| Summary: | <p>Q-balls are an example of non-topological soliton that can appear in the spectrum of scalar field theories. They are semi-classical states that minimise the energy for a given Noether charge. If isolated from other sectors, these spherically symmetric objects are kept absolutely stable by energy and Noether charge conservation. Though the properties of Q-balls cannot be determined analytically in general, progress can be made in two opposite limits: the thin-wall (large charge) limit; and the thick-wall (small charge) limit. Q-balls are both interesting phenomenologically and as formal objects in their own right, as evidenced by the large body of work on this subject.</p>
<p>This thesis represents a study on the formal properties of field theories, with the aim to determine the subclass of models that admit Q-ball solutions. To that end, its goals are two-fold. Firstly, to constrain the theories that possess stable Q-ball states by: (i) determining the differential equations that govern the VEV of the constituent scalar in the thin-wall limit, together with the physical properties of the resulting Q- ball; (ii) constraining the small-field expansions that lead to stable thick-wall Q-balls by demanding that the minimum of energy be classically stable against decay to the underlying quanta of the scalar field. Secondly, to determine whether stable Q-balls, in both the thick- and thin-wall limit, can form from scalar mesons, arising from the breaking of an approximate chiral symmetry, in the SM and in a specific BSM theory. We will not discuss the phenomenology of these theories in this thesis.</p>
<p>The content of this thesis is laid out in three parts. Part I is concerned with Q-balls in theories possessing only one scalar field, and comprises Chapters 2 and 3, whereas Part II is concerned with theories with multiple scalar fields, and comprises Chapters 4-6. In these parts, we perform an analysis to determine the existence of Q-ball states, and any constraints required by the theories that possess them. In particular, in Part I, the thick-wall analysis presents us with necessary conditions, whereas in Part II, the thick-wall analysis presents us with sufficient conditions. Fi- nally, Part III analyses theories when the underlying scalars of the theory are pseudo- Nambu-Goldstone bosons arising from the breaking of an approximate chiral sym- metry, as in the Standard Model – this final part comprises Chapters 7 and 8. We show that stable Q-balls are not part of the spectrum of the leading-order Chiral lagrangian, but that they can arise in the class of BSM models we study.</p>
<p>The bulk of the original work of this thesis can be found in Refs. [18,19,100–102], with the remaining work unpublished.</p>
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