The Dichotomous Nucleon: Some Radical Conjectures for the Large Nc Limit

TL;DR

This paper explores a novel approach to the large Nc limit in nucleon models, proposing that diquark pairing and the unpaired quark's wavefunction orthogonality can explain small axial coupling g_A, with implications for lattice simulations.

Contribution

It introduces a new conceptual framework where diquark pairing and wavefunction orthogonality lead to a small axial coupling in large Nc nucleon models, challenging existing assumptions.

Findings

Proposes diquark pairing as a mechanism for small g_A in large Nc limit.

Suggests orthogonal wavefunctions for unpaired quark and diquarks reduce energy costs.

Discusses potential tests via lattice simulations for different Nc and flavor numbers.

Abstract

We discuss some problems with the large Nc approximation for nucleons which arise if the axial coupling of the nucleon to pions is large, g_A \sim Nc. While g_A \sim Nc in non-relativistic quark and Skyrme models, it has been suggested that Skyrmions may collapse to a small size, r \sim 1/f_pi \sim Lambda_QCD^{-1}/sqrt(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 \sim Lambda_QCD. This naturally gives g_A \sim 1 and has other attractive features. In nature, the wavefunctions of the paired and unpaired quarks might only be approximately orthogonal; then g_A 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.