Deterministic Annealing

Another method to separate the quark flavours is based on the explicit reconstruction of decay vertices in the transverse plane. In the method of deterministic annealing [152], there is no definite assignment of tracks to vertices, but each track is assigned a weight with a range 0 to $1$ for each vertex candidate, using the weight function of [153]. The larger the distance of the track to a vertex candidate, the smaller the weight. A simultaneous fit to a primary and a secondary vertex is made, with all tracks of the event considered for the primary vertex, whereas only tracks associated to the jet axis contribute to the secondary vertex. The vertex configuration that minimizes the global fit $\chi^2$ is found iteratively.

Figure: The transverse distance between the primary and secondary vertex ($L_{xy}$) for events with two, three and four tracks associated with the secondary vertex. Superimposed on the data points are $c$, $b$ and light quark contributions that have been scaled by the results of the fit to the distributions $S_1$ and $S_2$ using the negative subtraction method as described in section 5.5.2 [43].

In fig.19 the decay length distributions are shown for events at large $Q^2$ with secondary vertices made up of two, three and four tracks, respectively. The decomposition into $uds$, $c$ and $b$ is indicated using the results from the fit of the negative subtraction method as described above in section 5.5.2. The fig.19 shows that the two methods give consistent results.