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Register a new userRealistic classical binding energies in the $omega$-Skyrme model
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Added by
Sven Bjarke Gudnason
Publication date
2020
fields
Physics
and research's language is
English
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An omega-meson extension of the Skyrme model - without the Skyrme term but including the pion mass - first considered by Adkins and Nappi is studied in detail for baryon numbers 1 to 8. The static problem is reformulated as a constrained energy minimisation problem within a natural geometric framework and studied analytically on compact domains, and numerically on Euclidean space. Using a constrained second-order Newton flow algorithm, classical energy minimisers are constructed for various values of the omega-pion coupling. At high coupling, these Skyrmion solutions are qualitatively similar to the Skyrmions of the standard Skyrme model with massless pions. At sufficiently low coupling, they show similarities with those in the lightly bound Skyrme model: the Skyrmions of low baryon number dissociate into lightly bound clusters of distinct 1-Skyrmions, and the classical binding energies for baryon numbers 2 through 8 have realistic values.
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We consider gauged skyrmions with boundary conditions which break the gauge from $mathrm{SU}(2)$ to $mathrm{U}(1)$ in models derived from Yang-Mills theory. After deriving general topological energy bounds, we approximate charge $1$ energy minimisers using KvBLL calorons with non-trivial asymptotic holonomy, use them to calibrate the model to optimise the ratio of energy to lower bound, and compare them with solutions to full numerical simulation. Skyrmions from calorons with non-trivial asymptotic holonomy exhibit a non-zero magnetic dipole moment, which we calculate explicitly, and compare with experimental values for the proton and the neutron. We thus propose a way to develop a physically realistic Skyrme-Maxwell theory, with the potential for exhibiting low binding energies.
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