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Register a new userMagnetic Vortices in the Abelian Higgs Model with Derivative Interactions
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We study the properties of a single magnetic vortex and magnetic vortex lattices in a generalization of the Abelian Higgs model containing the simplest derivative interaction that preserves the $U(1)$ gauge symmetry of the original model. The paper is motivated by the study of finite isospin chiral perturbation theory in a uniform, external : since pions are Goldstone bosons of QCD (due to chiral symmetry breaking by the QCD vacuum), they interact through momentum dependent terms. We introduce a uniform external magnetic field and find the asymptotic properties of single vortex solutions and compare them to the well-known solutions of the standard Abelian Higgs Model. Furthermore, we study the vortex lattice solutions near the upper critical field using the method of successive approximations, which was originally used by Abrikosov in his seminal paper on type-II superconductors. We find the vortex lattice structure, which remains hexagonal as in the standard Abelian Higgs model, and condensation energy of the vortex lattices relative to the normal vacuum (in a uniform magnetic field).
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A formulation of the linear $sigma$ model with derivative interactions is studied. The classical theory is on-shell equivalent to the $sigma$ model with the standard quartic Higgs potential. The mass of the scalar mode only appears in the quadratic part and not in the interaction vertices, unlike in the ordinary formulation of the theory. Renormalization of the model is discussed. A non power-counting renormalizable extension, obeying the defining functional identities of the theory, is presented. This extension is physically equivalent to the tree-level inclusion of a dimension six effective operator $partial_mu (Phi^dagger Phi) partial^mu (Phi^dagger Phi)$. The resulting UV divergences are arranged in a perturbation series around the power-counting renormalizable theory. The application of the formalism to the Standard Model in the presence of the dimension-six operator $partial_mu (Phi^dagger Phi) partial^mu (Phi^dagger Phi)$ is discussed.
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