Top Mass Measurements from Jets and the Tevatron Top-Quark Mass

TL;DR

This work addresses how to interpret and extract the top-quark mass from jet-based observables, emphasizing that the pole mass is ill-defined beyond nonperturbative effects and that short-distance schemes are essential. It develops a factorization framework for $e^+e^- \to t\bar t$ that maps observables to a short-distance mass, and introduces the MSR mass to handle scales much smaller than the top mass without introducing large perturbative uncertainties. The heavy-quark jet function and hemisphere soft function are analyzed in a renormalon-free setting, enabling controlled perturbative predictions and a clear separation of perturbative and nonperturbative shifts in observable peak positions. The implications for hadron colliders connect the Monte Carlo mass to a short-distance mass via the MSR scheme, enabling a reliable translation of the Tevatron top mass into the $\overline{\rm MS}$ framework with quantified scheme uncertainties.

Abstract

Theoretical issues are discussed for the measurement of the top-mass using jets, including perturbative and non-perturbative effects that relate experimental observables to the Lagrangian mass, and appropriate choices for mass schemes. Full account for these issues is given for e+e--> t-tbar using a factorization theorem for event shapes for massive quarks. Implications for the Tevatron top-mass measurement are discussed. A mass-scheme, the "MSR-mass", is introduced which allows for a precise description of observables sensitive to scales R << m, but at the same time does not introduce perturbative matching uncertainties in conversion to the MSbar mass.

Figures (4)

• Figure 1: Heavy quark jet-function up to NNLL order (top). Peak positions in the pole and jet-mass schemes (bottom). Plots from Jain:2008gb.
• Figure 2: Diagonal hemisphere soft function up to NNLO order in the $\delta\Delta=0$ scheme and scheme from Eq. (\ref{['dDelta']}). Plot from Hoang:2008fs.
• Figure 3: Diagonal invariant mass distribution at LL and NLL order (top). Peak position of the NLL distribution for different soft function models versus $Q/m$ (bottom). Vertical black lines indicate theory uncertainties and the colored bands linear extrapolations to $Q/m\to 0$. Plots from Fleming:2007xt.
• Figure 4: Converting the Tevatron top mass into the $\overline {\rm MS}$ scheme using the MSR scheme.