Baryon topology in hypersphere soliton model

Abstract

Exploiting a topological soliton on a hypersphere, we construct nucleon charge profile functions and find the density distributions for proton and neutron plotted versus the hypersphere third angle $\mu$. The neutron charge density is shown to possess a nontrivial $\mu$ dependence, consisting of both positive and negative charge density fractions. We next investigate the inner topology of the hypersphere soliton, by making use of the schematic M\"obius strips which are related with the tubular neighborhood of half-twist circle in the manifold $S^{3}$. In particular, we find that in the hypersphere soliton the nucleons are delineated in terms of a knot structure of two M\"obius strip type circles in $S^{3}$. Moreover, the two Hopf-linked M\"obius strip type circles in the hypersphere soliton are shown to correspond to (uu, d) in proton and (dd, u) in neutron, respectively, in the quark model.