Measurement of theb-quark fragmentation function inZ0decays

We present a measurement of the b-quark inclusive fragmentation function in $Z^0$ decays using a novel kinematic B-hadron energy reconstruction technique. The measurement was performed using 350 000 hadronic $Z^0$ events recorded in the SLD experiment at SLAC between 1997 and 1998. The small and stable SLC beam spot and the charge-coupled-device–based vertex detector were used to reconstruct B-decay vertices with high efficiency and purity, and to provide precise measurements of the kinematic quantities used in this technique. We measured the B energy with good efficiency and resolution over the full kinematic range. We compared the scaled B-hadron energy distribution with models of b-quark fragmentation and with several ad hoc functional forms. A number of models and functions are excluded by the data. The average scaled energy of weakly decaying B hadrons was measured to be $〈x_b〉=0.709\mathrm{}\pm 0.003\mathrm{}\left(\mathrm{stat}\right)\mathrm{}\pm 0.003\mathrm{}\left(\mathrm{syst}\right)\mathrm{}\pm 0.002\left(\mathrm{model}\right).\mathrm{}$