Results

 The main problem of the algorithm are events where a wrong primary vertex is selected with a large weight since this contributes to the tails in the Higgs mass distribution. Events with zero selected vertices at do not harm the mass resolution in comparison with using the calorimeter or beam spot information only. A high value for the cutoff on the quality (7.12) gives many events with zero vertices found; a low value of the cutoff returns the Higgs vertex in nearly every event but also many wrong vertex positions with similar or higher weights. Both effects are shown in fig. 7.8.

  

Figure 7.8: The fraction of the total weight that enters into the correct Higgs vertex as a function of the cutoff used for selecting vertex candidates. In (b) the fraction of events with no vertex selected as a function of the cutoff.

At high luminosity and without using the calorimeter pointing the optimal point for the Higgs signal significance, as defined in (7.8), is for a high value of the quality cut where a Higgs vertex candidate is found in 44% of the events and 30% of the weight enters into the correct Higgs vertex (or 68% of the weight in the events where at least one vertex is selected).

The optimisation of the cutoff is shown in fig. 7.9 for two different situations. The solid lines shows the situation where the calorimeter is used for the determination of the vertex position in case zero vertices are selected; the dashed lines shows the situation where just the average beam spot position is used. As expected, the global tracking is much more important for the case where the calorimeter pointing is not used. The significance of the Higgs signal is given as the relative improvement compared to the situation where no pointing information is used. The global tracking method has its best performance where the relative significance reaches its maximum.

  

Figure: Effect of changing the cutoff used to select the correct candidates for the H $\rightarrow$ $\gamma$$\gamma$ vertex. In (a) the Higgs mass resolution is shown as a function of the weight in the correct Higgs vertex and in (b) the mass resolution as a function of the fraction of events with zero selected vertices from the global tracking. In (c) and (d) the significance of the Higgs signal is normalised to the situation where no pointing information is used. The optimal cutoff to use is where the significance reaches its maximum. In each figure is shown results where the calorimeter pointing is used in the events with zero selected vertices (solid lines) and where only the beam spot position is used (dashed lines).

At low luminosity with much fewer background vertices a larger efficiency for picking the correct vertex is of course possible.