Nucleons as chiral solitons

TL;DR

The paper addresses how to derive a nonperturbative, relativistic description of the nucleon from QCD by using a large-Nc semiclassical framework where valence quarks are bound by a self-consistent chiral field. It develops and analyzes an effective chiral Lagrangian, explains the role of the Wess-Zumino term, and constructs the nucleon as a chiral quark soliton whose mass, profile, and quantum numbers emerge from minimizing the energy and rotating the soliton. It then applies this model to static properties, parton distributions, skewed distributions, and the light-cone wave function, showing qualitative and often quantitative agreement with data and making predictions such as large sea flavor asymmetry and skewed-density features. Overall, the Chiral Quark-Soliton Model offers a relativistic, 1/Nc-controlled nonperturbative framework that connects spontaneous chiral symmetry breaking to measurable nucleon structure, with clear predictions and testable consequences for future experiments.

Abstract

In the limit of large number of colors N the nucleon consisting of N quarks is heavy, and one can treat it semiclassically, like the large-Z Thomas--Fermi atom. The role of the semiclassical field binding the quarks in the nucleon is played by the pion or chiral field; its saddle-point distribution inside the nucleon is called the chiral soliton. The old Skyrme model for this soliton is an over-simplification. One can do far better by exploiting a realistic and theoretically-motivated effective chiral lagrangian presented in this paper. As a result one gets not only the static characteristics of the nucleon in a fair accordance with the experiment (such as masses, magnetic moments and formfactors) but also much more detailed dynamic characteristics like numerous parton distributions. We review the foundations of the Chiral Quark-Soliton Model of the nucleon as well as its recent applications to parton distributions, including the recently introduced `skewed' distributions, and to the nucleon wave function on the light cone.

Figures (8)

• Figure 1: Effective potential $V_{{\rm eff}}(r,t)=\ln\left[W(r,t)/W(r,t+a)\right]$ as function of $t$ at different values of $r$ from Ref.(35). The data points correspond (from bottom to top) to $r=0.65,\;0.98,\;1.30,\;1.62,\;1.95\;{\rm and}\; 2.25\;{\rm fm}$. The inverse coupling used $\beta=2.635$ corresponds to the lattice spacing $a=0.0541\;{\rm fm}$. Courtesy G.Bali.
• Figure 2: Quarks in a nucleon interacting via pion fields.
• Figure 3: Spectrum of the Dirac hamiltonian in trial pion field. The solid lines show occupied levels.
• Figure 4: Nucleon mass and its constituents as function of the soliton size. The short-dash line shows $3E_{{\rm level}}$, the long-dash line is $E_{{\rm field}}$, the solid line is their sum, ${\cal M}_N$.
• Figure 5: Singlet unpolarized structure functions $x\{[u(x)+d(x)]\pm[\bar{u}(x)+\bar{d}(x)]\}/2$ from Ref.(68) compared to the phenomenological parametrization of Ref.(70). The dashed line corresponds to the sum and the solid line corresponds to the difference of quark and antiquark distributions.