Role of instantons in a chiral confining model

In this paper we describe the role of instantons in a model of the nucleon called the chiral confining model (CCM). The effect of instantons is included through the ’t Hooft interaction. In general, confining models tend to give for the product of nucleon mass and quark rms radius, ${\mathit{M}}_{\mathit{N}}$〈${\mathit{r}}^2$ ${\mathrm{〉}}^{1/2}$, values in the range 6–8, while the experimental value is 3.48. In the CCM, in principle, the gluons have been integrated out in favor of mesons. Hence the N-Δ mass splitting must be understood in terms of the spin-isospin dependent forces generated by pion exchange. Unfortunately, one-pion exchange contributes only about 50 MeV or less to the N-Δ mass splitting. The ’t Hooft interaction is capable of resolving both these problems. The passage from QCD to the CCM modifies the strength of the ’t Hooft interaction and, at present, we do not know what it is. We fix it by fitting ${\mathit{M}}_{\mathit{N}}$-${\mathit{M}}_{\mathrm{\Delta }}$. With the strength so fixed we obtain values of ${\mathit{M}}_{\mathit{N}}$〈${\mathit{r}}^2$ ${\mathrm{〉}}^{1/2}$ in the range 4.4–5.1. A simple estimate of the correction for the motion of the center of mass of the nucleon, always present in any mean field calculation, reduces the value to 3.8–4.4. One hopes that the remaining discrepancy will be largely resolved when the mean-field approximation is improved by including quark-quark correlations.