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A4 family symmetry

Dekens, W.G. (2011) A4 family symmetry. Master's Thesis / Essay, Physics.

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Abstract

This thesis explores the role family symmetries might play in the interactions between elementary particles. In the last decade it has become clear that neutrinos, which come in three varieties called flavor, are able to change from one flavor to another, it is said that they oscillate. This indicates that neutrinos have a very small mass. From these oscillations the interactions between neutrinos with a definite mass and the weak force (responsible for radioactive decay) can be deduced. The story for the quarks is similar, although the interactions with the weak force are quite different. These interactions, especially those for the neutrinos, seem to follow a very specific pattern, called the mixing pattern. This pattern could either be due to chance or there might be a mechanism behind it. Family symmetries provide such a mechanism. A model with a family symmetry demands that all physics should be the same if the flavors (of the neutrinos or quarks) are interchanged in a certain way (dictated by the symmetry). It is called a family symmetry because each flavor relates to a different family of particles. A model with a family symmetry constrains the interactions that the model allows for. The goal is to implement a symmetry in such a way that the allowed interactions follow the same pattern seen in nature. This thesis focuses on models which use the group A4 to explain the mixing patterns. A4 is the symmetry group of a regular tetrahedron and is one of the simplest groups which can be used to try to reproduce the mixing patterns. Many models with this symmetry have been put forward in the literature. Some obtain the correct mixing pattern, but often a large number of additional fields (particles) is required to do so. In this thesis some of the simpler cases, with less additional fields, are discussed first. It is concluded from this discussion that these models are unsatisfactory; additional ingredients are required to get the right mixing patterns. After studying some examples from the literature, a new possibility, not yet present in the literature, is considered. In this case A4 is combined with a so called left-right model. In left-right models there is no difference between left and right at high energies. This symmetry between left and right is broken at lower energies, explaining why the weak force is observed to make a clear distinction between left and right. This type of model is used to provide additional ingredients so that the correct mixing patterns can be produced in combination with A4 . One of the simpler variants of the resulting model turns out to be unsatisfactory, as the right masses are not reproduced. However, in this simple case the right mixing patterns can be reproduced. This is an encouragement to further explore this type of model.

Item Type: Thesis (Master's Thesis / Essay)
Degree programme: Physics
Thesis type: Master's Thesis / Essay
Language: English
Date Deposited: 15 Feb 2018 07:46
Last Modified: 15 Feb 2018 07:46
URI: http://fse.studenttheses.ub.rug.nl/id/eprint/9755

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