Baryons with many colors and flavors.

Abstract

Using recently developed diagrammatic techniques, I derive some general results concerning baryons in the 1/N expansion, where N is the number of QCD colors. I show that the spin-flavor relations which hold for baryons in the large-N limit, as well as the form of the corrections to these relations at higher orders in 1/N, holed even if ${\mathit{N}}_{\mathit{F}}$/N\ensuremath{\sim}1, where ${\mathit{N}}_{\mathit{F}}$ is the number of light quark flavors. I also show that the amplitude for a baryon to emit n mesons is O(1/${\mathit{N}}^{\mathit{n}/2\mathrm{\ensuremath{-}}1}$), and that meson loops attached to baryon lines are unsupressed in the large-N limit, independent of ${\mathit{N}}_{\mathit{F}}$. For ${\mathit{N}}_{\mathit{F}}$>2, there are ambiguities in the extrapolation away from N=3 because the baryon flavor multiplets for a given spin grow with N. I argue that the 1/N expansion is valid for baryons with spin of order 1 and arbitrary flavor quantum numbers, including, e.g., baryons with isospin and/or strangeness O(N). This allows the formulation of a large-N expansion in which it is not necessary to identify the physical baryons with particular large-N states. SU(${\mathit{N}}_{\mathit{F}}$) symmetry can be made manifest to all orders in 1/N, yet group theory factors must be evaluated explicitly only for ${\mathit{N}}_{\mathit{F}}$=N=3. To illustrate this expansion, I consider the nonsinglet axial vector currents, baryon mass splittings, and matrix elements of s\ifmmode\bar\else\textasciimacron\fi{}s and s\ifmmode\bar\else\textasciimacron\fi{}${\ensuremath{\gamma}}_{\mathrm{\ensuremath{\mu}}}$${\ensuremath{\gamma}}_{5}$s in the nucleon.