Multi-Impact Parameter Method

Figure: Distribution of the negative logarithm of the multi impact parameter probability. The decomposition of the simulation into $b$ (shaded histogram), $c$ (dotted line), $uds$ (dashed line) is taken from the fit [45] (see text).

In this method, the impact parameters of all well measured, i.e.selected, tracks in a given jet are used to form a probability that the tracks come from the primary interaction point and not from the decay of a long lived particle. The quantity

$$P(S_i)=\frac{1}{\sqrt{2\pi}} \int_{S_i^2}^{\infty} e^{-t^2}dt,$$

can be interpreted as the probability that a track originates from the primary vertex. The probabilities for tracks with negative significances are set to unity. A multi impact parameter (MIP) probability $P_{MIP}$ is then constructed by combining the probabilities of the $N$ selected tracks within each jet:

$$P_{MIP}=\Pi \sum_{j=0}^{N-1} (- \ln \Pi)^j / j!,$$

where $j$ runs over all selected tracks and

$$\Pi=\prod_{i=1}^N P(S_i).$$

The distribution of the negative logarithm $-\log(P_{MIP})$ for both jets is shown in fig.18. The contributions from events containing $b$, $c$ and $uds$ quarks are determined by a fit [150,151] to the $-\log(P_{MIP})$ distribution, using the Monte Carlo expectations for the shapes of each of these quark flavours.