# 2008.11.18 Cluster isolation cuts: 2x1 vs. 2x2 vs. 3x3

Ilya Selyuzhenkov *November 18, 2008*

### Data sets:

### 2x1, 2x2, and 3x3 clusters definition:

**3x3 cluster**: tower energy sum for 3x3 patch around highest tower
**2x2 cluster**: tower energy sum for 2x2 patch

which are closest to 3x3 tower patch centroid.

**3x3 tower patch centroid** is defined based

on tower energies weighted wrt tower centers:

**centroid = sum{E_tow * r_tow} / sum{E_tow}**.

Here r_tow=(x_tow, y_tow) denotes tower center.
**2x1 cluster**: tower energy sum for high tower plus second highest tower in 3x3 patch
**r=0.7 energy** is calculated based on towers

within a radius of 0.7 (in delta phi and eta) from high tower

**Cuts applied**

all gamma-jet candidate selection cuts except 3x3/r=0.7 energy isolation cut

### Results for 2x1, 2x2, and 3x3 clusters

- Energy fraction in NxN cluster in r=0.7 radius

2x1, 2x2, 3x3 patch to jet radius of 0.7 energy ratios
- Yield vs. NxN cluster energy fraction in r=0.7

For a given cluster energy fraction yield is defined as an integral on the right
- Efficiency vs. NxN cluster energy fraction in r=0.7

For a given cluster energy fraction

efficiency is defined as the yield (on the right)

normalized by the total integral (total yield)

# Efficiency vs. NxN cluster energy fraction in r=0.7

## Efficiency vs. NxN cluster energy fraction in r=0.7

**Figure 1b:** 2x1/0.7 ratio

**Figure 2b:** 2x2/0.7 ratio

**Figure 3b:** 3x3/0.7 ratio

**Figure 4b:** 3x3/0.7 ratio but only using towers which passed jet finder threshold

# Energy fraction in NxN cluster within r=0.7 radius

## Energy fraction in NxN cluster within r=0.7 radius

**Figure 1a:** 2x1/0.7 ratio

**Figure 2a:** 2x2/0.7 ratio

**Figure 3a:** 3x3/0.7 ratio

**Figure 4a:** 3x3/0.7 ratio but only using towers which passed jet finder threshold

# Yield vs. NxN cluster energy fraction in r=0.7

## Yield vs. NxN cluster energy fraction in r=0.7

**Figure 1c:** 2x1/0.7 ratio

**Figure 2c:** 2x2/0.7 ratio

**Figure 3c:** 3x3/0.7 ratio

**Figure 4c:** 3x3/0.7 ratio but only using towers which passed jet finder threshold