Combination of CDF and DO results on the mass of the top quark using up to 8.7 fb^{-1} at the Tevatron
FFERMI NATIONAL ACCELERATOR LABORATORY
FERMILAB-CONF-13-164-PPD-TDTEVEWWG/top 2013/01CDF Note 10976DØ Note 6381August 2013
Combination of CDF and DØ results on themass of the top quark using up to 8 . − atthe Tevatron The Tevatron Electroweak Working Group for the CDF and DØ Collaborations Abstract
We summarize the current top-quark mass measurements from the CDF and DØ experi-ments at Fermilab. We combine published Run I (1992–1996) measurements with the mostprecise published and preliminary Run II (2001–2011) measurements based on data setscorresponding to up to 8 . − of p ¯ p collisions. Taking correlations of uncertainties intoaccount, and combining the statistical and systematic uncertainties, the resulting prelimi-nary Tevatron average mass of the top quark is M t = 173 . ± .
87 GeV /c , correspondingto a relative precision of 0 . The Tevatron Electroweak Working Group can be contacted at [email protected] information can be found at http://tevewwg.fnal.gov . a r X i v : . [ h e p - e x ] D ec Introduction
This note reports the Tevatron average top-quark mass obtained by combining the most pre-cise published and preliminary measurements of the top-quark mass. It is an update of thecombination presented in Ref. [1], where further details can be found. The ATLAS and CMScollaborations have also performed a combination of their most recent top quark mass mea-surements [2].The CDF and DØ collaborations have performed several direct experimental measurementsof the top-quark mass ( M t ) using data collected at the Tevatron proton-antiproton colliderlocated at the Fermi National Accelerator Laboratory. These pioneering measurements werefirst based on approximately 0 . − of Run I data [3]-[14] collected from 1992 to 1996, andincluded results from the decay channels tt → W + bW − b → qq (cid:48) bqq (cid:48) b (alljets), tt → W + bW − b → (cid:96)νbqq (cid:48) b ( (cid:96) +jets), and tt → W + bW − b → (cid:96) + νb(cid:96) − νb ( (cid:96)(cid:96) ), where (cid:96) = e or µ . Decays with τ → e, µ are included in the direct W → e and W → µ channels. In Run II (2001–2011), many top massmeasurements have been performed, and those considered here are the most recent results inthese channels, using up to 8 . − of data for CDF (corresponding to the full CDF Run IIdataset) [15, 16, 17, 18], and up to 5 . − of data for DØ [19, 20, 21]. The CDF analysisbased upon charged particle tracking for exploiting the transverse decay length of b -tagged jets( L XY ) and the transverse momentum of electrons and muons from W boson decays ( p lep T ) usesa data set corresponding to a luminosity of 1.9 fb − [22], and there are no plans to update thisanalysis. The DØ Run II measurements presented in this note include the most recent RunII measurement in the (cid:96)(cid:96) [21] channel using 5.4 fb − of data and in the (cid:96) +jets channel [20]with 3.6 fb − of data. Both results are now published. Since the combination performed in2011 [23], a new final state signature was introduced by CDF that requires events to possessmissing transverse energy ( (cid:54) E T ) and jets, but no identified lepton (“MEt”) [15, 24]. This sampleis statistically independent from the previous three CDF channels.With respect to the July 2011 combination [23] and the published version of the combina-tion [1], the Run II CDF measurement in the (cid:96) +jets channel has been updated using 8.7 fb − ofdata, an improved analysis technique, and improved jet energy resolution [16]. The CDF mea-surement in the MEt channel was updated to use the full Run II data set for CDF of 8.7 fb − of data as well [15]. The now published Run II CDF measurements in the (cid:96)(cid:96) channel [17] andalljets channel [18] are unchanged. The measurement based on charged particle tracking [22]was incorporated as described in the past combinations [23]. From the corresponding analysisonly the measurement of the top quark mass using the mean decay length L XY of B hadronsin b -tagged lepton+jets events has been used. It is independent of energy information in thecalorimeter, and its main source of systematic uncertainty is uncorrelated with the dominantones from the jet energy scale calibration in other measurements. This measurement of m t is essentially uncorrelated with the higher precision CDF result from the lepton+jets channel.The overlap between the data samples used for the decay-length method and the lepton+jetssample has therefore no effect. 2he Tevatron average top-quark mass is obtained by combining five published Run I mea-surements [4, 5, 7, 9, 12, 13] with four published Run II CDF results [16, 17, 18, 22], onepreliminary Run II CDF result [15], and two published Run II DØ results [20, 21]. This combi-nation supersedes previous combinations [23, 25, 26, 27, 28, 29, 30, 31, 32, 33].The definition and evaluation of the systematic uncertainties and the understanding of thecorrelations among channels, experiments, and Tevatron runs is the outcome of many years ofjoint work between the CDF and DØ collaborations and is described in detail elsewhere [1].The input measurements and uncertainty categories used in the combination are detailedin Sections 2 and 3, respectively. The correlations assumed in the combination are discussed inSection 4 and the resulting Tevatron average top-quark mass is given in Section 5. A summaryis presented in Section 6. Twelve measurements of M t used in this combination are shown in Table 1. The Run I mea-surements all have relatively large statistical uncertainties and their systematic uncertaintiesare dominated by the total jet energy scale (JES) uncertainty. In Run II both CDF and DØtake advantage of the larger tt samples available and employ new analysis techniques to reduceboth of these uncertainties. In particular, the Run II DØ analysis in the (cid:96) +jets channel andthe Run II CDF analyses in the (cid:96) +jets, alljets, and MEt channels constrain the response oflight-quark jets using the kinematic information from W → qq (cid:48) decays (so-called in situ cal-ibration) [9, 34]. Residual JES uncertainties associated with p T and η dependencies as wellas uncertainties specific to the response of b jets are treated separately. The Run II DØ (cid:96)(cid:96) measurement uses the JES determined in the (cid:96) +jets channel by in situ calibration [21].The DØ Run II (cid:96) +jets analysis uses the JES determined from the external calibrationderived from γ +jets events as an additional Gaussian constraint to the in situ calibration.Therefore, the total resulting JES uncertainty is split into one part obtained from the insitu calibration and another part determined from the external calibration. To do this, themeasurement without external JES constraint has been combined iteratively with a pseudo-measurement using the method of Refs. [35, 36] that uses only the external calibration in a waythat the combination gives the total JES uncertainty. The splitting obtained in this way is usedto assess both the statistical part of the JES uncertainty and the part of the JES uncertaintydue to the external calibration constraint [37].The L XY technique developed by CDF uses the decay length of B mesons from b -taggedjets. While the statistical sensitivity of this analysis is not as good as that of the more tradi-tional methods, this technique has the advantage that it is almost entirely independent of JES3able 1: Summary of the measurements used to determine the Tevatron average M t . Integratedluminosity ( (cid:82) L dt ) has units of fb − , and all other numbers are in GeV /c . The uncertaintycategories and their correlations are described in Section 3. The total systematic uncertaintyand the total uncertainty are obtained by adding the relevant contributions in quadrature.“n/a” stands for “not applicable”, “n/e” for “not evaluated”. Run I published Run II published Run II prel.CDF DØ CDF DØ CDF (cid:96) +jets (cid:96)(cid:96) alljets (cid:96) +jets (cid:96)(cid:96) (cid:96) +jets (cid:96)(cid:96) alljets Lxy (cid:96) +jets (cid:96)(cid:96)
MEt (cid:82) L dt In situ light-jet cali-bration (iJES) n/a n/a n/a n/a n/a 0.49 n/a 0.95 n/a 0.53 0.55 1.05Response to b / q / g jets (aJES) n/a n/a n/a 0.0 0.0 0.09 0.14 0.03 n/a 0.0 0.40 0.10Model for b jets(bJES) 0.6 0.8 0.6 0.7 0.7 0.16 0.33 0.15 n/a 0.07 0.20 0.17Out-of-cone correction(cJES) 2.7 2.6 3.0 2.0 2.0 0.21 2.13 0.24 0.36 n/a n/a 0.18Light-jet response (2)(dJES) 0.7 0.6 0.3 2.5 1.1 0.07 0.58 0.04 0.06 0.63 0.56 0.04Light-jet response (1)(rJES) 3.4 2.7 4.0 n/a n/a 0.48 2.01 0.38 0.24 n/a n/a 0.40Lepton modeling(LepPt) n/e n/e n/e n/e n/e 0.03 0.27 n/a n/a 0.17 0.35 n/aSignal modeling(Signal) 2.6 2.9 2.0 1.1 1.8 0.61 0.73 0.62 0.90 0.77 0.86 0.64Jet modeling(DetMod) 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.36 0.50 0.0Offset(UN/MI) n/a n/a n/a 1.3 1.3 n/a n/a n/a n/a n/a n/a n/aBackground fromtheory (BGMC) 1.3 0.3 1.7 1.0 1.1 0.12 0.24 0.0 0.80 0.18 0.0 0.0Background based ondata (BGData) 0.0 0.0 0.0 0.0 0.0 0.16 0.14 0.56 0.20 0.23 0.20 0.12Calibration method(Method) 0.0 0.7 0.6 0.6 1.1 0.00 0.12 0.38 2.50 0.16 0.51 0.31Multiple interactionsmodel (MHI) n/e n/e n/e n/e n/e 0.07 0.23 0.08 0.0 0.05 0.0 0.18Systematic uncertainty(Syst) 5.3 4.9 5.7 3.9 3.6 0.98 3.09 1.49 2.90 1.24 1.44 1.35Statistical uncertainty(Stat) 5.1 10.3 10.0 3.6 12.3 0.52 1.95 1.43 9.00 0.83 2.36 1.26Total uncertainty 7.3 11.4 11.5 5.3 12.8 1.11 3.79 2.06 9.46 1.50 2.76 1.85 uncertainties since it uses primarily tracking information.The DØ Run II (cid:96) +jets result is a combination of the published Run IIa (2002–2005) mea-surement [19] with 1 fb − of data and the result obtained with 2.6 fb − of data from Run IIb(2006–2007) [20]. This analysis includes an additional particle response correction on top ofthe standard in situ calibration. The DØ Run II (cid:96)(cid:96) result is based on a neutrino weightingtechnique using 5.4 fb − of Run II data [21].Table 1 lists the individual uncertainties of each result, subdivided into the categories de-scribed in the next Section. The correlations between the inputs are described in Section 4.4 Uncertainty Categories
We employ uncertainty categories similar to what was used for the previous Tevatron average [1,23], with small modifications to better account for their correlations. They are divided suchthat sources of systematic uncertainty that share the same or similar origin are combined asexplained in Ref. [1]. For example, the
Signal modeling ( Signal ) category discussed belowincludes the uncertainties from different systematic sources that are correlated due to theirorigin in the modeling of the simulated signal samples.Some systematic uncertainties have been separated into multiple categories to accommodatespecific types of correlations. For example, the jet energy scale (JES) uncertainty is subdividedinto six components to more accurately accommodate our best understanding of the relevantcorrelations between input measurements.For this note we use the new systematic naming scheme described in Ref. [1]. In parentheses,the old names of the systematic uncertainties are provided. There is a one-to-one matchingbetween the new and old systematic definitions of categories.
Statistical uncertainty (Statistics):
The statistical uncertainty associated with the M t de-termination. In situ light-jet calibration (iJES):
That part of the JES uncertainty that originates from in situ calibration procedures and is uncorrelated among the measurements. In the com-bination reported here, it corresponds to the statistical uncertainty associated with theJES determination using the W → qq (cid:48) invariant mass in the CDF Run II (cid:96) +jets, alljets,and MEt measurements and the DØ Run II (cid:96)(cid:96) and (cid:96) +jets measurements. For the DØRun II (cid:96) +jets measurement, it also includes the uncertainty coming from the MC/datadifference in jet response that is uncorrelated with the other DØ Run II measurements.Residual JES uncertainties arising from effects not considered in the in situ calibrationare included in other categories. Response to b/q/g jets (aJES):
That part of the JES uncertainty that originates fromaverage differences in detector electromagnetic over hadronic ( e/h ) response for hadronsproduced in the fragmentation of b -jets and light-quark jets. Model for b jets (bJES): That part of the JES uncertainty that originates from uncertain-ties specific to the modeling of b jets and that is correlated across all measurements. Forboth CDF and DØ this includes uncertainties arising from variations in the semileptonicbranching fractions, b -fragmentation modeling, and differences in the color flow between b -quark jets and light-quark jets. These were determined from Run II studies but back-propagated to the Run I measurements, whose Light-jet response (1) uncertainties ( rJES ,see below) were then corrected to keep the total JES uncertainty constant.5 ut-of-cone correction (cJES):
That part of the JES uncertainty that originates from mod-eling uncertainties correlated across all measurements. It specifically includes the model-ing uncertainties associated with light-quark fragmentation and out-of-cone corrections.For DØ Run II measurements, it is included in the
Light-jet response (2) (dJES) category.
Light-jet response (1) (rJES):
The remaining part of the JES uncertainty that covers theabsolute calibration for CDF’s Run I and Run II measurements. It also includes smallcontributions from the uncertainties associated with modeling multiple interactions withina single bunch crossing and corrections for the underlying event.
Light-jet response (2) (dJES):
That part of the JES uncertainty that includes DØ’s Run Iand Run II calibrations of absolute response (energy dependent), the relative response ( η -dependent), and the out-of-cone showering correction that is a detector effect. This uncer-tainty term for CDF includes only the small relative response calibration ( η -dependent)for Run I and Run II. Lepton modeling (LepPt):
The systematic uncertainty arising from uncertainties in thescale of lepton transverse momentum measurements. It was not considered as a source ofsystematic uncertainty in the Run I measurements.
Signal modeling (Signal):
The systematic uncertainty arising from uncertainties in tt mod-eling that is correlated across all measurements. This includes uncertainties from vari-ations of the amount of initial and final state radiation and from the choice of partondensity function used to generate the tt Monte Carlo samples that calibrate each method.For DØ, it also includes the uncertainty from higher-order corrections evaluated from acomparison of tt samples generated by M C@NLO [38] and A LPGEN [39], both inter-faced to H ERWIG [40, 41] for the simulation of parton showers and hadronization. In thiscombination, the systematic uncertainty arising from a variation of the phenomenologicaldescription of color reconnection (CR) between final state particles [42, 43] is included inthe
Signal modeling category. The CR uncertainty is obtained by taking the differencebetween the P YTHIA 6.4 tune “Apro” and the P YTHIA 6.4 tune “ACRpro” that differonly in the CR model. This uncertainty was not evaluated in Run I since the Monte Carlogenerators available at that time did not allow for variations of the CR model. Thesemeasurements therefore do not include this source of systematic uncertainty. Finally, thesystematic uncertainty associated with variations of the MC generator used to calibratethe mass extraction method is added. It includes variations observed when substituting P YTHIA [44, 45, 46] (Run I and Run II) or I SAJET [47] (Run I) for H ERWIG [40, 41]when modeling the tt signal. Jet modeling (DetMod):
The systematic uncertainty arising from uncertainties in the mod-eling of jet interactions in the detector in the MC simulation. For DØ this includes un-certainties from jet resolution and identification. Applying jet algorithms to MC events,CDF finds that the resulting efficiencies and resolutions closely match those in data. Thesmall differences propagated to M t lead to a negligible uncertainty of 0.005 GeV, whichis then ignored. 6 ackground based on data (BGData): This includes uncertainties associated with the mod-eling using data of the QCD multijet background in the alljets, MEt, and (cid:96) +jets channelsand the Drell-Yan background in the (cid:96)(cid:96) channel. This part is uncorrelated between ex-periments.
Background from theory (BGMC):
This systematic uncertainty on the background origi-nating from theory (MC) takes into account the uncertainty in modeling the backgroundsources. It is correlated between all measurements in the same channel, and includes un-certainties on the background composition, normalization, and shape of different compo-nents, e.g., the uncertainties from the modeling of the W +jets background in the (cid:96) +jetschannel associated with variations of the factorization scale used to simulate W +jetsevents. Calibration method (Method):
The systematic uncertainty arising from any source specificto a particular fit method, including the finite Monte Carlo statistics available to calibrateeach method.
Offset (UN/MI):
This uncertainty is specific to DØ and includes the uncertainty arising fromuranium noise in the DØ calorimeter and from the multiple interaction corrections to theJES. For DØ Run I these uncertainties were sizable, while for Run II, owing to the shortercalorimeter electronics integration time and in situ
JES calibration, these uncertaintiesare negligible.
Multiple interactions model (MHI):
The systematic uncertainty arising from a mismod-eling of the distribution of the number of collisions per Tevatron bunch crossing owingto the steady increase in the collider instantaneous luminosity during data-taking. Thisuncertainty has been separated from other sources to account for the fact that it is un-correlated between experiments.These categories represent the current preliminary understanding of the various sources ofuncertainty and their correlations. We expect these to evolve as we continue to probe eachmethod’s sensitivity to the various systematic sources with improving precision.
The following correlations are used for the combination: • The uncertainties in the
Statistical uncertainty (Stat) and
Calibration method (Method) categories are taken to be uncorrelated among the measurements.7able 2: The matrix of correlation coefficients used to determine the Tevatron average top-quarkmass.
Run I published Run II published Run II preliminaryCDF DØ CDF DØ CDF (cid:96) +jets (cid:96)(cid:96) alljets (cid:96) +jets (cid:96)(cid:96) (cid:96) +jets (cid:96)(cid:96) alljets L XY (cid:96) +jets (cid:96)(cid:96) MEtCDF-I (cid:96) +jets 1.00 0.29 0.32 0.26 0.11 0.49 0.54 0.25 0.07 0.21 0.12 0.27CDF-I (cid:96)(cid:96) (cid:96) +jets 0.26 0.15 0.14 1.00 0.16 0.22 0.27 0.12 0.05 0.14 0.07 0.12DØ-I (cid:96)(cid:96) (cid:96) +jets 0.49 0.29 0.30 0.22 0.11 1.00 0.48 0.29 0.08 0.30 0.18 0.33CDF-II (cid:96)(cid:96) L XY (cid:96) +jets 0.21 0.13 0.09 0.14 0.07 0.30 0.11 0.16 0.06 1.00 0.39 0.18DØ-II (cid:96)(cid:96) • The uncertainties in the
In situ light-jet calibration (iJES) category are taken to beuncorrelated among the measurements except for D0’s (cid:96)(cid:96) and (cid:96) +jets measurements, wherethis uncertainty is taken to be 100% correlated since the (cid:96)(cid:96) measurement uses the JEScalibration determined in (cid:96) +jets channel. • The uncertainties in the
Response to b / q / g jets (aJES) , Light-jet response (2) (dJES) , Lepton modeling (LepPt) , and
Multiple interactions model (MHI) categories are takento be 100% correlated among all Run I and all Run II measurements within the sameexperiment, but uncorrelated between Run I and Run II and uncorrelated between theexperiments. • The uncertainties in the
Light-jet response (1) (rJES) , Jet modeling (DetMod) , and
Offset(UN/MI) categories are taken to be 100% correlated among all measurements within thesame experiment but uncorrelated between the experiments. • The uncertainties in the
Backgrounds estimated from theory (BGMC) category are takento be 100% correlated among all measurements in the same channel. • The uncertainties in the
Backgrounds estimated from data (BGData) category are takento be 100% correlated among all measurements in the same channel and same run period,but uncorrelated between the experiments. • The uncertainties in the
Model for b jets (bJES) , Out-of-cone correction (cJES) , and
Sig-nal modeling (Signal) categories are taken to be 100% correlated among all measurements.Using the inputs from Table 1 and the correlations specified here, the resulting matrix of totalcorrelation coefficients is given in Table 2.The measurements are combined using a program implementing two independent meth-ods: a numerical χ minimization and the analytic best linear unbiased estimator (BLUE)8ethod [35, 36]. The two methods are mathematically equivalent. It has been checked thatthey give identical results for the combination. The BLUE method yields the decomposition ofthe uncertainty on the Tevatron M t average in terms of the uncertainty categories specified forthe input measurements [36]. The resultant combined value for the top-quark mass is M t = 173 . ± .
51 (stat) ± .
71 (syst) GeV /c . Adding the statistical and systematic uncertainties in quadrature yields a total uncertainty of0 .
87 GeV /c , corresponding to a relative precision of 0.50% on the top-quark mass. It has a χ of 8.5 for 11 degrees of freedom, corresponding to a probability of 67%, indicating goodagreement among all input measurements. The breakdown of the uncertainties is shown inTable 3. The total statistical and systematic uncertainties are reduced relative to the Summer2011 combination [23] and the published combination [1] due to the increase of the CDF datasamples in the (cid:96) +jets and MEt analyses and better treatment of JES corrections in the (cid:96) +jetsanalysis.The pull and weight for each of the inputs, as obtained from the combination with theBLUE method, are listed in Table 4. The input measurements and the resulting Tevatronaverage mass of the top quark are summarized in Fig. 1.The weights of some of the measurements are negative, which occurs if the correlationbetween two measurements is larger than the ratio of their total uncertainties. In these instancesthe less precise measurement will acquire a negative weight. While a weight of zero means thata particular input is effectively ignored in the combination, channels with a negative weightaffect the resulting M t central value and help reduce the total uncertainty [35]. To visualize theweight each measurement carries in the combination, Fig. 2 shows the absolute values of theweight of each measurement divided by the sum of the absolute values of the weights of all inputmeasurements. Negative weights are represented by bins with a different (grey) color. We note,that due to correlations between the uncertainties the relative weights of the different inputchannels may be significantly different from what one could expect from the total accuracy ofeach measurement as represented by error bars in Fig. 1.No input has an anomalously large pull. It is, however, still interesting to determine thetop-quark mass separately in the alljets, (cid:96) +jets, (cid:96)(cid:96) , and MEt channels (leaving out the L XY measurement). We use the same methodology, inputs, uncertainty categories, and correlationsas described above, but fit the four physical observables, M alljetst , M (cid:96) + jetst , M (cid:96)(cid:96) t , and M MEtt separately. The results of these combinations are shown in Figure 3 and Table 5.9able 3: Summary of the Tevatron combined average M t . The uncertainty categories aredescribed in the text. The total systematic uncertainty and the total uncertainty are obtainedby adding the relevant contributions in quadrature.Tevatron combined values (GeV/ c ) M t In situ light-jet calibration (iJES) 0.36Response to b / q / g jets (aJES) 0.09Model for b jets (bJES) 0.11Out-of-cone correction (cJES) 0.01Light-jet response (2) (dJES) 0.15Light-jet response (1) (rJES) 0.16Lepton modeling (LepPt) 0.05Signal modeling (Signal) 0.52Jet modeling (DetMod) 0.08Offset (UN/MI) 0.00Background from theory (BGMC) 0.06Background based on data (BGData) 0.13Calibration method (Method) 0.06Multiple interactions model (MHI) 0.07Systematic uncertainty (syst) 0.71Statistical uncertainty (stat) 0.51Total uncertainty 0.87Table 4: The pull and weight for each of the inputs, as obtained from the combination withthe BLUE method to determine the average top quark mass. Run I published Run II published Run II preliminaryCDF DØ CDF DØ CDF (cid:96) +jets (cid:96)(cid:96) alljets (cid:96) +jets (cid:96)(cid:96) (cid:96) +jets (cid:96)(cid:96) alljets Lxy (cid:96) +jets (cid:96)(cid:96)
MEtPull +0 . − .
51 +1 .
11 +1 . − . − . − . − . − .
67 1 .
42 +0 .
30 +0 . − . − . − . . − . . − . . .
22 +20 . . . Using the results of Table 5 we calculate the following chi-squared values including correla-tions: χ ( (cid:96) + jets − (cid:96)(cid:96) ) = 1 . / χ ( (cid:96) + jets − alljets) = 0 . / χ ( (cid:96) + jets − MEt) = 0 . / χ ( (cid:96)(cid:96) − alljets) = 0 . / χ ( (cid:96)(cid:96) − MEt) = 1 . /
1, and χ (alljets − MEt) = 0 . /
1. Thesecorrespond to chi-squared probabilities of 25%, 79%, 74%, 52%, 27%, and 66% respectively,indicating that the top-quark mass determined in each decay channel is consistent in all cases.To test the influence of the choices in modeling the correlations, we performed a cross-check by changing all non-diagonal correlation coefficients of the correlation matrix defined in10able 5: Summary of the combination of the 12 measurements by CDF and DØ in terms offour physical quantities, the mass of the top quark in the alljets, (cid:96) +jets, (cid:96)(cid:96) , and MEt decaychannels. Parameter Value (GeV /c ) Correlations M alljetst M (cid:96) + jetst M (cid:96)(cid:96) t M MEtt M alljetst . ± . M (cid:96) + jetst . ± . M (cid:96)(cid:96) t . ± . M MEtt . ± . .
19 GeV /c shift of the top-quark mass and reduces the totaluncertainty negligibly. The chosen approach is therefore conservative.We also performed separate combinations of all the CDF and DØ measurements. The resultsof these combinations are 172 . ± .
93 GeV /c for CDF and 174 . ± .
42 GeV /c for DØ.Taking all correlations into account, we calculate the chi-square value χ ( CDF − D Ø) = 2 . / An update of the combination of measurements of the mass of the top quark from the Teva-tron experiments CDF and DØ has been presented. This preliminary combination includes fivepublished Run I measurements, six published Run II measurements, and one preliminary Run IImeasurement, but the majority of these measurements are not yet performed on the full datasetsavailable. Taking into account the statistical and systematic uncertainties and their correlations,the preliminary result for the Tevatron average is M t = 173 . ± .
51 (stat) ± .
71 (syst) GeV /c ,where the total uncertainty is obtained assuming Gaussian systematic uncertainties. The cen-tral value is 0.02 GeV/ c higher than our July 2012 average [1] of M t = 173 . ± .
94 GeV/ c .Adding in quadrature the statistical and systematic uncertainties yields a total uncertainty of0 .
87 GeV /c which represents an improvement of 8%.The mass of the top quark is now known with a relative precision of 0.50%, limited by thesystematic uncertainties, which are dominated by the jet energy scale uncertainty. This resultwill be further improved when all analysis channels from CDF and DØ using the full Run IIdata set are finalized. 11 Acknowledgments
We thank the Fermilab staff and the technical staffs of the participating institutions for theirvital contributions. This work was supported by DOE and NSF (USA), CONICET and UBA-CyT (Argentina), CNPq, FAPERJ, FAPESP and FUNDUNESP (Brazil), CRC Program, CFI,NSERC and WestGrid Project (Canada), CAS and CNSF (China), Colciencias (Colombia),MSMT and GACR (Czech Republic), Academy of Finland (Finland), CEA and CNRS/IN2P3(France), BMBF and DFG (Germany), Ministry of Education, Culture, Sports, Science andTechnology (Japan), World Class University Program, National Research Foundation (Korea),KRF and KOSEF (Korea), DAE and DST (India), SFI (Ireland), INFN (Italy), CONACyT(Mexico), NSC(Republic of China), FASI, Rosatom and RFBR (Russia), Slovak R&D Agency(Slovakia), Ministerio de Ciencia e Innovaci´on, and Programa Consolider-Ingenio 2010 (Spain),The Swedish Research Council (Sweden), Swiss National Science Foundation (Switzerland),FOM (The Netherlands), STFC and the Royal Society (UK), and the A.P. Sloan Foundation(USA). 12 (GeV/c t M150 160 170 180 190 200015
CDF March'07 – – – ( Tevatron combination * – – – ( syst) – stat – ( CDF-II MET+Jets * – – – ( CDF-II track – – – ( CDF-II alljets – – – ( CDF-I alljets – – – ( DØ-II lepton+jets – – – ( CDF-II lepton+jets – – – ( DØ-I lepton+jets – – – ( CDF-I lepton+jets – – – ( DØ-II dilepton – – – ( CDF-II dilepton – – – ( DØ-I dilepton – – – ( CDF-I dilepton – – – ( Mass of the Top Quark (* preliminary)
March 2013 /dof = 8.5/11 (67%) c Figure 1: Summary of the input measurements and resulting Tevatron average mass of the topquark. 13 nalysis f o r a ll m eas u r e m e n t s ⎢ i w e i gh t ⎢ ∑ / ⎢ i w e i gh t ⎢ C D F - II l e p t o n + j e t s D Ø - II l e p t o n + j e t s C D F - II M E T + J e t s C D F - II a llj e t s C D F - I l e p t o n + j e t s D Ø - II d il e p t o n C D F - I d il e p t o n C D F - I a llj e t s D Ø - I l e p t o n + j e t s C D F - II d il e p t o n C D F - II t r a c k D Ø - I d il e p t o n March 2013Preliminary positive weights absolute value ofnegative weights
Figure 2: Relative weights of the input measurements in the combination. The relative weightshave been obtained by dividing the absolute value of each measurement weight by the sum overall measurements of the absolute values of the weights. Negative weights are represented bytheir absolute value, but using a grey color. 14 (GeV/c t M168 169 170 171 172 173 174 175 176 177 178 17907.3 CDF March'07 – – – ( Tevatroncombination * – – – ( syst) – stat – ( MET+Jets * – – – ( Alljets – – – ( Dilepton – – – ( Lepton+jets – – – ( Mass of the Top Quark in Different Decay Channels (* preliminary)
March 2013
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