Precise Measurement of theb-Quark Fragmentation Function inZ0Boson Decays

We have developed a new technique for inclusive reconstruction of the energy of $B$ hadrons. The excellent efficiency and resolution of this technique allow us to make the most precise determination of the $b$-quark fragmentation function, using $e^{+}{e}^{-}\to Z^0$ decays recorded in the SLAC Large Detector experiment. We compared our measurement with the predictions of a number of fragmentation models. We excluded several of these models and measured the average scaled energy of weakly decaying $B$ hadrons to be $〈x_B〉=0.714\mathrm{}\pm 0.005\left(\mathrm{stat}\right)\pm 0.007\left(\mathrm{syst}\right)\pm 0.002$ (model dependence).