Skyrmions in models with pions and rho mesons

Carlos Naya,Paul Sutcliffe

doi:10.1007/jhep05(2018)174

Abstract

A problem with the standard Skyrme model is that Skyrmion binding energies are around 15%, being much larger than the order 1% binding energies of the nuclei that they aim to describe. Here we consider theories that extend the standard Skyrme model of pions by including rho mesons, via dimensional deconstruction of Yang-Mills theory with an extra dimension. We report the first results of parallel numerical computations of multi-Skyrmions in theories of this type, including a model that reduces Skyrmion energies below those of the standard Skyrme model whilst retaining exactly the same Faddeev-Bogomolny energy bound. We compute all Skyrmions with baryons numbers up to 12 and find that the inclusion of rho mesons reduces binding energies to less than 4%, and therefore moves Skyrmion theory closer to experimental data. Furthermore, we find that this dramatic reduction in binding energies is obtained without changing the qualitative features of the Skyrmions, such as their symmetries.

Highlights

JHEP05(2018)174 that to date only the single Skyrmion has been computed in this model, so multi-Skyrmion solutions and their binding energies are unknown
We report the first results of parallel numerical computations of multiSkyrmions in theories of this type, including a model that reduces Skyrmion energies below those of the standard Skyrme model whilst retaining exactly the same Faddeev-Bogomolny energy bound
We present the results of parallel numerical computations of Skyrmions for all baryons numbers from one to twelve and find that binding energies are dramatically reduced from the 15% in the standard Skyrme model to less than 4%

Summary

Including rho mesons in the Skyrme model

The standard Skyrme model is a nonlinear theory of pions in which the pion fields (π1, π2, π3) are combined into the Skyrme field U ∈ SU(2) as. Where φ(z) is a real-valued odd function satisfying the boundary condition φ(∞) = 1 and α is a positive normalization constant Substituting this restricted form into the Yang-Mills energy (2.5), and integrating out the fourth dimension, the energy EYM defines a theory of pions and rho mesons with the energy given by Eπ,ρ = Eπ + Eρ + Eint, where. A motivation for a new parameter set is to obtain an extension of the standard Skyrme model in which the Faddeev-Bogomolny bound survives the inclusion of rho mesons by virtue of the fact that it coincides exactly with the Yang-Mills derived energy bound.

Numerical results for Skyrmions

Findings

Conclusion