Measurements of cross section and asymmetry for $e^{+}{e}^{-}\to b\overline{b}$ and heavy quark fragmentation at KEK TRISTAN

Using 773 muons found in hadronic events from 142 ${\mathrm{pb}}^{-1\mathrm{}}$ of data at a c.m. energy of 57.8 GeV, we extract the cross section and forward-backward charge asymmetry for the $e^{+}{e}^{-}\to b\overline{b}$ process, and the heavy quark fragmentation function parameters for the Peterson model. For the analysis of the $e^{+}{e}^{-}\to b\overline{b}$ process, we use a method in which the behavior of the $c$ quark and lighter quarks is assumed, with only that of the $b$ quark left indeterminate. The cross section and asymmetry for $e^{+}{e}^{-}\to b\overline{b}$ are found to be $R_b = 0.57 \pm 0.06\left(\mathrm{stat}\right) \pm 0.08\left(\mathrm{syst}\right)$ and $A_b = -0.59\mathrm{} \pm 0.09 \pm 0.09$, respectively. They are consistent with the standard model predictions. For the study of the fragmentation function we use the variable $〈x_E〉$, the fraction of the beam energy carried by the heavy hadrons. We obtain ${〈x_E〉}_c={0.56}_{-0.05-0.03\mathrm{}}^{+0.04+0.03\mathrm{}}$ and ${〈x_E〉}_b={0.65}_{-0.04-0.06\mathrm{}}^{+0.06+0.05\mathrm{}}$, respectively. These are in good agreement with previously measured values.