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Lecture 13

Monte Carlo and Sampling Methods

PHYS 398: Data Analysis for Physics

Fall 2023

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Monte Carlo Integration Example:

Particle Physics at High-Energy Particle Colliders

Fall 2023

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CERN’s Large Hadron Collider (LHC)

Mont Blanc

Lake Geneva

Mont Blanc

  • At the LHC, counter-rotating proton beams cross with a frequency of 40 MHz
  • The beams consist of ~2500 bunches of O(100 billion) protons per bunch that are steered into one another

→ Each pp collision produces of O(103) particles!

  • These beams are squeezed to increase the collision rate and therefore increase the chance of producing interesting but rare physics for discovery science

→ comes with a price: multiple pp interactions per bunch crossing (“pile-up”)

that can obscure the most interesting (hard scattering) physics

Fall 2023

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CERN’s Large Hadron Collider (LHC)

Mont Blanc

Lake Geneva

Mont Blanc

Fall 2023

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Fall 2023

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Born-Level Cross Section

Fall 2023

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LHC Experiments

ALICE

ATLAS

LHCb

CMS

Lake Geneva

Mont Blanc

Fall 2023

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Matrix Element Method

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Ab initio calculation of an approximate probability density function 𝓟𝞷 (𝙭|𝞪) for an event with observed final-state particle momenta 𝙭 to be due to a process 𝞷 with theory parameters 𝞪

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Dynamics from QFT→ Correlations from physics

𝓟𝞷 (𝙭|𝞪) can be used in a number of ways to search for new phenomena at particle colliders

Sample Likelihood

(e.g. 𝞪 measurements via max. likelihood)

Neyman-Pearson Discriminant

(e.g. process search, hypothesis test)