# TechReport: Regarding 2-D Trigger in Belle-II

Introduction to **the system of 2-D Trigger in Belle-II**.

This report is written for non-physics-background peoples.

Hoping engineering-background peoples can easily understand *the system of 2-D Trigger in Belle-II* after reading this report.

I'll divide the content into 4 parts to illustrate:

* Central Drift Chamber (CDC)
* System architecture
* Hough-space: defined the curves which may be a track
* Clustering: ensure the curve is vaild.

## 1 Central Drift Chamber (CDC)


* z-axis: Particle injection direction
* [x, y]-axis: Slices of plane where perpendicular to z-axis, it also can be expressed by polar coordinates(r-phi), here is protagonist in 2D-trigger.

### 1.1 Simplified diagram of CDC top view


#### 1.1.1 Configuration of Superlayer[n]

* Superlayer{ 0, 2, 4, 6, 8 }: Used in 2D-Trigger
* Superlayer{ 1, 3, 5, 7 }: Used in 3D-Trigger

#### 1-1-1. Trigger segment

One trigger segment consist of 5 sublayer(also is a 1 superlayer)


## 2. Basic system architecture


## 3 Hough-space

## 3.1 Theorem

Refer to here

https://hackmd.io/@BelleII-CDC-Trig-NTU-DeWei/SJQsCpPlD

## 3.2 Fix formular(curve-space) for CDC

In [previous(3.1)](##3.1-Theorem):


New:


1. Substitute from $x^2+y^2$ to $r_{TS}$
2. $\phi_0$ = $90deg$

### 3.3 Hough-Voting

Concept:

Implementation:


## 4 Clustering

### 4.1 Result of finding center is nonideal

After [Hough-Voting](#33-Hough-Voting),

we can find the center of circle to rebuild curve,

but it is so ideal,

in actual experiments, noise-triggered may occur.

* Ideal triggered

* Nonideal triggered (noise-triggered)

### 4.2 Solved noised-triggered - using cluster algorithm

#### 4.2.1 Principle


* Since slope of curve in Hough-place only exist *positive*

#### 4.2.2 Step

1. Two squares are disconnected if they fall into any of the categories(Picture is example for disconnect)


2. Checking the cluster within a block.


###### tags: `TechReport` `DeWei` `2D`