The most precise top quark mass measurements use kinematic reconstruction methods, determining the top mass parameter of a Monte Carlo event generator m MC t . Because of hadronization and parton-shower dynamics, relating m MC t to a field theory mass is difficult. We present a calibration procedure to determine this relation using hadron level QCD predictions for observables with kinematic mass sensitivity. The highest precision measurements are based on direct reconstruction methods exploiting kinematic properties related to the top quark mass, and are based on multivariate fits that depend on a maximum amount of information on the top decay final states. This includes template and matrix element fits for distributions such as the measured invariant mass. These observables are highly differential, depending on experimental cuts and jet dynamics. Multipurpose Monte Carlo (MC) event generators are employed to do the analysis, and the results are influenced by both perturbative and nonperturbative QCD effects. Thus, the measured mass is the top mass parameter m MC t contained in the particular MC event generator. Its interpretation may also depend in part on the MC tuning and the observables used in the analysis.The systematic uncertainties from MC modeling are a dominant uncertainty in the above measurements, but do not address how m MC t is related to a mass parameter defined precisely in quantum field theory that can be globally used for higher-order predictions. The relation is nontrivial because it requires an understanding of the interplay between the partonic components of the MC generator (hard matrix elements and parton shower) and the hadronization model. In the context of top quark mass determinations, it is often assumed that MC generators should be considered as models whose partonic components and hadronization models are, through the tuning procedure, capable of describing experimental data to a precision that is higher than that of their partonic input.In the past m MC t has been frequently identified with the pole mass. This is compatible with parton-shower implementations for massive quarks, but a direct identification is disfavored because of sensitivity to nonperturbative effects from below the MC shower cutoff, Λ c ∼ 1 GeV. Also, the pole mass has an OðΛ QCD Þ renormalon ambiguity, while m MC t does not (since partonic information is not employed below Λ c ). It has been argued [4,5] can be calibrated into a field theory mass scheme through a fit of MC predictions to hadron level QCD computations for observables closely related to the distributions that enter the experimental analyses. In this Letter we provide a precise quantitative study on the interpretation of m MC t in terms of the MSR and pole mass schemes based on a hadron level prediction for the variable τ 2 for the production of a boosted top-antitop quark pair in e þ e − annihilation. It is defined aswhere the sum is over the 3-momenta of all final state particles, the maximum defines the thrust axisñ t , and Q is the center-of-ma...

We determine the MS charm quark mass from a charmonium QCD sum rules analysis. On the theoretical side we use input from perturbation theory at O(α 3 s ). Improvements with respect to previous O(α 3 s ) analyses include (1) an account of all available e + e − hadronic cross section data and (2) a thorough analysis of perturbative uncertainties. Using a data clustering method to combine hadronic cross section data sets from different measurements we demonstrate that using all available experimental data up to c.m. energies of 10.538 GeV allows for determinations of experimental moments and their correlations with small errors and that there is no need to rely on theoretical input above the charmonium resonances. We also show that good convergence properties of the perturbative series for the theoretical sum rule moments need to be considered with some care when extracting the charm mass and demonstrate how to set up a suitable set of scale variations to obtain a proper estimate of the perturbative uncertainty. As the final outcome of our analysis we obtain m c (m c ) = 1.282 ± (0.006) stat ± (0.009) syst ± (0.019) pert ± (0.010) αs ± (0.002) GG GeV. The perturbative error is an order of magnitude larger than the one obtained in previous O(α 3 s ) sum rule analyses.

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We present new determinations of the MS charm quark mass using relativistic QCD sum rules at O(α 3 s ) from the moments of the vector and the pseudoscalar current correlators. We use available experimental measurements from e + e − collisions and lattice simulation results, respectively. Our analysis of the theoretical uncertainties is based on different implementations of the perturbative series and on independent variations of the renormalization scales for the mass and the strong coupling. Taking into account the resulting set of series to estimate perturbative uncertainties is crucial, since some ways to treat the perturbative expansion can exhibit extraordinarily small scale dependence when the two scales are set equal. As an additional refinement, we address the issue that double scale variation could overestimate the perturbative uncertainties. We supplement the analysis with a test that quantifies the convergence rate of each perturbative series by a single number. We find that this convergence test allows to determine an overall and average convergence rate that is characteristic for the series expansions of each moment, and to discard those series for which the convergence rate is significantly worse. We obtain m c (m c ) = 1.288 ± 0.020 GeV from the vector correlator. The method is also applied to the extraction of the MS bottom quark mass from the vector correlator. We compute the experimental moments including a modeling uncertainty associated to the continuum region where no data is available. We obtain m b (m b ) = 4.176 ± 0.023 GeV.