CMS 101 Concepts

By : Sudhir Malik,

Guillermo Fidalgo, Roy Cruz, Tetiana Mazurets

Outline

• Exploration of CMS through iSpy
• Part 1: Large Hadron Collider
• LHC facts
• Bunches
• Luminosity
• Part 2: CMS Detector
• CMS Coordinate System
• 4-momentum and transverse momentum
• Missing transverse momentum
• Trigger system: Motivation and Functionality of L1 and HLT
• Part 3: A Bit of Theory
• Units in HEP
• Lessons From Quantum Mechanics and Special Relativity
• Feynman Diagrams, Matrix Elements
• Transition Rate and Cross-Section

What is the charge?

If v and B are perpendicular then

Remember the sub-detector colors!

Large Hadron Collider

• Let’s take a closer look at CMS…

Part 1: The Large Hadron Collider

The Large Hadron Collider

• Largest and most powerful particle accelerator in the world.
• Accelerates particles to almost the speed of light.
• It is a tool of discovery that we use to probe our best theories to the limit.
• It’s an engineering feat!
• 27 km ring
• ~1,200 are superconducting dipoles using > 11,000 Amps. (27000m / 1200 ~ 22m)
• The magnets have enough energy to melt 15 tons of copper.
• Particles are kept in a high vacuum more empty then space.
• The magnets are cooled to less than 2 Kelvin (-456 °F).

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Distance per bunch

27,000m / 3,600 bunches = 7.5m/bunch

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Time per bunch crossing

(7.5m/bunch ) / 3x10^8 m/s = 2.5 x 10^-8 s / bunch

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Collision frequency is 1/Time

= 1/ 2.5x10^-8 = 40 x 10^6 Hz = 40 MHz

Bunches

• We don’t accelerate/collide individual protons.
• Travel as a bag of protons (bunch)
• We accelerate proton bunches, each bunch is precisely separated.
• Most of the particles graze each other. We are more interested in head on collisions.
• 1 event = 1 bunch crossing
• 1 bunch crossing is currently >20 primary interactions.

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Pileup

• 1 bunch crossing ~50 interactions.
• From these even more particles and unintended collisions can occur (pileup)
• Currently around 50
• HL - LHC could be up to 200
• This gets further broken down into two types of pileup
• In-time
• From current bunch crossing
• Out-of-time
• From nearby bunch crossing

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Luminosity and Cross Section

• Cross Section is a measurement of area.
• Probability of interaction is proportional to the area of within which particles interact.
• We therefore borrow the term to mean probability.
• Unit is the barn ( ) which is about the size of Uranium nucleus.
• Luminosity measure how tightly beams of particles are compressed. Higher means higher chances of collisions.
• Unit is the inverse barn per second

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• number of events per second

Part 2: The CMS Detector

The CMS Detector

• Tracker: reconstructs the paths of charged particles in the center of the CMS detector
• ECAL/HCAL: measures energies of charged particles and composite particles (hadrons) respectively
• Muon chambers: measures the trajectory, momentum, and identifies muons (200 times heavier than electron)
• Forward Calorimeter: measures the energy of particles produced at small angles relative to the beam line

CMS coordinate system

• We define a Cartesian coordinate system where
• x: Points towards the center of the LHC
• y: Points skyward
• z: Points counter clockwise when viewing the LHC from the sky
• If you treat CMS as a cylindrical 2D surface, you can define any point on that surface using just two variables. We typically use:
• eta: Describes angle between beamline and trajectory
• phi: Angle between x and the xy projection

Basic Physical Observables

• Pseudo rapidity
• Describes the angle between the particle trajectory with respect to the axis of the beam.
• Why not just the angle itself?
• η is approximately invariant under Lorentz boost along the beam axis
• Mathematical definition

Basic Physical Observables

• In classical mechanics, momentum is defined as

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• In another non-accelerating (i.e. inertial) reference frame, the transformation of classical momentum is described by Galilean transformations.
• These transformations only apply if the velocities involved are << c and are just approximations for more general transformation at this limit.
• In this limit, energy and classical momentum are individually conserved quantities

Basic Physical Observables

• A more accurate description is given by SR, which states that in a given reference frame it is not the classical momentum that is conserved, but the 4-momentum

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4-momentum conserved in a closed system (collider):

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Why do we need a collider then?

• In proton-proton (pp) collisions at the LHC, weakly interacting neutral particles often evade detection. Yet, their existence can be deduced from an imbalance in momentum observed in the plane perpendicular to the beam, known as missing transverse momentum

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was instrumental in the discovery of the W and Z bosons in the 1980s and continues to play a crucial role in searches for new particles like those predicted by supersymmetry.

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Trigger system

• Trigger required to reduce data rate to a level we can read out, store, and process
• Trigger is critical
• Can only analyze events that were selected
• No way to go back and recover missed events!
• In CMS, there is one bunch crossing is every 25 ns which produced multiple collisions. Let’s calculate the frequency necessary to operate in these conditions.

Hardware based (L1) trigger

• The primary role of the L1 Trigger is to quickly reduce the data rate from the raw collision rate of 40 MHz to < 100kHz

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• It analyzes basic detector information to decide almost instantaneously (within less than 4 μs) whether an event is potentially interesting enough to keep for further analysis

• List of active trigger algorithms (L1 seeds) with specific thresholds used to select events is called “trigger menu”
• Data is from calorimeters and a muon chamber

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Software based (HLT) Trigger

• The main purpose to reduce the volume of collision data that must be stored and analyzed by applying sophisticated software algorithms to select only the most scientifically valuable events.
• Reduces the data rate from 100 kHz to ~ 1 kHz
• HLT receives the full event information (including tracking)
• A L1 seed starts algorithms for given HLT paths
• Any event passing one of the paths is stored in a “primary dataset” (ex. SingleMuon, JetHT, DoubleEG etc.)
• Data is from the whole reconstruction

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Part 3: A Bit of Theory

Units in HEP

• In SI, we commonly used units of
• kg: mass
• m: distance
• s: time
• These units is cumbersome in HEP!
• Mass of the proton in kilograms = ~1.67E-27 kg
• Radius of the proton in meters = ~0.84E-15 m
• Equations like Einstein’s energy-mass relation and the de Broglie wavelength shows that we can express these in terms of energy
• We typically use eV (= 1.60E-19 Joules): increase in potential energy for an electron crossing a distance with a electric potential difference of 1V
• Mass of the proton in MeV/c² = 938.1 MeV/c²

Units in HEP

• The physical constants in many equations are ugly enough, now we’re adding more!?

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• To simplify our lives (and our equations), in HEP we use natural units

Units in HEP

What can we learn from QM?

• From QM we know that
• The universe is not deterministic. E.g.: Before measurement, a particle may exist in a “superposition” of many different states with different positions.
• Particles are described by wavefunctions, complex valued functions which contain the information about the position, momentum, energy, etc. of the particle.
• We cannot say that the particle has this or that position, momentum, etc. until it is measured.
• There are also some fundamental equations that come from QM

Quantum Field Theory

• Particles are described by quantum field theory (QFT) which is SR + QM
• Quantum Chromodynamics
• Electroweak Theory (QED + Weak)
• QFT describes particles as fields (a value at every point in space-time)
• Different types of fields describe particles with different properties
• Spin-0: Scalar fields (Higgs)
• Spin-½: Fermionic fields (Quarks and leptons)
• Spin-1: Gauge fields (Photons, W^± and Z⁰ and gluons)
• Particles are localized excitations of these fields. There is a fields for every types of particle (electron field, Higgs field, photon field, etc.)

Quantum Electrodynamics

• Quantum electrodynamics
• P. Dirac laid the groundwork in 1928, R. Feynman, J. Schwinger, T. Shin’ichiro developed it in the 1940s.
• Describes how charged particles and photons interact
• Two fields: photon field and electron field

Feynman Diagrams

• Processes in QED (and other QFTs) can be described using Feynman diagrams which are their pictorial representations****
• Electron: straight line with arrow
• Photon: squiggly line
• Horizontal axis corresponds to time
• Vertices: Points where lines intersect. Represents interaction between fields. Interaction must conserve charge, momentum

QED Example: e⁺e^- → e⁺e^-

• We can only directly observe what comes in and what comes out.
• But what happens in the middle? There are infinite possibilities! (Literally)
• Remember, this is a quantum mechanical system, so there is a chance that anything* could have happened

QED Example: e⁺e^- → e⁺e^-

=

+

+

+...

QED Example: e⁺e^- → e⁺e^-

• So what happened in between? All of them “happened” in superposition.
• Note: The more complex the intermediate steps from initial to final state are, the lower the probability the the process happened in that particular way.
• Keep in mind: Just because you can draw it, doesn’t mean its possible

VS

Oh no…

Feynman Diagrams

• So, how do we deal with all of this? How can all of these Kindergarden drawings be useful if there’s so many?
• Feynman diagrams are not just cute little pictures, but actual mathematical tools!
• They represent the perturbative expansion of the matrix elements for particle interactions
• M_fi, the transition matrix element, represents the probability (amplitude) of a certain process happening (e.g. e⁺e^- → e⁺e^-). It can be expanded similarly to a Taylor series
• Feynman diagrams represent these expansion terms and a certain set of rules allow us to find the mathematical expression from the diagram

Feynman Diagrams

• These expansion terms are obtained directly from Feynman diagrams.
• Each vertex adds a coupling constant factor

QED coupling constant < 1

Cross-Section and Rate

• Knowing M_fi allows us to measure other key values
• Cross-section: measure of the probability that a specific phenomenon will happen

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• Decay/Transition rate: measure of the probability per unit time that a type of phenomena will happen

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• With these quantities, we can make predictions about the expected amount of events we will see.

Simulations

• So how can the analyst deal with all of this!?
• We know we can use theory to make predictions. However, as you can deduce, computing by hand would take too long, so we simulate (and approximate)!
• Common simulations tools include:
• MadGraph5: Calculates the Feynman diagrams for a given initial and final states in order to compute the matrix elements and cross-section numerically.
• Pythia: For simulation of parton showering and hadronization
• GEANT4: For simulating how particles interact with our detector

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Simulations

• “State” refers to the quantum state of the system.
• System: mess of gluons, and quarks when the protons collide.
• A model (e.g. SM, SUSY, dark sector models, etc.), given the initial conditions (mess of gluons + quarks or one of its immediate products), predicts that certain phenomena can occur with varying probabilities.

What’s next?

• There’s much more to say about how this all comes together in an analysis.
• Through phenomenological considerations and the predicted topology of an desired signal, one can make cuts on kinematic values.
• On Monday, we will be doing an “analysis” where we will find out the mass of the Higgs from H → ZZ → 4l where these concepts we introduced will be useful.

Backup Slides

References

1. Goldfarb, S., Anthony, K. Broad as a barn. Nat. Phys. 15, 414 (2019). https://doi.org/10.1038/s41567-019-0490-z
2. https://twiki.cern.ch/twiki/bin/view/CMSPublic/LumiPublicResults#Run_3_charts_of_luminosity
3. ​

What is this talk about?

Example process: H → ZZ → 4l

• Setting the stage: Suppose we are an analyst that wishes to measure the mass of the Higgs through the H → ZZ → 4l decay mode.

First slide (abstract)

https://cms.physicsmasterclasses.org/pages/cmswz.html

https://quarknet.org/sites/default/files/InvMass.pdf

https://quarknet.org/page/geometry-collider-detector

https://www.screencast.com/t/9kI1CMWFXK

https://www.i2u2.org/elab/cms/library/resources.jsp?options=project

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What is this talk about?

• Starting off, when you hear particle physicists talk, it sounds like a different language with millions of acronyms.
• E.g.: MET, pt, CaloJets, etc.
• At the end of this presentation, we hope that you will be able to understand these concepts to the point where you can engage in these conversations and be able to navigate HEP literature with more ease.
• We will do this by telling you a story…