On the Light Massive Flavor Dependence of the Large Order Asymptotic Behavior and the Ambiguity of the Pole Mass

We provide a systematic renormalization group formalism for the mass effects in the relation of the pole mass $m_Q^{\rm pole}$ and short-distance masses such as the $\overline{\rm MS}$ mass $\overline{m}_Q$ of a heavy quark $Q$, coming from virtual loop insertions of massive quarks lighter than $Q$. The formalism reflects the constraints from heavy quark symmetry and entails a combined matching and evolution procedure that allows to disentangle and successively integrate out the corrections coming from the lighter massive quarks and the momentum regions between them and to precisely control the large order asymptotic behavior. With the formalism we systematically sum logarithms of ratios of the lighter quark masses and $m_Q$, relate the QCD corrections for different external heavy quarks to each other, predict the ${\cal O}(\alpha_s^4)$ virtual quark mass corrections in the pole-$\overline{\rm MS}$ mass relation, calculate the pole mass differences for the top, bottom and charm quarks with a precision of around $20$ MeV and analyze the decoupling of the lighter massive quark flavors at large orders. The summation of logarithms is most relevant for the top quark pole mass $m_t^{\rm pole}$, where the hierarchy to the bottom and charm quarks is large. We determine the ambiguity of the pole mass for top, bottom and charm quarks in different scenarios with massive or massless bottom and charm quarks in a way consistent with heavy quark symmetry, and we find that it is $250$ MeV. The ambiguity is larger than current projections for the precision of top quark mass measurements in the high-luminosity phase of the LHC.Comment: 45 pages + appendix, 6 figures, v2: journal versio

The MSR Mass and the O(ΛQCD){\cal O}(\Lambda_{\rm QCD}) Renormalon Sum Rule

We provide a detailed description and analysis of a low-scale short-distance mass scheme, called the MSR mass, that is useful for high-precision top quark mass determinations, but can be applied for any heavy quark $Q$. In contrast to earlier low-scale short-distance mass schemes, the MSR scheme has a direct connection to the well known $\overline{\rm MS}$ mass commonly used for high-energy applications, and is determined by heavy quark on-shell self-energy Feynman diagrams. Indeed, the MSR mass scheme can be viewed as the simplest extension of the $\overline{\rm MS}$ mass concept to renormalization scales $\ll m_Q$. The MSR mass depends on a scale $R$ that can be chosen freely, and its renormalization group evolution has a linear dependence on $R$, which is known as R-evolution. Using R-evolution for the MSR mass we provide details of the derivation of an analytic expression for the normalization of the ${\cal O}(\Lambda_{\rm QCD})$ renormalon asymptotic behavior of the pole mass in perturbation theory. This is referred to as the ${\cal O}(\Lambda_{\rm QCD})$ renormalon sum rule, and can be applied to any perturbative series. The relations of the MSR mass scheme to other low-scale short-distance masses are analyzed as well.Comment: 42 pages + appendices, 6 figures, v2: Refs and Appendix B added, Fig.3 changed from nl=4 to nl=5, v3: journal versio

Monte Carlo Top Quark Mass Calibration

The most precise top quark mass measurements use kinematic reconstruction methods, determining the top mass parameter of a Monte Carlo event generator, $m_t^{\rm MC}$. Due to the complicated interplay of hadronization and parton shower dynamics in Monte Carlo event generators relevant for kinematic reconstruction, relating $m_t^{\rm MC}$ to field theory masses is a non-trivial task. In this talk we report on a calibration procedure to determine this relation using hadron level QCD predictions for 2-Jettiness in $e^+e^-$ annihilation, an observable which has kinematic top mass sensitivity and a close relation to the invariant mass of the particles coming from the top decay. The theoretical ingredients of the QCD prediction are reviewed. Fitting $e^+e^-$ 2-Jettiness calculations at NLL/NNLL order to PYTHIA 8.205, we find that $m_t^{\rm MC}$ agrees with the MSR mass $m_{t,1\,{\rm GeV}}^{\rm MSR}$ within uncertainties. At NNLL we find $m_t^{\rm MC} = m_{t,1\,{\rm GeV}}^{\rm MSR} + (0.18 \pm 0.22)\,{\rm GeV}$. $m_t^{\rm MC}$ can differ from the pole mass $m_t^{\rm pole}$ by up to $600\,{\rm MeV}$, and using the pole mass generally leads to larger uncertainties. At NNLL we find $m_t^{\rm MC} = m_t^{\rm pole} + (0.57 \pm 0.28)\,{\rm GeV}$ as the fit result. In contrast, converting $m_{t,1\,{\rm GeV}}^{\rm MSR}$ obtained at NNLL to the pole mass gives a result for $m_t^{\rm pole}$ that is substantially larger and incompatible with the fit result. We also explain some theoretical aspects relevant for employing the C-parameter as an alternative calibration observable.Comment: Talk presented at the 13th International Symposium on Radiative Corrections (RADCOR 2017), St. Gilgen, Austria, 24-29 September 2017. 7 pages, 1 figur

Top Quark Mass Calibration for Monte Carlo Event Generators

United States. Department of Energy (DE-SC0011090

On the Light Massive Flavor Dependence of the Top Quark Mass

We provide a systematic renormalization group formalism for the mass effects in the relation of the pole mass and short-distance masses such as the MS mass of a heavy quark Q, coming from virtual loop insertions of massive quarks lighter than Q with the main focus on the top quark. The formalism reflects the constraints from heavy quark symmetry and entails a combined matching and evolution procedure that allows to disentangle and successively integrate out the corrections coming from the lighter massive quarks and the momentum regions between them and also to precisely control the large order asymptotic behavior. With the formalism we systematically sum logarithms of ratios of the lighter quark masses and heavy quark mass, predict the O α s 4 virtual quark mass corrections in the pole- MS ̅ mass relation and calculate the pole mass differences for the top, bottom and charm quarks with a precision of around 20 MeV

Calibration of the top quark mass for Monte-Carlo event generators

© Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0). The most precise top quark mass measurements use kinematic reconstruction methods, determining the top mass parameter of a Monte Carlo event generator, mtMC. Due to the complicated interplay of hadronization and parton shower dynamics in Monte Carlo event generators, relating mtMC to field theory masses is a non-trivial task. In this talk we present a calibration procedure to determine this relation using hadron level QCD predictions for 2-Jettiness in e+e- annihilation, an observable which has kinematic top mass sensitivity and has a close relation to the invariant mass of the particles coming from the top decay. The theoretical ingredients of the QCD prediction are explained. Fitting e+e- 2-Jettiness calculations at NLL/NNLL order to PYTHIA 8.205, we find that mtMC agrees with the MSR mass at the scale 1 GeV within uncertainties, mtMC ≃ mtMSR1GeV, but differs from the pole mass by 900/600 MeV

Top quark mass calibration for Monte-Carlo event generators

The most precise top quark mass measurements use kinematic reconstruction methods, determining the top mass parameter of a Monte Carlo event generator, mMCt. Due to the complicated interplay of hadronization and parton shower dynamics in Monte Carlo event generators, relating mMCt to field theory masses is a non-trivial task. In this talk we present a calibration procedure to determine this relation using hadron level QCD predictions for 2-Jettiness in e+e- annihilation, an observable which has kinematic top mass sensitivity and has a close relation to the invariant mass of the particles coming from the top decay. The theoretical ingredients of the QCD prediction are explained. Fitting e+e- 2-Jettiness calculations at NLL/NNLL order to PYTHIA 8.205, we find that mMCt agrees with the MSR mass at the scale 1 GeV within uncertainties, mMCt mMSRt;1GeV, but differs from the pole mass by 900/600MeV

Summing logarithms and factorization for massive quark initiated jets and the Pythia top quark mass

© Copyright owned by the author(s) under the terms of the Creative Commons. The most precise top quark mass measurements use kinematic reconstruction methods, determining the top mass parameter of a Monte Carlo event generator, mtMC. Due to the complicated interplay of hadronization and parton shower dynamics in Monte Carlo event generators, relating mtMC to field theory masses is a non-trivial task. In this talk we present a calibration procedure to determine this relation using hadron level QCD predictions for 2-Jettiness in e+e- annihilation, an observable which has kinematic top mass sensitivity and has a close relation to the invariant mass of the particles coming from the top decay. The theoretical ingredients of the QCD prediction are explained. Fitting e+e-2-Jettiness calculations at NLL/NNLL order to PYTHIA 8.205, we find that mtMC agrees with the MSR mass at the scale 1 GeV within uncertainties, mtMC≃ mtMCmt, IGeVMSR, but differs from the pole mass by 900/600MeV

Top Quark Mass Calibration for Monte Carlo Event Generators

The most precise top quark mass measurements use kinematic reconstruction methods, determining the top mass parameter of a Monte Carlo event generator, $m_t^{\rm MC}$. Due to hadronization and parton shower dynamics, relating $m_t^{\rm MC}$ 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. Fitting $e^+e^-$ 2-Jettiness calculations at NLL/NNLL order to Pythia 8.205, $m_t^{\rm MC}$ differs from the pole mass by $900$/$600$ MeV, and agrees with the MSR mass within uncertainties, $m_t^{\rm MC}\simeq m_{t,1\,{\rm GeV}}^{\rm MSR}$