Physics

Physics
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6 minute read

This section starts by describing the LHC accelerator at CERN and evidence found by the experiments suggesting existence of a Higgs Boson. The huge number of authors on a paper, remarks on histograms and Feynman diagrams is followed by an accelerator picture gallery. The next unit is devoted to Python experiments looking at histograms of Higgs Boson production with various forms of shape of signal and various background and with various event totals. Then random variables and some simple principles of statistics are introduced with explanation as to why they are relevant to Physics counting experiments. The unit introduces Gaussian (normal) distributions and explains why they seen so often in natural phenomena. Several Python illustrations are given. Random Numbers with their Generators and Seeds lead to a discussion of Binomial and Poisson Distribution. Monte-Carlo and accept-reject methods. The Central Limit Theorem concludes discussion.

Looking for Higgs Particles

Bumps in Histograms, Experiments and Accelerators

This unit is devoted to Python and Java experiments looking at histograms of Higgs Boson production with various forms of shape of signal and various background and with various event totals. The lectures use Python but use of Java is described.

  • Presentation Higgs (20)

  • <{gitcode}/physics/mr-higgs/higgs-classI-sloping.py>

Particle Counting

We return to particle case with slides used in introduction and stress that particles often manifested as bumps in histograms and those bumps need to be large enough to stand out from background in a statistically significant fashion.

We give a few details on one LHC experiment ATLAS. Experimental physics papers have a staggering number of authors and quite big budgets. Feynman diagrams describe processes in a fundamental fashion.

Experimental Facilities

We give a few details on one LHC experiment ATLAS. Experimental physics papers have a staggering number of authors and quite big budgets. Feynman diagrams describe processes in a fundamental fashion.

This lesson gives a small picture gallery of accelerators. Accelerators, detection chambers and magnets in tunnels and a large underground laboratory used fpr experiments where you need to be shielded from background like cosmic rays.

Resources

Looking for Higgs Particles: Python Event Counting for Signal and Background (Part 2)

This unit is devoted to Python experiments looking at histograms of Higgs Boson production with various forms of shape of signal and various background and with various event totals.

Files:

  • <{gitcode}/physics/mr-higgs/higgs-classI-sloping.py>
  • <{gitcode}/physics/number-theory/higgs-classIII.py>
  • <{gitcode}/physics/mr-higgs/higgs-classII-uniform.py>

Event Counting

We define event counting data collection environments. We discuss the python and Java code to generate events according to a particular scenario (the important idea of Monte Carlo data). Here a sloping background plus either a Higgs particle generated similarly to LHC observation or one observed with better resolution (smaller measurement error).

Monte Carlo

This uses Monte Carlo data both to generate data like the experimental observations and explore effect of changing amount of data and changing measurement resolution for Higgs.

Resources

Random Variables, Physics and Normal Distributions

We introduce random variables and some simple principles of statistics and explains why they are relevant to Physics counting experiments. The unit introduces Gaussian (normal) distributions and explains why they seen so often in natural phenomena. Several Python illustrations are given. Java is currently not available in this unit.

  • Presentation Higgs (39)
  • <{gitcode}/physics/number-theory/higgs-classIII.py>

Statistics Overview and Fundamental Idea: Random Variables

We go through the many different areas of statistics covered in the Physics unit. We define the statistics concept of a random variable.

Physics and Random Variables

We describe the DIKW pipeline for the analysis of this type of physics experiment and go through details of analysis pipeline for the LHC ATLAS experiment. We give examples of event displays showing the final state particles seen in a few events. We illustrate how physicists decide whats going on with a plot of expected Higgs production experimental cross sections (probabilities) for signal and background.

Statistics of Events with Normal Distributions

We introduce Poisson and Binomial distributions and define independent identically distributed (IID) random variables. We give the law of large numbers defining the errors in counting and leading to Gaussian distributions for many things. We demonstrate this in Python experiments.

Gaussian Distributions

We introduce the Gaussian distribution and give Python examples of the fluctuations in counting Gaussian distributions.

Using Statistics

We discuss the significance of a standard deviation and role of biases and insufficient statistics with a Python example in getting incorrect answers.

Resources

Random Numbers, Distributions and Central Limit Theorem

We discuss Random Numbers with their Generators and Seeds. It introduces Binomial and Poisson Distribution. Monte-Carlo and accept-reject methods are discussed. The Central Limit Theorem and Bayes law concludes discussion. Python and Java (for student - not reviewed in class) examples and Physics applications are given.

Files:

  • <{gitcode}/physics/calculated-dice-roll/higgs-classIV-seeds.py>

Generators and Seeds

We define random numbers and describe how to generate them on the computer giving Python examples. We define the seed used to define to specify how to start generation.

Binomial Distribution

We define binomial distribution and give LHC data as an example of where this distribution valid.

Accept-Reject

We introduce an advanced method accept/reject for generating random variables with arbitrary distributions.

Monte Carlo Method

We define Monte Carlo method which usually uses accept/reject method in typical case for distribution.

Poisson Distribution

We extend the Binomial to the Poisson distribution and give a set of amusing examples from Wikipedia.

Central Limit Theorem

We introduce Central Limit Theorem and give examples from Wikipedia.

Interpretation of Probability: Bayes v. Frequency

This lesson describes difference between Bayes and frequency views of probability. Bayes’s law of conditional probability is derived and applied to Higgs example to enable information about Higgs from multiple channels and multiple experiments to be accumulated.

Resources

\TODO{integrate physics-references.bib}

SKA – Square Kilometer Array

Professor Diamond, accompanied by Dr. Rosie Bolton from the SKA Regional Centre Project gave a presentation at SC17 “into the deepest reaches of the observable universe as they describe the SKA’s international partnership that will map and study the entire sky in greater detail than ever before.”

A summary article about this effort is available at:

Last modified June 17, 2021 : add aliasses (6b7beab5)