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 $1/N$, hold even if $N_F/N\sim 1$, where $N_F$ is the number of light quark flavors. I also show that the amplitude for a baryon to emit $n$ mesons is $O(1/N^{n/2-1})$, and that meson loops attached to baryon lines are unsupressed in the large-$N$ limit, independent of $N_F$. For $N_F>2$, 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 $O(1)$ and {\it 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. $SU(N_F)$ symmetry can be made manifest to all orders in $1/N$, yet group theory factors must be evaluated explicitly only for $N_F=N=3$. To illustrate this expansion, I consider the non-singlet axial currents, baryon mass splittings, and matrix elements of $\text{mybar}ss$ and $\text{mybar}s{\text{gam}}_{\mu }{\text{gam}}_{5}s$ in the nucleon.

Comments: 19 pages, plain TeX, 4 uuencoded postscrip figures, LBL-35539, NSF-ITP-94-42