Rotational-vibrational coupling in the BPS Skyrme model of baryons

C Adam,C Naya,J Sanchez-Guillen,A Wereszczynski

doi:10.1016/j.physletb.2013.09.045

C Adam, C Naya + Show 2 more

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https://doi.org/10.1016/j.physletb.2013.09.045

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Abstract

We calculate the rotational-vibrational spectrum in the BPS Skyrme model for the hedgehog skyrmion with baryon number one. The resulting excitation energies for the nucleon and delta Roper resonances are slightly above their experimental values. Together with the fact that in the standard Skyrme model these excitation energies are significantly lower than the experimental ones, this provides strong evidence for the conjecture that the inclusion of the BPS Skyrme model is required for a successful quantitative description of physical properties of baryons and nuclei.

Highlights

The Skyrme model [1] provides a means to describe the low energy regime of QCD where the baryons and nuclei are topological excitations of the group-valued meson field U
If we stay within the BPS Skyrme model, which contains only the sextic and the potential terms, the masses are slightly too high in comparison to the experimental data
The BPS Skyrme model, simple and integrable, provides better agreement than the usual Skyrme model, built out of the sigma model term and the Skyrme term, which gives excitation masses which are lower than the true values

Summary

INTRODUCTION

The Skyrme model [1] provides a means to describe the low energy regime of QCD where the baryons and nuclei are topological excitations of the group-valued meson field U. The energies of the atomic nuclei are with a very good agreement linear in the baryon number Such a ”hard core” of Skyrme type effective models should be based on a BPS theory. The BPS Skyrme model is a realization of this idea It consists of two terms: the sextic part L6 which is the baryon currents squared and a potential L0 = V [14]. The BPS Skyrme model provides the required scaling properties of the energy E and radius R with the baryon charge B: E ∼ B and R ∼ B1/3 It has a very large (infinite) group of symmetries [16], which is a subgroup of the SDiff(S3) on the target space. Roper resonance energies in the standard Skyrme model have been calculated in [19], [20], [21] and, for the SU(3) Skyrme model, in [22]

We start with the BPS Skyrme Lagrangian

The Hamiltonian is given by the following formula

CONCLUSIONS