The dichotomous nucleon: Some radical conjectures for the large Nc limit

We discuss some problems with the large Nc approximation for nucleons which arise if the axial coupling of the nucleon to pions is large, gA∼Nc. While gA∼Nc in non-relativistic quark and Skyrme models, it has been suggested that Skyrmions may collapse to a small size, r∼1/fπ∼ΛQCD−1/Nc. (This is also the typical scale over which the string vertex moves in a string vertex model of the baryon.) We concentrate on the case of two flavors, where we suggest that to construct a nucleon with a small axial coupling, that most quarks are bound into colored diquark pairs, which have zero spin and isospin. For odd Nc, this leaves one unpaired quark, which carries the spin and isospin of the nucleon. If the unpaired quark is in a spatial wavefunction orthogonal to the wavefunctions of the scalar diquarks, then up to logarithms of Nc, the unpaired quark only costs an energy ∼ΛQCD. This naturally gives gA∼1 and has other attractive features. In nature, the wavefunctions of the paired and unpaired quarks might only be approximately orthogonal; then gA depends weakly upon Nc. This dichotomy in wave functions could arise if the unpaired quark orbits at a size which is parametrically large in comparison to that of the diquarks. We discuss possible tests of these ideas from numerical simulations on the lattice, for two flavors and three and five colors; the extension of our ideas to more than three or more flavors is not obvious, though.