Measurements of the Z Partial Decay Width into $c\overline{c}$ and Multiplicity of Charm Quarks per b Decay

The partial decay width $R_c$ of the $Z$ into $c\bar{c}$ quark pair and the number of charm quarks $n_c$ per $b$ decay are measured with the DELPHI detector at \mbox{LEP 1}. Particle identification provides clear $D^0$, $D^+$, $D_s^+$ and $\Lambda_c^+$ signatures. The charm hadron production rate is measured in each channel by a fit to the scaled energy, impact parameter information and the invariant mass spectrum. Two measurements of $R_c$ are presented, from the $D^{*+}$ production rate and from the overall charm counting, including strange charm baryon production, in $c\bar{c}$ events. The multiplicity $n_c$, which includes hidden $c\bar{c}$ and strange charm baryon production, is inferred from the charm counting in $b\bar{b}$ events. The final results are $R_c = 0.1665 \pm 0.0095$ and $n_c = 1.166 \pm 0.086$.