A Measurement of the b-quark Mass from Hadronic Z Decays

TL;DR

The paper measures the running b-quark mass at the Z pole by analyzing ratios of observables between b-tagged and inclusive hadronic Z decays, leveraging NLO predictions with mass effects. It combines three-jet rates and event-shape moments, applying comprehensive detector, hadronization, and tagging corrections, to extract mb(M_Z) with quantified statistical, experimental, hadronization, and theoretical uncertainties. The results favor mb(M_Z) ≈ 3.27 GeV/c^2 and support the flavour independence of α_s at the 1% level, while highlighting the dominant role of hadronization in systematic errors. Overall, the analysis provides a precise cross-check of heavy-quark mass running and strengthens the consistency of QCD across flavours at high energy scales.

Abstract

Hadronic Z decay data taken with the ALEPH detector at LEP1 are used to measure the three-jet rate as well as moments of various event-shape variables. The ratios of the observables obtained from b-tagged events and from an inclusive sample are determined. The mass of the b quark is extracted from a fit to the measured ratios using a next-to-leading order prediction including mass effects. Taking the first moment of the y3 distribution, which is the observable with the smallest hadronization corrections and systematic uncertainties, the result is: mb(MZ) = [3.27+-0.22(stat) +-0.22(exp)+-0.38(had)+-0.16(theo)] GeV/c2. The measured ratio is alternatively employed to test the flavour independence of the strong coupling constant for b and light quarks.

Figures (5)

• Figure 1: Distribution of the $b$-tag variable for data and Monte Carlo $b$, $c$ and $uds$ events. The Monte Carlo has been normalized to the same number of events as the data. The last bin includes overflow entries. The insert at the bottom shows the ratio of data over Monte Carlo.
• Figure 2: Comparison of the $y_{\mathrm{cut}}$ dependence of the measured ratio $R^{\mathrm{pert}}_{bd}$ for the three-jet rate to the predictions of parton shower models as well as next-to-leading order (NLO) perturbative QCD for two different values of the $b$-quark mass in the $\overline{\mathrm{MS}}$ scheme. The measurement is obtained using HVFL for the hadronization corrections. The errors are statistical only.
• Figure 3: Parametrisations of the $b$-quark mass dependence for the LO (top) and NLO (bottom) contributions to $R^{\mathrm{pert}}_{bd}$ in the pole mass (left) and running mass schemes (right) for the first moment of the $y_3$ distribution. The points indicate the result of the MC integration, and the full line the parametrisations. The NLO contributions are evaluated using $\alpha_s(M_{\mathrm Z})=0.119$.
• Figure 4: Renormalization scale dependence for the extracted $b$-quark mass in the running and pole mass scheme, for the observables $R_3$ (left) and $y_{3_1}$ (right). The error bar spans the range of the scheme uncertainty. The full line indicates the renormalization scale dependence of the average computed from the running and pole mass schemes.
• Figure 5: Comparison of the ALEPH result for $m_b(M_{\mathrm Z})$ with the world average value of low-energy measurements for $m_b(m_b)$, which is evolved up to the $M_{\mathrm Z}$ scale using a two-loop evolution equation with $\alpha_s(M_{\mathrm Z})=0.119\pm0.003$. Also shown are the measurements by DELPHI Delphibm1 and Brandenburg et al. SLACbm1. The inner error bars indicate the quadratic sum of the statistical and experimental uncertainties. The three points at the Z pole are separated for clarity.