[Paper Review] The Skyrme Model for Baryons

J. Schechter, H. Weigel|ArXiv.org|Jul 29, 1999

Quantum Chromodynamics and Particle Interactions3 references16 citations

TL;DR

This paper reviews the Skyrme model, which describes baryons as topological solitons (Skyrmions) in an effective meson field theory. By extending the model to include vector mesons and applying chiral symmetry principles, it provides a zero-parameter description of baryon properties—demonstrating improved agreement with experimental data, particularly in resolving the proton spin puzzle through vector meson dominance and improved scattering phase shifts.

ABSTRACT

We review the Skyrme model approach which treats baryons as solitons of an effective meson theory. We start out with a historical introduction and a concise discussion of the original two flavor Skyrme model and its interpretation. Then we develop the theme, motivated by the large $N_C$ approximation of QCD, that the {\it effective} Lagrangian of QCD is in fact one which contains just mesons of all spins. When this Lagrangian is (at least approximately) determined from the meson sector it should then yield a zero parameter description of the baryons. We next discuss the concept of chiral symmetry and the technology involved in handling the three flavor extension of the model at the collective level. This material is used to discuss properties of the light baryons based on three flavor meson Lagrangians containing just pseudoscalars and also pseudoscalars plus vectors. The improvements obtained by including vectors are exemplified in the treatment of the {\it proton spin puzzle}.

Motivation & Objective

• To provide a comprehensive review of the Skyrme model as a soliton-based description of baryons in effective field theory.
• To extend the original two-flavor Skyrme model to three flavors, incorporating chiral symmetry and its spontaneous breaking.
• To demonstrate how including vector mesons in the effective Lagrangian leads to improved agreement with experimental observables, such as nucleon radii and spin structure.
• To show that the soliton approach yields a zero-parameter description of baryons once the meson sector is fixed, with baryon properties derived from collective quantization.
• To address the proton spin puzzle by showing that vector meson exchange naturally accounts for the observed quark spin content in the nucleon.

Proposed method

• Formulate the Skyrme Lagrangian using a non-linear realization of chiral symmetry with the SU(3)×SU(3) group and the unitary matrix U representing pion fields.
• Apply the large $N_C$ approximation to motivate a generalized effective Lagrangian containing mesons of all spins, with the Skyrme term stabilizing the soliton.
• Use collective coordinate quantization to promote the classical Skyrmion solution to a quantum state with correct baryon number and spin quantum numbers.
• Incorporate vector mesons (e.g., $\rho$) via vector meson dominance, modifying the current algebra and improving the description of electromagnetic and axial currents.
• Construct the soliton solution in the three-flavor case using the SU(3) flavor group and compute matrix elements of baryon currents, including electromagnetic and axial currents.
• Perform meson-baryon scattering calculations using small fluctuations around the soliton, replacing contact interactions with $\rho$-exchange to stabilize phase shifts at high momentum.

Experimental results

Research questions

• RQ1 How can baryons be consistently described as topological solitons in an effective meson field theory?
• RQ2 What improvements does including vector mesons bring to the description of nucleon properties such as radii and spin structure?
• RQ3 To what extent can the Skyrme model provide a zero-parameter description of baryons once the meson sector is fixed?
• RQ4 How does the inclusion of vector mesons resolve the issue of linearly rising phase shifts in meson-baryon scattering?
• RQ5 Can the soliton model explain the proton spin puzzle through the contribution of quark and gluonic currents in a chiral framework?

Key findings

• The inclusion of vector mesons in the Skyrme model increases the isoscalar radius by approximately $0.35\,{\rm fm}^2$, significantly improving agreement with experimental data.
• Vector meson exchange replaces the contact interaction in the Skyrme model, leading to a saturation of phase shifts at high momentum transfer instead of linear growth.
• The model successfully describes the proton spin puzzle by attributing the observed small quark spin polarization to the chiral soliton structure and vector meson contributions.
• The effective Lagrangian with pseudoscalars and vectors yields a more realistic description of short-distance nucleon structure, consistent with vector meson dominance.
• The collective quantization of the Skyrmion in the three-flavor case provides a consistent framework for computing baryon matrix elements with minimal input.
• The model achieves a zero-parameter description of baryons once the meson Lagrangian is fixed, with all baryon properties derived from soliton dynamics and symmetry constraints.