Lifetime Tag

Vertex detectors can be used to detect vertices displaced from the primary interaction point. For charm mesons with lifetimes between 0.4 and 1 ps the typical spatial separation between their production vertex and the decay vertex is given by their $c\tau$ of 120 to 315 $\mu$m.

In a recent analysis at HERA, a complete reconstruction of charmed mesons was performed in combination with a lifetime tag to reduce the combinatorial backgrounds [6]. A sketch of the reconstruction procedure for the reconstruction of the long-lived $D^{\pm}$ meson candidates is shown in fig.13. The main difficulty in the 3-body decays of the $D^{\pm}$ into $K^{\mp }\pi ^{\pm }\pi ^{\pm }$ is the combinatorial background which is large due to the large number of combinations of tracks that can wrongly be assigned to one of the decay particles. The signal-to-background ratio can drastically be improved by use of a lifetime tag in which it is required that the tracks originate from a common displaced vertex. The vertex displacement is measured in the $r$-$\phi$ plane. In fig.14 the mass spectrum is shown without and with the cut $S_l > 8$ on the vertex displacement. Here, $S_l$ is the significance of the displacement, i.e. the distance between the primary and secondary vertices divided by the uncertainty of the distance measurement.

Figure: Reconstruction of a $D^+$ meson candidate by reconstruction the vertex from the decay particles $K^{\mp }\pi ^{\pm }\pi ^{\pm }$. The displacement of the secondary vertex is used to enhance the fraction of signal events in the sample (see fig.14).

Figure: Invariant mass distribution $m(K\pi \pi )$ for $D^{\pm } \rightarrow K^{\mp }\pi ^{\pm }\pi ^{\pm }$ decay candidates, a) before and b) after a cut on the decay length significance $S_l > 8$ [6].