Inclusive Analysis of the b Quark Fragmentation Function in Z Decays at LEP

TL;DR

This study delivers a highly precise, model-independent measurement of the mean B-hadron scaled energy $⟨x_E⟩$ in Z decays using inclusively reconstructed B hadrons from OPAL data. By combining two unfolding methods and cross-validating with model-dependent fits, the authors show $⟨x_E⟩ = 0.7193 \pm 0.0016\,(stat)^{+0.0038}_{-0.0033}\,(syst)$, consistent with ALEPH and SLD within uncertainties. The results favor string-inspired fragmentation functions (Bowler/Lund) and a one-parameter Kartvelishvili description over Peterson/Collins-Spiller, while HERWIG's cluster model is disfavoured; this work provides a stringent benchmark for hadronisation models in heavy-flavor physics. The methodologies and detailed systematic studies enhance the reliability of B-hadron energy distributions as inputs for precision QCD tests and heavy-flavor analyses.

Abstract

A study of b quark hadronisation is presented using inclusively reconstructed B hadrons in about four million hadronic Z decays recorded in 1992-2000 with the OPAL detector at LEP. The data are compared to different theoretical models, and fragmentation function parameters of these models are fitted. The average scaled energy of weakly decaying B hadrons is determined to be <xe>=0.7193+-0.0016(stat)+0.0036-0.0031(syst)

Figures (9)

• Figure 1: Distribution of the jet b-tagging discriminant in data (points with error bars) and Monte Carlo (histograms). The contributions from $\mathrm{b}$ jets, $\mathrm{c}$ jets, and light quark or gluon jets are shown as open, hatched, and black area respectively. Jets with a b-tagging discriminant above 0.8 in a jet in the opposite hemisphere are retained for analysis.
• Figure 2: a) Dependence of the $\mathrm{B}$ hadron energy resolution (black circles) and reconstruction bias (open circles) on the generated $\mathrm{B}$ hadron energy. b) Dependence of the $\mathrm{B}$ hadron reconstruction efficiency on the generated $\mathrm{B}$ hadron energy.
• Figure 3: Results of the fit to the data of various hadronisation models for JETSET 7.4. The points with error bars are the uncorrected reconstructed scaled energy distribution in the 1994 data sample. Only statistical errors are shown. The histogram represents the best match as obtained from the respective fragmentation function fits. Background from charm jets is shown as hatched histogram, and light quark and gluon background is indicated by the black area. Charm jets are preferentially passing the selection if the $\mathrm{c}$ quark flight length is large due to a large boost. The mean energy of reconstructed charm candidates is therefore close to that of $\mathrm{b}$ jets.
• Figure 4: Results of the fit to the data of various hadronisation models for JETSET 7.4. The points with error bars are the uncorrected reconstructed scaled energy distribution in the 1994 data sample. Only statistical errors are shown. The histogram represents the best match as obtained from the respective fragmentation function fits. Background from charm jets is shown as hatched histogram, and light quark and gluon background is indicated by the black area. Charm jets are preferentially passing the selection if the $\mathrm{c}$ quark flight length is large due to a large boost. The mean energy of reconstructed charm candidates is therefore close to that of $\mathrm{b}$ jets.
• Figure 5: Result of the fit to the data of the Collins-Spiller hadronisation model for JETSET 7.4. The points with error bars are the uncorrected reconstructed scaled energy distribution in the 1994 data sample. Only statistical errors are shown. The histogram represents the best match as obtained from the fragmentation function fit. Background from charm jets is shown as hatched histogram, and light quark and gluon background is indicated by the black area. Charm jets are preferentially passing the selection if the $\mathrm{c}$ quark flight length is large due to a large boost. The mean energy of reconstructed charm candidates is therefore close to that of $\mathrm{b}$ jets.