---
# System prepended metadata

title: 'TechReport: Regarding 2-D Trigger in Belle-II'
tags: [2D, TechReport, DeWei]

---

# 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)

![CDC](https://i.imgur.com/8CHgTUf.png)

* 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

![tv-cdc](https://i.imgur.com/76ji87i.png)

#### 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)

![sl-arch](https://i.imgur.com/lTzcIkm.png)

## 2. Basic system architecture

![base-arch](https://i.imgur.com/AHqNhr0.png)

## 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):

![](https://i.imgur.com/s1HttVT.png)

New:

![](https://i.imgur.com/ASBbKYf.png)

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

### 3.3 Hough-Voting

Concept:
![Hough-voting](https://i.imgur.com/iBRdnE4.png)


Implementation:

![Hough-voting-impl](https://i.imgur.com/rlGnwJD.png)


## 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
![Ideal-triggered](https://i.imgur.com/OfM7qCS.png)

* Nonideal triggered (noise-triggered)
![NONIdeal-triggered](https://i.imgur.com/Hh0KqGx.png)

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

#### 4.2.1 Principle

![](https://i.imgur.com/DkcUYYx.png)


* 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)

    ![](https://i.imgur.com/gT2HPgt.png)

2. Checking the cluster within a block.

    ![](https://i.imgur.com/U3efNto.png)


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