What are split clusters ?

(i) Upstream materials in front of PMD

(ii) Limiations of the clustering algorithm

How to find a split cluster ?

The alogrithm for associating a cluster with an ID is as follows :

Step - I

If a cluster formed by a photon track then it is given an Id = 1 If a cluster has been formed by a hadron track then it is given an Id = 8

Step - II

In a photon cluster, there may be one photon track or many.

(a) If the cluster has a photon track which does NOT have a split track (track multiplicity = 1). We assign that cluster an Id = 1, irrespective of whether the cluster has any other photon track in it.

(b) For clusters which does not have a track with track multiplicity = 1, we assign the track which has deposited the largest energy to that cluster.

So one cluster is associated with only one track.

Step - III

For photon clusters which have associated photon tracks which belong to more than one clusters, we do the following :

(i) If the energy of the clusters > 2 MIP EDEP, then the cluster with smaller number of cells in a cluster is a split cluster and is given cluster Id = 2

(ii) If the energy of any one of the clusters or both < 2 MIP EDEP, then the cluster with smaller energy is called a split cluster and given a cluster Id = 2.

For both the above cases, the other cluster has Id = 1.

Information on track multiplicity :

CLICK ON THE FIGURES

What is track multiplicity ?

Track multiplicity is defined as the number of clusters associated with a particular track in an event . For e.g.

(a) Track multiplicity = 1 implies no split cluster (particluar track is associated with one cluster only).

(b) Track multiplicity = 2 implies that, track is associated with two different clusters (one original cluster & other its split cluster).

(c) Track multiplicity = 3 or more implies that, track is associated with 3 or more clusters (one original & rest are its split clusters).

First plot shows the track multiplicity distribution over 700 events. We can see that a particular track is associated with 15 clusters.

Second plot shows the percentage track multiplicity. We can see that 55 % of the tracks in an event are associated with single cluster. 25 % of the track in an event are defined as split cluster. 10 % of the track in an event are having more than one split partners.

Third plot shows the variation of track multiplicity on an event by event basis as a function of impact parameter.

Some plots which shows that this logic is working :

CLICK ON THE FIGURES

This plot shows the Number of cells distribution for cluster finally given an Id = 1 and their corresponding split cluster number of cells. You will find that the split cluster number of cells never exceed that of the corresponding Original cluster (indicated by the line) for cases where cluster edep of both are greater than 2 MIP.

This plot shows the Cluster Edep and the Edep of the corresponding split clusters. You will find that the split cluster edep is mostly lower than the corresponding original cluster Edep.

CLICK ON THE FIGURES

Some informations obtained from analysis of split clusters :

This plot shows the event-by-event variation of fraction of split cluster with impact parameter of the event. Fraction of split cluster is defined as : Total number of split cluster in the event / (Total clusters with cluster Id = 1 + cluster Id = 2 )

This plot shows the fraction of split cluster and how it varies with different cuts based on number of cells in a cluster and cluster Edep.

This plot shows the event-by-event variation of fraction of gamma clusters and how it varies with different cuts based on number of cells in a cluster and cluster Edep. Fraction of gamma cluster is defined as : Total number of gamma cluster in the event after cut / (Total clusters with cluster Id = 1 before any cut)

We find that the fraction of split cluster decreases from 45% to 20% with a EDEP cut of 3 MIP, but the corresponding gamma clusters decreases from 70% to 55%.

This plot shows the separation of split clusters from it's parent cluster in units of eta, phi and radial distance. We feel that we need to merge the closeby clusters or tune the refine cluster part of the clustering routine.

Some informations obtained from analysis of split clusters in PMD ONLY case:

This plot shows the fraction of split cluster and how it varies with different cuts based on number of cells in a cluster and cluster Edep for PMD only case. It seems that 27% of split clusters are due to either geometry of the detector and/or the clustering algorithm. This is because we say 45% split cluster for PMD with ALL detectors ON case.

This plot shows the separation of split clusters from it's parent cluster in units of eta, phi and radial distance for PMD only case. We feel that we need to merge the closeby clusters or tune the refine cluster part of the clustering routine.