Skyrmions in models with pions and rho mesons

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 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 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.

Vibrational modes of Skyrmions

“…A modified model with low classical binding energies (such as those developed in Refs. [10][11][12][13][14][15][16][17]) will also have lower vibrational frequencies and hence more realistic quantum states. In addition, and especially in the lightly bound models, the potential energy may be significantly anharmonic-a difficult feature to account for.…”

“…where m is the dimensionless pion mass which we fix as m ¼ 1. One may modify the Lagrangian in a number of ways [10][11][12][13][14][15][16][17]. For static, finite energy configurations the potential term ensures that Φ ¼ ð1; 0; 0; 0Þ at spatial infinity.…”

B=5 Skyrmion as a two-cluster system

“…One is to include vector mesons in the Lagrangian. Recently it was shown that inclusion of the rho meson reduces the classical binding energy by two-thirds, while retaining the symmetry group of each Skyrmion up to baryon number eight [22]. If one integrates out the mesons, a term which contains sixth order derivatives of the pion field appears [23].…”

Exploring the generalized loosely bound Skyrme model

“…Hence, if such a bound could be saturated, then classically the binding energy would vanish exactly. In the last decade, this approach has been taken in three different directions: the vector meson Skyrme model [12][13][14], the BPS-Skyrme model [15,16] and the lightly/loosely bound Skyrme models [17][18][19].…”