Study of charm production in Z decays

The production rates of \({\mathrm{D}}^{*\pm}\), \({\mathrm{D}}_{\rm{s}}^{* \pm}\), \({\mathrm{D}}^{\pm}\), \({\mathrm{D}}^0 / \bar{{\mathrm{D}}}^0\), \({\mathrm{D}}_{\rm{s}}^{\pm}\), and \(\Lambda_{\rm c}^{+}/{\bar{\Lambda}}_{\rm c}^{-}\) in \({\rm Z} \rightarrow {\mathrm c} \bar{{\mathrm c}}\) decays are measured using the LEP I data sample recorded by the ALEPH detector. The fractional energy spectrum of the \({\mathrm{D}}^{*\pm}\) is well described as the sum of three contributions: charm hadronisation, b hadron decays and gluon splitting into a pair of heavy quarks. The probability for a c quark to hadronise into a \({\mathrm{D}}^{*+}\) is found to be \(f({\mathrm c} \to{\mathrm{D}}^{*+}) = 0.233 \pm 0.010 \mathrm{(stat.)} \pm 0.011\mathrm{(syst.)}\). The average fraction of the beam energy carried by \({\mathrm{D}}^{*\pm}\) mesons in \({\rm Z} \to{\rm c \bar c}\) events is measured to be \({\langle X_E ({\mathrm{D}}^{*\pm}) \rangle}_{{\mathrm c} \bar{{\mathrm c}}} =0.4878 \pm 0.0046 \mathrm{(stat.)} \pm 0.0061 \mathrm{(syst.)}.\) The \({\mathrm{D}}^{*\pm}\) energy and the hemisphere mass imbalance distributions are simultaneously used to measure the fraction of hadronic Z decays in which a gluon splits to a \({\mathrm c} \bar{{\mathrm c}}\) pair: \(\bar{n}_{\mathrm{g} \to{\mathrm c}\bar{{\mathrm c}}} = (3.23 \pm 0.48 \mathrm{(stat.)} \pm 0.53 \mathrm{(syst.)})\%.\) The ratio of the Vector/(Vector+Pseudoscalar) production rates in charmed mesons is found to be \(P_V = 0.595\pm0.045\). The fractional decay width of the Z into \({\mathrm c}\bar{{\mathrm c}}\) pairs is determined from the sum of the production rates for various weakly decaying charmed states to be \({\rm R_c} =0.1738 \pm 0.0047{\rm (stat.)} \pm 0.0116 {\rm (syst.)}.\)