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 $m_t^{\mathrm{MC}}$. Because of hadronization and parton-shower dynamics, relating $m_t^{\mathrm{MC}}$ 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 next-to-leading-logarithmic and next-to-next-to-leading-logarithmic order to pythia 8.205, $m_t^{\mathrm{MC}}$ differs from the pole mass by 900 and 600 MeV, respectively, and agrees with the MSR mass within uncertainties, $m_t^{\mathrm{MC}}\simeq m_{t,1\mathrm{GeV}}^{\mathrm{MSR}}$.

Figure 1

Distribution of best-fit mass values from the scan over parameters describing perturbative uncertainties. Results are shown for cross sections employing the MSR mass $m_t^{\mathrm{MSR}}(1\mathrm{GeV})$ (top two panels) and the pole mass $m_t^{\mathrm{pole}}$ (bottom two panels), both at $\mathrm{N}\mathrm{N}\mathrm{LL}$ and NLL. The pythia data sets use $m_t^{\mathrm{MC}}=173\mathrm{GeV}$ as an input (vertical red lines).

Figure 2

Comparison of pythia samples with $10^7$ events and $m_t^{\mathrm{MC}}=173\mathrm{GeV}$ (red dots) to the theoretical prediction in the MSR scheme at $\mathrm{N}\mathrm{N}\mathrm{L}\mathrm{L}$ for $m_t^{\mathrm{MSR}}(1\mathrm{GeV})=172.81\mathrm{GeV}$ and ${\mathrm{\Omega }}_1=0.44\mathrm{GeV}$. The blue band shows the perturbative uncertainty from a random scan over 500 profile functions. Vertical error bars on the pythia points are obtained by a global rescaling of pythia statistical uncertainties such that the average ${\chi }_{\min }^2/\mathrm{d}\mathrm{o}\mathrm{f}=1$ and roughly indicate the incompatibility uncertainties on the cross sections. Horizontal error bars are related to the $\mathrm{N}{}^2\mathrm{LL}$ incompatibility uncertainty in the MSR mass shown in Table 1.

Figure 3

Dependence of the $\mathrm{N}\mathrm{N}\mathrm{L}\mathrm{L}$ fit result for the MSR mass on the input $m_t^{\mathrm{MC}}$ value in pythia. The error bars show the total calibration uncertainty. The red solid lines correspond to the weighted average of the individual results. The red shaded area shows the average of the individual uncertainties.