2.7. Properties of the Top Quark
2.7.4. Previous Measurements of the Top Quark Mass
Since its discovery in 1995, the top quark mass has been measured using a variety of different techniques. With the understanding of detector performance and over 20 years of run time, the top quark mass became the most well known mass of any quark. The precision of the mass is of the order of 0.5% from the latest Tevatron combination [3]. Top quark mass measurements have either been made from direct or indirect evidence. Some of the different types of measurements are described in the following list:
2. Physics
Distribution Fitting Methods: where the use of a distribution which is significantly de-pendent on top quark mass is utilized to extract the top quark mass in data. The signal and background distributions, S(xi|mt, ) and B(xi|mt, ) respectively, are templates of a given distribution which depends on mt. Therefore, a dependence against the mass can be measured by a fit of these distributions against data. Using the example of the binned likelihood, L(mt, , fs), a fit is made which is depen-dent on the signal fraction fs and on signal and background distributions which are dependent on the top quark mass and nuisance variables () such as the JES.
L(mt, , fs) =
N
X
i=1
[fsS(xi|mt, ) + (1−fs)B(xi|mt, )]. (2.51) Extensions to the simple 1-d model employ the dependence of the signal and back-ground distributions (S(xi|mt, ) andB(xi|mt, ) respectively) on a nuisance param-eter, such as the JES. This improves the sensitivity to the top quark mass by adding an extra dimension to the fit for the JES. The most precise alljets measurement was performed at CDF using this method [72]:
malljetstop = 172.5±1.4 (stat.)±1.5 (syst.) GeV/c2. (2.52) Templates were created for variations in top mass and JES and a 2-dimensional fit was performed. Another powerful extension to this method is the so-called “ideogram method” which uses the event-by-event top mass resolution. Such a method is performed at DØ. The resulting top mass from this method performed at DØ in the lepton + jets channel is [73]:
mideogramtop = 173.7±4.4 (stat.+ JES) +2.1−2.0 (syst.) GeV/c2. (2.53) The ideogram method has also been used by the CMS collaboration in the µ+ jets channel using a reconstruction similar to what has been previously performed at DØ [74]. The resulting mass measurement uses the full 2011 dataset of 4.7 fb−1, and results in a top mass value of [75]:
mCM S ideogram
top = 172.6±0.6 (stat.+ JES)±1.2 (syst.) GeV/c2. (2.54) The uncertainty is slightly underestimated as underlying event and colour reconnec-tion systematic uncertainties were not evaluated. As a result, the analysis is still only preliminary and expected to have slightly larger uncertainties. To date, this is the most precise LHC top mass measurement.
Neutrino Re-Weighting Methods: involve analyzing a kinematically under-constrained system due to the two missing neutrinos. Integration over the neutrino rapidity is performed. Since the JES is not able to be calibrated in the dilepton channel, a correction may be taken from the t¯t→ l+jets events. This allows the correction for the JES in dilepton events. The most recent measurement at DØ gives a top quark mass of [76]:
mdileptontop = 174.0±2.4 (stat.)±1.4 (syst.) GeV/c2, (2.55) when using a correction obtained from lepton + jets events. This is the most precise measurement in the dilepton channel.
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2.7. Properties of the Top Quark
Integration Methods: better known as Matrix Element Methods (MEM), which use in-tegration over the parton-level quantities. The method was introduced by DØ in 2004 [77]. It is especially powerful when only limited data is available since it is very CPU intensive as integration is made over several quantities per event and is non-trivial. The probability of observingx per event is given as:
P(x|a) = 1
σi(a) ·dσi(x|a)
dx , (2.56)
where σi(a) is the cross section of the process,x are the observables and a are the set of parameters. This method has given the most precise measurement ever made of the top quark mass [78].
ml+jetstop = 173.0±1.2 GeV/c2 (2.57) Its DØ counterpart is found at [79]. The method is one of the most precise methods to measure the top mass. Essentially the events are fit within aχ2minimization, where distributions of detector transfer functions and event modeling are considered. This results in a significantly improved estimator. The drawback to such an analysis is the required understanding of the detector and modeling of signal density functions.
Also the minimization may be non-trivial and a significant amount of CPU time is required. As a result, this method has not yet been applied on LHC data.
Indirect via the Cross Section: which uses the measuredt¯tcross section to indirectly cal-culate the top quark mass. This method assumes the SM theoretical description of the mass dependence to the cross section and higher order corrections to the theoret-ical cross section. It has been performed at the Tevatron in [80, 81]. The correlation between mass and cross section can be seen in Figure 2.20, where several different approximate NNLO cross section calculations are given with their intersection at different possible mass values.
Figure 2.20.: Relationship of several NNLO theoretical cross sections to the t quark mass inpp collisions at√
s= 7 TeV. Figure taken from [82].
2. Physics
Using the measured ATLAS t¯tcross section value, and theKidonakis et. al. calcu-lation, the top quark mass was calculated to be at ATLAS [82]:
mσtt¯t = 166.2+7.8−7.2 GeV. (2.58) However, this mass is different from the MM C mentioned in the other measurements of the top quark mass as it uses a renormalization scale.
These measurements, along with many others, have all played a roll in the evolution of the top mass shown in Figure 2.21. Depicted are the measurements of the top mass and the increase in precision over time, beginning with indirect searches ate+e− colliders and evidence from electroweak fits up until the year 1995. Afterwards, the numbers begin to converge at approximately 175 GeV/c2 after the first measurement at the two experiments at the Tevatron. All of this culminates with a very precise direct top quark mass measurement. The final points on the graph show the first produced analyses from ATLAS and CMS, which are measurements performed on data collected in 2010 and 2011 [83, 84].
Figure 2.21.: Evolution of the top mass measurement as a result of direct and indirect searches over the past 20 years. Updated in 2012.
The current top mass measurement precision is dominated by the Tevatron. At present, there is no top mass measurements made at the LHC in the world average calculation.
The current world average of the top quark mass, calculated in 2011 [3], is:
173.2±0.6 (stat.)±0.8 (syst.) GeV/c2 (2.59) Several of the measurements performed at both DØ and CDF are highlighted by channel and experiment in Figure 2.22. Many analyses are used in the calculation of the top quark mass world average, from several channels at both the Tevatron experiments.
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2.7. Properties of the Top Quark
2) (GeV/c mtop
150 160 170 180 190 200
0 15
CDF March’07 12.4 ± 2.7 (± 1.5 ± 2.2)
Tevatron combination * 173.2 ± 0.9(± 0.6 ± 0.8) syst) stat ± (±
CDF-II MET+Jets * 172.3 ± 2.6(± 1.8 ± 1.8)
CDF-II track 166.9 ± 9.5(± 9.0 ± 2.9) CDF-II alljets * 172.5 ± 2.1(± 1.4 ± 1.5)
CDF-I alljets 186.0 ±11.5(±10.0 ± 5.7)
DØ-II lepton+jets 174.9 ± 1.5(± 0.8 ± 1.2) CDF-II lepton+jets 173.0 ± 1.2(± 0.6 ± 1.1)
DØ-I lepton+jets 180.1 ± 5.3(± 3.9 ± 3.6)
CDF-I lepton+jets 176.1 ± 7.4(± 5.1 ± 5.3)
DØ-II dilepton 174.0 ± 3.1(± 1.8 ± 2.5)
CDF-II dilepton 170.6 ± 3.8(± 2.2 ± 3.1)
DØ-I dilepton 168.4 ±12.8(±12.3 ± 3.6)
CDF-I dilepton 167.4 ±11.4(±10.3 ± 4.9)
Mass of the Top Quark
(* preliminary) July 2011
/dof = 8.3/11 (68.5%) χ2
Figure 2.22.: Current world average of the top quark mass. The combination uses Tevatron results only. The measurements from all decay channels in both experiments are used to maximize the knowledge of the top quark mass.
Figure taken from [3].