Effective Field Theories for Non-topological Solitons and the Standard Model 4 views

We employ effective field theory frameworks to study both non-topological solitons and lepton-flavor-violating phenomena. Bosons carrying a conserved charge can form stable bound states in the presence of attractive self-interactions. For large charge $Q$, these configurations admit a classical description as $Q$-balls, whose properties are determined by a non-linear differential equation. We study $Q$-balls in arbitrary polynomial single-scalar-field potentials both numerically and analytically, highlighting universal features that depend only weakly on the details of the potential. Such polynomial potentials can arise from renormalizable models with additional heavy or light scalar fields. We further revisit non-topological solitons in the Friedberg--Lee--Sirlin model, a renormalizable two-field construction involving a complex scalar carrying a conserved charge and a real-scalar mediator. We provide analytic approximations to the underlying equations and compare their properties to those of $Q$-ball solutions. Exploiting the structural similarity between $Q$-ball equations and Euclidean vacuum-decay bounce solutions, we reformulate the problem using the tunneling potential approach. This method replaces the field profile with an energy-based description and provides a framework for obtaining approximate and, in some cases, exact solutions. On the phenomenological side, we study charged lepton flavor violation within the Standard Model Effective Field Theory. While operators inducing neutrinoless muon and tau decays are tightly constrained, operators that violate lepton flavor by two units are more difficult to probe. We derive constraints from lepton-flavor-universality observables and discuss prospects for future searches at Belle II and future collider facilities. Finally, we investigate lepton flavor violation by three units. Such processes arise at higher mass dimension and lead to signatures in leptonic decays and tau processes such as $\tau \to eee\bar{\mu}\bar{\mu}$ and $\tau \to \mu\mu\mu\bar{e}\bar{e}$. Observable rates require light new particles and imply clean collider signatures that remain largely unexplored.

PHD (Doctor of Philosophy)

Particle Physics; Non-topological Solitons; Q-balls; Lepton Flavor Violation; Charged Lepton Flavor Violation; Standard Model Effective Field Theory; Effective Field Theory

English

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2026-04-30