Theoretical physics is a branch of physics which employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict natural phenomena. Keywords particle physics variable space relative entropy particle accelerator actual observation. Each random variable is characterized by its probability distribution function or probability density function generically called pdf. Final report on particle analysis for gunshot residue detection prepared by g. So, i hope you have gathered enough courage to embark upon a journey to learn one of the most beautiful, enthralling and in particular experimentally passed all the test of time and successful subjects in the history of physics ever, particle. Thomson discovered the electron in 1897 and the electron remains the prototype of an elementary particle, while many other particles discovered between then and today have lost that status. A word on subjective and objective bayesian priors lecture 2. The history of elementary particle physics is only 100 years old. Kyle cranmer nyu cern academic training, feb 25, 2009 statistics plays a vital role in science, it is the way that we quantify our knowledge and uncertainty. Practical statistics for particle physicists cern publishing. Particle physics studies the smallest pieces of matter, 1 110.
It was a geometric representation of real particle data, such as the likelihood that two colliding gluons will turn into four gluons. Handbook on statistical distributions for experimentalists. Atoms were postulated long ago by the greek philosopher democritus, and until the beginning of the 20 th century, atoms were thought to be the fundamental indivisible building blocks of all forms of matter. Unfortunately, the research literature in this field is clearly inaccessible to undergraduates, and although there are now several excellent graduate texts. Results show how two proposed theories compare to the standard model and how the likelihood ratio varies as a function of a physical parameter e. Introduction to statistics and data analysis for physicists. Statistical methods in particle physics ws 201718 k. Data analysis and statistical methods in experimental. In particle physics usually an event is the result of a collision, as recorded by our. In statistics an event is a subset of the sample space. We developed the group theoretic tools needed to understand the basic construction of gauge theory, as well as the physical concepts and tools to understand the structure of the standard model of particle physics as a gauge theory. Particle filters pf are widely used in the vision literature for visual object tracking.
Modern particle physics makes a large use of relatively new sciences. Center for cosmology and particle physics, physics department, new. We present inference techniques for this case that combine the insight that additional latent information can be. Statistical methods in particle physics heidelberg university. In particle physics there are various elements of uncertainty. There is a lot of power in the likelihood function applied to physics using the complex likelihood derived from the complex logarithm. The likelihood ratio is the maximum power test, that maximize the discovery potential the maximum likelihood ml is the best estimator in the case of parametric statistics problems the likelihood ratio permits to match toghether different experiments and to realize the neyman frequentist scheme. Testing for goodness of t the 2 distribution the quantity.
Obviously in particle physics, all three kinds of uncertainties are at play. Lyons, statistics for nuclear and particle physics, cup, 1986. On page 101, likelihood functions are given for determining how many pions and kaons there are in a sample of events for which particle identi. If a particle and antiparticle come across each other, they annihilate. Data analysis and statistical methods in experimental particle physics thomasr. Soon after, the rutherford experiment, executed by geiger and marsden, proved the untenability of the thomson atom and the atom, or better the nucleus, becomes understoodinitscorrectform. In several concrete cases, an event in statistics may correspond to many possible collision events. Further discussion and applications to particle physics.
However, the selection and the tuning of the observation pdf or likelihood function involved in the. Note that the definition implies that the coverage probability p. In this model, three of the four fundamental forces of physics are described, along with gauge bosons, the particles that mediate those forces. Statistical methods for particle physics lecture 2.
Feynman developed a diagram technique for representing processes in particle physics. If we use the conversion factor given in the table above, we get 1 b 2570. Pdf testing theories in particle physics using maximum. For continuous x, its probability density function pdf px is defined as. History of the particle physics modern particle physics began in the early 20th century as an exploration into the structure of the atom. But if weve gone that far, it would be irresponsible not to include a discussion of supersymmetry and supergravity, and so on and so on. Likelihood is a central concept of statistical analysis and its foundation is the likelihood principle. Testing theories in particle physics using maximum likelihood. Aachen 2014 statistics for particle physics, lecture 3. While, there are several efforts being made in theoretical particle physics, in an attempt to develop the models, theoretical framework, and mathematical tools to. In particle physics it is expressed in a unit called barn b. The standard model of particle physics andrea romanino associate professor, sissa. For theories that are equally, proportionally, discrete, or continuously likely a likelihood ratio can be created and optimized in order to reveal their computationally unified dynamics.
In scientific fields as diverse as particle physics, genetics, and epidemiology, complex computer simulations provide the most accurate description of phenomena, but the corresponding likelihood function cannot be computed. This is a major challenge for statistical inference. Our range of resources, including impacting journals and awardwinning ebooks, cover all interface areas between particle and nuclear physics, including particle and nuclear astrophysics and cosmology. Encyclopedia of applied high energy and particle physics 2009. Elementary particle physics lecture notes spring 2002. Going hand in hand with technological advances, particle physics now has extended its reach to studies of the. In statistics, we are interested in using a given sample of data to make inferences about a probabilistic model, e. Soon came the rutherford atom and the nucleus and the bohr quantization. Soon came the rutherford atom and the nucleus and the bohr. We discuss this concept in more detail than usually done in textbooks and base the treatment of inference problems as far as possible on the likelihood function only, as is common in the majority of the nuclear and particle physics community. In bayesian statistics, interpretation of probability extended to. This note is an introduction to the standard model of particle physics, the strong and electroweak interactions between the basic constituents of the world, quarks and leptons, via the exchange of gluons, photons and w and z particles. Often a likelihood ratio is used as the test statistic t for a double test. Free particle physics books download ebooks online textbooks.
Cowan istep 2016, beijing statistics for particle physics lecture 2 page 6 likelihood ratio for 2d example neymanpearson lemma says best critical region for classification is determined by the likelihood ratio. A key feature of collider physics is that events resulting from particle collisions are independent of each other, and provide a quasiperfect laboratory of quantummechanical probability processes. Many analyses in particle physics do not use likelihood functions. The standard model of particle physics, which classifies elementary particles into several groups, is at the core of modern physics. The dirac equation, interaction by particle exchange, electron positron annihilation, electron proton elastic scattering, deep inelastic scattering, symmetries and the quark model, quantum chromodynamics, va and the weak interaction, leptonic weak interactions, neutrino oscillations, weak interactions of quarks. Electromagnetism probably the best understood force macroscopic. Testing theories in particle physics using maximum.
Although the word particle can refer to various types of very small objects e. The book has originated from the authors attempts during many years to provide themselves and their students working for a degree in experimen tal particle physics with practical knowledge of statistical analysis methods and some further insight required for research in this field. Statistical methods for particle physics royal holloway. In fact for many systematics a gaussian pdf is hard to. In particle physics, cls represents a statistical method for setting upper limits also called exclusion limits on model parameters, a particular form of interval estimation used for parameters that can take only nonnegative values. Once the pdf is known a random variable is completely assigned. These lectures provide a basic introduction to the standard model sm of particle physics. All that was to say that ive decided to make this a long term project as a post particle physicist hobby. If the distribution of x is continuous then this should be replaced by an equality.
The science of particle physics surged forward with the invention of particle accelerators that could accelerate protons or electrons to high energies and smash them into nuclei to the surprise of scientists, a whole host of new particles were produced in these collisions. I believe the time has come to integrate elementary particle physics into the standard undergraduate curriculum. Particle physics also known as high energy physics is a branch of physics that studies the nature of the particles that constitute matter and radiation. Time runs from left to right arrow directed towards the right indicates a particle, and otherwise antiparticle at every vertex, momentum, angular. Shannon and fisher information, correlation, information geometry, cramerrao bound. Basic concepts particle physics feynman diagrams in 1940s, r. Particle physics with standard model, diagram, formulas. Parametric and nonparametric probability density functions. Equivalently we can use any monotonic function of this as a test statistic, e. The discovery of the atomic nucleus in the gold foil experiment of geiger, marsden, and rutherford was the foundation of the field. Field computation for accelerator magnets analytical and numerical methodsfor electromagnetic design and optimization 2010 isbn 9783527407699 stock, r. Pdf a selfadaptive likelihood function for tracking. In particle physics usually an event is the result of a collision, as recorded by our experiment. Cowan invisibles 2014 statistics for particle physics 5 distribution, likelihood, model suppose the outcome of a measurement is x.
Although gravity isnt technically included in the standard model, theoretical physicists are working to extend the. The likelihood function for the entire experiment assuming the backgroundonly hypothesis h 0 is. Contents preface vii introduction 1 elementary particle physics 1 how do you produce elementary particles. In particle physics, we deal with crosssections often. This chapter gives an overview of statistical methods used in highenergy physics. Pdf a selfadaptive likelihood function for tracking with. Particle physics sits at the forefront of our search for the ultimate structure of matter at the smallest scale, but in the process it has also learned to question the nature of our space and time in which they exist. Elementary particle physics is barely 108 years old. Antiparticles were predicted in 1930 by dirac, and discovered 2 years later e2 4. Mining gold from implicit models to improve likelihood. Elementary particle physics from theory to experiment. Suppose we have a pdf characterized by one or more parameters. Systematic errors estimation likelihood maximum likelihood examples least squares straight line fit bayesian statistics confidence levels hypothesis testing 020312 statistical. Part i 40 was primarily an algebraic exposition of gauge theories.
One can then speak of a probability density function p. This particle physics booklet includes the summary tables plus essential tables. Standard model of particle physics the standard model sm of particle physics gottfried and weisskopf, 1984 was developed throughout the 20th century, although the current formulation was essentially. In fact for many systematics a gaussian pdf is hard to defend more on this later. The probability density or mass function or distribution of x, which may depend on parameters.
In the context of experimental particle physics, such an outcome could be. Particle physics practical statistics for particle physics. Although cls are said to refer to confidence levels, the methods name is. A stable particle a in free space moving or at rest particle traveling backwards in time antiparticle traveling forwards in time a stable antiparticle a in free space moving or at rest nb here time runs upwards the choice is merely a convention and has no other meaning. Elementary particle physics lecture notes 2014 bobby samir acharya march 4, 2014 1.
152 724 1402 689 33 320 1339 1391 1239 1407 1024 1096 470 829 941 1192 321 579 320 71 617 1039 6 29 1493 1283 827 1239 1212 655 1395 35 258 1211 1346 379 1081 826 1362