MDS Reconstruction

Overview

Teaching: 30 min
Exercises: 180 min

Questions

• What is Muon Detector Shower (MDS)?

• How are MDS reconstructed?

Objectives

• Understand how are MDS reconstructed: the input, the algorithm, the output

• Visualize MDS reconstruction

• Calculate cluster properties

• Calculate MDS reconstruction efficiency with respect to LLP decay position

Ingredient of MDS: Rechits

MDS is a cluster of rechits in the muon system. The main reason for using rechit is that rechit provides sufficient granularity to capture the high-multiplicity nature of the showers coming from LLPs.

What is a rechit?

CSCs consist of arrays of positively-charged anode wires crossed with negatively-charged copper cathode strips within a gas volume.

When muons pass through, they knock electrons off the gas atoms, which flock to the anode wires creating an avalanche of electrons.

Positive ions move away from the wire and towards the copper cathode, also inducing a charge pulse in the strips, at right angles to the wire direction.

Because the strips and the wires are perpendicular, we get two position coordinates for each passing particle.

Figure 3.1

Illustration of a CSC chamber.

Discussion 3.1 :rechits

Can you think of some of the properties of a rechit?

Solution:

The most relevant ones for MDS are: position(x,y,z,eta,phi) and time.

Are there disadvantage/limitation for using rechit as the inputs of MDS?

Solution:

The reconstruction of rechits from the anode/cathode pulses are designed for a single muon, thus it can miss some details about how the shower is developed.

A dedicated machine learning algorithm maybe able to extract those details for even better MDS reconstruction.

Since multiplicity is the most important feature of MDS, the limitation of using rechits is very minimal.

How are CSC chambers arranged?

CSC chambers are arranged into 4 different stations, interleaved with the steel of the flux-return yoke.

Figure 3.2

Illustration of CMS Muon System.

Open a notebook

For this part, open the notebook called MDS_reconstruction.ipynb to learn how to access and visualize the rechits.

Clustering algorithm

DBSCAN(Density-Based Spatial Clustering of Applications with Noise) is a widely-used, generic clustering algorithm.

It has two parameters, minPts for minimum points to be a cluster and dR for the distance between points.

For clustering MDS, the rechits are the input points and we are clustering in the eta-phi space.

We choose minPts = 50, dR = 0.2. minPts = 50 because it’s more than 2x of the typical number of hits created by a muon in CSC(< 24 hits).

Figure 3.3

Illustration of DBSCAN algorithm. In this diagram, minPts = 4.

Point A and the other red points are core points, because the area surrounding these points in an ε radius contain at least 4 points (including the point itself). Because they are all reachable from one another, they form a single cluster.

Points B and C are not core points, but are reachable from A (via other core points) and thus belong to the cluster as well.

Point N is a noise point that is neither a core point nor directly-reachable.

Cluster properties

Cluster properties are computed from constituent rechits. Here are the descriptions of some key cluster properties:

• Cluster position: average of input rechit positions
• Cluster time: average of input rechit wire time and strip time
• Cluster nStation10: number of stations with at least 10 input rechits in this cluster
• Cluster avgStation10: average station number weighted by number of rechits, using stations with at least 10 input rechits
• Cluster nME11/12: number of rechits coming from ME11 or ME12 in this cluster

Exercise: compute cluster properties

Following the definitions above, complete the function computeCluster, computeStationProp and computeME11_12.

Exercise: plot cluster properties

Plot the cluster properties of background and signal clusters.

To compute for signal clusters,

• run the DBScan functions with signal rechits
• store the output in a new variable called s_cls
• add an addition line in samples for plotting

Try to read and understand the plotting code as well.

Discussion 3.2: cluster properties

Which variables can be used to distinguish between signal and background?

Solution:

You should be able to see the N_rechits, time, and ME11_12 distributions are very different between signal and background.

Placing some cuts on these variables should give us separation of signal events from background!

MDS reconstruction efficiency

When an LLP decay in CSC, we want to know

• how often it can make an MDS cluster (this is cluster efficiency) and
• where does the LLP decay when this happens

In this part, we will make a plot of MDS efficiency as a function LLP decay position and try to understand it.

Open a notebook

For this part, continue to the section MDS reconstruction efficiency for signal to calculate the MDS reconstruction efficiency with respect to the LLP decay position.

Discussion 3.3

Why does the efficiency drops off at the two ends of the muon detectors?

How does the efficiency varies between the muon stations? Do you understand why?

Make a 2D histogram to confirm your understanding!

Key Points

• MDS is a cluster of rechits in the muon system, clustered by the DBSCAN algorithm

• MDS properties are computed from the input rechits(e.g. position,time & station) and are very powerful of rejecting background

• MDS reconstruction efficiency depends on where the LLP decays with respect to the steel, since the decay particles require small amount of steel to initiate the shower and are detected only in the active gas chambers