7.5 Primary Interaction Vertex
7.5.1 The NC Optimal Vertex
The NC optimal vertex approach is making use of information from the scattered electron candidate and aims for the best estimation of the primary interaction ver- tex position, ZOptimalNC, and validation of the scattered electron measured in the calorimeter with the tracker information. For that the following information in gen- eral is available:
• The electron cluster. An identification efficiency for the scattered electron is very high (see Section 7.2) if the electron is in acceptance of the LAr calorime- ter. The cluster position provides a good estimation of the position of the electron entry point on the surface of the calorimeter.
• The DTRA track linked to the electron cluster (see Fig. 7.14a). This track fit- ted to the reconstructed primary interaction vertex provides reliable estimation of the electron properties and indicates that one can trust the reconstructed vertex position, if the track points to the electron cluster.
7.5. PRIMARY INTERACTION VERTEX 83
Figure 7.13: Example of the DTNV event. The scattered electron gives an isolated cluster of high energy in the calorimeter and a DTNV track. The HFS interacts with the beam pipe downstream to the proton beam direction providing multiple tracks and a fake primary vertex.
• The DTNV track linked to the electron cluster (see Fig. 7.14b). This track provides unbiased (but not the most precise) and robust estimation of the electron properties. The DTNV vertex is the point on the beam line most close to the propagation of the DTNV track to the beam line. The distance dca of the closest approach of this propagation to the beam line should be reasonably small: dca <2 cm.
• The CJC vertex obtained in the vertex fit. It is the best estimation of the vertex position if it is not spoiled by the secondary interactions.
• The CIP hits. They can help for the electron verification if the electron track is completely lost (neither DTRA, nor DTNV electron tracks are reconstructed). In general, the CJC vertex obtained in the vertex fit, which involves all recon- structed tracks in the event, is the best estimation of the primary vertex position. Therefore, if the vertex fit has converged and the DTRA track associated with the scattered electron points to the electron cluster in the LAr calorimeter, the vertex position is taken from the vertex fit. The matching between the DTRA track and the electron cluster is illustrated in Fig. 7.14a. If the distance DDTRA is below 12 cm (12 cm is a characteristic size of a calorimetric cell in the LAr calorimeter), the electron cluster is considered to be validated by the DTRA track and the event is classified as Optimal—DTRA with zOptimalNC=zCJC.
If the vertex fit has failed or there is no DTRA track pointing to the electron cluster, a DTNV track pointing to the electron cluster within 12 cm, see Fig. 7.14b, is considered. If there is the DTNV vertex (and the CJC vertex is not constructed) and
the DTNV track, the event is classified as Optimal—DTNV withzOptimalNC =zDTNV. If the CJC vertex is available, the choice of the primary vertex relies on the analysis of the CJC and DTNV vertex positions.
cluster DTRA track Fitted vertex beamline cluster DTNV track beamline d < 2 cm D D (a) (b)
Figure 7.14: Schematic view of the (a) DTRA and (b) DTNV tracks, vertex and cluster with the essential parameters definition.
The CJC and DTNV vertices distributions for the cases, where the CJC was reconstructed but the DTRA track is missed, are shown in Fig. 7.15 together with the difference between these two. The CJC vertex has a big non-physical “tail” at large values of theZCJC. At the same time the DTNV vertex distribution demonstrates a good agreement between data and MC and follows the profile of the proton bunch.
[cm] CJC z -100-80-60 -40 -20 0 20 40 60 80 100 ev N 500 1000 1500 2000 2500 3000 3500 4000 [cm] DTNV z -100-80 -60 -40 -20 0 20 40 60 80 100 ev N 500 1000 1500 2000 2500 3000 3500 4000 [cm] DTNC - z CJC z -50 -40 -30-20 -10 0 10 20 30 40 50 ev N 500 1000 1500 2000 2500 3000 3500 4000 data MC (a) (b) (c)
Figure 7.15: Distributions of the vertex z position of the (a) CJC vertices, (b)
DTNV vertices and (c) difference between them for events without DTRA track pointing to the electron cluster.
The distributions for the CJC and DTNV vertices for different regions of the ∆ZCJC-DTNV=ZCJC−ZDTNV distribution are shown in Fig. 7.16. In the case when the CJC and DTNV vertices are close, −10 < ∆ZCJC-DTNV < 10 cm (“central” region of ∆ZCJC-DTNV distribution, Fig. 7.16 b, e) both vertices demonstrate good agreement between data and MC and centered around zero. Here one assumes that the vertex fit provides the right vertex position, and ZOptimalNC=ZCJC is taken.
If the distance between the CJC and DTNV vertices is more than 10 cm, we gen- erally rely on the DTNV vertex, and suppose that the CJC vertex was constructed with the tracks from the secondary interaction of the HFS particle with the beam
7.5. PRIMARY INTERACTION VERTEX 85 (‘‘left’’) [cm] DTNV z -100-80-60 -40 -20 0 20 40 60 80 100 ev N 50 100 150 200 250 (‘‘centre’’) [cm] DTNV z -100-80 -60 -40 -20 0 20 40 60 80 100 ev N 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 (‘‘right’’) [cm] DTNV z -100-80 -60-40 -20 0 20 40 60 80 100 ev N 200 400 600 800 1000 1200 1400 (‘‘left’’) [cm] CJC z -100-80-60 -40 -20 0 20 40 60 80 100 ev N 50 100 150 200 250 (‘‘centre’’) [cm] CJC z -100-80 -60 -40 -20 0 20 40 60 80 100 ev N 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 (‘‘right’’) [cm] CJC z -100-80 -60-40 -20 0 20 40 60 80 100 ev N 200 400 600 800 1000 1200 1400 data MC (a) (b) (c) (d) (e) (f)
Figure 7.16: Distributions of the CJC and DTNV vertices for the different regions of the ∆ZCJC-DTNV variable.
pipe. The region of ∆ZCJC-DTNV>10 cm (marked as “right”, Fig. 7.16 c, f) is pop- ulated with the events where these nuclear interactions occurred. The CJC vertex is completely spoiled while DTNV vertex demonstrates good agreement between data and MC and peaks around zero. In this region one takes ZOptimalNC=ZDTNV.
In the region of ∆ZCJC-DTNV <−10 cm (marked as “left”, Fig. 7.16 a, d) if the DTNV vertex is reasonably close to the nominal interaction point (namely ZDTNV < 20 cm) we rely on it and takeZOptimalNC=ZDTNV, otherwise the CJC vertex is taken. In Fig. 7.17 a typical event with far forward DTNV vertex (ZDTNV>20 cm) is shown with the distribution for the ZCJC for such cases. The CJC vertex looks reasonable though the electron DTRA track is lost.
If an event is not classified as Optimal—DTRA or Optimal—DTNV, but the vertex fit has converged, one tries to validate this vertex with the CIP hits. It could happen that the electron track is lost in the reconstruction despite one measures correctly the electron cluster and the vertex. On the line between the vertex and the cluster one searches for hits in the CIP chamber which has a good segmentation in the z direction. If two or more such hits are found, the situation is recognized as the NC event with the electron track lost and one assumes ZOptimalNC = ZCJC. These events are classified as Optimal—CJC.
If none of the approaches above to get the vertex position is successful, the event is classified as NoVertex event and will not pass the NC selection.
After all, four classes of events are identified
• DTRA events where the vertex fit converged and the electron DTRA track matches well to the electron cluster.
• DTNV events where the vertex comes from the DTNV track reconstruction and the electron DTNV track matches well to the electron cluster. If the
[cm] CJC z -100-80 -60 -40 -20 0 20 40 60 80 100 ev N 5 10 15 20 25 30 35 40 45 50 data MC
Figure 7.17: For the case ∆ZCJC-DTNV<−10 cm andZDTNV>20 cm: event display with a typical event (left plot) and distribution of the CJC vertices for the whole HERA II sample (right plot).
primary vertex position is changed (DTNV vertex is taken), the hadronic final state variables, calculated with the reconstructed vertex position, should be re-calculated, see Section 7.6.5.
• CJC events where the DTRA and DTNV tracks are lost, but the CJC vertex is reliable and electron is verified by the CIP hits on the expected trajectory of the electron.
• NoVertex events where no Optimal vertex is found. In this subsample we re- quire γh < 30◦ if the CJC vertex is not reconstructed. The rejected events (with γh ≥ 30◦) were scanned visually and were identified as non-ep back- ground with the E − Pz distribution which does not peak around 55 GeV. Here we formally assume ZOptimalNC= 0.
For these four classes the distributions of γh, log10(xeΣ′), E − Pz, Pthad/Pte, Ee/EDA variables are shown in Fig. 7.18. These distributions for the DTRA, DTNV and CJC samples demonstrate a good agreement between data and MC. The NoVer- tex sample behaves as expected for the NC events with a peak in theE−Pz distri- bution around 55 GeV. It causes an inefficiency of the Optimal Vertex procedure. Statistics of the DTRA sample is roughly forty times larger than that of the DTNV and CJC samples, and the NoVertex sample statistics is two times smaller.
The DTNV events are concentrate at a region of low γh or high x where the hadronic final state goes in the forward direction with the following nuclear interac- tions. They were restored with the Optimal Vertex procedure and pass now the NC selection cut |Zvtx|<35 cm.