� Top quark mass definitions and their measurements Hiroshi Yokoya (University of Toyama) 6th Meeting of Toyama Higgs Working Group, 07.07.2013, Toyama
� • Top-quark mass history and present arXiv:1305.3939 ATLAS-CONF-2012-095 • The value of the top-quark mass is important, because, 1. It is one of the parameters with large uncertainty in the SM. 2. It is a key parameter for the high-scale behavior of the SM. 3. It is also a key parameter for the scale of the BSM physics.
� • RGE of Higgs quartic coupling m t is important to calculate the scale at which the SM break down. • Higgs mass in the MSSM
� • Definition of the mass with renormalization Pole mass : defined as the position of the pole in the propagator, but for the quarks confined, it may not be meaningful nor well-defined. Convergence of perturbative series is known to be slow. MSbar mass : defined as minimum subtraction of the divergent term, unphysical mass, just a parameter in the Lagrangian . Convergence better than pole scheme. Threshold masses : → important at the ILC related to the bound-state mass near threshold
� • RGE and matching condition (finite renormalization) : 3-loop in QCD, O(α, α*α s ) known • Recent topics : Jegerlehner et al. (13) In the presence of EW correction, MSbar mass may be defined with running VEV. large running effect due to tadpoles
� Top-quark mass measurement at colliders arXiv:1305.3939 ATLAS-CONF-2012-095
� The best channel is the Lepton+Jets channel, using 3-jet invariant-mass. (less BG, easy to reconstruct mass) : lepton + E T + 4-jets (2 b-tagged) /
� Template Method • Calculate distributions of some observables using MC simulation (Pythia, HERWIG,,,) by changing the input mass. (Template) • Fit the observed distribution with Templates and find the best values.
� • Is the mass measured by bjj invariant-mass pole mass? ? Since quark is a colored object while jets consist of colorless hadrons, four-momentum of jets cannot be that of a quark, and the bjj invariant-mass cannot be the pole mass. [However, the difference may be small ~O(hundreds MeV), because the color neutralization can be achieved by small-momentum quarks/gluons.]
�� Moreover, there are many ISR/FSR hadrons at hadron colliders, which come in to the jet constituents, and consequently change the peak of the invariant-mass distributions. Estimations of these effects are difficult. Therefore, we rely on the MC simulation for this part. Different MC generators give different invariant-mass distributions, then we → → → → MC mass (Pythia mass) obtain different mass value as the best fit.
�� • The other methods for determining top-quark mass without conceptual problem Direct measurements : Langenfeld, Moch, Uwer (09) • Top-quark production cross-section Alekhin, Djouadi, Moch (12) • Top-quark kinematical distributions Dowling, Moch (13) • Threshold scan at the ILC • … Indirect measurements : • EW precision test •
�� Top-quark mass in the EW precision measurements: MSbar or pole mass, depending on which scheme the observables are calculated.
�� Method using the top-quark pair-production cross-section known up to NNLO Barnreuther,Czakon,Mitov (12) Czakon,Fiedler,Mitov (13) It is known that the convergence is better in MSbar scheme than in pole mass scheme. Uncertainties come from PDF and strong coupling constant.
�� NNLO(QCD) Alekhin, Djouadi, Moch (12) A few GeV errors still exist, but the pole masses seem to be consistent with the value obtained by the “MC mass method”. EW correction in the MSbar scheme has not yet available.
�� Threshold scan at the ILC At the ILC, top-quark mass can be measured very accurately in the well-defined definition, by performing “Threshold Scan” Threshold Scan : measure the energy dependence of the total cross-sections at the threshold region where the tt bound-state is formed. The (threshold) mass can be measured in 30~50 MeV accuracy. By converting it to the MSbar scheme, the mass is determined in 100MeV accuracies. This is the best accurate method for the top- quark mass determination ever proposed.
�� Summary : • Top-quark mass is an important parameter in the SM. • In QFT, these are defined with renormalization scheme (Pole, MSbar,,,). • Currently measured mass should be close to the pole mass but not exactly for sure. We don’t know how much it is different. • A well-defined mass determination by using the total cross-sections, etc, has been started. • The most accurate top-quark mass determination will be achieved by “threshold scan” at the ILC.
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