Determination of the b Quark Mass at the Z Mass Scale

TL;DR

This work determines the running b-quark mass at the Z mass scale by comparing mass-sensitive 3-jet rates in Z decays to massive QCD predictions, using seven jet finders and a b-tagging technique based on displaced vertices. The analysis yields mbbar(mZ) = 2.67 ± stat 0.03 GeV +0.29/−0.37 GeV (syst) ±0.19 GeV (theo), which, when evolved to mb, gives mbbar(mb) ≈ 3.95 GeV, consistent with threshold measurements and supporting the QCD-predicted running of the quark mass. A constant-mass hypothesis is disfavored at 3.9 standard deviations, underscoring the scale dependence of mb in the MSbar scheme. The result aligns with prior Z-pole determinations and the PDG world average, providing a precise validation of quark-mass running predicted by QCD at high energy scales.

Abstract

In hadronic decays of Z bosons recorded with the OPAL detector at LEP, events containing b quarks were selected using the long lifetime of b flavoured hadrons. Comparing the 3-jet rate in b events with that in d,u,s and c quark events, a significant difference was observed. Using Order(alpha_s squared) calculations for massive quarks, this difference was used to determine the b quark mass in the MSbar renormalisation scheme at the scale of the Z boson mass. By combining the results from seven different jet finders the running b quark mass was determined to be mb(MZ) = (2.67 +/- 0.03(stat) +0.29/-0.37(syst) +/- 0.19(theo.)) GeV. Evolving this value to the b quark mass scale itself yields mb(mb) = (3.95 +0.52/-0.62) GeV, consistent with results obtained at the b quark production threshold. This determination confirms the QCD expectation of a scale dependent quark mass. A constant mass is ruled out by 3.9 standard deviations.

Figures (7)

• Figure 1: Distribution of the decay length significance $L/\sigma_L$ for data (points) and simulation (histograms). The contributions from the d, u or s and c quark events in the simulation are shown by different hatching, b quark events are shown by the open histogram. The vertical line indicates the cut chosen to select b quark events. The statistical uncertainty is also shown.
• Figure 2: In a) and b) the correction factors of the $B_3$ ratio for detector effects, ${\cal C}_{\mathrm{det}}$, and in c) and d) for hadronisation effects, ${\cal C}_{\mathrm{had}}$, are shown as a function of $y_{\mathrm{cut}}$ for the DURHAM (left column) and JADE E0 (right column) jet finders. The error bars show the statistical uncertainty of the Monte Carlo. The dashed vertical lines indicate the $y_{\mathrm{cut}}$ values chosen to determine the b quark mass.
• Figure 3: a) and b) show the efficiency $\epsilon_3(y_{\mathrm{cut}})$ for b quark 3-jet events for the DURHAM (left) and JADE E0 (right column) jet finders. Overlaid as a dotted line is $\epsilon$, the tagging efficiency for all b quark events; c) and d) show the fake tag rates $f_3(y_{\mathrm{cut}})$ for light quark 3-jet events for both jet finders. Overlaid is the fake tag rate $f$ for all light quark events. The error bars describe the statistical uncertainty of the Monte Carlo. The dashed vertical lines indicate the $y_{\mathrm{cut}}$ values chosen to determine the b quark mass.
• Figure 4: The uncorrected a) and b), and the corrected c) and d) $B_3$ ratios for the DURHAM and the JADE E0 jet finders. The uncertainties include the effect of finite statistics in both data and Monte Carlo. There is a substantial correlation between adjacent bins. The dashed vertical lines indicate the $y_{\mathrm{cut}}$ values chosen for the determination of the b quark mass. The bands in c) and d) display the total systematic and the statistical uncertainty added in quadrature.
• Figure 5: For each jet finder the fit to the theoretical prediction, Eq. (\ref{['b3_2_mb']}), is shown together with each measured double ratio $B_3$ displayed on the y-axis. The b quark mass can be read from the x-axis. The band represents the total uncertainty for the double ratio and b quark mass. In a) JADE, b) DURHAM, c) JADE E0, d) JADE P, e) JADE P0, f) JADE E and in g) GENEVA schemes are shown. No lower bound on the b quark mass for the JADE P scheme is shown as this bound reaches the physical limit of a vanishing b quark mass. The arrows in a) and c) indicate, how two positively correlated systematic uncertainties on $B_3$ turn into negatively correlated ones in $\overline{m}_{\mathrm{b}}$.