4.1 Overview of Method

This analysis uses data from electron-positron collisions at LEP with centre of mass energies at or near the $\ensuremathbox{\mathrm{Z^0}}$ pole, recorded by the DELPHI detector. The detector is described in chapter 2. The data capture and its subsequent analysis common to all DELPHI measurements are detailed, respectively, in sections 2.10 and 2.11 and references therein.

From this reconstructed data, hadronic events were selected and $\ensuremathbox{\mathrm{J/\psi}}\ensuremathbox{\rightarrow}\ensuremathbox{\mu^+ \mu^-}$ candidates were searched for in these events. Initially, very loose $\ensuremathbox{\mathrm{J/\psi}}$ cuts were applied in order to provide samples of both signal and background candidates, as well as allowing for easier tuning of cuts later on. Detailed information on each of these candidates (both muon parameters and tagging information as well as the reconstructed parameters of the putative $\ensuremathbox{\mathrm{J/\psi}}$) was written to disk for interactive analysis.

By selecting candidates with reconstructed mass close to the $\ensuremathbox{\mathrm{J/\psi}}$ mass, $\ensuremathbox{M_{\ensuremathbox{\mathrm{J/\psi}}}}$, a fairly pure sample of $\ensuremathbox{\mathrm{J/\psi}}$s was obtained. By parameterizing the distribution of reconstructed masses over a larger range, the purity of the signal sample was measured. Samples of events with the `wrong' mass or charge were used to model the background in the signal sample.

Since the distance the $\ensuremathbox{\mathrm{J/\psi}}$ travels over its lifetime is negligible compared to our experimental resolution, the $\ensuremathbox{\mathrm{J/\psi}}$ decay point, measured from the crossing point of the two muons' (extrapolated) trajectories, was used to determine the $\ensuremathbox{\mathrm{J/\psi}}$'s production point. If this is significantly removed from the electron-positron collision point (coincident with the $\ensuremathbox{\mathrm{Z^0}}$ decay point), the presence of a relatively long-lived intermediate in the decay chain is indicated. Assuming this is a B-hadron (see chapter 1) and that its momentum can be determined, estimates of the B decay times can be made. Their distribution should be near-exponential, but for the experimental resolution, after correcting for the background contamination. The expected similarity of the different B-hadron lifetimes allows us to assume a single exponential. The decay constant allows us to measure the mean lifetime of B-hadrons decaying to $\ensuremathbox{\mathrm{J/\psi}}$s. Any excess near zero decay time indicates the presence of $\ensuremathbox{\mathrm{J/\psi}}$s produced directly (or via short-lived intermediaries) from the $\ensuremathbox{\mathrm{Z^0}}$ decay.