Methods for primary vertex determination

 The primary vertex is with the parameters of the beam spot alone defined with a precision of 5.6 cm along the beam axis. The precision can be improved using the shower development in the calorimeter. The method is to reconstruct the barycentre of the shower in the first and second sampling of the calorimeter. The direction of the photon is found from simple pointing between the two positions [4].

In events with converted photons the position of the primary vertex can be identified from the reconstructed conversion.

  

Figure: An illustration of primary vertex identification in H $\rightarrow$ $\gamma$$\gamma$ events. In (a) the vertex is identified from pointing in the calorimeter, in (b) from the reconstruction of a converted photon and in (c) from the tracks in the underlying events.

A third method is to identify the position of the primary vertex from the charged tracks of the event underlying the H $\rightarrow$ $\gamma$$\gamma$ decay. These particles are from initial and final state radiation and share the main vertex with the Higgs particle. At low luminosity this method is quite simple, only a few other primary vertices are present in the detector; at high luminosity there will be on average 23 additional primary vertices from the pile-up events and the situation is more complicated. The task is to pick up the correct primary vertex. All three vertex reconstruction methods are illustrated in fig. 7.2.