calibrated top quark mass, accounting only for the statistical uncertainty, when performed exclusively in each event category. 
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Figure 6f:
Template fits to the observed ${m_{\mathrm {svl}}} $ distributions for the three dilepton channels ($ {\mathrm{ e } \mu } $, ${\mathrm{ e } \mathrm{ e } } $, ${\mu \mu } $ from (a,b,c) to (d,e,f) to (g,h,i)), and for exactly three, four, and five tracks assigned to the secondary vertex (from (a,d,g) to (b,e,h) to (c,f,i)). The top panels show the binbybin difference between the observed data and the fit result, divided by the statistical uncertainty (pull). The inset shows the scan of the negative loglikelihood as a function of the calibrated top quark mass, accounting only for the statistical uncertainty, when performed exclusively in each event category. 
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Figure 6g:
Template fits to the observed ${m_{\mathrm {svl}}} $ distributions for the three dilepton channels ($ {\mathrm{ e } \mu } $, ${\mathrm{ e } \mathrm{ e } } $, ${\mu \mu } $ from (a,b,c) to (d,e,f) to (g,h,i)), and for exactly three, four, and five tracks assigned to the secondary vertex (from (a,d,g) to (b,e,h) to (c,f,i)). The top panels show the binbybin difference between the observed data and the fit result, divided by the statistical uncertainty (pull). The inset shows the scan of the negative loglikelihood as a function of the calibrated top quark mass, accounting only for the statistical uncertainty, when performed exclusively in each event category. 
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Figure 6h:
Template fits to the observed ${m_{\mathrm {svl}}} $ distributions for the three dilepton channels ($ {\mathrm{ e } \mu } $, ${\mathrm{ e } \mathrm{ e } } $, ${\mu \mu } $ from (a,b,c) to (d,e,f) to (g,h,i)), and for exactly three, four, and five tracks assigned to the secondary vertex (from (a,d,g) to (b,e,h) to (c,f,i)). The top panels show the binbybin difference between the observed data and the fit result, divided by the statistical uncertainty (pull). The inset shows the scan of the negative loglikelihood as a function of the calibrated top quark mass, accounting only for the statistical uncertainty, when performed exclusively in each event category. 
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Figure 6i:
Template fits to the observed ${m_{\mathrm {svl}}} $ distributions for the three dilepton channels ($ {\mathrm{ e } \mu } $, ${\mathrm{ e } \mathrm{ e } } $, ${\mu \mu } $ from (a,b,c) to (d,e,f) to (g,h,i)), and for exactly three, four, and five tracks assigned to the secondary vertex (from (a,d,g) to (b,e,h) to (c,f,i)). The top panels show the binbybin difference between the observed data and the fit result, divided by the statistical uncertainty (pull). The inset shows the scan of the negative loglikelihood as a function of the calibrated top quark mass, accounting only for the statistical uncertainty, when performed exclusively in each event category. 
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Figure 7a:
Template fits to the observed ${m_{\mathrm {svl}}} $ distributions for the semileptonic channels ($ {\mathrm{ e } } $ and ${\mu } $ from (a,b,c) to (d,e,f) to (g,h,i)), and for exactly three, four, and five tracks assigned to the secondary vertex (from (a,d,g) to (b,e,h) to (c,f,i)). The top panels show the binbybin difference between the observed data and the fit result, divided by the statistical uncertainty (pull). The inset shows the scan of the negative loglikelihood as a function of the calibrated top quark mass, accounting only for the statistical uncertainty, when performed exclusively in each event category. 
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Figure 7b:
Template fits to the observed ${m_{\mathrm {svl}}} $ distributions for the semileptonic channels ($ {\mathrm{ e } } $ and ${\mu } $ from (a,b,c) to (d,e,f) to (g,h,i)), and for exactly three, four, and five tracks assigned to the secondary vertex (from (a,d,g) to (b,e,h) to (c,f,i)). The top panels show the binbybin difference between the observed data and the fit result, divided by the statistical uncertainty (pull). The inset shows the scan of the negative loglikelihood as a function of the calibrated top quark mass, accounting only for the statistical uncertainty, when performed exclusively in each event category. 
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Figure 7c:
Template fits to the observed ${m_{\mathrm {svl}}} $ distributions for the semileptonic channels ($ {\mathrm{ e } } $ and ${\mu } $ from (a,b,c) to (d,e,f) to (g,h,i)), and for exactly three, four, and five tracks assigned to the secondary vertex (from (a,d,g) to (b,e,h) to (c,f,i)). The top panels show the binbybin difference between the observed data and the fit result, divided by the statistical uncertainty (pull). The inset shows the scan of the negative loglikelihood as a function of the calibrated top quark mass, accounting only for the statistical uncertainty, when performed exclusively in each event category. 
png pdf 
Figure 7d:
Template fits to the observed ${m_{\mathrm {svl}}} $ distributions for the semileptonic channels ($ {\mathrm{ e } } $ and ${\mu } $ from (a,b,c) to (d,e,f) to (g,h,i)), and for exactly three, four, and five tracks assigned to the secondary vertex (from (a,d,g) to (b,e,h) to (c,f,i)). The top panels show the binbybin difference between the observed data and the fit result, divided by the statistical uncertainty (pull). The inset shows the scan of the negative loglikelihood as a function of the calibrated top quark mass, accounting only for the statistical uncertainty, when performed exclusively in each event category. 
png pdf 
Figure 7e:
Template fits to the observed ${m_{\mathrm {svl}}} $ distributions for the semileptonic channels ($ {\mathrm{ e } } $ and ${\mu } $ from (a,b,c) to (d,e,f) to (g,h,i)), and for exactly three, four, and five tracks assigned to the secondary vertex (from (a,d,g) to (b,e,h) to (c,f,i)). The top panels show the binbybin difference between the observed data and the fit result, divided by the statistical uncertainty (pull). The inset shows the scan of the negative loglikelihood as a function of the calibrated top quark mass, accounting only for the statistical uncertainty, when performed exclusively in each event category. 
png pdf 
Figure 7f:
Template fits to the observed ${m_{\mathrm {svl}}} $ distributions for the semileptonic channels ($ {\mathrm{ e } } $ and ${\mu } $ from (a,b,c) to (d,e,f) to (g,h,i)), and for exactly three, four, and five tracks assigned to the secondary vertex (from (a,d,g) to (b,e,h) to (c,f,i)). The top panels show the binbybin difference between the observed data and the fit result, divided by the statistical uncertainty (pull). The inset shows the scan of the negative loglikelihood as a function of the calibrated top quark mass, accounting only for the statistical uncertainty, when performed exclusively in each event category. 
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Figure 8a:
Variation of the simulated ${m_{\mathrm {svl}}} $ shape with systematic effects: reweighting of the simulated top quark ${p_{\mathrm {T}}} $ shape to the observed distribution, separately for correct and wrong leptonvertex pairings (a); and different b quark fragmentation function shapes (b). The bottom panels in the two plots show the ratios between the top quark ${p_{\mathrm {T}}} $ reweighted and nominal shapes for the correct and wrong pairings (a), and between the various fragmentation models and the central Z2* LEP $r_{\mathrm{ b } }$ tune (b). 
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Figure 8b:
Variation of the simulated ${m_{\mathrm {svl}}} $ shape with systematic effects: reweighting of the simulated top quark ${p_{\mathrm {T}}} $ shape to the observed distribution, separately for correct and wrong leptonvertex pairings (a); and different b quark fragmentation function shapes (b). The bottom panels in the two plots show the ratios between the top quark ${p_{\mathrm {T}}} $ reweighted and nominal shapes for the correct and wrong pairings (a), and between the various fragmentation models and the central Z2* LEP $r_{\mathrm{ b } }$ tune (b). 
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Figure 9:
Impact of the average b quark fragmentation, $< {p_{\mathrm {T}}} (\mathrm{B} )/ {p_{\mathrm {T}}} ( \mathrm{b} ) > $, on the extracted ${m_{\mathrm{ t } }}$ value, for various different fragmentation shapes. The horizontal band represents the contribution of the b quark fragmentation model to the systematic uncertainty in the measurement of the top quark mass, which is estimated from the Z2* LEP $r_{\mathrm{ b } }$ ${\pm }$ variations. A linear fit to the effects on the different variations (the line in the figure) suggests a relative change in the measured top quark mass of 0.61 GeV for each percent change in average momentum transfer. 
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Figure 10:
Results of the ${m_{\mathrm{ t } }}$ measurement in the individual channels and their combination. Smaller and thicker error bars show the statistical uncertainty, whereas the thinner bars show the combined statistical and systematic uncertainty. The right panel shows the extracted mass when performing the analysis in separate track multiplicity bins, combining the lepton channels. 
Tables  
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Table 1:
Number of observed events and expected purity of top quark production ($ {\mathrm{ t \bar{t} } } $ and single top quarks) for the five channels investigated in this analysis. 
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Table 2:
Summary of the systematic uncertainties in the final measurement. In cases where there are two variations of one source of uncertainty, the first and second numbers correspond, respectively, to the down and up variations. The total uncertainties are taken as the separate quadratic sum of all positive and negative shifts. For the contributions marked with a (*), the shift of the single variation including its sign is given, but the uncertainty is counted symmetrically in both up and down directions for the total uncertainty calculation. 
Summary 
A novel measurement of the top quark mass has been presented, using an observable that relies entirely on the reconstruction of charged particles. It shows minimal sensitivity to experimental sources of uncertainty. The final result yields a value of $ m_{\mathrm{t}} =$ 173.68 $^{+1.59}_{0.99}$ GeV, equivalent to a precision of well below one percent. The overall uncertainty is dominated by the b quark fragmentation modeling uncertainty of $+1.00/0.54$ GeV and the uncertainty in the modeling of the top quark $p_{\mathrm{T}}$ of +0.82 GeV. Experimental uncertainties related to the understanding of jet energy scales only affect the event acceptance and are therefore virtually irrelevant to the final result. Studies of the b quark fragmentation with reconstructed secondary vertices and inclusively reconstructed charm quark mesons are used to select the central b quark fragmentation shape and to validate the systematic uncertainty. With the significantly larger data sets becoming available for analysis from the current 13 TeV run of the LHC, this method could be extended to constrain the b quark fragmentation, using the properties of the secondary vertices or charmed mesons, while measuring the top quark mass. This is expected to lead to a significant reduction of the overall uncertainty. Furthermore, theoretical uncertainties related to kinematic properties of top quarks and scale choices in QCD calculations are expected to decrease with the next generation of Monte Carlo event generators. Finally, this result is complementary to standard measurements relying on kinematic properties of jets. The precision of such analyses is typically limited by the uncertainty from the modeling of hadronization effects, influencing the understanding of the jet energy scale, while not much affected by the choice of b quark fragmentation model and the modeling of top quark kinematic properties. Therefore, a combination of this result with standard measurements could optimally benefit from independent sources of systematic uncertainties. 
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37  CMS Collaboration  Particleflow event reconstruction in CMS and performance for jets, taus, and $ E_{\mathrm{T}}^{\text{miss}} $  CDS  
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