May the force be with you Part-1 :Jet Tagging using Deep Learning

Jet Tagging using Deep Learning is a riveting topic, a rare gem in the field of Deep Learning.

This Bread Crumb learning trail will help you follow this topic irrespective of your comfort level with physics (particle physics), mathematics & Deep Learning. This is for everyone : )

It's a fancy way of saying this is a collection of other people's work. Better to learn from smarter peeps .

Part 1 is prerequisite to actual coding and implemetation of jet tagging classification system.

What is the smallest thing in the universe?

[a] This is a TED-Ed on standard model.

This video explains composition of the atom and the other two forces (Weak force and Strong Force ) which keep an atom together (or causes Beta decay. In Beta decay energy and particle are both emitted).

Four types of fundamental forces and their messanger:

• Gravitational Force ( Gravitron - hypothetical)
• Electromagnetic Force (Photon)
• Strong Force (Gluon)
• Weak Force (Boson)

Analogy between electromagnetic force - photon and weak force -W,Z Boson is very useful. Bosons like photons of our world ( Yey!!! photon are in team human not team quantum) are messanger particle carrying electromagnetic(photon) & weak force(boson) respectively. Important difference is that unlike photons a boson has mass. As per Quantum Field Theory(QFT) photon as 0 mass Boson with Spin 1 ( And we lose photon to team quantum).

Side note : There are four kinds of Quatum Field Theories, Each trying to explain 3 fundamental forces through Quantum Mechanics.

• Quantum Chromodynamics (QCD)
• Electroweak Theory (EWT)
• Quantum Electrodynamics (QED)
• Quantum Flavordynamics (QFD)

Also in quantum physics all particles have vibrations( frequencies). Blame?Louis de Broglie (1923) for stunning work on wave-particle duality.

ALERT: Photons don't have mass however a pair of photon system has an invriant mass.

Life Hack: Keep saying invariant mass I bet you will feel really intelligent.

What is p- value:

Video by StatQuest explaining p value (Part of hypothesis testing used in explaining results of experiemnts performed in LHC)

The Higgs Discovery Explained:

3.5 part youtube series by CERN

[a] Produce

Part 1 is about the need to produce high energy particles inside LHC (Bosons). Our aim here is confirm presence of particles as predicted by standard model and study them( There are several objectives however this is an oversimplification for sake of learning). In this case we want to expermimentally find Higgs Boson which will then confirm presense of Higgs field. There are 2 major challanges :

• Finders are not keepers: We can't study Boson created in nature (universe). So we go for create your own particle model. Hence 27 km long experimental apparatus is required.

• Is it a Higgs Boson ?: Even if LHC manages to create a particle it's not possible to directly confirm if particle was created. This is covered in detect and analyse section below.

Einstein's equation E = mc2 plays a central role in this process. This video explains why collision of these high energy particles is such a tough job. Business of collision is all about studying what will happen and with what probability. Before shutdown LHC (It will be up and running from July 2022 onwards) was targetting 40million collisions/ second, each bunch has 30 protons. Rate of production of Boson was one in Billion collision.

[b] Detect

Part 2 is very interesting. Bosons can't be detected directly as they immediately decay into other particles almost instantly after getting produced. Take this decay path for example Higgs Boson --> Decay into Something --> Final Decay to 2 photons. These 2 special photons are very important, These photons are what experiments detect.

Experiments measure energy of these two special photons (travelling in opposite direction).

Using law of energy conservation we can identify if these 2 photons are ordinary photons produced regularly in LHC or 2 special photons which are product of decay from Higgs Boson which was produced inside LHC.

Basically Einstein is back again, using energy of photons we can find invariant mass of Higgs Boson (E=mc2) (Note: general form of the equation is used in this setup)

Higgs Boson with momentum: A practical problem

The calculation described in above section is valid only if the particle is stationary when it decays, It is called centre of mass reference frame. However in most cases Higgs Boson has momentum whereas the detector is stationary. This section describes how to get from Detector Reference Frame to Center of Mass reference frame.

[c] Analyse:

Part 3 again a very interesting section and deals heavily with hypothesis testing. Steps followed so far

• Step1: Detect 2 special photons.
• Step2: Calculate Invariant mass of these 2 special photons system.
• Step3: If photons came from decay of Higgs Boson then this is the mass of Higgs Boson.

Question: What if two photon pairs are actually from an unrelated event?

Our expectation is that Invariant mass of photon pair system from unrelated event will be a random number. LHC experiments in this case are simply a sequence of trials just like trials in probability such as rolling of dice. Instead of dice rolls LHC experiments are calculating Invariant mass of particle.

A plot of Events vs Mass of photon pair is created after performing these experiments. If it's a smooth decreasing curve then most likely Higgs Boson was not discovered. However if a bump in the graph is recorded chances are that Higgs Boson was produced and peak of bump is mass of Higgs Boson. Yey we found a new particle !!! Maybe :)

Credit :

Huilin Qu: Jet Tagging in the Era of Deep Learning

CMS Detector

This section starts with explanation of CMS Detector. (Transverse Slice of CMS showing various components/ subsystems of detector and their functions)

Jets?

Oops wrong Jet

Right then Jets!

Jets are collimated spray of particles. How is a jet formed inside LHC?

Inside the LHC protons moving at high speed collide with each other ( It's not actual collision, more like an interaction or meet & greet). Some constituents of protons break apart interact with surrounding particles and form a shower of fast moving hadrons. ( See small article by Sarah Charley)

Jet Tagging is trying to identify origin of Jets. In terms of machine learning it a classification problem. Jet tagging is used as an handle to probe interesting events.

Detailed Breakdown of video with timestamp is given below:

1:37 Large Hadron Collider setup

LHC is located between border of Switzerland & France. Several experiments at the Large Hadron Collider (LHC) use detectors to analyse the myriad of particles produced by collisions in the accelerator: ATLAS, CMS, ALICE. ( My favourite experiment is Alpha which studies anti-matter system an anti-hydrogen but for now back to CMS & ATLAS)

2:03 CMS Detector explanation (Transverse slice of CMS showing various components/ sub-systems of the detector and their functions)

3:00 Particle flow algorithm to reconstruct full event.

3:48 Why Jets?

5:13 What kind of particles initiate Jet Tagging? Jet Tagging as a classification problem in machine learning

3 types of tagging

- Jet flavour tagging: Distinguish Jets from bottom quarks, charm quarks or light flavoured quarks or gluon jets.

- Tagging Hadronic decay of Tao leptons.

- Boosted Jets: Takes advantage of both structure and flavor.

Particles are produced with very high momentum and high Lorentz boost particles end up coming very close to each other. In Boosted Jet Tagging we are trying to identify decay path such as t-->Wq-->qqq or h/W/Z-->qq and reject as background jets from single quark or gluon which are ubiquitously produced during interactions.

7:26 Main focus is on boosted jet tagging.

Example Hadronic decay of highly Lorentz-boosted heavy particles (Higgs/W/Z/top) lead to large- radius jets with distinctive characteristics:

-Different radiation pattern (“substructure”) such as 3-prong(top), 2- prong(W/Z/H) or 1-prong(gluon/light flavour).

9:33

Approach 1: Convert Jets to 2D/3D Images and use Computer Vision. Use convolution Neural Network (CNN)

Approach 2: Convert to Sequence and use Natural Language Processing. Use Recurrent Neural Network , eg GRU/LSTM or 1D CNN.

11:22 DeepAk8 Architecture : Advance deep learning architecture for boosted jet tagging.

14:48 ParticleNet :Point Cloud Representation of a Jet?

Treat Jet as unordered set of particles.

Based on Dynamic Graph CNN

Next Part 2: Will Feature actual coding and implementation ( including datasets and representation and other aspects). We will refer two lectures

1. Deep Learning for Particle Physics by Lewis Tunstall :
2. Jet Tagging in Era of Deep Learning by Huilin Qu.