# Presentation: 686302

## A Study on Cluster Resolution

-  Neighborhood ***hit density gradients*** are proposed as a means for
-   	-- identifying cluster boundaries
- 	-- implementing a cluster split/merge strategy
-  Relies on the inspection of “calorimeter domains” – collections of
-   connected cells gang’ed as projective towers. Currently coded in
-   “box form”  ( *n **x** m** x** l* ) cells as segmented in (*theta,phi,layer*).
-  A tool to be used as a sup-
-   port to clustering algorithms.
-  Equally applicable to both
-   analogue and digital readouts.

*A. Maciel (NIU), Simulation & E-flow Wshop , NIU, November 7-9, 2002*

- γ1

- γ2

***neighborhood hit density gradients***

-    box of 4x4 cells.
-  Locate (4 x 4 x all) domain with highest
-    energy (or #hits).
-  Inspect neighborhood w/ grads; i.e. find
-   (Rmin, Gmin) and (Rmax,Gmax).
-  If Gmax > *k**Gmin, then a secondary cluster
-    is declared found (currently using* k* = 2 ).
-  Rmin & Rmax determine a search area for
-    “next-hottest” (4 x 4 x all) domain.
-  Cross check that γ**2** cluster also “sees” γ**1**
-  Use both sets of R&G(min,max) to re-size clusters.

- γ**1**

- search area for  γ**2**

*Cluster ID Calorimeter Domain Methods*

***Rmin+1***

***Rmin***

***Rmax***

***Rmax + size***

***Gmin***

***Gmax***

*A. Maciel (NIU), Simulation & E-flow Wshop , NIU, November 7-9, 2002*

## π0 ( 10GeV )    γ γ           5K single-π0 events

-  γ γ distance,
- generated (cm)

-  γ γ distance,
- reconstructed
- (#of cells)

- 5000 events
- superimposed

- (#of cells)

- 1= layers  0 -- 9
- 2= layers 10--19

- π0 ( 10*GeV *)    γ γ           5K single-π0 events

*neighborhood 2 is tested*
*if neighborhood 1 fails*

***1 cell = 0.5 cm***

*A. Maciel (NIU), Simulation & E-flow Wshop , NIU, November 7-9, 2002*

## Generated (upper)   .vs.  “Reconstructed” (lower)

***inefficiency***

*GeV*

*A. Maciel (NIU), Simulation & E-flow Wshop , NIU, November 7-9, 2002*

## Domain (Projective Box) Energy Resolution

*A. Maciel (NIU), Simulation & E-flow Wshop , NIU, November 7-9, 2002*

## γ1 pre-cluster

- Layer energy centroid position fluctuations across layers (distances in cell units)

- γ**1** pre-cluster

- γ**1** re-sized

- γ**2** pre-cluster

- γ**2** re-sized

*A. Maciel (NIU), Simulation & E-flow Wshop , NIU, November 7-9, 2002*

## A  series  of  event  displays  for  10GeV  π0  γ γ

***with the associated****** ******neighborhood gradients***
***analysis as an illustration of the method.***

## Event 81

- Evt# 81
- Gamma1:  ThetaBin=420   PhiBin=213
- Reco  Energy = 4.87
- MC    Energy =  5.28
- Gamma2:  ThetaBin=417   PhiBin=204
- Reco  Energy = 4.39
- MC    Energy = 4.72

- Example of a ~symmetric decay

**Neighborhood Grads**

## γ1 “looks at” γ2

- Event 81

- γ1 “looks at” γ2
- layers used: 0--9

- γ2 “looks at” γ1
- layers used: 0--9

- distance, in number of cells

- distance, in number of cells

## Event 36

- Example of an asymmetric decay
- Evt# 36
- Rmin1 = 4 , Rmax1 = 9
- Rmin2 = 36, Rmax2 = 9   , DeltaR = 10
- Gamma1:   ThetaBin=420   PhiBin=288
- Box-Reco Energy=8.09    ( MC = 8.88 )
- Gamma2:   ThetaBin=410   PhiBin=289
- Box-Reco Energy=1.33    ( MC = 1.12 )

**Neighborhood Grads**

## γ1 “looks at” γ2

- Event 36

- γ1 “looks at” γ2
- layers used: 0--9

- γ2 “looks at” γ1
- layers used: 0--9

- distance, in number of cells

- distance, in number of cells

## γ1

- Event 48

- Evt# 48    (how it can get tricky...)
- Gamma1  Energy=8.10    MC =  9.50
- Gamma2  Energy=0.31    MC =  0.50

- γ1

- γ2

- “dirt”

**Neighborhood Grads**

## γ1 “looks at” γ2

- Event 48

- γ1 “looks at” γ2
- layers used: 0--9

- γ2 “looks at” γ1
- layers used: 0--9

- distance, in number of cells

- distance, in number of cells

- “dirt”

- “dirt”

- γ1

- γ2

- γ2

- γ1

- Note: “Grads” search was cylindrical (as opposed to directional, in theta and phi)

## Event 184

**Neighborhood Grads**

-     Evt# 184  ( A case of extreme asymmetry )
-     Gamma1: ThetaBin=419   PhiBin=1603
-     Reco Energy=9.45    ***MC Energy = 9.98***
-     Gamma2: ThetaBin=414   PhiBin=1588
-     Reco Energy=0.050  ***MC Energy=0.021***

## γ1

- γ1

- γ2

- γ2

**layers 0—9  cannot **
**detect  gamma_2**

**layers 10—19  **

**layers 20—29  **

**layers 0—9  **

- Rmin1 = 10 , Rmax1 = 13
- hsize1 = 13  , DeltaR = 15

- (*) clearly, any level of noise here turns this into an inefficiency...

- (*)

## Event 284

-    Evt# 284   (Gamma_2 is a late shower)
-    Gamma1: ThetaBin=419   PhiBin=1492
-    Reco Energy=7.91    MC Energy=8.04
-    Gamma2: ThetaBin=417   PhiBin=1483
-    Reco Energy=2.15     MC Energy=1.96

**Neighborhood Grads**

## γ1

- Rmin2 = 4
- Rmax2 = 8
- DeltaR = 9

- Rmin1 = 4
- Rmax1 = 7
- hsize1 = 5

- γ1

**layers 0—9  cannot **
**detect  gamma_2**

- γ1

- γ2

- γ2

- γ1

**layers 20—29  **

**layers 10—19  **

**layers 0—9  **

- γ1

- γ2

## EM Shower Characteristics in the “SD” Detector Model

-  The next two slides display shower profiles for electrons and gammas respectively
-  Profiles are averaged over samples of 5000 monochromatic single particles (10GeV)
-  All plots are longitudinal profiles, where the x-axis labels the layer number
- 	-- Energy deposition per layer	-- Layer hosting hottest cell
- 	-- Number of hits per layer		-- Layer mean square radius (*)

- (*) definition;

*A. Maciel (NIU), Simulation & E-flow Wshop , NIU, November 7-9, 2002*

## SD – 10GeV single  γ’s  in Em-Cal   (5k evts.)

- SD – 10GeV single  γ’s  in Em-Cal   (5k evts.)

***GeV***

**n.of cells**

***energy-weighted***
***transverse shower***
***radius (in #of cells)***

***shower-max***

***hit-max***

*A. Maciel (NIU), Simulation & E-flow Wshop , NIU, November 7-9, 2002*